Principles of
Corporate Finance

THE MCGRAW-HILL/IRWIN SERIES IN FINANCE, INSURANCE, AND REAL ESTATE

Stephen A. Ross, Franco Modigliani Professor of Finance and Economics, Sloan School of Management, Massachusetts Institute of Technology, Consulting Editor

Financial Management

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Fourteenth Edition

Brealey, Myers, and Allen

Principles of Corporate Finance

Eleventh Global Edition

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Fundamentals of Corporate Finance

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Brooks

FinGame Online 5.0

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Case Studies in Finance: Managing for Corporate Value Creation

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Principles of
Corporate Finance

ELEVENTH GLOBAL EDITION

Richard A. Brealey

Professor of Finance

London Business School

Stewart C. Myers

Robert C. Merton (1970) Professor of Finance

Sloan School of Management

Massachusetts Institute of Technology

Franklin Allen

Nippon Life Professor of Finance

The Wharton School

University of Pennsylvania

Principles of Corporate Finance

Richard A Brealey, Stewart C Myers, Franklin Allen

ISBN-13 9780077151560

ISBN-10 0077151569

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ISBN-13 9780077151560

ISBN-10 0077151569

© 2014. Exclusive rights by The McGraw-Hill Companies, Inc. for manufacture and export. This book cannot be re-exported from the country to which it is sold by McGraw-Hill.

To Our Parents

About the Authors

   Richard A. Brealey

Professor of Finance at the London Business School. He is the former president of the European Finance Association and a former director of the American Finance Association. He is a fellow of the British Academy and has served as a special adviser to the Governor of the Bank of England and director of a number of financial institutions. Other books written by Professor Brealey include Introduction to Risk and Return from Common Stocks.

   Stewart C. Myers

Robert C. Merton (1970) Professor of Finance at MIT’s Sloan School of Management. He is past president of the American Finance Association and a research associate of the National Bureau of Economic Research. His research has focused on financing decisions, valuation methods, the cost of capital, and financial aspects of government regulation of business. Dr. Myers is a director of Entergy Corporation and The Brattle Group, Inc. He is active as a financial consultant.

   Franklin Allen

Nippon Life Professor of Finance at the Wharton School of the University of Pennsylvania. He is past president of the American Finance Association, Western Finance Association, and Society for Financial Studies. His research has focused on financial innovation, asset price bubbles, comparing financial systems, and financial crises. He is a scientific adviser at Sveriges Riksbank (Sweden’s central bank).

Preface

This book describes the theory and practice of corporate finance. We hardly need to explain why financial managers have to master the practical aspects of their job, but we should spell out why down-to-earth managers need to bother with theory.

Managers learn from experience how to cope with routine problems. But the best managers are also able to respond to change. To do so you need more than time-honored rules of thumb; you must understand why companies and financial markets behave the way they do. In other words, you need a theory of finance.

Does that sound intimidating? It shouldn’t. Good theory helps you to grasp what is going on in the world around you. It helps you to ask the right questions when times change and new problems need to be analyzed. It also tells you which things you do not need to worry about. Throughout this book we show how managers use financial theory to solve practical problems.

Of course, the theory presented in this book is not perfect and complete—no theory is. There are some famous controversies where financial economists cannot agree. We have not glossed over these disagreements. We set out the arguments for each side and tell you where we stand.

Much of this book is concerned with understanding what financial managers do and why. But we also say what financial managers should do to increase company value. Where theory suggests that financial managers are making mistakes, we say so, while admitting that there may be hidden reasons for their actions. In brief, we have tried to be fair but to pull no punches.

This book may be your first view of the world of modern finance theory. If so, you will read first for new ideas, for an understanding of how finance theory translates into practice, and occasionally, we hope, for entertainment. But eventually you will be in a position to make financial decisions, not just study them. At that point you can turn to this book as a reference and guide.

   Changes in the Eleventh Edition

We are proud of the success of previous editions of Principles, and we have done our best to make the eleventh global edition even better.

What is new in the eleventh global edition? Of course, a large part of the changes in any edition consist of adding some updated data here and a new example there. However, we have rewritten and refreshed several basic chapters. Content remains much the same, but we think that the revised chapters are simpler and flow better.

•  Chapter 1 has grown over the years as major new developments in the financial world seem to demand some reference and comment. In this edition we have sought to make the chapter a more focused introduction to corporate finance. It concentrates on the decisions that corporations need to make and the financial objectives that govern these decisions. It also introduces five basic themes that return again and again throughout the book.

•  Chapter 3 introduces bond valuation. We rewrote and simplified some of the material, such as the discussion of duration. The last section of the chapter includes an introduction to default risk. The tribulations of the eurozone and the default by the Greek government on its bonds are reminders that default is not just a concern for holders of corporate debt. So we discuss briefly the risk of default for both corporate and sovereign borrowers. (We discuss corporate debt and default risk in more detail in Chapter 23.)

•  Chapter 4 is concerned with the valuation of common stocks. We start by explaining how individual stocks are valued and go on to look at the problem of valuing the entire company. These days many firms do not pay dividends and use excess cash to repurchase stock. In this edition we provide more guidance on valuing these companies.

•  Chapter 6 explains how to calculate the present value of new investments. We cover the same material in this chapter as in previous editions, but we include a longer discussion of the differences between cash flows and accounting profits. We think that this will provide readers with a clearer understanding of how to derive cash-flow forecasts.

•  The financial manager spends a large part of his time interacting with financial institutions and markets. In Chapter 14 we expand our discussion of these institutions. We describe the main forms of institutions, we look at their economic role, and we use the crisis of 2007–2009 to review what happens when financial institutions and markets cease to function well.

•  We substantially rewrote Chapter 16, which looks at payout policy. We review both how much companies should pay out and whether they should do so by means of a dividend payment or stock repurchase. We also return to an issue that we introduced in Chapter 4 and look in more detail at how to value a company when repurchases are important.

•  Chapter 24, which previously looked at the different kinds of long-term debt, now also looks at short-term debt such as bank loans. Many of the issues about debt design such as the role of covenants apply to both short- and long-term debt.

•  In earlier editions we discussed bank debt in the chapter on working capital management. One advantage of moving this discussion to Chapter 24 is that we have the luxury in Chapter 30 of being able to look more broadly at working capital. For example, we now include a discussion of the cash conversion cycle and show how it is affected by management decisions.

The first edition of this book appeared in 1981. Basic principles are the same now as then, but the last three decades have also generated important changes in theory and practice. Research in finance has focused less on what financial managers should do, and more on understanding and interpreting what they do in practice. In other words, finance has become more positive and less normative. For example, we now have careful surveys of firms’ capital investment practices and payout and financing policies. We review these surveys and look at how they cast light on competing theories.

Many financial decisions seem less clear-cut than they were 20 or 30 years ago. It no longer makes sense to ask whether high payouts are always good or always bad, or whether companies should always borrow less or more. The right answer is, “It depends.” Therefore we set out pros and cons of different policies. We ask, “What questions should the financial manager ask when setting financial policy?” You will, for example, see this shift in emphasis when we discuss payout decisions in Chapter 16.

This edition builds on other changes from earlier editions. We recognize that financial managers work more than ever in an international environment and therefore need to be familiar with international differences in financial management and in financial markets and institutions. Chapters 27 (Managing International Risks) and 33 (Governance and Corporate Control around the World) are exclusively devoted to international issues. We have also found more and more opportunities in other chapters to draw cross-border comparisons or use non-U.S. examples. We hope that this material will both provide a better understanding of the wider financial environment and be useful to our many readers around the world.

As every first-grader knows, it is easier to add than to subtract. To make way for new topics we needed to make some judicious pruning. We will not tell you where we cut out material, because we hope that the deletions will be invisible.

The biggest change in this edition is not to the printed text but to the Beyond the Page digital extensions and applications (see Pedagogical Features, below). These pieces are an integral part of the e-versions of the book, but they are also easily accessible via the Web using the QR codes and shortcut URLs provided. They provide additional examples, applications, spreadsheet programs, and opportunities to explore topics in more depth.

BEYOND THE PAGE

● ● ● ● ●

Principles of corporate finance

mhhe.com/bma

The QR codes are easy to use. First, use your smartphone to download any QR-enabled barcode reader from your provider’s marketplace. Focus your smartphone’s camera on any code in the book, and you’ll be able to access the online chapter content instantly. Try the code above now!

Additional examples include:

•  Chapter 2 Do you need to learn how to use a financial calculator? The “Beyond the Page” financial calculator application shows how to do so.

•  Chapter 3 Would you like to calculate a bond’s duration, see how it predicts the effect of small interest rate changes on bond price, calculate the duration of a common stock, or learn how to adjust for convexity? The duration application for Figure 3.2 allows you to do so.

•  Chapter 9 How about measuring the betas of the Fama-French three-factor model for U.S. stocks? The “Beyond the Page” beta estimation application does this.

•  Chapter 15 There was not space in the chapter to include a real IPO prospectus, but you can go “Beyond the Page” to learn more.

•  Chapter 19 The book briefly describes the flow-to-equity method for valuing businesses, but using the method can be tricky. We provide an application that guides you through the procedure.

•  Chapter 20 The Black-Scholes “Beyond the Page” application provides an option calculator. It also shows how to estimate the option’s sensitivity to changes in the inputs.

•  Chapter 28 Would you like to view the most recent financial statements for different U.S. companies and calculate their financial ratios? There is an application that will do this for you.

We believe that the opportunity to add additional content and applications such as these will increasingly widen the type of material that can be made available and help the reader to decide how deeply he or she wishes to explore a topic.

   Making Learning Easier

Each chapter of the book includes an introductory preview, a summary, and an annotated list of suggested further reading. The list of possible candidates for further reading is now voluminous. Rather than trying to list every important article, we largely listed survey articles or general books. We give more specific references in footnotes.

Each chapter is followed by a set of basic problems, intermediate problems on both numerical and conceptual topics, and a few challenge problems. Answers to the odd-numbered basic problems appear in the Appendix at the end of the book.

We included a “Finance on the Web” section in chapters where it makes sense to do so. This section now houses a number of Web Projects, along with new Data Analysis problems. These exercises seek to familiarize the reader with some useful websites and to explain how to download and process data from the Web.

The book also contains 12 end-of-chapter Mini-Cases. These include specific questions to guide the case analyses. Answers to the mini-cases are available to instructors on the book’s website.

Spreadsheet programs such as Excel are tailor-made for many financial calculations. Several chapters include boxes that introduce the most useful financial functions and provide some short practice questions. We show how to use the Excel function key to locate the function and then enter the data. We think that this approach is much simpler than trying to remember the formula for each function.

We conclude the book with a glossary of financial terms.

The 34 chapters in this book are divided into 11 parts. Parts 1 to 3 cover valuation and capital investment decisions, including portfolio theory, asset pricing models, and the cost of capital. Parts 4 to 8 cover payout policy, capital structure, options (including real options), corporate debt, and risk management. Part 9 covers financial analysis, planning, and working-capital management. Part 10 covers mergers and acquisitions, corporate restructuring, and corporate governance around the world. Part 11 concludes.

We realize that instructors will wish to select topics and may prefer a different sequence. We have therefore written chapters so that topics can be introduced in several logical orders. For example, there should be no difficulty in reading the chapters on financial analysis and planning before the chapters on valuation and capital investment.

   Acknowledgments

We have a long list of people to thank for their helpful criticism of earlier editions and for assistance in preparing this one. They include Faiza Arshad, Aleijda de Cazenove Balsan, Kedran Garrison, Robert Pindyck, Sara Salem, and Gretchen Slemmons at MIT; Elroy Dimson, Paul Marsh, Mike Staunton, and Stefania Uccheddu at London Business School; Lynda Borucki, Michael Barhum, Marjorie Fischer, Larry Kolbe, Michael Vilbert, Bente Villadsen, and Fiona Wang at The Brattle Group, Inc.; Alex Triantis at the University of Maryland; Adam Kolasinski at the University of Washington; Simon Gervais at Duke University; Michael Chui at China International Capital Corporation; Pedro Matos at the University of Southern California; Yupana Wiwattanakantang at Hitotsubashi University; Nickolay Gantchev, Tina Horowitz, and Chenying Zhang at the University of Pennsylvania; Julie Wulf at Harvard University; Jinghua Yan at Tykhe Capital; Roger Stein at Moody’s Investor Service; Bennett Stewart at EVA Dimensions; and James Matthews at Towers Perrin.

We want to express our appreciation to those instructors whose insightful comments and suggestions were invaluable to us during the revision process:

Ibrahim Affaneh Indiana University of Pennsylvania

Neyaz Ahmed University of Maryland

Alexander Amati Rutgers University, New Brunswick

Anne Anderson Lehigh University

Noyan Arsen Koc University

Anders Axvarn Gothenburg University

John Banko University of Florida, Gainesville

Michael Barry Boston College

Jan Bartholdy ASB, Denmark

Penny Belk Loughborough University

Omar Benkato Ball State University

Eric Benrud University of Baltimore

Ronald Benson University of Maryland, University College

Peter Berman University of New Haven

Tom Boulton Miami University of Ohio

Edward Boyer Temple University

Alon Brav Duke University

Jean Canil University of Adelaide

Robert Carlson Bethany College

Chuck Chahyadi Eastern Illinois University

Fan Chen University of Mississippi

Celtin Ciner University of North Carolina, Wilmington

John Cooney Texas Tech University

Charles Cuny Washington University, St. Louis

John Davenport Regent University

Ray DeGennaro University of Tennessee, Knoxville

Adri DeRidder Gotland University

William Dimovski Deakin University, Melbourne

David Ding Nanyang Technological University

Robert Duvic University of Texas at Austin

Alex Edmans University of Pennsylvania

Susan Edwards Grand Valley State University

Riza Emekter Robert Morris University

Robert Everett Johns Hopkins University

Dave Fehr Southern New Hampshire University

Donald Flagg University of Tampa

Frank Flanegin Robert Morris University

Zsuzanna Fluck Michigan State University

Connel Fullenkamp Duke University

Mark Garmaise University of California, Los Angeles

Sharon Garrison University of Arizona

Christopher Geczy University of Pennsylvania

George Geis University of Virginia

Stuart Gillan University of Delaware

Felix Goltz Edhec Business School

Ning Gong Melbourne Business School

Levon Goukasian Pepperdine University

Gary Gray Pennsylvania State University

C. J. Green Loughborough University

Mark Griffiths Thunderbird, American School of International Management

Re-Jin Guo University of Illinois, Chicago

Ann Hackert Idaho State University

Winfried Hallerbach Erasmus University, Rotterdam

Milton Harris University of Chicago

Mary Hartman Bentley College

Glenn Henderson University of Cincinnati

Donna Hitscherich Columbia University

Ronald Hoffmeister Arizona State University

James Howard University of Maryland, College Park

George Jabbour George Washington University

Ravi Jagannathan Northwestern University

Abu Jalal Suffolk University

Nancy Jay Mercer University

Thadavillil (Nathan) Jithendranathan University of Saint Thomas

Kathleen Kahle University of Arizona

Jarl Kallberg NYU, Stern School of Business

Ron Kaniel Duke University

Steve Kaplan University of Chicago

Eric Kelley University of Arizona

Arif Khurshed Manchester Business School

Ken Kim University of Wisconsin, Milwaukee

Jiro Eduoard Kondo Northwestern University Kellogg School of Management

C. R. Krishnaswamy Western Michigan University

George Kutner Marquette University

Dirk Laschanzky University of Iowa

Scott Lee Texas A&M University

Bob Lightner San Diego Christian College

David Lins University of Illinois, Urbana

Brandon Lockhart University of Nebraska, Lincoln

David Lovatt University of East Anglia

Greg Lucado University of the Sciences in Philadelphia

Debbie Lucas Northwestern University

Brian Lucey Trinity College, Dublin

Suren Mansinghka University of California, Irvine

Ernst Maug Mannheim University

George McCabe University of Nebraska

Josie McLaren, University of Newcastle

Eric McLaughlin California State University, Pomona

Joe Messina San Francisco State University

Tim Michael University of Houston, Clear Lake

Dag Michalson Bl, Oslo

Franklin Michello Middle Tennessee State University

Peter Moles University of Edinburgh

Katherine Morgan Columbia University

James Nelson East Carolina University

James Owens West Texas A&M University

Darshana Palkar Minnesota State University, Mankato

Claus Parum Copenhagen Business School

Dilip Patro Rutgers University

John Percival University of Pennsylvania

Birsel Pirim University of Illinois, Urbana

Latha Ramchand University of Houston

Rathin Rathinasamy Ball State University

Raghavendra Rau Purdue University

Joshua Raugh University of Chicago

Charu Reheja Wake Forest University

Thomas Rhee California State University, Long Beach

Tom Rietz University of Iowa

Robert Ritchey Texas Tech University

Michael Roberts University of Pennsylvania

Mo Rodriguez Texas Christian University

John Rozycki Drake University

Frank Ryan San Diego State University

Marc Schauten Eramus University

Brad Scott Webster University

Nejat Seyhun University of Michigan

Jay Shanken Emory University

Chander Shekhar University of Melbourne

Hamid Shomali Golden Gate University

Richard Simonds Michigan State University

Bernell Stone Brigham Young University

John Strong College of William & Mary

Avanidhar Subrahmanyam University of California, Los Angeles

Tim Sullivan Bentley College

Shrinivasan Sundaram Ball State University

Chu-Sheng Tai Texas Southern University

Tom Tallerico Dowling College

Stephen Todd Loyola University, Chicago

Walter Torous University of California, Los Angeles

Emery Trahan Northeastern University

Gary Tripp Southern New Hampshire University

Ilias Tsiakas University of Warwick

Narendar V. Rao Northeastern University

David Vang St. Thomas University

Steve Venti Dartmouth College

Joseph Vu DePaul University

John Wald Rutgers University

Chong Wang Naval Postgraduate School

Faye Wang University of Illinois, Chicago

Kelly Welch University of Kansas

Jill Wetmore Saginaw Valley State University

Patrick Wilkie University of Virginia

Matt Will University of Indianapolis

David Williams Texas A&M University, Commerce

Art Wilson George Washington University

Shee Wong University of Minnesota, Duluth

Bob Wood Tennessee Tech University

Fei Xie George Mason University

Minhua Yang University of Central Florida

David Zalewski Providence College

Chenying Zhang University of Pennsylvania

This list is surely incomplete. We know how much we owe to our colleagues at the London Business School, MIT’s Sloan School of Management, and the University of Pennsylvania’s Wharton School. In many cases, the ideas that appear in this book are as much their ideas as ours.

We would also like to thank all those at McGraw-Hill/Irwin who worked on the book, including Michele Janicek and Chuck Synovec, Executive Brand Managers; Noelle Bathurst, Development Editor; Melissa Caughlin, Executive Marketing Manager; Jennifer Jelinski, Marketing Specialist; Rachel Townsend, Content Project Manager; Laurie Entringer, Designer; and Michael McCormick, Senior Buyer.

Finally, we record the continuing thanks due to our wives, Diana, Maureen, and Sally, who were unaware when they married us that they were also marrying the Principles of Corporate Finance.

Richard A. Brealey

Stewart C. Myers

Franklin Allen

Guided Tour

Pedagogical Features

   Chapter Overview

Each chapter begins with a brief narrative and outline to explain the concepts that will be covered in more depth. Useful websites related to material for each Part are provided on the book’s website at www.mcgraw-hill.co.uk/textbooks/brealey

   Finance in Practice Boxes

Relevant news articles from financial publications appear in various chapters throughout the text. Aimed at bringing real-world flavor into the classroom, these boxes provide insight into the business world today.

   Numbered Examples

Numbered and titled examples are called out within chapters to further illustrate concepts. Students can learn how to solve specific problems step-by-step and apply key principles to answer concrete questions and scenarios.

   “Beyond the Page” Interactive Content and Applications

New to this edition! Additional resources and hands-on applications are just a click away. Students can scan the in-text QR codes or use the direct Web address to learn more about key concepts and try out calculations, tables, and figures when they go “Beyond the Page.”

Excel Treatment

   Spreadsheet Functions Boxes

These boxes provide detailed examples of how to use Excel spreadsheets when applying financial concepts. Questions that apply to the spreadsheet follow for additional practice.

   Excel Exhibits

Select tables are set as spreadsheets, and the corresponding Excel files are also available on the book’s website at www.mcgraw-hill.co.uk/textbooks/brealey

End-of-Chapter Features

   Problem Sets

For the eleventh edition, topic labels have been added to each end-of-chapter problem to enable easy assignment creation for instructors and reinforcement for students. These end-of-chapter problems give students hands-on practice with the key concepts. The content is organized by level of difficulty: Basic, Intermediate, and Challenge. Answers to the odd-numbered basic problems are included at the back of the book.

   Excel Problems

Most chapters contain problems, denoted by an icon, specifically linked to Excel spreadsheets that are available on the book’s website at www.mcgraw-hill.co.uk/textbooks/brealey

   Finance on the Web Section

Featured in select chapters, this section includes Web exercises that give students the opportunity to explore financial websites on their own to gain familiarity and apply chapter concepts. These problems provide an easy method of including current, real-world data into the classroom.

   Mini-Cases

To enhance concepts discussed within a chapter, mini-cases are included in select chapters so students can apply their knowledge to real-world scenarios.

Supplements

In this edition, we have gone to great lengths to ensure that our supplements are equal in quality and authority to the text itself.

FOR THE INSTRUCTOR

The following supplements are available to you via the book’s website at www.mcgraw-hill.co.uk/textbooks/brealey and are password protected for security. Print copies are available through your McGraw-Hill representative.

Instructor’s Manual

The Instructor’s Manual was extensively revised and updated by Catherine Teutsch of the University of Colorado. It contains an overview of each chapter, teaching tips, learning objectives, challenge areas, key terms, and an annotated outline that provides references to the PowerPoint slides.

Test Bank

The Test Bank, revised by Frank Ryan of San Diego State University, contains hundreds of multiple-choice and short answer/discussion questions, updated based on the revisions of the authors. The level of difficulty varies, as indicated by the easy, medium, or difficult labels.

Computerized Test Bank

McGraw-Hill’s EZ Test is a flexible and easy-to-use electronic testing program. The program allows you to create tests from book-specific items. It accommodates a wide range of question types and you can add your own questions. Multiple versions of the test can be created and any test can be exported for use with course management systems such as WebCT, BlackBoard, or PageOut. EZ Test Online gives you a place to easily administer your EZ Test–created exams and quizzes online. The program is available for Windows and Macintosh environments.

PowerPoint Presentations

Catherine Teutsch also prepared the PowerPoint presentations, which contain exhibits, outlines, key points, and summaries in a visually stimulating collection of slides. You can edit, print, or rearrange the slides to fit the needs of your course.

Solutions Manual

ISBN 9780077502478; MHID 0077502477

The Solutions Manual, carefully revised by Peter Crabb of Northwest Nazarene University, contains solutions to all basic, intermediate, and challenge problems found at the end of each chapter. This supplement can be purchased by your students with your approval or can be packaged with this text at a discount. Please contact your McGraw-Hill representative for additional information.

Finance Video Series DVD

ISBN 9780073363653; MHID 0073363650

The McGraw-Hill Finance Video Series is a complete video library designed to be added points of discussion to your class. You will find examples of how real businesses face hot topics like mergers and acquisitions, going public, time value of money, and careers in finance.

   Online Support

ONLINE LEARNING CENTER

www.mcgraw-hill.co.uk/textbooks/brealey

Find a wealth of information online! This site contains information about the book and the authors as well as teaching and learning materials for the instructor and student, including:

•  “Beyond the Page” content A wealth of additional examples, explanations, and applications are available for quick access on the website. Each “Beyond the Page” feature is called out in the text with a QR code or icon that links directly to the OLC.

•  Excel templates There are templates for select exhibits, as well as various end-of-chapter problems that have been set as Excel spreadsheets—all denoted by an icon. They correlate with specific concepts in the text and allow students to work through financial problems and gain experience using spreadsheets. Also refer to the valuable Useful Spreadsheet Functions Boxes that are sprinkled throughout the text for some helpful prompts on working in Excel.

•  Online quizzes These multiple-choice questions are provided as an additional testing and reinforcement tool for students. Each quiz is organized by chapter to test the specific concepts presented in that particular chapter. Immediate scoring of the quiz occurs upon submission and the correct answers are provided.

•  Interactive FinSims This valuable asset consists of multiple simulations of key financial topics. Ideal for students to reinforce concepts and gain additional practice to strengthen skills.

MCGRAW-HILL’s CONNECT FINANCE

Less Managing. More Teaching. Greater Learning.

Images McGraw-Hill’s Connect Finance is an online assignment and assessment solution that connects students with the tools and resources they’ll need to achieve success.

McGraw-Hill’s Connect Finance helps prepare students for their future by enabling faster learning, more efficient studying, and higher retention of knowledge.

McGraw-Hill’s Connect Finance Features

ImagesConnect Finance offers a number of powerful tools and features to make managing assignments easier, so faculty can spend more time teaching. With Connect Finance, students can engage with their coursework anytime and anywhere, making the learning process more accessible and efficient. Connect Finance offers the features described here.

Simple Assignment Management

With Connect Finance creating assignments is easier than ever, so you can spend more time teaching and less time managing. The assignment management function enables you to

•  Create and deliver assignments easily with selectable end-of-chapter questions and test bank items.

•  Streamline lesson planning, student progress reporting, and assignment grading to make classroom management more efficient than ever.

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Contents

Preface

Part One: Value

1  Introduction to Corporate Finance

1-1    Corporate Investment and Financing Decisions

Investment Decisions/Financing Decisions/What Is a Corporation?/The Role of the Financial Manager

1-2    The Financial Goal of the Corporation

Shareholders Want Managers to Maximize Market Value/A Fundamental Result/The Investment Trade-off/Should Managers Look After the Interests of Their Shareholders?/Agency Problems and Corporate Governance

1-3    Preview of Coming Attractions

Summary

Problem Sets

Appendix: Why Maximizing Shareholder Value Makes Sense

2  How to Calculate Present Values

2-1    Future Values and Present Values

Calculating Future Values/Calculating Present Values/Valuing an Investment Opportunity/Net Present Value/Risk and Present Value/Present Values and Rates of Return/Calculating Present Values When There Are Multiple Cash Flows/The Opportunity Cost of Capital

2-2    Looking for Shortcuts—Perpetuities and Annuities

How to Value Perpetuities/How to Value Annuities/Valuing Annuities Due/Calculating Annual Payments/Future Value of an Annuity

2-3    More Shortcuts—Growing Perpetuities and Annuities

Growing Perpetuities/Growing Annuities

2-4    How Interest Is Paid and Quoted

Continuous Compounding

Summary

Problem Sets

Finance on the Web

3  Valuing Bonds

3-1    Using the Present Value Formula to Value Bonds

A Short Trip to Paris to Value a Government Bond/On to the United States: Semiannual Coupons and Bond Prices

3-2    How Bond Prices Vary with Interest Rates

Duration and Volatility

3-3    The Term Structure of Interest Rates

Spot Rates, Bond Prices, and the Law of One Price/Measuring the Term Structure/Why the Discount Factor Declines as Futurity Increases—and a Digression on Money Machines

3-4    Explaining the Term Structure

Expectations Theory of the Term Structure/Introducing Risk/Inflation and Term Structure

3-5    Real and Nominal Rates of Interest

Indexed Bonds and the Real Rate of Interest/ What Determines the Real Rate of Interest?/Inflation and Nominal Interest Rates

3-6    The Risk of Default

Corporate Bonds and Default Risk/Sovereign Bonds and Default Risk

Summary

Further Reading

Problem Sets

Finance on the Web

4  The Value of Common Stocks

4-1    How Common Stocks Are Traded

Trading Results for GE

4-2    How Common Stocks Are Valued

Valuation by Comparables/Stock Prices and Dividends

4-3    Estimating the Cost of Equity Capital

Using the DCF Model to Set Gas and Electricity Prices/Dangers Lurk in Constant-Growth Formulas

4-4    The Link Between Stock Price and Earnings per Share

Calculating the Present Value of Growth Opportunities for Fledgling Electronics

4-5    Valuing a Business by Discounted Cash Flow

Valuing the Concatenator Business/Valuation Format/Estimating Horizon Value/ A Further Reality Check/Free Cash Flow, Dividends, and Repurchases

Summary

Problem Sets

Finance on the Web

Mini-Case: Bok Sports

5  Net Present Value and Other Investment Criteria

5-1    A Review of the Basics

Net Present Value’s Competitors/Three Points to Remember about NPV/NPV Depends on Cash Flow, Not on Book Returns

5-2    Payback

Discounted Payback

5-3    Internal (or Discounted-Cash-Flow) Rate of Return

Calculating the IRR/The IRR Rule/Pitfall 1— Lending or Borrowing?/Pitfall 2—Multiple Rates of Return/Pitfall 3—Mutually Exclusive Projects/Pitfall 4—What Happens When There Is More than One Opportunity Cost of Capital?/ The Verdict on IRR

5-4    Choosing Capital Investments When Resources Are Limited

An Easy Problem in Capital Rationing/Uses of Capital Rationing Models

Summary

Further Reading

Problem Sets

Mini-Case: Vegetron’s Cfo Calls Again

6  Making Investment Decisions with the Net Present Value Rule

6-1    Applying the Net Present Value Rule

Rule 1: Only Cash Flow Is Relevant/Rule 2: Estimate Cash Flows on an Incremental Basis/Rule 3: Treat Inflation Consistently/Rule 4: Separate Investment and Financing Decisions

6-2    Example—IM&C’s Fertilizer Project

Separating Investment and Financing Decisions/Investments in Working Capital/A Further Note on Depreciation/A Final Comment on Taxes/Project Analysis/Calculating NPV in Other Countries and Currencies

6-3    Using the NPV Rule to Choose among Projects

Problem 1: The Investment Timing Decision/Problem 2: The Choice between Long- and Short-Lived Equipment/Problem 3: When to Replace an Old Machine/Problem 4: Cost of Excess Capacity

Summary

Problem Sets

Mini-Case: New Economy Transport (A) and (B)

Part Two: Risk

7  Introduction to Risk and Return

7-1    Over a Century of Capital Market History in One Easy Lesson

Arithmetic Averages and Compound Annual Returns/Using Historical Evidence to Evaluate Today’s Cost of Capital/Dividend Yields and the Risk Premium

7-2    Measuring Portfolio Risk

Variance and Standard Deviation/Measuring Variability/How Diversification Reduces Risk

7-3    Calculating Portfolio Risk

General Formula for Computing Portfolio Risk/Limits to Diversification

7-4    How Individual Securities Affect Portfolio Risk

Market Risk Is Measured by Beta/Why Security Betas Determine Portfolio Risk

7-5    Diversification and Value Additivity

Summary

Further Reading

Problem Sets

Finance on the Web

8  Portfolio Theory and the Capital Asset Pricing Model

8-1    Harry Markowitz and the Birth of Portfolio Theory

Combining Stocks into Portfolios/We Introduce Borrowing and Lending

8-2    The Relationship Between Risk and Return

Some Estimates of Expected Returns/Review of the Capital Asset Pricing Model/What If a Stock Did Not Lie on the Security Market Line?

8-3    Validity and Role of the Capital Asset Pricing Model

Tests of the Capital Asset Pricing Model/Assumptions behind the Capital Asset Pricing Model

8-4    Some Alternative Theories

Arbitrage Pricing Theory/A Comparison of the Capital Asset Pricing Model and Arbitrage Pricing Theory/The Three-Factor Model

Summary

Further Reading

Problem Sets

Finance on the Web

Mini-Case: John and Marsha on Portfolio Selection

9  Risk and the Cost of Capital

9-1    Company and Project Costs of Capital

Perfect Pitch and the Cost of Capital/Debt and the Company Cost of Capital

9-2    Measuring the Cost of Equity

Estimating Beta/The Expected Return on Union Pacific Corporation’s Common Stock/Union Pacific’s After-Tax Weighted-Average Cost of Capital/Union Pacific’s Asset Beta

9-3    Analyzing Project Risk

What Determines Asset Betas?/Don’t Be Fooled by Diversifiable Risk/Avoid Fudge Factors in Discount Rates/Discount Rates for International Projects

9-4    Certainty Equivalents—Another Way to Adjust for Risk

Valuation by Certainty Equivalents/When to Use a Single Risk-Adjusted Discount Rate for Long-Lived Assets/A Common Mistake/When You Cannot Use a Single Risk-Adjusted Discount Rate for Long-Lived Assets

Summary

Further Reading

Problem Sets

Finance on the Web

Mini-Case: The Jones Family, Incorporated

Part Three: Best Practices in Capital Budgeting

10  Project Analysis

10-1  The Capital Investment Process

Project Authorizations—and the Problem of Biased Forecasts/Postaudits

10-2  Sensitivity Analysis

Value of Information/Limits to Sensitivity Analysis/Scenario Analysis/Break-Even Analysis/Operating Leverage and the Break-Even Point

10-3  Monte Carlo Simulation

Simulating the Electric Scooter Project

10-4  Real Options and Decision Trees

The Option to Expand/The Option to Abandon/Production Options/Timing Options/More on Decision Trees/Pro and Con Decision Trees

Summary

Further Reading

Problem Sets

Mini-Case: Waldo County

11  Investment, Strategy, and Economic Rents

11-1  Look First to Market Values

The Mercedes and the Movie Star

11-2  Economic Rents and Competitive Advantage

11-3  Marvin Enterprises Decides to Exploit a New Technology—an Example

Forecasting Prices of Gargle Blasters/The Value of Marvin’s New Expansion/Alternative Expansion Plans/The Value of Marvin Stock/The Lessons of Marvin Enterprises

Summary

Further Reading

Problem Sets

Mini-Case: Ecsy-Cola

12  Agency Problems, Compensation, and Performance Measurement

12-1  Incentives and Compensation

Agency Problems in Capital Budgeting/Agency Problems and Risk Taking/Monitoring/Management Compensation/Incentive Compensation/Monitoring Pay for Performance

12-2  Measuring and Rewarding Performance: Residual Income and EVA

Pros and Cons of EVA

12-3  Biases in Accounting Measures of Performance

Example: Measuring the Profitability of the Nodhead Supermarket/Measuring Economic Profitability/Do the Biases Wash Out in the Long Run?/What Can We Do about Biases in Accounting Profitability Measures?/Earnings and Earnings Targets

Summary

Further Reading

Problem Sets

Part Four: Financing Decisions and Market Efficiency

13  Efficient Markets and Behavioral Finance

13-1  We Always Come Back to NPV

Differences between Investment and Financing Decisions

13-2  What Is an Efficient Market?

A Startling Discovery: Price Changes Are Random/Three Forms of Market Efficiency/Efficient Markets: The Evidence

13-3  The Evidence Against Market Efficiency

Do Investors Respond Slowly to New Information?/Bubbles and Market Efficiency

13-4  Behavioral Finance

Limits to Arbitrage/Incentive Problems and the Subprime Crisis

13-5  The Six Lessons of Market Efficiency

Lesson 1: Markets Have No Memory/Lesson 2: Trust Market Prices/Lesson 3: Read the Entrails/Lesson 4: There Are No Financial Illusions/Lesson 5: The Do-It-Yourself Alternative/Lesson 6: Seen One Stock, Seen Them All/What If Markets Are Not Efficient? Implications for the Financial Manager

Summary

Further Reading

Problem Sets

Finance on the Web

14  An Overview of Corporate Financing

14-1  Patterns of Corporate Financing

Do Firms Rely Too Much on Internal Funds?/ How Much Do Firms Borrow?

14-2  Common Stock

Voting Procedures/Dual-Class Shares and Private Benefits/Equity in Disguise/ Preferred Stock

14-3  Debt

Debt Comes in Many Forms/A Debt by Any Other Name/Variety’s the Very Spice of Life

14-4  Financial Markets and Institutions

Financial Markets/Financial Intermediaries/Investment Funds/Financial Institutions

14-5  The Role of Financial Markets and Intermediaries

The Payment Mechanism/Borrowing and Lending/Pooling Risk/Information Provided by Financial Markets/The Financial Crisis of 2007–2009

Summary

Further Reading

Problem Sets

Finance on the Web

15  How Corporations Issue Securities

15-1  Venture Capital

The Venture Capital Market

15-2  The Initial Public Offering

Arranging an Initial Public Offering/The Sale of Marvin Stock/The Underwriters/Costs of a New Issue/Underpricing of IPOs/Hot New-Issue Periods

15-3  Alternative Issue Procedures for IPOs

Types of Auction: A Digression

15-4  Security Sales by Public Companies

General Cash Offers/International Security Issues/The Costs of a General Cash Offer/Market Reaction to Stock Issues/Rights Issues

15-5  Private Placements and Public Issues

Summary

Further Reading

Problem Sets

Finance on the Web

Appendix: Marvin’s New-Issue Prospectus

Part Five: Payout Policy and Capital Structure

16  Payout Policy

16-1  Facts About Payout

How Firms Pay Dividends/How Firms Repurchase Stock

16-2  The Information Content of Dividends and Repurchases

The Information Content of Share Repurchases

16-3  Dividends or Repurchases? The Payout Controversy

Payout Policy Is Irrelevant in Perfect Capital Markets/Dividends or Repurchases? An Example/Stock Repurchases and DCF Models of Share Price/Dividends and Share Issues

16-4  The Rightists

Payout Policy, Investment Policy, and Management Incentives

16-5  Taxes and the Radical Left

Empirical Evidence on Dividends and Taxes/Alternative Tax Systems/Taxes and Payout— A Summary

16-6  Payout Policy and the Life Cycle of the Firm

Payout and Corporate Governance

Summary

Further Reading

Problem Sets

17  Does Debt Policy Matter?

17-1  The Effect of Financial Leverage in a Competitive Tax-free Economy

Enter Modigliani and Miller/The Law of Conservation of Value/An Example of Proposition

17-2  Financial Risk and Expected Returns

Proposition 2/How Changing Capital Structure Affects Beta

17-3  The Weighted-Average Cost of Capital

Two Warnings/Rates of Return on Levered Equity—The Traditional Position/Today’s Unsatisfied Clienteles Are Probably Interested in Exotic Securities/Imperfections and Opportunities

17-4  A Final Word on the After-Tax Weighted-Average Cost of Capital

Summary

Further Reading

Problem Sets

18  How Much Should a Corporation Borrow?

18-1  Corporate Taxes

How Do Interest Tax Shields Contribute to the Value of Stockholders’ Equity?/Recasting Johnson & Johnson’s Capital Structure/MM and Taxes

18-2  Corporate and Personal Taxes

18-3  Costs of Financial Distress

Bankruptcy Costs/Evidence on Bankruptcy Costs/Direct versus Indirect Costs of Bankruptcy/Financial Distress without Bankruptcy/ Debt and Incentives/Risk Shifting: The First Game/Refusing to Contribute Equity Capital: The Second Game/And Three More Games, Briefly/What the Games Cost/Costs of Distress Vary with Type of Asset/The Trade-off Theory of Capital Structure

18-4  The Pecking Order of Financing Choices

Debt and Equity Issues with Asymmetric Information/Implications of the Pecking Order/The Trade-off Theory vs. the Pecking-Order Theory—Some Evidence/The Bright Side and the Dark Side of Financial Slack/Is There a Theory of Optimal Capital Structure?

Summary

Further Reading

Problem Sets

Finance on the Web

19  Financing and Valuation

19-1  The After-Tax Weighted-Average Cost of Capital

Review of Assumptions

19-2  Valuing Businesses

Valuing Rio Corporation/Estimating Horizon Value/WACC vs. the Flow-to-Equity Method

19-3  Using WACC In Practice

Some Tricks of the Trade/Mistakes People Make in Using the Weighted-Average Formula/Adjusting WACC when Debt Ratios and Business Risks Differ/Unlevering and Relevering Betas/The Importance of Rebalancing/The Modigliani–Miller Formula, Plus Some Final Advice

19-4  Adjusted Present Value

APV for the Perpetual Crusher/Other Financing Side Effects/APV for Businesses/APV for International Investments

19-5  Your Questions Answered

Summary

Further Reading

Problem Sets

Finance on the Web

Appendix: Discounting Safe, Nominal Cash Flows

Part Six: Options

20  Understanding Options

20-1  Calls, Puts, and Shares

Call Options and Position Diagrams/Put Options/Selling Calls, Puts, and Shares/Position Diagrams Are Not Profit Diagrams

20-2  Financial Alchemy with Options

Spotting the Option

20-3  What Determines Option Values?

Risk and Option Values

Summary

Further Reading

Problem Sets

Finance on the Web

21  Valuing Options

21-1  A Simple Option-Valuation Model

Why Discounted Cash Flow Won’t Work for Options/Constructing Option Equivalents from Common Stocks and Borrowing/Valuing the Apple Put Option

21-2  The Binomial Method for Valuing Options

Example: The Two-Step Binomial Method/ The General Binomial Method/The Binomial Method and Decision Trees

21-3  The Black–Scholes Formula

Using the Black–Scholes Formula/The Risk of an Option/The Black–Scholes Formula and the Binomial Method

21-4  Black–Scholes in Action

Executive Stock Options/Warrants/ Portfolio Insurance/Calculating Implied Volatilities

21-5  Option Values at a Glance

21-6  The Option Menagerie

Summary

Further Reading

Problem Sets

Finance on the Web

Mini-Case: Bruce Honiball’s Invention

22  Real Options

22-1  The Value of Follow-On Investment Opportunities

Questions and Answers about Blitzen’s Mark II/ Other Expansion Options

22-2  The Timing Option

Valuing the Malted Herring Option/Optimal Timing for Real Estate Development

22-3  The Abandonment Option

Bad News for the Perpetual Crusher/Abandonment Value and Project Life/Temporary Abandonment

22-4  Flexible Production and Procurement

Aircraft Purchase Options

22-5  Investment in Pharmaceutical R&D

22-6  A Conceptual Problem?

Practical Challenges

Summary

Further Reading

Problem Sets

Part Seven: Debt Financing

23  Credit Risk and the Value of Corporate Debt

23-1  Yields on Corporate Debt

What Determines the Yield Spread?

23-2  The Option to Default

How the Default Option Affects a Bond’s Risk and Yield/A Digression: Valuing Government Financial Guarantees

23-3  Bond Ratings and the Probability of Default

23-4  Predicting the Probability of Default

Credit Scoring/Market-Based Risk Models

23-5  Value at Risk

Summary

Further Reading

Problem Sets

Finance on the Web

24  The Many Different Kinds of Debt

24-1  Long-Term Bonds

Bond Terms/Security and Seniority/Asset-Backed Securities/Sinking Funds/Call Provisions/Bond Covenants/Privately Placed Bonds/Foreign Bonds, Eurobonds, and Global Bonds

24-2  Convertible Securities and Some Unusual Bonds

The Value of a Convertible at Maturity/Forcing Conversion/Why Do Companies Issue Convertibles?/Valuing Convertible Bonds/ A Variation on Convertible Bonds: The Bond–Warrant Package/Innovation in the Bond Market

24-3  Bank Loans

Commitment/Maturity/Rate of Interest/Syndicated Loans/Security/Debt Covenants

24-4  Commercial Paper and Medium-Term Notes

Commercial Paper/Medium-Term Notes

Summary

Further Reading

Problem Sets

Mini-Case: The Shocking Demise of Mr. Thorndike

Appendix: Project Finance

25  Leasing

25-1  What Is a Lease?

25-2  Why Lease?

Sensible Reasons for Leasing/Some Dubious Reasons for Leasing

25-3  Operating Leases

Example of an Operating Lease/Lease or Buy?

25-4  Valuing Financial Leases

Example of a Financial Lease/Who Really Owns the Leased Asset?/Leasing and the Internal Revenue Service/A First Pass at Valuing a Lease Contract/The Story So Far

25-5  When Do Financial Leases Pay?

Leasing around the World

25-6  Leveraged Leases

Summary

Further Reading

Problem Sets

Part Eight: Risk Management

26  Managing Risk

26-1  Why Manage Risk?

Reducing the Risk of Cash Shortfalls or Financial Distress/Agency Costs May Be Mitigated by Risk Management/The Evidence on Risk Management

26-2  Insurance

26-3  Reducing Risk with Options

26-4  Forward and Futures Contracts

A Simple Forward Contract/Futures Exchanges/The Mechanics of Futures Trading/Trading and Pricing Financial Futures Contracts/Spot and Futures Prices—Commodities/More about Forward Contracts/Homemade Forward Rate Contracts

26-5  Swaps

Interest Rate Swaps/Currency Swaps/Total Return Swaps

26-6  How to Set Up a Hedge

Hedging Interest Rate Risk/Hedge Ratios and Basis Risk

26-7  Is “Derivative” A Four-Letter Word?

Summary

Further Reading

Problem Sets

Finance on the Web

Mini-Case: Rensselaer Advisers

27  Managing International Risks

27-1  The Foreign Exchange Market

27-2  Some Basic Relationships

Interest Rates and Exchange Rates/The Forward Premium and Changes in Spot Rates/Changes in the Exchange Rate and Inflation Rates/Interest Rates and Inflation Rates/Is Life Really That Simple?

27-3  Hedging Currency Risk

Transaction Exposure and Economic Exposure

27-4  Exchange Risk and International Investment Decisions

The Cost of Capital for International Investments/Do Some Countries Have a Lower Cost of Capital?

27-5  Political Risk

Summary

Further Reading

Problem Sets

Finance on the Web

Mini-Case: Exacta, s.a.

Part Nine: Financial Planning and Working Capital Management

28  Financial Analysis

28-1  Financial Ratios

28-2  Financial Statements

28-3  Home Depot’s Financial Statements

The Balance Sheet/The Income Statement

28-4  Measuring Home Depot’s Performance

Economic Value Added (EVA)/Accounting Rates of Return/Problems with EVA and Accounting Rates of Return

28-5  Measuring Efficiency

28-6  Analyzing the Return on Assets: The Du Pont System

The Du Pont System

28-7  Measuring Leverage

Leverage and the Return on Equity

28-8  Measuring Liquidity

28-9  Interpreting Financial Ratios

Summary

Further Reading

Problem Sets

Finance on the Web

29  Financial Planning

29-1  Links Between Short-Term and Long-Term Financing Decisions

29-2  Tracing Changes in Cash

The Cash Cycle

29-3  Cash Budgeting

Preparing the Cash Budget: Inflows/Preparing the Cash Budget: Outflows

29-4  The Short-Term Financing Plan

Options for Short-Term Financing/ Dynamic’s Financing Plan/Evaluating the Plan/A Note on Short-Term Financial Planning Models

29-5  Long-Term Financial Planning

Why Build Financial Plans?/ A Long-Term Financial Planning Model for Dynamic Mattress/Pitfalls in Model Design/Choosing a Plan

29-6  Growth and External Financing

Summary

Further Reading

Problem Sets

Finance on the Web

30  Working Capital Management

30-1  The Operating and Cash Conversion Cycles

30-2  Inventories

30-3  Credit Management

Terms of Sale/The Promise to Pay/Credit Analysis/The Credit Decision/Collection Policy

30-4  Cash

How Purchases Are Paid For/Speeding Up Check Collections/International Cash Management/Paying for Bank Services

30-5  Marketable Securities

Calculating the Yield on Money-Market Investments/Yields on Money-Market Investments/The International Money Market/Money-Market Instruments

Summary

Further Reading

Problem Sets

Finance on the Web

Part Ten: Mergers, Corporate Control, and Governance

31  Mergers

31-1  Sensible Motives for Mergers

Economies of Scale/Economies of Vertical Integration/Complementary Resources/Surplus Funds/Eliminating Inefficiencies/Industry Consolidation

31-2  Some Dubious Reasons for Mergers

Diversification/Increasing Earnings per Share: The Bootstrap Game/Lower Financing Costs

31-3  Estimating Merger Gains and Costs

Right and Wrong Ways to Estimate the Benefits of Mergers/More on Estimating Costs—What If the Target’s Stock Price Anticipates the Merger?/Estimating Cost When the Merger Is Financed by Stock/Asymmetric Information

31-4  The Mechanics of a Merger

Mergers, Antitrust Law, and Popular Opposition/The Form of Acquisition/Merger Accounting/ Some Tax Considerations

31-5  Proxy Fights, Takeovers, and the Market for Corporate Control

Proxy Contests/Takeovers/Oracle Bids for PeopleSoft/Takeover Defenses/Who Gains Most in Mergers?

31-6  Mergers and the Economy

Merger Waves/Do Mergers Generate Net Benefits?

Summary

Further Reading

Problem Sets

Appendix: Conglomerate Mergers and Value Additivity

32  Corporate Restructuring

32-1  Leveraged Buyouts

The RJR Nabisco LBO/Barbarians at the Gate?/Leveraged Restructurings/LBOs and Leveraged Restructurings

32-2  Fusion and Fission in Corporate Finance

Spin-offs/Carve-outs/Asset Sales/Privatization and Nationalization

32-3  Private Equity

Private-Equity Partnerships/Are Private-Equity Funds Today’s Conglomerates?

32-4  Bankruptcy

Is Chapter 11 Efficient?/Workouts/Alternative Bankruptcy Procedures

Summary

Further Reading

Problem Sets

33  Governance and Corporate Control Around the World

33-1  Financial Markets and Institutions

Investor Protection and the Development of Financial Markets

33-2  Ownership, Control, and Governance

Ownership and Control in Japan/Ownership and Control in Germany/European Boards of Directors/Shareholders versus Stakeholders/Ownership and Control in Other Countries/Conglomerates Revisited

33-3  Do These Differences Matter?

Risk and Short-termism/Growth Industries and Declining Industries/Transparency and Governance

Summary

Further Reading

Problem Sets

Part Eleven: Conclusion

34  Conclusion: What We Do and Do Not Know about Finance

34-1  What We Do Know: The Seven Most Important Ideas in Finance

1. Net Present Value/2. The Capital Asset Pricing Model/3. Efficient Capital Markets/ 4. Value Additivity and the Law of Conservation of Value/5. Capital Structure Theory/6. Option Theory/7. Agency Theory

34-2  What We Do Not Know: 10 Unsolved Problems in Finance

1. What Determines Project Risk and Present Value?/2. Risk and Return—What Have We Missed?/3. How Important Are the Exceptions to the Efficient-Market Theory?/4. Is Management an Off-Balance-Sheet Liability?/5. How Can We Explain the Success of New Securities and New Markets?/6. How Can We Resolve the Payout Controversy?/7. What Risks Should a Firm Take?/8. What Is the Value of Liquidity?/9. How Can We Explain Merger Waves?/10. Why Are Financial Systems So Prone to Crisis?

34-3  A Final Word

APPENDIX

GLOSSARY

INDEX

Note: Present value tables are available on the book’s website, www.mcgraw-hill.co.uk/textbooks/brealey

Part 1 Value

Introduction to Corporate Finance

This book is about how corporations make financial decisions. We start by explaining what these decisions are and what they are seeking to accomplish.

Corporations invest in real assets, which generate income. Some of these assets, such as plant and machinery, are tangible; others, such as brand names and patents, are intangible. Corporations finance their investments by borrowing, by retaining and reinvesting cash flow, and by selling additional shares of stock to the corporation’s shareholders. Thus the corporation’s financial manager faces two broad financial questions: First, what investments should the corporation make? Second, how should it pay for those investments? The investment decision involves spending money; the financing decision involves raising it.

A large corporation may have hundreds of thousands of shareholders. These shareholders differ in many ways, such as their wealth, risk tolerance, and investment horizon. Yet we shall see that they usually share the same financial objective. They want the financial manager to increase the value of the corporation and its current stock price.

Thus the secret of success in financial management is to increase value. That is easy to say, but not very helpful. Instructing the financial manager to increase value is like advising an investor in the stock market to “buy low, sell high.” The problem is how to do it.

There may be a few activities in which one can read a textbook and then just “do it,” but financial management is not one of them. That is why finance is worth studying. Who wants to work in a field where there is no room for judgment, experience, creativity, and a pinch of luck? Although this book cannot guarantee any of these things, it does cover the concepts that govern good financial decisions, and it shows you how to use the tools of the trade of modern finance.

This chapter begins with specific examples of recent investment and financing decisions made by well-known corporations. The chapter ends by stating the financial goal of the corporation, which is to increase, and ideally to maximize, its market value. We explain why this goal makes sense. The middle of the chapter covers what a corporation is and what its financial managers do.

Financial managers add value whenever the corporation can earn a higher return than shareholders can earn for themselves. The shareholders’ investment opportunities outside the corporation set the standard for investments inside the corporation. Financial managers therefore refer to the opportunity cost of the capital contributed by shareholders.

Managers are of course human beings, with their own interests and circumstances; they are not always the perfect servants of shareholders. Therefore corporations must combine governance rules and procedures with appropriate incentives to make sure that all managers and employees—not just the financial managers—pull together to increase value.

Good governance and appropriate incentives also help block out temptations to increase stock price by illegal or unethical means. Thoughtful shareholders do not want the maximum possible stock price. They want the maximum honest stock price.

This chapter introduces five themes that return again and again, in various forms and circumstances, throughout the book:

1.  Corporate finance is all about maximizing value.

2.  The opportunity cost of capital sets the standard for investment decisions.

3.  A safe dollar is worth more than a risky dollar.

4.  Smart investment decisions create more value than smart financing decisions.

5.  Good governance matters.

 1-1   Corporate Investment and Financing Decisions

To carry on business, a corporation needs an almost endless variety of real assets. These do not drop free from a blue sky; they need to be paid for. The corporation pays for the real assets by selling claims on them and on the cash flow that they will generate. These claims are called financial assets or securities. Take a bank loan as an example. The bank provides the corporation with cash in exchange for a financial asset, which is the corporation’s promise to repay the loan with interest. An ordinary bank loan is not a security, however, because it is held by the bank and not sold or traded in financial markets.

Take a corporate bond as a second example. The corporation sells the bond to investors in exchange for the promise to pay interest on the bond and to pay off the bond at its maturity. The bond is a financial asset, and also a security, because it can be held and traded by many investors in financial markets. Securities include bonds, shares of stock, and a dizzying variety of specialized instruments. We describe bonds in Chapter 3, stocks in Chapter 4, and other securities in later chapters.

This suggests the following definitions:

But these equations are too simple. The investment decision also involves managing assets already in place and deciding when to shut down and dispose of assets if profits decline. The corporation also has to manage and control the risks of its investments. The financing decision includes not just raising cash today but also meeting obligations to banks, bondholders, and stockholders that contributed financing in the past. For example, the corporation has to repay its debts when they become due. If it cannot do so, it ends up insolvent and bankrupt. Sooner or later the corporation will also want to pay out cash to its shareholders.¹

Let’s go to more specific examples. Table 1.1 lists nine corporations from all over the world. We have chosen very large public corporations that you are probably already familiar with. You have probably filled up at an Exxon gas station, shopped at Walmart, or used Crest toothpaste.

   TABLE 1.1 Examples of recent investment and financing decisions by major public corporations.

Investment Decisions

The second column of Table 1.1 shows an important recent investment decision for each corporation. These investment decisions are often referred to as capital budgeting or capital expenditure (CAPEX) decisions, because most large corporations prepare an annual capital budget listing the major projects approved for investment. Some of the investments in Table 1.1, such as Walmart’s new stores or Union Pacific’s new locomotives, involve the purchase of tangible assets—assets that you can touch and kick. However, corporations also need to invest in intangible assets, such as research and development (R&D), advertising, and marketing. For example, GlaxoSmithKline and other major pharmaceutical companies invest billions every year on R&D for new drugs. Similarly, consumer goods companies such as Procter & Gamble invest huge sums in advertising and marketing their products. These outlays are investments because they build brand recognition and reputation for the long run.

Today’s capital investments generate future cash returns. Sometimes the cash inflows last for decades. For example, many U.S. nuclear power plants, which were initially licensed by the Nuclear Regulatory Commission to operate for 40 years, are now being re-licensed for 20 more years, and may be able to operate efficiently for 80 years overall.

Yet a stream of cash inflows lasting for 40-plus years may still not be enough. For example, the Southern Company has received authorization to build two new nuclear plants. The cost of the plants has been estimated (perhaps optimistically) at $14 billion. Construction will take seven years (perhaps also an optimistic estimate). Thus Southern, if it goes ahead, will have to invest at least $14 billion and wait at least seven years for any cash return. The longer it has to wait for cash to flow back in, the greater the cash inflow required to justify the investment. Thus the financial manager has to pay attention to the timing of cash inflows, not just to their cumulative amount.

Of course not all investments have distant payoffs. For example, Walmart spends about $40 billion each year to stock up its stores and warehouses before the holiday season. The company’s return on this investment comes within months as the inventory is drawn down and the goods are sold.

In addition, financial managers know (or quickly learn) that cash returns are not guaranteed. An investment could be a smashing success or a dismal failure. For example, the Iridium communications satellite system, which offered instant telephone connections worldwide, soaked up $5 billion of investment before it started operations in 1998. It needed 400,000 subscribers to break even, but attracted only a small fraction of that number. Iridium defaulted on its debt and filed for bankruptcy in 1999. The Iridium system was sold a year later for just $25 million. (Iridium has recovered and is now profitable and expanding, however.)³

Among the contenders for the all-time worst investment was the purchase of Chrysler by Daimler-Benz in 1998 for $40 billion. The German firm planned to turn Chrysler into a company to rival General Motors and Ford. But the new DaimlerChrysler quickly found that selling both luxury and economy-priced cars wasn’t so easy. By 2003 Daimler’s share price had fallen by 70% since the acquisition. Business Week called the merger a “colossal mistake” and reported DaimlerChrysler’s biggest shareholder, Deutsche Bank, openly wanted out after losing some $15 billion in the deal. Daimler eventually sold Chrysler to Cerberus Capital Management for $6 billion in 2007, $34 billion less than it originally paid.

Financial managers do not make major investment decisions in solitary confinement. They may work as part of a team of engineers and managers from manufacturing, marketing, and other business functions. Also, do not think of the financial manager as making billion-dollar investments on a daily basis. Most investment decisions are smaller and simpler, such as the purchase of a truck, machine tool, or computer system. Corporations make thousands of these smaller investment decisions every year. The cumulative amount of small investments can be just as large as that of the occasional big investments, such as those shown in Table 1.1.

Financing Decisions

The third column of Table 1.1 lists a recent financing decision by each corporation. A corporation can raise money from lenders or from shareholders. If it borrows, the lenders contribute the cash, and the corporation promises to pay back the debt plus a fixed rate of interest. If the shareholders put up the cash, they do not get a fixed return, but they hold shares of stock and therefore get a fraction of future profits and cash flow. The shareholders are equity investors, who contribute equity financing. The choice between debt and equity financing is called the capital structure decision. Capital refers to the firm’s sources of long-term financing.

The financing choices available to large corporations seem almost endless. Suppose the firm decides to borrow. Should it borrow from a bank or borrow by issuing bonds that can be traded by investors? Should it borrow for 1 year or 20 years? If it borrows for 20 years, should it reserve the right to pay off the debt early if interest rates fall? Should it borrow in Paris, receiving and promising to repay euros, or should it borrow dollars in New York? As Table 1.1 shows, Procter & Gamble borrowed Japanese yen, but it could have borrowed dollars or euros instead.

Corporations raise equity financing in two ways. First, they can issue new shares of stock. The investors who buy the new shares put up cash in exchange for a fraction of the corporation’s future cash flow and profits. Second, the corporation can take the cash flow generated by its existing assets and reinvest the cash in new assets. In this case the corporation is reinvesting on behalf of existing stockholders. No new shares are issued.

What happens when a corporation does not reinvest all of the cash flow generated by its existing assets? It may hold the cash in reserve for future investment, or it may pay the cash back to its shareholders. Table 1.1 shows that in 2010 GlaxoSmithKline paid cash dividends of $3.2 billion. In the same year Exxon Mobil paid back $12 billion to its stockholders by repurchasing shares. This was in addition to $9 billion paid out as cash dividends. The decision to pay dividends or repurchase shares is called the payout decision. We cover payout decisions in Chapter 16.

In some ways financing decisions are less important than investment decisions. Financial managers say that “value comes mainly from the asset side of the balance sheet.” In fact the most successful corporations sometimes have the simplest financing strategies. Take Microsoft as an example. It is one of the world’s most valuable corporations. At the end of 2011, Microsoft shares traded for $26 each. There were about 8.4 billion shares outstanding. Therefore Microsoft’s overall market value—its market capitalization or market cap—was $26 × 8.4 = $218 billion. Where did this market value come from? It came from Microsoft’s product development, from its brand name and worldwide customer base, from its research and development, and from its ability to make profitable future investments. The value did not come from sophisticated financing. Microsoft’s financing strategy is very simple: it carries no debt to speak of and finances almost all investment by retaining and reinvesting cash flow.

Financing decisions may not add much value, compared with good investment decisions, but they can destroy value if they are stupid or if they are ambushed by bad news. For example, when real estate mogul Sam Zell led a buyout of the Chicago Tribune in 2007 the newspaper took on about $8 billion of additional debt. This was not a stupid decision, but it did prove fatal. As advertising revenues fell away in the recession of 2008, the Tribune could no longer service its debt. In December 2008 it filed for bankruptcy with assets of $7.6 billion and debts of $12.9 billion.

Business is inherently risky. The financial manager needs to identify the risks and make sure they are managed properly. For example, debt has its advantages, but too much debt can land the company in bankruptcy, as the Chicago Tribune discovered. Companies can also be knocked off course by recessions, by changes in commodity prices, interest rates and exchange rates, or by adverse political developments. Some of these risks can be hedged or insured, however, as we explain in Chapters 26 and 27.

What Is a Corporation?

We have been referring to “corporations.” Before going too far or too fast, we need to offer some basic definitions. Details follow in later chapters.

A corporation is a legal entity. In the view of the law, it is a legal person that is owned by its shareholders. As a legal person, the corporation can make contracts, carry on a business, borrow or lend money, and sue or be sued. One corporation can make a takeover bid for another and then merge the two businesses. Corporations pay taxes—but cannot vote!

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Zipcar’s articles

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In the U.S., corporations are formed under state law, based on articles of incorporation that set out the purpose of the business and how it is to be governed and operated.⁴ For example, the articles of incorporation specify the composition and role of the board of directors.⁵ A corporation’s directors are elected by the shareholders. They choose and advise top management and must sign off on some corporate actions, such as mergers and the payment of dividends to shareholders.

A corporation is owned by its shareholders but is legally distinct from them. Therefore the shareholders have limited liability, which means that they cannot be held personally responsible for the corporation’s debts. When the U.S. financial corporation Lehman Brothers failed in 2008, no one demanded that its stockholders put up more money to cover Lehman’s massive debts. Shareholders can lose their entire investment in a corporation, but no more.

When a corporation is first established, its shares may be privately held by a small group of investors, perhaps the company’s managers and a few backers. In this case the shares are not publicly traded and the company is closely held. Eventually, when the firm grows and new shares are issued to raise additional capital, its shares are traded in public markets such as the New York or London stock exchanges. Such corporations are known as public companies. Most well-known corporations in the U.S. are public companies with widely dispersed shareholdings. In other countries, it is more common for large corporations to remain in private hands, and many public companies may be controlled by just a handful of investors. The latter category includes such well-known names as Fiat, Peugeot, Benetton, L’Oréal, and the Swatch Group.

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Zipcar’s bylaws

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A large public corporation may have hundreds of thousands of shareholders, who own the business but cannot possibly manage or control it directly. This separation of ownership and control gives corporations permanence. Even if managers quit or are dismissed and replaced, the corporation survives. Today’s stockholders can sell all their shares to new investors without disrupting the operations of the business. Corporations can, in principle, live forever, and in practice they may survive many human lifetimes. One of the oldest corporations is the Hudson’s Bay Company, which was formed in 1670 to profit from the fur trade between northern Canada and England. The company still operates as one of Canada’s leading retail chains.

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S-corporations

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The separation of ownership and control can also have a downside, for it can open the door for managers and directors to act in their own interests rather than in the stockholders’ interest. We return to this problem later in the chapter.

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Other Forms of Business Organization

  Corporations do not have to be prominent, multinational businesses such as those listed in Table 1.1. You can organize a local plumbing contractor or barber shop as a corporation if you want to take the trouble. But most corporations are larger businesses or businesses that aspire to grow. Small “mom-and-pop” businesses are usually organized as sole proprietorships.

What about the middle ground? What about businesses that grow too large for sole proprietorships but don’t want to reorganize as corporations? For example, suppose you wish to pool money and expertise with some friends or business associates. The solution is to form a partnership and enter into a partnership agreement that sets out how decisions are to be made and how profits are to be split up. Partners, like sole proprietors, face unlimited liability. If the business runs into difficulties, each partner can be held responsible for all the business’s debts.

Partnerships have a tax advantage. Partnerships, unlike corporations, do not have to pay income taxes. The partners simply pay personal income taxes on their shares of the profits.

Some businesses are hybrids that combine the tax advantage of a partnership with the limited liability advantage of a corporation. In a limited partnership, partners are classified as general or limited. General partners manage the business and have unlimited personal liability for its debts. Limited partners are liable only for the money they invest and do not participate in management.

You will also encounter limited liability partnerships (LLPs) or, equivalently, limited liability companies (LLCs). These are partnerships in which all partners have limited liability.

Another U.S. variation on the theme is the professional corporation (PC), which is commonly used by doctors, lawyers, and accountants. In this case, the business has limited liability, but the professionals can still be sued personally, for example, for malpractice.

Most large investment banks such as Morgan Stanley and Goldman Sachs started life as partnerships. But eventually these companies and their financing requirements grew too large for them to continue as partnerships, and they reorganized as corporations. The partnership form of organization does not work well when ownership is widespread and separation of ownership and management is essential.

There are other disadvantages to being a corporation. One is the cost, in both time and money, of managing the corporation’s legal machinery. These costs are particularly burdensome for small businesses. There is also an important tax drawback to corporations in the United States. Because the corporation is a separate legal entity, it is taxed separately. So corporations pay tax on their profits, and shareholders are taxed again when they receive dividends from the company or sell their shares at a profit. By contrast, income generated by businesses that are not incorporated is taxed just once as personal income.

Almost all large and medium-sized businesses are corporations, but the nearby box describes how smaller businesses may be organized.

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The financial managers

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The Role of the Financial Manager

What is the essential role of the financial manager? Figure 1.1 gives one answer. The figure traces how money flows from investors to the corporation and back to investors again. The flow starts when cash is raised from investors (arrow 1 in the figure). The cash could come from banks or from securities sold to investors in financial markets. The cash is then used to pay for the real assets (investment projects) needed for the corporation’s business (arrow 2). Later, as the business operates, the assets generate cash inflows (arrow 3). That cash is either reinvested (arrow 4a) or returned to the investors who furnished the money in the first place (arrow 4b). Of course, the choice between arrows 4a and 4b is constrained by the promises made when cash was raised at arrow 1. For example, if the firm borrows money from a bank at arrow 1, it must repay this money plus interest at arrow 4b.

   FIGURE 1.1 Flow of cash between financial markets and the firm’s operations. Key: (1) Cash raised by selling financial assets to investors; (2) cash invested in the firm’s operations and used to purchase real assets; (3) cash generated by the firm’s operations; (4a) cash reinvested; (4b) cash returned to investors.

You can see examples of arrows 4a and 4b in Table 1.1. Walmart financed its investment in new stores by reinvesting earnings (arrow 4a). Exxon Mobil decided to return cash to shareholders by buying back its stock (arrow 4b). It could have chosen instead to pay the money out as additional cash dividends.

Notice how the financial manager stands between the firm and outside investors. On the one hand, the financial manager helps manage the firm’s operations, particularly by helping to make good investment decisions. On the other hand, the financial manager deals with investors—not just with shareholders but also with financial institutions such as banks and with financial markets such as the New York Stock Exchange.

 1-2   The Financial Goal of the Corporation

Shareholders Want Managers to Maximize Market Value

Walmart has nearly 300,000 shareholders. There is no way that these shareholders can be actively involved in management; it would be like trying to run New York City by town meetings. Authority has to be delegated to professional managers. But how can Walmart’s managers make decisions that satisfy all the shareholders? No two shareholders are exactly the same. They differ in age, tastes, wealth, time horizon, risk tolerance, and investment strategy. Delegating the operation of the firm to professional managers can work only if the shareholders have a common objective. Fortunately there is a natural financial objective on which almost all shareholders agree: Maximize the current market value of shareholders’ investment in the firm.

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B-corporations

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A smart and effective manager makes decisions that increase the current value of the company’s shares and the wealth of its stockholders. This increased wealth can then be put to whatever purposes the shareholders want. They can give their money to charity or spend it in glitzy nightclubs; they can save it or spend it now. Whatever their personal tastes or objectives, they can all do more when their shares are worth more.

Maximizing shareholder wealth is a sensible goal when the shareholders have access to well-functioning financial markets.⁶ Financial markets allow them to share risks and transport savings across time. Financial markets give them the flexibility to manage their own savings and investment plans, leaving the corporation’s financial managers with only one task: to increase market value.

A corporation’s roster of shareholders usually includes both risk-averse and risk-tolerant investors. You might expect the risk-averse to say, “Sure, maximize value, but don’t touch too many high-risk projects.” Instead, they say, “Risky projects are OK, provided that expected profits are more than enough to offset the risks. If this firm ends up too risky for my taste, I’ll adjust my investment portfolio to make it safer.” For example, the risk-averse shareholders can shift more of their portfolios to safer assets, such as U.S. government bonds. They can also just say good-bye, selling shares of the risky firm and buying shares in a safer one. If the risky investments increase market value, the departing shareholders are better off than if the risky investments were turned down.

A Fundamental Result

The goal of maximizing shareholder value is widely accepted in both theory and practice. It’s important to understand why. Let’s walk through the argument step by step, assuming that the financial manager should act in the interests of the firm’s owners, its stockholders.

1.  Each stockholder wants three things:

a.  To be as rich as possible, that is, to maximize his or her current wealth.

b.  To transform that wealth into the most desirable time pattern of consumption either by borrowing to spend now or investing to spend later.

c.  To manage the risk characteristics of that consumption plan.

2.  But stockholders do not need the financial manager’s help to achieve the best time pattern of consumption. They can do that on their own, provided they have free access to competitive financial markets. They can also choose the risk characteristics of their consumption plan by investing in more- or less-risky securities.

3.  How then can the financial manager help the firm’s stockholders? There is only one way: by increasing their wealth. That means increasing the market value of the firm and the current price of its shares.

Economists have proved this value-maximization principle with great rigor and generality. After you have absorbed this chapter, take a look at its Appendix, which contains a further example. The example, though simple, illustrates how the principle of value maximization follows from formal economic reasoning.

We have suggested that shareholders want to be richer rather than poorer. But sometimes you hear managers speak as if shareholders have different goals. For example, managers may say that their job is to “maximize profits.” That sounds reasonable. After all, don’t shareholders want their company to be profitable? But taken literally, profit maximization is not a well-defined financial objective for at least two reasons:

1.  Maximize profits? Which year’s profits? A corporation may be able to increase current profits by cutting back on outlays for maintenance or staff training, but those outlays may have added long-term value. Shareholders will not welcome higher short-term profits if long-term profits are damaged.

2.  A company may be able to increase future profits by cutting this year’s dividend and investing the freed-up cash in the firm. That is not in the shareholders’ best interest if the company earns only a modest return on the money.

The Investment Trade-off

OK, let’s take the objective as maximizing market value. But why do some investments increase market value, while others reduce it? The answer is given by Figure 1.2, which sets out the fundamental trade-off for corporate investment decisions. The corporation has a proposed investment project (a real asset). Suppose it has cash on hand sufficient to finance the project. The financial manager is trying to decide whether to invest in the project. If the financial manager decides not to invest, the corporation can pay out the cash to shareholders, say as an extra dividend. (The investment and dividend arrows in Figure 1.2 are arrows 2 and 4b in Figure 1.1.)

   FIGURE 1.2 The firm can either keep and reinvest cash or return it to investors. (Arrows represent possible cash flows or transfers.) If cash is reinvested, the opportunity cost is the expected rate of return that shareholders could have obtained by investing in financial assets.

Assume that the financial manager is acting in the interests of the corporation’s owners, its stockholders. What do these stockholders want the financial manager to do? The answer depends on the rate of return on the investment project and on the rate of return that the stockholders can earn by investing in financial markets. If the return offered by the investment project is higher than the rate of return that shareholders can get by investing on their own, then the shareholders would vote for the investment project. If the investment project offers a lower return than shareholders can achieve on their own, the shareholders would vote to cancel the project and take the cash instead.

Figure 1.2 could apply to Walmart’s decisions to invest in new retail stores, for example. Suppose Walmart has cash set aside to build 100 new stores in 2014. It could go ahead with the new stores, or it could choose to cancel the investment project and instead pay the cash out to its stockholders. If it pays out the cash, the stockholders can then invest for themselves.

Suppose that Walmart’s new-stores project is just about as risky as the U.S. stock market and that investment in the stock market offers a 10% expected rate of return. If the new stores offer a superior rate of return, say 20%, then Walmart’s stockholders would be happy to let Walmart keep the cash and invest it in the new stores. If the new stores offer only a 5% return, then the stockholders are better off with the cash and without the new stores; in that case, the financial manager should turn down the investment project.

As long as a corporation’s proposed investments offer higher rates of return than its shareholders can earn for themselves in the stock market (or in other financial markets), its shareholders will applaud the investments and its stock price will increase. But if the company earns an inferior return, shareholders boo, stock price falls, and stockholders demand their money back so that they can invest on their own.

In our example, the minimum acceptable rate of return on Walmart’s new stores is 10%. This minimum rate of return is called a hurdle rate or cost of capital. It is really an opportunity cost of capital because it depends on the investment opportunities available to investors in financial markets. Whenever a corporation invests cash in a new project, its shareholders lose the opportunity to invest the cash on their own. Corporations increase value by accepting all investment projects that earn more than the opportunity cost of capital.

Notice that the opportunity cost of capital depends on the risk of the proposed investment project. Why? It’s not just because shareholders are risk-averse. It’s also because shareholders have to trade off risk against return when they invest on their own. The safest investments, such as U.S. government debt, offer low rates of return. Investments with higher expected rates of return—the stock market, for example—are riskier and sometimes deliver painful losses. (The U.S. stock market was down 38% in 2008, for example.) Other investments are riskier still. For example, high-tech growth stocks offer the prospect of higher rates of return but are even more volatile.

Notice too that the opportunity cost of capital is generally not the interest rate that the company pays on a loan from a bank. If the company is making a risky investment, the opportunity cost is the expected return that investors can achieve in financial markets at the same level of risk. The expected return on risky securities is normally well above the interest rate on a bank loan.

Managers look to the financial markets to measure the opportunity cost of capital for the firm’s investment projects. They can observe the opportunity cost of capital for safe investments by looking up current interest rates on safe debt securities. For risky investments, the opportunity cost of capital has to be estimated. We start to tackle this task in Chapter 7.

Should Managers Look After the Interests of Their Shareholders?

We have described managers as the agent of shareholders, who want them to maximize their wealth. But perhaps this begs the questions: Is it desirable for managers to act in the selfish interests of their shareholders? Does a focus on enriching the shareholders mean that managers must act as greedy mercenaries riding roughshod over the weak and helpless?

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Ethical dilemmas

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Most of this book is devoted to financial policies that increase value. None of these policies requires gallops over the weak and helpless. In most instances, little conflict arises between doing well (maximizing value) and doing good. Profitable firms are those with satisfied customers and loyal employees; firms with dissatisfied customers and a disgruntled workforce will probably end up with declining profits and a low stock price.

Most established corporations can add value by building long-term relationships with their customers and establishing a reputation for fair dealing and financial integrity. When something happens to undermine that reputation, the costs can be enormous.

So, when we say that the objective of the firm is to maximize shareholder wealth, we do not mean that anything goes. The law deters managers from making blatantly dishonest decisions, but most managers are not simply concerned with observing the letter of the law or with keeping to written contracts. In business and finance, as in other day-to-day affairs, there are unwritten rules of behavior. These rules make routine financial transactions feasible, because each party to the transaction has to trust the other to keep to his or her side of the bargain.⁷

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A Trojan Horse

  Eurozone countries are threatened with hefty fines if their total government debt exceeds 60% of GDP or if they run a budget deficit of more than 3% of GDP. Greece has never managed to stick to this 60% debt limit, and only once in the past 20 years has it adhered to the 3% deficit ceiling.

When it comes to totting up its debts, the Greek government has shown remarkable ingenuity. But in 2001, shortly after joining the Eurozone, Greece entered into an unusually imaginative scheme that would remove about 2% of the country’s debts from its accounts. It did so by entering into a number of swap transactions with the investment bank, Goldman Sachs. We explain swaps in Chapter 26, but a simple example will illustrate how the scheme worked. Suppose Greece borrows $10 billion, which it then swaps into euros. This means that Greece pays the $10 billion over to Goldman Sachs and receives euros in exchange. From then on Goldman pays Greece enough dollars to service its dollar loan, and in return Greece makes a series of euro payments to Goldman. Such an arrangement is a normal part of government financing. Europe’s governments obtain funds from investors around the world by borrowing dollars or yen. But they need euros to pay their daily bills. The swap allows them to get those euros. What was unusual about the Greek government deal with Goldman Sachs was that the swap was arranged so that Greece got more than $10 billion worth of euros up front — but, of course, had to pay back correspondingly more euros in the future. Those extra euros that it received and the extra euros that it promised to pay in the future were in effect additional debt but they were buried in the swap and did not appear in the official statistics.

The deal with Goldman was a good bit more complicated than our simple example suggests. It also included a separate contract that linked Greece’s payments to future rates of interest. As interest rates fell after 2001, that bet began to sour, and within 4 years the debt had almost doubled in size.

There was nothing illegal about the Greek deal. Nor was it the first Eurozone country to disguise its borrowing in this way, for Italy had used a similar subterfuge in 1995. However, when the deal was uncovered, many observers felt that the Greek government had behaved unethically. Goldman Sachs also was criticized for participating in the subterfuge and for constructing a scheme that was highly profitable to them but poorly understood by the Greek government.

Of course trust is sometimes misplaced. Charlatans and swindlers are often able to hide behind booming markets. It is only “when the tide goes out that you learn who’s been swimming naked.”⁸ The tide went out in 2008 and a number of frauds were exposed. One notorious example was the Ponzi scheme run by the New York financier Bernard Madoff.⁹ Individuals and institutions put about $65 billion in the scheme before it collapsed in 2008. (It’s not clear what Madoff did with all this money, but much of it was apparently paid out to early investors in the scheme to create an impression of superior investment performance.) With hindsight, the investors should not have trusted Madoff or the financial advisers who steered money to Madoff.

Madoff’s Ponzi scheme was (we hope) a once-in-a-lifetime event.¹⁰ It was astonishingly unethical, illegal, and bound to end in tears. More complex ethical issues were raised by the banking crisis of 2007–2009. Look, for example, at the box on the previous page that describes a deal involving the investment bank Goldman Sachs. Some observers believed that Goldman’s actions reflected all that is worst on Wall Street, but others argued that Goldman was simply following its client’s wishes.

Agency Problems and Corporate Governance

We have emphasized the separation of ownership and control in public corporations. The owners (shareholders) cannot control what the managers do, except indirectly through the board of directors. This separation is necessary but also dangerous. You can see the dangers. Managers may be tempted to buy sumptuous corporate jets or to schedule business meetings at tony resorts. They may shy away from attractive but risky projects because they are worried more about the safety of their jobs than about maximizing shareholder value. They may work just to maximize their own bonuses, and therefore redouble their efforts to make and resell flawed subprime mortgages.

Conflicts between shareholders’ and managers’ objectives create agency problems. Agency problems arise when agents work for principals. The shareholders are the principals; the managers are their agents. Agency costs are incurred when (1) managers do not attempt to maximize firm value and (2) shareholders incur costs to monitor the managers and constrain their actions.

Agency problems can sometimes lead to outrageous behavior. For example, when Dennis Kozlowski, the CEO of Tyco, threw a $2 million 40th birthday bash for his wife, he charged half of the cost to the company. This of course was an extreme conflict of interest, as well as illegal. But more subtle and moderate agency problems arise whenever managers think just a little less hard about spending money when it is not their own.

Later in the book we will look at how good systems of governance ensure that shareholders’ pockets are close to the managers’ hearts. This means well-designed incentives for managers, standards for accounting and disclosure to investors, requirements for boards of directors, and legal sanctions for self-dealing by management. When scandals happen, we say that corporate governance has broken down. When corporations compete effectively and ethically to deliver value to shareholders, we are comforted that governance is working properly.

 1-3   Preview of Coming Attractions

Figure 1.2 illustrates how the financial manager can add value for the firm and its shareholders. He or she searches for investments that offer rates of return higher than the opportunity cost of capital. But that search opens up a treasure chest of follow-up questions.

•  Is a higher rate of return on investment always better? Not always, for two reasons. First, a lower-but-safer return can be better than a higher-but-riskier return. Second, an investment with a higher percentage return can generate less value than a lower-return investment that is larger or lasts longer. We show how to calculate the present value (PV) of a stream of cash flows in Chapter 2. Present value is a workhorse concept of corporate finance that shows up in almost every chapter.

•  How do I calculate the rate of return? The rate of return is calculated from the cash inflows and outflows generated by the investment project. See Chapters 2 and 5.

•  What are the cash flows? The future cash flows from an investment project should sum up all cash inflows and outflows caused by the decision to invest. Cash flows are calculated after corporate taxes are paid. They are the free cash flows that can be paid out to shareholders or reinvested on their behalf. Chapter 6 explains free cash flows in detail.

•  How does the financial manager judge whether cash-flow forecasts are realistic? As Niels Bohr, the 1922 Nobel Laureate in Physics, observed, “Prediction is difficult, especially if it’s about the future.” But good financial managers take care to assemble relevant information and to purge forecasts of bias and thoughtless optimism. See Chapters 6 and 9 through 11.

•  How do we measure risk? We look to the risks borne by shareholders, recognizing that investors can dilute or eliminate some risks by holding diversified portfolios (Chapters 7 and 8).

•  How does risk affect the opportunity cost of capital? Here we need a theory of risk and return in financial markets. The most widely used theory is the Capital Asset Pricing Model (Chapters 8 and 9).

•  What determines value in financial markets? We cover valuation of bonds and common stocks in Chapters 3 and 4. We will return to valuation principles again and again in later chapters. As you will see, corporate finance is all about valuation.

•  Where does financing come from? Broadly speaking, from borrowing or from cash invested or reinvested by stockholders. But financing can get complicated when you get down to specifics. Chapter 14 gives an overview of financing. Chapters 23 through 25 cover sources of debt financing, including financial leases, which are debt in disguise.

•  Debt or equity? Does it matter? Not in a world of perfect financial markets. In the real world, the choice between debt and equity does matter, but for many possible reasons, including taxes, the risks of bankruptcy, information differences, and incentives. See Chapters 17 and 18.

That’s enough questions to start, but you can see certain themes emerging. For example, corporate finance is “all about valuation,” not only for the reasons just listed, but because value maximization is the natural financial goal of the corporation. Another theme is the importance of the opportunity cost of capital, which is established in financial markets. The financial manager is an intermediary, who has to understand financial markets as well as the operations and investments of the corporation.

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SUMMARY

Corporations face two principal financial decisions. First, what investments should the corporation make? Second, how should it pay for the investments? The first decision is the investment decision; the second is the financing decision.

The stockholders who own the corporation want its managers to maximize its overall value and the current price of its shares. The stockholders can all agree on the goal of value maximization, so long as financial markets give them the flexibility to manage their own savings and investment plans. Of course, the objective of wealth maximization does not justify unethical behavior. Shareholders do not want the maximum possible stock price. They want the maximum honest share price.

How can financial managers increase the value of the firm? Mostly by making good investment decisions. Financing decisions can also add value, and they can surely destroy value if you screw them up. But it’s usually the profitability of corporate investments that separates value winners from the rest of the pack.

Investment decisions involve a trade-off. The firm can either invest cash or return it to shareholders, for example, as an extra dividend. When the firm invests cash rather than paying it out, shareholders forgo the opportunity to invest it for themselves in financial markets. The return that they are giving up is therefore called the opportunity cost of capital. If the firm’s investments can earn a return higher than the opportunity cost of capital, stock price increases. If the firm invests at a return lower than the opportunity cost of capital, stock price falls.

Managers are not endowed with a special value-maximizing gene. They will consider their own personal interests, which creates a potential conflict of interest with outside shareholders. This conflict is called a principal–agent problem. Any loss of value that results is called an agency cost.

Investors will not entrust the firm with their savings unless they are confident that management will act ethically on their behalf. Successful firms have governance systems that help to align managers’ and shareholders’ interests.

Remember the following five themes, for you will see them again and again throughout this book:

1.  Corporate finance is all about maximizing value.

2.  The opportunity cost of capital sets the standard for investments.

3.  A safe dollar is worth more than a risky dollar.

4.  Smart investment decisions create more value than smart financing decisions.

5.  Good governance matters.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Investment and financing decisions Read the following passage: “Companies usually buy (a) assets. These include both tangible assets such as (b) and intangible assets such as (c). To pay for these assets, they sell (d) assets such as (e). The decision about which assets to buy is usually termed the (f) or (g) decision. The decision about how to raise the money is usually termed the (h) decision.” Now fit each of the following terms into the most appropriate space: financing, real, bonds, investment, executive airplanes, financial, capital budgeting, brand names.

2.  Investment and financing decisions Which of the following are real assets, and which are financial?

a.  A share of stock.

b.  A personal IOU.

c.  A trademark.

d.  A factory.

e.  Undeveloped land.

f.  The balance in the firm’s checking account.

g.  An experienced and hardworking sales force.

h.  A corporate bond.

3.  Investment and financing decisions Vocabulary test. Explain the differences between:

a.  Real and financial assets.

b.  Capital budgeting and financing decisions.

c.  Closely held and public corporations.

d.  Limited and unlimited liability.

4.  Corporations Which of the following statements always apply to corporations?

a.  Unlimited liability.

b.  Limited life.

c.  Ownership can be transferred without affecting operations.

d.  Managers can be fired with no effect on ownership.

INTERMEDIATE

  5.  Separation of ownership In most large corporations, ownership and management are separated. What are the main implications of this separation?

  6.  Opportunity cost of capital F&H Corp. continues to invest heavily in a declining industry. Here is an excerpt from a recent speech by F&H’s CFO:

We at F&H have of course noted the complaints of a few spineless investors and uninformed security analysts about the slow growth of profits and dividends. Unlike those confirmed doubters, we have confidence in the long-run demand for mechanical encabulators, despite competing digital products. We are therefore determined to invest to maintain our share of the overall encabulator market. F&H has a rigorous CAPEX approval process, and we are confident of returns around 8% on investment. That’s a far better return than F&H earns on its cash holdings.

The CFO went on to explain that F&H invested excess cash in short-term government securities, which are almost entirely risk-free but offered only a 4% rate of return.

a.  Is a forecasted 8% return in the encabulator business necessarily better than a 4% safe return on short-term government securities? Why or why not?

b.  Is F&H’s opportunity cost of capital 4%? How in principle should the CFO determine the cost of capital?

  7.  Corporate goals We can imagine the financial manager doing several things on behalf of the firm’s stockholders. For example, the manager might:

a.  Make shareholders as wealthy as possible by investing in real assets.

b.  Modify the firm’s investment plan to help shareholders achieve a particular time pattern of consumption.

c.  Choose high- or low-risk assets to match shareholders’ risk preferences.

d.  Help balance shareholders’ checkbooks.

But in well-functioning capital markets, shareholders will vote for only one of these goals. Which one? Why?

   8.  Maximizing shareholder value Ms. Espinoza is retired and depends on her investments for her income. Mr. Liu is a young executive who wants to save for the future. Both are stockholders in Scaled Composites, LLC, which is building SpaceShipOne to take commercial passengers into space. This investment’s payoff is many years away. Assume it has a positive NPV for Mr. Liu. Explain why this investment also makes sense for Ms. Espinoza.

   9.  Ethical issues The box on page 11 describes the controversial involvement of Goldman Sachs in a financing deal with Greece. The deal was perfectly legal, but many regarded it as unethical. Was the fault solely that of the Greek government or was Goldman partly to blame? There is some indication that the government did not fully understand the bet that it was placing on future interest rates. Did Goldman have a responsibility to ensure that it did?

10.  Agency issues Why might one expect managers to act in shareholders’ interests? Give some reasons.

11.  Agency issues Many firms have devised defenses that make it more difficult or costly for other firms to take them over. How might such defenses affect the firm’s agency problems? Are managers of firms with formidable takeover defenses more or less likely to act in the shareholders’ interests rather than their own? What would you expect to happen to the share price when management proposes to institute such defenses?

12.  Ethical issues Most managers have no difficulty avoiding blatantly dishonest actions. But sometimes gray areas, where it is debatable whether an action is unethical and unacceptable, exist. Suggest an important ethical dilemma that companies may face. What principles should guide their decision?

APPENDIX ● ● ● ● ●

Why Maximizing Shareholder Value Makes Sense

We have suggested that well-functioning financial markets allow different investors to agree on the objective of maximizing value. This idea is sufficiently important that we need to pause and examine it more carefully.

BEYOND THE PAGE

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Foundations of NPV

brealey.mhhe.com/c01

How Financial Markets Reconcile Preferences for Current vs. Future Consumption

Suppose that there are two possible investors with entirely different preferences. Think of A as an ant, who wishes to save for the future, and of G as a grasshopper, who would prefer to spend all his wealth on some ephemeral frolic, taking no heed of tomorrow. Suppose that each has a nest egg of exactly $100,000 in cash. G chooses to spend all of it today, while A prefers to invest it in the financial market. If the interest rate is 10%, A would then have 1.10 × $100,000 = $110,000 to spend a year from now. Of course, there are many possible intermediate strategies. For example, A or G could choose to split the difference, spending $50,000 now and putting the remaining $50,000 to work at 10% to provide 1.10 × $50,000 = $55,000 next year. The entire range of possibilities is shown by the green line in Figure 1A.1.

In our example, A used the financial market to postpone consumption. But the market can also be used to bring consumption forward in time. Let’s illustrate by assuming that instead of having cash on hand of $100,000, our two friends are due to receive $110,000 each at the end of the year. In this case A will be happy to wait and spend the income when it arrives. G will prefer to borrow against his future income and party it away today. With an interest rate of 10%, G can borrow and spend $110,000/1.10 = $100,000. Thus the financial market provides a kind of time machine that allows people to separate the timing of their income from that of their spending. Notice that with an interest rate of 10%, A and G are equally happy with cash on hand of $100,000 or an income of $110,000 at the end of the year. They do not care about the timing of the cash flow; they just prefer the cash flow that has the highest value today ($100,000 in our example).

Investing in Real Assets

In practice individuals are not limited to investing in financial markets; they may also acquire plant, machinery, and other real assets. For example, suppose that A and G are offered the opportunity to invest their $100,000 in a new business that a friend is founding. This will produce a one-off surefire payment of $121,000 next year. A would clearly be happy to invest in the business. It will provide her with $121,000 to spend at the end of the year, rather than the $110,000 that she gets by investing her $100,000 in the financial market. But what about G, who wants money now, not in one year’s time? He too is happy to invest, as long as he can borrow against the future payoff of the investment project. At an interest rate of 10%, G can borrow $110,000 and so will have an extra $10,000 to spend today. Both A and G are better off investing in their friend’s venture. The investment increases their wealth. It moves them up from the green to the maroon line in Figure 1A.1.

Why can both A and G spend more by investing $100,000 in their friend’s business? Because the business provides a return of $21,000, or 21%, whereas they would earn only $10,000, or 10%, by investing their money in the capital market.

A Crucial Assumption

The key condition that allows A and G to agree to invest in the new venture is that both have access to a well-functioning, competitive capital market, in which they can borrow and lend at the same rate. Whenever the corporation’s shareholders have equal access to competitive capital markets, the goal of maximizing market value makes sense.

It is easy to see how this rule would be damaged if we did not have such a well-functioning capital market. For example, suppose that G could not easily borrow against future income. In that case he might well prefer to spend his cash today rather than invest it in the new venture. If A and G were shareholders in the same enterprise, A would be happy for the firm to invest, while G would be clamoring for higher current dividends.

No one believes unreservedly that capital markets function perfectly. Later in this book we discuss several cases in which differences in taxation, transaction costs, and other imperfections must be taken into account in financial decision making. However, we also discuss research indicating that, in general, capital markets function fairly well. In this case maximizing shareholder value is a sensible corporate objective. But for now, having glimpsed the problems of imperfect markets, we shall, like an economist in a shipwreck, simply assume our life jacket and swim safely to shore.

QUESTIONS

1.  Maximizing shareholder value Look back to the numerical example graphed in Figure 1A.1. Suppose the interest rate is 20%. What would the ant (A) and grasshopper (G) do if they both start with $100,000? Would they invest in their friend’s business? Would they borrow or lend? How much and when would each consume?

2.  Maximizing shareholder value Answer this question by drawing graphs like Figure 1A.1. Casper Milktoast has $200,000 available to support consumption in periods 0 (now) and 1 (next year). He wants to consume exactly the same amount in each period. The interest rate is 8%. There is no risk.

a.  How much should he invest, and how much can he consume in each period?

b.  Suppose Casper is given an opportunity to invest up to $200,000 at 10% risk-free. The interest rate stays at 8%. What should he do, and how much can he consume in each period?

   FIGURE 1A.1 The green line shows the possible spending patterns for the ant and grasshopper if they invest $100,000 in the capital market. The red line shows the possible spending patterns if they invest in their friend’s business. Both are better off by investing in the business as long as the grasshopper can borrow against the future income.

___________

¹We have referred to the corporation’s owners as “shareholders” and “stockholders.” The two terms mean exactly the same thing and are used interchangeably. Corporations are also referred to casually as “companies,” “firms,” or “businesses.” We also use these terms interchangeably.

²LVMH Moët Hennessy Louis Vuitton (usually abbreviated to LVMH) markets perfumes and cosmetics, wines and spirits, watches, and other fashion and luxury goods. And, yes, we know what you are thinking, but LVMH really is short for Moët Hennessy Louis Vuitton.

³The private investors who bought the bankrupt system concentrated on aviation, maritime, and defense markets rather than retail customers. In 2010 it arranged $1.8 billion in new financing to replace and upgrade its satellite system.

⁴In the U.S., corporations are identified by the label “Corporation,” “Incorporated,” or “Inc.,” as in US Airways Group, Inc. The UK identifies public corporations by “plc” (short for “Public Limited Corporation”). French corporations have the suffix “SA” (“Société Anonyme”). The corresponding labels in Germany are “GmbH” (“Gesellschaft mit beschränkter Haftung”) or “AG” (“Aktiengesellschaft”).

⁵The corporation’s bylaws set out in more detail the duties of the board of directors and how the firm should conduct its business.

⁶Here we use “financial markets” as shorthand for the financial sector of the economy. Strictly speaking, we should say “access to well-functioning financial markets and institutions.” Many investors deal mostly with financial institutions, for example, banks, insurance companies, or mutual funds. The financial institutions in turn engage in financial markets, including the stock and bond markets. The institutions act as financial intermediaries on behalf of individual investors.

⁷See L. Guiso, L. Zingales, and P. Sapienza, “Trusting the Stock Market,” Journal of Finance 63 (December 2008), pp. 2557–600. The authors show that an individual’s lack of trust is a significant impediment to participation in the stock market. “Lack of trust” means a subjective fear of being cheated.

⁸The quotation is from Warren Buffett’s annual letter to the shareholders of Berkshire Hathaway, March 2008.

⁹Ponzi schemes are named after Charles Ponzi who founded an investment company in 1920 that promised investors unbelievably high returns. He was soon deluged with funds from investors in New England, taking in $1 million during one three-hour period. Ponzi invested only about $30 of the money that he raised, but used part of the cash provided by later investors to pay generous dividends to the original investors. Within months the scheme collapsed and Ponzi started a five-year prison sentence.

¹⁰Ponzi schemes pop up frequently, but none has approached the scope and duration of Madoff’s.

Part 1 Value

How to Calculate Present Values

Companies invest in lots of things. Some are tangible assets—that is, assets you can kick, like factories, machinery, and offices. Others are intangible assets, such as patents or trademarks. In each case the company lays out some money now in the hope of receiving even more money later.

Individuals also make investments. For example, your college education may cost you $40,000 per year. That is an investment you hope will pay off in the form of a higher salary later in life. You are sowing now and expecting to reap later.

Companies pay for their investments by raising money and, in the process, assuming liabilities. For example, they may borrow money from a bank and promise to repay it with interest later. You also may have financed your investment in a college education by borrowing money that you plan to pay back out of that fat salary.

All these financial decisions require comparisons of cash payments at different dates. Will your future salary be sufficient to justify the current expenditure on college tuition? How much will you have to repay the bank if you borrow to finance your degree?

In this chapter we take the first steps toward understanding the relationship between the values of dollars today and dollars in the future. We start by looking at how funds invested at a specific interest rate will grow over time. We next ask how much you would need to invest today to produce a specified future sum of money, and we describe some shortcuts for working out the value of a series of cash payments.

The term interest rate sounds straightforward enough, but rates can be quoted in different ways. We, therefore, conclude the chapter by explaining the difference between the quoted rate and the true or effective interest rate.

Once you have learned how to value cash flows that occur at different points in time, we can move on in the next two chapters to look at how bonds and stocks are valued. After that we will tackle capital investment decisions at a practical level of detail.

For simplicity, every problem in this chapter is set out in dollars, but the concepts and calculations are identical in euros, yen, or any other currency.

 2-1   Future Values and Present Values

Calculating Future Values

Money can be invested to earn interest. So, if you are offered the choice between $100 today and $100 next year, you naturally take the money now to get a year’s interest. Financial managers make the same point when they say that money has a time value or when they quote the most basic principle of finance: a dollar today is worth more than a dollar tomorrow.

Suppose you invest $100 in a bank account that pays interest of r = 7% a year. In the first year you will earn interest of .07 × $100 = $7 and the value of your investment will grow to $107:

By investing, you give up the opportunity to spend $100 today, but you gain the chance to spend $107 next year.

If you leave your money in the bank for a second year, you earn interest of .07 × $107 = $7.49 and your investment will grow to $114.49:

Notice that in the second year you earn interest on both your initial investment ($100) and the previous year’s interest ($7). Thus your wealth grows at a compound rate and the interest that you earn is called compound interest.

If you invest your $100 for t years, your investment will continue to grow at a 7% compound rate to $100 × (1.07)t. For any interest rate r, the future value of your $100 investment will be

The higher the interest rate, the faster your savings will grow. Figure 2.1 shows that a few percentage points added to the interest rate can do wonders for your future wealth. For example, by the end of 20 years $100 invested at 10% will grow to $100 × (1.10)20 = $672.75. If it is invested at 5%, it will grow to only $100 × (1.05)20 = $265.33.

Calculating Present Values

We have seen that $100 invested for two years at 7% will grow to a future value of 100 × 1.072 = $114.49. Let’s turn this around and ask how much you need to invest today to produce $114.49 at the end of the second year. In other words, what is the present value (PV) of the $114.49 payoff?

   FIGURE 2.1 How an investment of $100 grows with compound interest at different interest rates.

You already know that the answer is $100. But, if you didn’t know or you forgot, you can just run the future value calculation in reverse and divide the future payoff by (1.07)2:

In general, suppose that you will receive a cash flow of Ct dollars at the end of year t. The present value of this future payment is

The rate, r, in the formula is called the discount rate, and the present value is the discounted value of the cash flow, Ct. You sometimes see this present value formula written differently. Instead of dividing the future payment by (1 + r)t, you can equally well multiply the payment by 1/(1 + r)t. The expression 1/(1 + r)t is called the discount factor. It measures the present value of one dollar received in year t. For example, with an interest rate of 7% the two-year discount factor is

Investors are willing to pay $.8734 today for delivery of $1 at the end of two years. If each dollar received in year 2 is worth $.8734 today, then the present value of your payment of $114.49 in year 2 must be

The longer you have to wait for your money, the lower its present value. This is illustrated in Figure 2.2. Notice how small variations in the interest rate can have a powerful effect on the present value of distant cash flows. At an interest rate of 5%, a payment of $100 in year 20 is worth $37.69 today. If the interest rate increases to 10%, the value of the future payment falls by about 60% to $14.86.

   FIGURE 2.2 Present value of a future cash flow of $100. Notice that the longer you have to wait for your money, the less it is worth today.

Valuing an Investment Opportunity

How do you decide whether an investment opportunity is worth undertaking? Suppose you own a small company that is contemplating construction of a suburban office block. The cost of buying the land and constructing the building is $700,000. Your company has cash in the bank to finance construction. Your real-estate adviser forecasts a shortage of office space and predicts that you will be able to sell next year for $800,000. For simplicity, we will assume initially that this $800,000 is a sure thing.

The rate of return on this one-period project is easy to calculate. Divide the expected profit ($800,000 – 700,000 = $100,000) by the required investment ($700,000). The result is 100,000/700,000 = .143, or 14.3%.

Figure 2.3 summarizes your choices. (Note the resemblance to Figure 1.2 in the last chapter.) You can invest in the project, or pay cash out to shareholders, who can invest on their own. We assume that they can earn a 7% profit by investing for one year in safe assets (U.S. Treasury debt securities, for example). Or they can invest in the stock market, which is risky but offers an average return of 12%.

   FIGURE 2.3 Your company can either invest $700,000 in an office block and sell it after 1 year for $800,000, or it can return the $700,000 to shareholders to invest in the financial markets.

What is the opportunity cost of capital, 7% or 12%? The answer is 7%: That’s the rate of return that your company’s shareholders could get by investing on their own at the same level of risk as the proposed project. Here the level of risk is zero. (Remember, we are assuming for now that the future value of the office block is known with certainty.) Your shareholders would vote unanimously for the investment project, because the project offers a safe return of 14% versus a safe return of only 7% in financial markets.

The office-block project is therefore a “go,” but how much is it worth and how much will the investment add to your wealth? The project produces a cash flow at the end of one year. To find its present value we discount that cash flow by the opportunity cost of capital:

Suppose that as soon as you have bought the land and paid for the construction, you decide to sell your project. How much could you sell it for? That is an easy question. If the venture will return a surefire $800,000, then your property ought to be worth its PV of $747,664 today. That is what investors in the financial markets would need to pay to get the same future payoff. If you tried to sell it for more than $747,664, there would be no takers, because the property would then offer an expected rate of return lower than the 7% available on government securities. Of course, you could always sell your property for less, but why sell for less than the market will bear? The $747,664 present value is the only feasible price that satisfies both buyer and seller. Therefore, the present value of the property is also its market price.

Net Present Value

The office building is worth $747,664 today, but that does not mean you are $747,664 better off. You invested $700,000, so the net present value (NPV) is $47,664. Net present value equals present value minus the required investment:

In other words, your office development is worth more than it costs. It makes a net contribution to value and increases your wealth. The formula for calculating the NPV of your project can be written as:

Remember that C0, the cash flow at time 0 (that is, today) is usually a negative number. In other words, C0 is an investment and therefore a cash outflow. In our example, C0 = – $700,000.

When cash flows occur at different points in time, it is often helpful to draw a time line showing the date and value of each cash flow. Figure 2.4 shows a time line for your office development. It sets out the net present value calculation assuming that the discount rate r is 7%.¹

   FIGURE 2.4 Calculation showing the NPV of the office development.

Risk and Present Value

We made one unrealistic assumption in our discussion of the office development: Your real estate adviser cannot be certain about the profitability of an office building. Those future cash flows represent the best forecast, but they are not a sure thing.

If the cash flows are uncertain, your calculation of NPV is wrong. Investors could achieve those cash flows with certainty by buying $747,664 worth of U.S. government securities, so they would not buy your building for that amount. You would have to cut your asking price to attract investors’ interest.

Here we can invoke a second basic financial principle: A safe dollar is worth more than a risky dollar. Most investors dislike risky ventures and won’t invest in them unless they see the prospect of a higher return. However, the concepts of present value and the opportunity cost of capital still make sense for risky investments. It is still proper to discount the payoff by the rate of return offered by a risk-equivalent investment in financial markets. But we have to think of expected payoffs and the expected rates of return on other investments.²

Not all investments are equally risky. The office development is more risky than a government security but less risky than a start-up biotech venture. Suppose you believe the project is as risky as investment in the stock market and that stocks are expected to provide a 12% return. Then 12% is the opportunity cost of capital for your project. That is what you are giving up by investing in the office building and not investing in equally risky securities.

Now recompute NPV with r = .12:

The office building still makes a net contribution to value, but the increase in your wealth is smaller than in our first calculation, which assumed that the cash flows from the project were risk-free.

The value of the office building depends, therefore, on the timing of the cash flows and their risk. The $800,000 payoff would be worth just that if you could get it today. If the office building is as risk-free as government securities, the delay in the cash flow reduces value by $52,336 to $747,664. If the building is as risky as investment in the stock market, then the risk further reduces value by $33,378 to $714,286.

Unfortunately, adjusting asset values for both time and risk is often more complicated than our example suggests. Therefore, we take the two effects separately. For the most part, we dodge the problem of risk in Chapters 2 through 6, either by treating all cash flows as if they were known with certainty or by talking about expected cash flows and expected rates of return without worrying how risk is defined or measured. Then in Chapter 7 we turn to the problem of understanding how financial markets cope with risk.

Present Values and Rates of Return

We have decided that constructing the office building is a smart thing to do, since it is worth more than it costs. To discover how much it is worth, we asked how much you would need to invest directly in securities to achieve the same payoff. That is why we discounted the project’s future payoff by the rate of return offered by these equivalent-risk securities—the overall stock market in our example.

We can state our decision rule in another way: your real estate venture is worth undertaking because its rate of return exceeds the opportunity cost of capital. The rate of return is simply the profit as a proportion of the initial outlay:

The cost of capital is once again the return foregone by not investing in financial markets. If the office building is as risky as investing in the stock market, the return foregone is 12%. Since the 14.3% return on the office building exceeds the 12% opportunity cost, you should go ahead with the project.

Building the office block is a smart thing to do, even if the payoff is just as risky as the stock market. We can justify the investment by either one of the following two rules:³

• Net present value rule. Accept investments that have positive net present values.

• Rate of return rule. Accept investments that offer rates of return in excess of their opportunity costs of capital.

Both rules give the same answer, although we will encounter some cases in Chapter 5 where the rate of return rule is unreliable. In those cases, you should use the net present value rule.

Calculating Present Values When There Are Multiple Cash Flows

One of the nice things about present values is that they are all expressed in current dollars—so you can add them up. In other words, the present value of cash flow (A + B) is equal to the present value of cash flow A plus the present value of cash flow B.

Suppose that you wish to value a stream of cash flows extending over a number of years. Our rule for adding present values tells us that the total present value is:

This is called the discounted cash flow (or DCF) formula. A shorthand way to write it is

where ∑ refers to the sum of the series. To find the net present value (NPV) we add the (usually negative) initial cash flow:

EXAMPLE 2.1 • Present Values with Multiple Cash Flows

Your real estate adviser has come back with some revised forecasts. He suggests that you rent out the building for two years at $30,000 a year, and predicts that at the end of that time you will be able to sell the building for $840,000. Thus there are now two future cash flows—a cash flow of C1 = $30,000 at the end of one year and a further cash flow of C2 = (30,000 + 840,000) = $870,000 at the end of the second year.

The present value of your property development is equal to the present value of C1 plus the present value of C2. Figure 2.5 shows that the value of the first year’s cash flow is C1/(1 + r) = 30,000/1.12 = $26,786 and the value of the second year’s flow is C2/(1 + r)2 = 870,000/1.122 = $693,559. Therefore our rule for adding present values tells us that the total present value of your investment is:

   FIGURE 2.5 Calculation showing the NPV of the revised office project.

It looks as if you should take your adviser’s suggestion. NPV is higher than if you sell in year 1:

Your two-period calculations in Example 2.1 required just a few keystrokes on a calculator. Real problems can be much more complicated, so financial managers usually turn to financial calculators especially programmed for present value calculations or to computer spreadsheet programs. A box near the end of the chapter introduces you to some useful Excel functions that can be used to solve discounting problems.

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Introduction to financial calculators

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The Opportunity Cost of Capital

By investing in the office building you are giving up the opportunity to earn an expected return of 12% in the stock market. The opportunity cost of capital is therefore 12%. When you discount the expected cash flows by the opportunity cost of capital, you are asking how much investors in the financial markets are prepared to pay for a security that produces a similar stream of future cash flows. Your calculations showed that these investors would need to pay $720,344 for an investment that produces cash flows of $30,000 at year 1 and $870,000 at year 2. Therefore, they won’t pay any more than that for your office building.

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Introduction to Excel

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Confusion sometimes sneaks into discussions of the cost of capital. Suppose a banker approaches. “Your company is a fine and safe business with few debts,” she says. “My bank will lend you the $700,000 that you need for the office block at 8%.” Does this mean that the cost of capital is 8%? If so, the project would be even more worthwhile. At an 8% cost of capital, PV would be 30,000/1.08 + 870,000/1.082 = $773,663 and NPV = $773,663 – $700,000 = + $73,663.

But that can’t be right. First, the interest rate on the loan has nothing to do with the risk of the project: it reflects the good health of your existing business. Second, whether you take the loan or not, you still face the choice between the office building and an equally risky investment in the stock market. The stock market investment could generate the same expected payoff as your office building at a lower cost. A financial manager who borrows $700,000 at 8% and invests in an office building is not smart, but stupid, if the company or its shareholders can borrow at 8% and invest the money at an even higher return. That is why the 12% expected return on the stock market is the opportunity cost of capital for your project.

 2-2   Looking for Shortcuts—Perpetuities and Annuities

How to Value Perpetuities

Sometimes there are shortcuts that make it easy to calculate present values. Let us look at some examples.

On occasion, the British and the French have been known to disagree and sometimes even to fight wars. At the end of some of these wars the British consolidated the debt they had issued during the war. The securities issued in such cases were called consols. Consols are perpetuities. These are bonds that the government is under no obligation to repay but that offer a fixed income for each year to perpetuity. The British government is still paying interest on consols issued all those years ago. The annual rate of return on a perpetuity is equal to the promised annual payment divided by the present value:⁴

We can obviously twist this around and find the present value of a perpetuity given the discount rate r and the cash payment C:

The year is 2030. You have been fabulously successful and are now a billionaire many times over. It was fortunate indeed that you took that finance course all those years ago. You have decided to follow in the footsteps of two of your heroes, Bill Gates and Warren Buffet. Malaria is still a scourge and you want to help eradicate it and other infectious diseases by endowing a foundation to combat these diseases. You aim to provide $1 billion a year in perpetuity, starting next year. So, if the interest rate is 10%, you are going to have to write a check today for

Two warnings about the perpetuity formula. First, at a quick glance you can easily confuse the formula with the present value of a single payment. A payment of $1 at the end of one year has a present value of 1/(1 + r). The perpetuity has a value of 1/r. These are quite different.

Second, the perpetuity formula tells us the value of a regular stream of payments starting one period from now. Thus your $10 billion endowment would provide the foundation with its first payment in one year’s time. If you also want to provide an up-front sum, you will need to lay out an extra $1 billion.

Sometimes you may need to calculate the value of a perpetuity that does not start to make payments for several years. For example, suppose that you decide to provide $1 billion a year with the first payment four years from now. Figure 2.6 provides a timeline of these payments. Think first about how much they will be worth in year 3. At that point the endowment will be an ordinary perpetuity with the first payment due at the end of the year. So our perpetuity formula tells us that in year 3 the endowment will be worth $1/r = $1/.1 = $10 billion. But it is not worth that much now. To find today’s value we need to multiply by the three-year discount factor 1/(1 + r)3 = 1/(1.1)3 = .751. Thus, the “delayed” perpetuity is worth $10 billion × .751 = $7.51 billion. The full calculation is:

   FIGURE 2.6 This perpetuity makes a series of payments of $1 billion a year starting in year 4.

How to Value Annuities

An annuity is an asset that pays a fixed sum each year for a specified number of years. The equal-payment house mortgage or installment credit agreement are common examples of annuities. So are interest payments on most bonds, as we see in the next chapter.

You can always value an annuity by calculating the value of each cash flow and finding the total. However, it is often quicker to use a simple formula that states that if the interest rate is r, then the present value of an annuity that pays $C a period for each of t periods is:

The expression in brackets shows the present value of $1 a year for each of t years. It is generally known as the t-year annuity factor.

If you are wondering where this formula comes from, look at Figure 2.7. It shows the payments and values of three investments.

   FIGURE 2.7 An annuity that makes payments in each of years 1 through 3 is equal to the difference between two perpetuities.

Row 1 The investment in the first row provides a perpetual stream of $1 starting at the end of the first year. We have already seen that this perpetuity has a present value of 1/r.

Row 2 Now look at the investment shown in the second row of Figure 2.7. It also provides a perpetual stream of $1 payments, but these payments don’t start until year 4. This stream of payments is identical to the payments in row 1, except that they are delayed for an additional three years. In year 3, the investment will be an ordinary perpetuity with payments starting in one year and will therefore be worth 1/r in year 3. To find the value today, we simply multiply this figure by the three-year discount factor. Thus

Row 3 Finally, look at the investment shown in the third row of Figure 2.7. This provides a level payment of $1 a year for each of three years. In other words, it is a three-year annuity. You can also see that, taken together, the investments in rows 2 and 3 provide exactly the same cash payments as the investment in row 1. Thus the value of our annuity (row 3) must be equal to the value of the row 1 perpetuity less the value of the delayed row 2 perpetuity:

Remembering formulas is about as difficult as remembering other people’s birthdays. But as long as you bear in mind that an annuity is equivalent to the difference between an immediate and a delayed perpetuity, you shouldn’t have any difficulty.⁵

EXAMPLE 2.2 • Costing an Installment Plan

Most installment plans call for level streams of payments. Suppose that Tiburon Autos offers an “easy payment” scheme on a new Toyota of $5,000 a year, paid at the end of each of the next five years, with no cash down. What is the car really costing you?

First let us do the calculations the slow way, to show that, if the interest rate is 7%, the present value of these payments is $20,501. The time line in Figure 2.8 shows the value of each cash flow and the total present value. The annuity formula, however, is generally quicker; you simply need to multiply the $5,000 cash flow by the annuity factor:

   FIGURE 2.8 Calculations showing the year-by-year present value of the installment payments.

EXAMPLE 2.3 • Winning Big at the Lottery

In August 2006 eight lucky meatpackers from Nebraska pooled their money to buy Powerball lottery tickets and won a record $365 million. We suspect that the winners received unsolicited congratulations, good wishes, and requests for money from dozens of more or less worthy charities, relations, and newly devoted friends. In response, they could fairly point out that the prize wasn’t really worth $365 million. That sum was to be paid in 30 equal annual installments of $12.167 million each. Assuming that the first payment occurred at the end of one year, what was the present value of the prize? The interest rate at the time was 6.0%.

These payments constitute a 30-year annuity. To value this annuity we simply multiply $12.167 million by the 30-year annuity factor:

At an interest rate of 6.0%, the annuity factor is

The present value of the cash payments is $12.167 × 13.765 = $167.5 million, much below the well-trumpeted prize, but still not a bad day’s haul.

Lottery operators generally make arrangements for winners with big spending plans to take an equivalent lump sum. In our example the winners could either take the $365 million spread over 30 years or receive $167.5 million up front. Both arrangements had the same present value.

Valuing Annuities Due

When we used the annuity formula to value the Powerball lottery prize in Example 2.3, we presupposed that the first payment was made at the end of one year. In fact, the first of the 30 yearly payments was made immediately. How does this change the value of the prize?

If we discount each cash flow by one less year, the present value is increased by the multiple (1 + r). In the case of the lottery prize the value becomes 167.5 × (1 + r) = 167.5 × 1.060 = $177.5 million.

A level stream of payments starting immediately is called an annuity due. An annuity due is worth (1 + r) times the value of an ordinary annuity.

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Calculating Annual Payments

Annuity problems can be confusing on first acquaintance, but you will find that with practice they are generally straightforward. For example, here is a case where you need to use the annuity formula to find the amount of the payment given the present value.

EXAMPLE 2.4 • Paying Off a Bank Loan

Bank loans are paid off in equal installments. Suppose that you take out a four-year loan of $1,000. The bank requires you to repay the loan evenly over the four years. It must therefore set the four annual payments so that they have a present value of $1,000. Thus,

Suppose that the interest rate is 10% a year. Then

Let’s check that this annual payment is sufficient to repay the loan. Table 2.1 provides the calculations. At the end of the first year, the interest charge is 10% of $1,000, or $100. So $100 of the first payment is absorbed by interest, and the remaining $215.47 is used to reduce the loan balance to $784.53.

   TABLE 2.1 An example of an amortizing loan. If you borrow $1,000 at an interest rate of 10%, you would need to make an annual payment of $315.47 over four years to repay that loan with interest.

Next year, the outstanding balance is lower, so the interest charge is only $78.45. Therefore $315.47 – $78.45 = $237.02 can be applied to paying off the loan. Because the loan is progressively paid off, the fraction of each payment devoted to interest steadily falls over time, while the fraction used to reduce the loan increases. By the end of year 4, the amortization is just enough to reduce the balance of the loan to zero.

Loans that involve a series of level payments are known as amortizing loans. “Amortizing” means that part of the regular payment is used to pay interest on the loan and part is used to reduce the amount of the loan.

EXAMPLE 2.5 • Calculating Mortgage Payments

Most mortgages are amortizing loans. For example, suppose that you take out a $250,000 house mortgage from your local savings bank when the interest rate is 12%. The bank requires you to repay the mortgage in equal annual installments over the next 30 years.

Thus,

Figure 2.9 shows that in the early years, almost all of the mortgage payment is eaten up by interest and only a small fraction is used to reduce the amount of the loan. Even after 15 years, the bulk of the annual payment goes to pay the interest on the loan. From then on, the amount of the loan begins to decline rapidly.

   FIGURE 2.9 Mortgage amortization. This figure shows the breakdown of mortgage payments between interest and amortization.

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Try It! Figure 2.9: The amortzation schedule

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Future Value of an Annuity

Sometimes you need to calculate the future value of a level stream of payments.

EXAMPLE 2.6 • Saving to Buy a Sailboat

Perhaps your ambition is to buy a sailboat; something like a 40-foot Beneteau would fit the bill very well. But that means some serious saving. You estimate that, once you start work, you could save $20,000 a year out of your income and earn a return of 8% on these savings. How much will you be able to spend after five years?

We are looking here at a level stream of cash flows—an annuity. We have seen that there is a shortcut formula to calculate the present value of an annuity. So there ought to be a similar formula for calculating the future value of a level stream of cash flows.

Think first how much your savings are worth today. You will set aside $20,000 in each of the next five years. The present value of this five-year annuity is therefore equal to

Once you know today’s value of the stream of cash flows, it is easy to work out its value in the future. Just multiply by (1.08)5:

You should be able to buy yourself a nice boat for $117,000.

In Example 2.6 we calculate the future value of an annuity by first calculating its present value and then multiplying by (1 + r)t. The general formula for the future value of a level stream of cash flows of $1 a year for t years is, therefore,

There is a general point here. If you can find the present value of any series of cash flows, you can always calculate future value by multiplying by (1 + r)t:

 2-3   More Shortcuts—Growing Perpetuities and Annuities

Growing Perpetuities

You now know how to value level streams of cash flows, but you often need to value a stream of cash flows that grows at a constant rate. For example, think back to your plans to donate $10 billion to fight malaria and other infectious diseases. Unfortunately, you made no allowance for the growth in salaries and other costs, which will probably average about 4% a year starting in year 1. Therefore, instead of providing $1 billion a year in perpetuity, you must provide $1 billion in year 1, 1.04 × $1 billion in year 2, and so on. If we call the growth rate in costs g, we can write down the present value of this stream of cash flows as follows:

Fortunately, there is a simple formula for the sum of this geometric series.⁶ If we assume that r is greater than g, our clumsy-looking calculation simplifies to

Therefore, if you want to provide a perpetual stream of income that keeps pace with the growth rate in costs, the amount that you must set aside today is

You will meet this perpetual-growth formula again in Chapter 4, where we use it to value the stock of mature, slowly growing companies.

Growing Annuities

You are contemplating membership in the St. Swithin’s and Ancient Golf Club. The annual membership fee for the coming year is $5,000, but you can make a single payment today of $12,750, which will provide you with membership for the next three years. Which is the better deal? The answer depends on how rapidly membership fees are likely to increase over the three-year period. For example, suppose that the annual fee is payable at the end of each year and is expected to increase by 6% per annum. The discount rate is 10%.

The problem is to calculate the present value of the three-year stream of growing payments. The first payment occurs at the end of year 1 and is C = $5,000. Thereafter, the payments grow at the rate of g = .06 each year. Thus in year 2 the expected payment is $5,000 × 1.06, and in year 3 it is $5,000 × 1.062. Of course, you could calculate these cash flows and discount them at 10%. The alternative is to use the following formula for the present value of a growing annuity:⁷

   TABLE 2.2 Some useful shortcut formulas.

In our golf club example, the present value of the membership fees for the next three years is

If you can find the cash, you would be better off paying now for a three-year membership.

Too many formulas are bad for the digestion. So we will stop at this point and spare you any more of them. The formulas discussed so far appear in Table 2.2.

 2-4   How Interest Is Paid and Quoted

In our examples we have assumed that cash flows occur only at the end of each year. This is sometimes the case. For example, in France and Germany the government pays interest on its bonds annually. However, in the United States and Britain government bonds pay interest semiannually. So if the interest rate on a U.S. government bond is quoted as 10%, the investor in practice receives interest of 5% every six months.

If the first interest payment is made at the end of six months, you can earn an additional six months’ interest on this payment. For example, if you invest $100 in a bond that pays interest of 10% compounded semiannually, your wealth will grow to 1.05 × $100 = $105 by the end of six months and to 1.05 × $105 = $110.25 by the end of the year. In other words, an interest rate of 10% compounded semiannually is equivalent to 10.25% compounded annually. The effective annual interest rate on the bond is 10.25%.

Let’s take another example. Suppose a bank offers you an automobile loan at an annual percentage rate, or APR, of 12% with interest to be paid monthly. This means that each month you need to pay one-twelfth of the annual rate, that is, 12/12 = 1% a month. Thus the bank is quoting a rate of 12%, but the effective annual interest rate on your loan is 1.0112 – 1 = .1268, or 12.68%.⁸

Our examples illustrate that you need to distinguish between the quoted annual interest rate and the effective annual rate. The quoted annual rate is usually calculated as the total annual payment divided by the number of payments in the year. When interest is paid once a year, the quoted and effective rates are the same. When interest is paid more frequently, the effective interest rate is higher than the quoted rate.

In general, if you invest $1 at a rate of r per year compounded m times a year, your investment at the end of the year will be worth [1 +(r/m)]m and the effective interest rate is [1 + (r/m)]m – 1. In our automobile loan example r = .12 and m = 12. So the effective annual interest rate was [1 + .12/12]12 – 1 = .1268, or 12.68%.

Continuous Compounding

Instead of compounding interest monthly or semiannually, the rate could be compounded weekly (m = 52) or daily (m = 365). In fact there is no limit to how frequently interest could be paid. One can imagine a situation where the payments are spread evenly and continuously throughout the year, so the interest rate is continuously compounded.⁹ In this case m is infinite.

It turns out that there are many occasions in finance when continuous compounding is useful. For example, one important application is in option pricing models, such as the Black–Scholes model that we introduce in Chapter 21. These are continuous time models. So you will find that most computer programs for calculating option values ask for the continuously compounded interest rate.

It may seem that a lot of calculations would be needed to find a continuously compounded interest rate. However, think back to your high school algebra. You may recall that as m approaches infinity [1 + (r/m)]m approaches (2.718)r. The figure 2.718—or e, as it is called—is the base for natural logarithms. Therefore, $1 invested at a continuously compounded rate of r will grow to er = (2.718)r by the end of the first year. By the end of t years it will grow to ert = (2.718)rt.

Example 1 Suppose you invest $1 at a continuously compounded rate of 11% (r = .11) for one year (t = 1). The end-year value is e.11, or $1.116. In other words, investing at 11% a year continuously compounded is exactly the same as investing at 11.6% a year annually compounded.

Example 2 Suppose you invest $1 at a continuously compounded rate of 11% (r = .11) for two years (t = 2). The final value of the investment is ert = e.22, or $1.246.

Sometimes it may be more reasonable to assume that the cash flows from a project are spread evenly over the year rather than occurring at the year’s end. It is easy to adapt our previous formulas to handle this. For example, suppose that we wish to compute the present value of a perpetuity of C dollars a year. We already know that if the payment is made at the end of the year, we divide the payment by the annually compounded rate of r:

If the same total payment is made in an even stream throughout the year, we use the same formula but substitute the continuously compounded rate.

Suppose the annually compounded rate is 18.5%. The present value of a $100 perpetuity, with each cash flow received at the end of the year, is 100/.185 = $540.54. If the cash flow is received continuously, we must divide $100 by 17%, because 17% continuously compounded is equivalent to 18.5% annually compounded (e.17 = 1.185). The present value of the continuous cash flow stream is 100/.17 = $588.24. Investors are prepared to pay more for the continuous cash payments because the cash starts to flow in immediately.

Example 3 After you have retired, you plan to spend $200,000 a year for 20 years. The annually compounded interest rate is 10%. How much must you save by the time you retire to support this spending plan?

Let us first do the calculations assuming that you spend the cash at the end of each year. In this case we can use the simple annuity formula that we derived earlier:

Thus, you will need to have saved nearly $1¾ million by the time you retire.

Instead of waiting until the end of each year before you spend any cash, it is more reasonable to assume that your expenditure will be spread evenly over the year. In this case, instead of using the annually compounded rate of 10%, we must use the continuously compounded rate of r = 9.53% (e.0953 = 1.10). Therefore, to cover a steady stream of expenditure, you need to set aside the following sum:¹⁰

USEFUL SPREADSHEET FUNCTIONS

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Discounting Cash Flows

  Spreadsheet programs such as Excel provide built-in functions to solve discounted-cash-flow (DCF) problems. You can find these functions by pressing fx on the Excel toolbar. If you then click on the function that you wish to use, Excel asks you for the inputs that it needs. At the bottom left of the function box there is a Help facility with an example of how the function is used.

Here is a list of useful functions for DCF problems and some points to remember when entering data:

• FV: Future value of single investment or annuity.

• PV: Present value of single future cash flow or annuity.

• RATE: Interest rate (or rate of return) needed to produce given future value or annuity.

• NPER: Number of periods (e.g., years) that it takes an investment to reach a given future value or series of future cash flows.

• PMT: Amount of annuity payment with a given present or future value.

• NPV: Calculates the value of a stream of negative and positive cash flows. (When using this function, note the warning below.)

• XNPV: Calculates the net present value at the date of the first cash flow of a series of cash flows occurring at uneven intervals.

• EFFECT: The effective annual interest rate, given the quoted rate (APR) and number of interest payments in a year.

• NOMINAL: The quoted interest rate (APR) given the effective annual interest rate.

All the inputs in these functions can be entered directly as numbers or as the addresses of cells that contain the numbers.

Three warnings:

1.  PV is the amount that needs to be invested today to produce a given future value. It should therefore be entered as a negative number. Entering both PV and FV with the same sign when solving for RATE results in an error message.

2.  Always enter the interest or discount rate as a decimal value (e.g., .05 rather than 5%).

3.  Use the NPV function with care. Better still, don’t use it at all. It gives the value of the cash flows one period before the first cash flow and not the value at the date of the first cash flow.

Spreadsheet Questions

The following questions provide opportunities to practice each of the Excel functions.

1. (FV) In 1880 five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelly. One hundred and thirteen years later the granddaughters of two of the trackers claimed that this reward had not been paid. If the interest rate over this period averaged about 4.5%, how much would the A$100 have accumulated to?

2. (PV) Your company can lease a truck for $10,000 a year (paid at the end of the year) for six years, or it can buy the truck today for $50,000. At the end of the six years the truck will be worthless. If the interest rate is 6%, what is the present value of the lease payments? Is the lease worthwhile?

3. (RATE) Ford Motor stock was one of the victims of the 2008 credit crisis. In June 2007, Ford stock price stood at $9.42. Eighteen months later it was $2.72. What was the annual rate of return over this period to an investor in Ford stock?

4. (NPER) An investment adviser has promised to double your money. If the interest rate is 7% a year, how many years will she take to do so?

5. (PMT) You need to take out a home mortgage for $200,000. If payments are made annually over 30 years and the interest rate is 8%, what is the amount of the annual payment?

6. (XNPV) Your office building requires an initial cash outlay of $370,000. Suppose that you plan to rent it out for three years at $20,000 a year and then sell it for $400,000. If the cost of capital is 12%, what is its net present value?

7. (EFFECT) Banque Nationale Supérieure pays 6.2% interest compounded annually. Banque Nationale Principale pays 6% interest compounded monthly. Which bank offers the higher effective annual interest rate?

8. (NOMINAL) What monthly compounded interest rate would Banque Nationale Principale need to pay on savings deposits to provide an effective rate of 6.2%?

To support a steady stream of outgoings, you must save an additional $83,600.

Often in finance we need only a ballpark estimate of present value. An error of 5% in a present value calculation may be perfectly acceptable. In such cases it doesn’t usually matter whether we assume that cash flows occur at the end of the year or in a continuous stream. At other times precision matters, and we do need to worry about the exact frequency of the cash flows.

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SUMMARY

Firms can best help their shareholders by accepting all projects that are worth more than they cost. In other words, they need to seek out projects with positive net present values. To find net present value we first calculate present value. Just discount future cash flows by an appropriate rate r, usually called the discount rate, hurdle rate, or opportunity cost of capital:

Net present value is present value plus any immediate cash flow:

Remember that C₀ is negative if the immediate cash flow is an investment, that is, if it is a cash outflow.

The discount rate r is determined by rates of return prevailing in capital markets. If the future cash flow is absolutely safe, then the discount rate is the interest rate on safe securities such as U.S. government debt. If the future cash flow is uncertain, then the expected cash flow should be discounted at the expected rate of return offered by equivalent-risk securities. (We talk more about risk and the cost of capital in Chapters 7 to 9.)

Cash flows are discounted for two simple reasons: because (1) a dollar today is worth more than a dollar tomorrow and (2) a safe dollar is worth more than a risky one. Formulas for PV and NPV are numerical expressions of these ideas.

Financial markets, including the bond and stock markets, are the markets where safe and risky future cash flows are traded and valued. That is why we look to rates of return prevailing in the financial markets to determine how much to discount for time and risk. By calculating the present value of an asset, we are estimating how much people will pay for it if they have the alternative of investing in the capital markets.

You can always work out any present value using the basic formula, but shortcut formulas can reduce the tedium. We showed how to value an investment that makes a level stream of cash flows forever (a perpetuity) and one that produces a level stream for a limited period (an annuity). We also showed how to value investments that produce growing streams of cash flows.

When someone offers to lend you a dollar at a quoted interest rate, you should always check how frequently the interest is to be paid. For example, suppose that a $100 loan requires six-month payments of $3. The total yearly interest payment is $6 and the interest will be quoted as a rate of 6% compounded semiannually. The equivalent annually compounded rate is (1.03)² – 1 = .061, or 6.1%. Sometimes it is convenient to assume that interest is paid evenly over the year, so that interest is quoted as a continuously compounded rate.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Future values At an interest rate of 12%, the six-year discount factor is .507. How many dollars is $.507 worth in six years if invested at 12%?

2.  Discount factors If the PV of $139 is $125, what is the discount factor?

3.  Present values If the cost of capital is 9%, what is the PV of $374 paid in year 9?

4.  Present values A project produces a cash flow of $432 in year 1, $137 in year 2, and $797 in year 3. If the cost of capital is 15%, what is the project’s PV?

5.  Futures values If you invest $100 at an interest rate of 15%, how much will you have at the end of eight years?

6.  Perpetuities An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9%, what is the NPV?

7.  Growing perpetuities A common stock will pay a cash dividend of $4 next year. After that, the dividends are expected to increase indefinitely at 4% per year. If the discount rate is 14%, what is the PV of the stream of dividend payments?

8.  Perpetuities and annuities The interest rate is 10%.

a.  What is the PV of an asset that pays $1 a year in perpetuity?

b.  The value of an asset that appreciates at 10% per annum approximately doubles in seven years. What is the approximate PV of an asset that pays $1 a year in perpetuity beginning in year 8?

c.  What is the approximate PV of an asset that pays $1 a year for each of the next seven years?

d.  A piece of land produces an income that grows by 5% per annum. If the first year’s income is $10,000, what is the value of the land?

9.  Future values and annuities

a.  The cost of a new automobile is $10,000. If the interest rate is 5%, how much would you have to set aside now to provide this sum in five years?

b.  You have to pay $12,000 a year in school fees at the end of each of the next six years. If the interest rate is 8%, how much do you need to set aside today to cover these bills?

c.  You have invested $60,476 at 8%. After paying the above school fees, how much would remain at the end of the six years?

10.  Continuous compounding The continuously compounded interest rate is 12%.

a.  You invest $1,000 at this rate. What is the investment worth after five years?

b.  What is the PV of $5 million to be received in eight years?

c.  What is the PV of a continuous stream of cash flows, amounting to $2,000 per year, starting immediately and continuing for 15 years?

11.  Compounding intervals You are quoted an interest rate of 6% on an investment of $10 million. What is the value of your investment after four years if interest is compounded:

a.  Annually?

b.  Monthly? or

c.  Continuously?

INTERMEDIATE

12.  Present values What is the PV of $100 received in:

a.  Year 10 (at a discount rate of 1%)?

b.  Year 10 (at a discount rate of 13%)?

c.  Year 15 (at a discount rate of 25%)?

d.  Each of years 1 through 3 (at a discount rate of 12%)?

13.  Discount factors and present values

a.  If the one-year discount factor is .905, what is the one-year interest rate?

b.  If the two-year interest rate is 10.5%, what is the two-year discount factor?

c.  Given these one- and two-year discount factors, calculate the two-year annuity factor.

d.  If the PV of $10 a year for three years is $24.65, what is the three-year annuity factor?

e.  From your answers to (c) and (d), calculate the three-year discount factor.

14.  Present values A factory costs $800,000. You reckon that it will produce an inflow after operating costs of $170,000 a year for 10 years. If the opportunity cost of capital is 14%, what is the net present value of the factory? What will the factory be worth at the end of five years?

15.  Present values A machine costs $380,000 and is expected to produce the following cash flows:

If the cost of capital is 12%, what is the machine’s NPV?

16.  Growing annuities  Yasuo Obuchi is 30 years of age and his salary next year will be ¥4,000,000. He forecasts that his salary will increase at a steady rate of 5% per annum until his retirement at age 60.

a.  If the discount rate is 8%, what is the PV of these future salary payments?

b.  If Mr Obuchi saves 5% of his salary each year and invests these savings at an interest rate of 8%, how much will he have saved by age 60?

c.  If he plans to spend these savings in even amounts over the subsequent 20 years, how much can he spend each year?

17.  Present values A factory costs $400,000. It will produce an inflow after operating costs of $100,000 in year 1, $200,000 in year 2, and $300,000 in year 3. The opportunity cost of capital is 12%. Calculate the NPV.

18.  Present values Halcyon Lines is considering the purchase of a new bulk carrier for $8 million. The forecasted revenues are $5 million a year and operating costs are $4 million. A major refit costing $2 million will be required after both the fifth and tenth years. After 15 years, the ship is expected to be sold for scrap at $1.5 million. If the discount rate is 8%, what is the ship’s NPV?

19.  Present values As winner of a breakfast cereal competition, you can choose one of the following prizes:

a.  $100,000 now.

b.  $180,000 at the end of five years.

c.  $11,400 a year forever.

d.  $19,000 for each of 10 years.

e.  $6,500 next year and increasing thereafter by 5% a year forever.

If the interest rate is 12%, which is the most valuable prize?

20.  Annuities Siegfried Basset is 65 years of age and has a life expectancy of 12 more years. He wishes to invest $20,000 in an annuity that will make a level payment at the end of each year until his death. If the interest rate is 8%, what income can Mr. Basset expect to receive each year?

21.  Annuities David and Helen Zhang are saving to buy a boat at the end of five years. If the boat costs $20,000 and they can earn 10% a year on their savings, how much do they need to put aside at the end of years 1 through 5?

22.  Annuities Kangaroo Autos is offering free credit on a new $10,000 car. You pay $1,000 down and then $300 a month for the next 30 months. Turtle Motors next door does not offer free credit but will give you $1,000 off the list price. If the rate of interest is 10% a year (about .83% a month), which company is offering the better deal?

23.  Present values Recalculate the NPV of the office building venture in Example 2.1 at interest rates of 5, 10, and 15%. Plot the points on a graph with NPV on the vertical axis and the discount rates on the horizontal axis. At what discount rate (approximately) would the project have zero NPV? Check your answer.

24.  Perpetuities and continuous compounding If the interest rate is 7%, what is the value of the following three investments?

a.  An investment that offers you $100 a year in perpetuity with the payment at the end of each year.

b.  A similar investment with the payment at the beginning of each year.

c.  A similar investment with the payment spread evenly over each year.

25.  Perpetuities and annuities Refer back to Sections 2-3 through 2-4. If the rate of interest is 8% rather than 10%, how much would you need to set aside to provide each of the following?

a.  $1 billion at the end of each year in perpetuity.

b.  A perpetuity that pays $1 billion at the end of the first year and that grows at 4% a year.

c.  $1 billion at the end of each year for 20 years.

d.  $1 billion a year spread evenly over 20 years.

26.  Continuous compounding How much will you have at the end of 20 years if you invest $100 today at 15% annually compounded? How much will you have if you invest at 15% continuously compounded?

27.  Perpetuities You have just read an advertisement stating, “Pay us $100 a year for 10 years and we will pay you $100 a year thereafter in perpetuity.” If this is a fair deal, what is the rate of interest?

28.  Compounding intervals Which would you prefer?

a.  An investment paying interest of 12% compounded annually.

b.  An investment paying interest of 11.7% compounded semiannually.

c.  An investment paying 11.5% compounded continuously.

Work out the value of each of these investments after 1, 5, and 20 years.

29.  Compounding intervals A leasing contract calls for an immediate payment of $100,000 and nine subsequent $100,000 semiannual payments at six-month intervals. What is the PV of these payments if the annual discount rate is 8%?

30.  Annuities Several years ago The Wall Street Journal reported that the winner of the Massachusetts State Lottery prize had the misfortune to be both bankrupt and in prison for fraud. The prize was $9,420,713, to be paid in 19 equal annual installments. (There were 20 installments, but the winner had already received the first payment.) The bankruptcy court judge ruled that the prize should be sold off to the highest bidder and the proceeds used to pay off the creditors.

a.  If the interest rate was 8%, how much would you have been prepared to bid for the prize?

b.  Enhance Reinsurance Company was reported to have offered $4.2 million. Use Excel to find the return that the company was looking for.

31.  Amortizing loans A mortgage requires you to pay $70,000 at the end of each of the next eight years. The interest rate is 8%.

a.  What is the present value of these payments?

b.  Calculate for each year the loan balance that remains outstanding, the interest payment on the loan, and the reduction in the loan balance.

32.  Growing annuities You estimate that by the time you retire in 35 years, you will have accumulated savings of $2 million. If the interest rate is 8% and you live 15 years after retirement, what annual level of expenditure will those savings support?

Unfortunately, inflation will eat into the value of your retirement income. Assume a 4% inflation rate and work out a spending program for your retirement that will allow you to increase your expenditure in line with inflation.

33.  Annuities The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate PV for each of the following cases.

a.  The annuity payments arrive at one-year intervals. The first payment arrives one year from now.

b.  The first payment arrives in six months. Following payments arrive at one-year intervals (i.e., at 18 months, 30 months, etc.).

34.  Annuities Dear Financial Adviser,

My spouse and I are each 62 and hope to retire in three years. After retirement we will receive $7,500 per month after taxes from our employers’ pension plans and $1,500 per month after taxes from Social Security. Unfortunately our monthly living expenses are $15,000. Our social obligations preclude further economies.

We have $1,000,000 invested in a high-grade, tax-free municipal-bond mutual fund. The return on the fund is 3.5% per year. We plan to make annual withdrawals from the mutual fund to cover the difference between our pension and Social Security income and our living expenses. How many years before we run out of money?

Sincerely,

Luxury Challenged

Marblehead, MA

You can assume that the withdrawals (one per year) will sit in a checking account (no interest). The couple will use the account to cover the monthly shortfalls.

35.  Present values Your firm’s geologists have discovered a small oil field in central Hong Kong. The field is forecasted to produce a cash flow of C1 = $HK20 million in the first year. You estimate that you could earn an expected return of r = 12% from investing in stocks with a similar degree of risk to your oil field. Therefore, 12% is the opportunity cost of capital.

What is the present value? The answer, of course, depends on what happens to the cash flows after the first year. Calculate present value for the following cases:

a.  The cash flows are forecasted to continue forever, with no expected growth or decline.

b.  The cash flows are forecasted to continue for 20 years only, with no expected growth or decline during that period.

c.  The cash flows are forecasted to continue forever, increasing by 3% per year because of inflation.

d.  The cash flows are forecasted to continue for 20 years only, increasing by 3% per year because of inflation.

36.  Amortizing loans Suppose that you take out a $200,000, 20-year mortgage loan to buy a condo. The interest rate on the loan is 6%, and payments on the loan are made annually at the end of each year.

a.  What is your annual payment on the loan?

b.  Construct a mortgage amortization table in Excel similar to Table 2.1, showing the interest payment, the amortization of the loan, and the loan balance for each year.

c.  What fraction of your initial loan payment is interest? What about the last payment? What fraction of the loan has been paid off after 10 years? Why is the fraction less than half?

37.  PV of annuities at high discount rates Interest rates in developed countries are mostly in single digits, but double-digit rates are common in developing countries. In October 2012, for example, interest rates on 5-year government bonds were about 14.5% in Egypt and 16% in Nigeria. If you skip ahead to Fig. 27-4, you will see that high inflation pushed the short-term interest rate in the Ukraine up to 16%. Thus it’s useful to see how much PVs fall when interest rates climb from, say, 5% to 15%. Calculate the PVs of the following cash-flow streams at these two interest rates.

a.  A 10-year annuity of $100 per year.

b.  A 10-year annuity due of $100 per year (first cash flow arrives immediately). How does the switch from a standard annuity to an annuity due increase PV if the interest rate is 15% instead of 5%?

c.  A 20-year annuity starting at $100 per year but growing at 5% per year.

d.  A 20-year annuity starting at $100 per year but declining at 5% per year.

CHALLENGE

38.  Future values and continuous compounding Here are two useful rules of thumb. The “Rule of 72” says that with discrete compounding the time it takes for an investment to double in value is roughly 72/interest rate (in percent). The “Rule of 69” says that with continuous compounding the time that it takes to double is exactly 69.3/interest rate (in percent).

a.  If the annually compounded interest rate is 12%, use the Rule of 72 to calculate roughly how long it takes before your money doubles. Now work it out exactly.

b.  Can you prove the Rule of 69?

39.  Annuities Use Excel to construct your own set of annuity tables showing the annuity factor for a selection of interest rates and years.

40.  Declining perpetuities and annuities You own an oil pipeline that will generate a $2 million cash return over the coming year. The pipeline’s operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows are expected to decline by 4% per year. The discount rate is 10%.

a.  What is the PV of the pipeline’s cash flows if its cash flows are assumed to last forever?

b.  What is the PV of the cash flows if the pipeline is scrapped after 20 years?

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FINANCE ON THE WEB

Finance.yahoo.com is a marvelous source of stock price data. You should get used to using it.

1.  Go to finance.yahoo.com and look up the most recent stock prices and the prices five years ago for Amazon (AMZN), Microsoft (MSFT), Google (GOOG), and Apple (AAPL). What was the compound rate of growth in the price of each stock over the five-year period? If each price continues to grow at the same rate for the next five years, what will be the price at the end of that period?

2.  You need to have accumulated savings of $2 million by the time that you retire in 20 years. You currently have savings of $200,000. How much do you need to save each year to meet your goal? Find the savings calculator on finance.yahoo.com to check your answer.

___________

¹You sometimes hear lay people refer to “net present value” when they mean “present value,” and vice versa. Just remember, present value is the value of the investment today; net present value is the addition that the investment makes to your wealth.

²We define “expected” more carefully in Chapter 9. For now think of expected payoff as a realistic forecast, neither optimistic nor pessimistic. Forecasts of expected payoffs are correct on average.

³You might check for yourself that these are equivalent rules. In other words, if the return of $100,000/$700,000 is greater than r, then the net present value – $700,000 + [$800,000/(1 + r)] must be greater than 0.

⁴You can check this by writing down the present value formula

Now let C/(1 + r) = a and 1/(1 + r) = x. Then we have (1) PV = a(1 + x + x² + . . .). Multiplying both sides by x, we have (2) PVx = a(x + x2 + . . .). Subtracting (2) from (1) gives us PV(1 – x) = a. Therefore, substituting for a and x,

Multiplying both sides by (1 + r) and rearranging gives

⁵Some people find the following equivalent formula more intuitive:

⁶We need to calculate the sum of an infinite geometric series PV = a(1 + x + x2 + · · ·) where a = C1/(1 + r) and x = (1 + g)/(1 + r). In footnote 4 we showed that the sum of such a series is a/(1 – x). Substituting for a and x in this formula,

⁷We can derive the formula for a growing perpetuity by taking advantage of our earlier trick of finding the difference between the values of two perpetuities. Imagine three investments (A, B, and C) that make the following dollar payments:

Investments A and B are growing perpetuities; A makes its first payment of $1 in year 1, while B makes its first payment of $(1 + g)3 in year 4. C is a three-year growing annuity; its cash flows are equal to the difference between the cash flows of A and B. You know how to value growing perpetuities such as A and B. So you should be able to derive the formula for the value of growing annuities such as C:

If r = g, then the formula blows up. In that case, the cash flows grow at the same rate as the amount by which they are discounted. Therefore, each cash flow has a present value of C/(1 + r) and the total present value of the annuity equals t × C/(1 + r). If r < g, then this particular formula remains valid.

⁸In the U.S., truth-in-lending laws oblige the company to quote an APR that is calculated by multiplying the payment each period by the number of payments in the year. APRs are calculated differently in other countries. For example, in the European Union APRs must be expressed as annually compounded rates, so consumers know the effective interest rate that they are paying.

⁹When we talk about continuous payments, we are pretending that money can be dispensed in a continuous stream like water out of a faucet. One can never quite do this. For example, instead of paying out $1 billion every year to combat malaria, you could pay out about $1 million every 8¾ hours or $10,000 every 5¼ minutes or $10 every 31/6 seconds but you could not pay it out continuously. Financial managers pretend that payments are continuous rather than hourly, daily, or weekly because (1) it simplifies the calculations and (2) it gives a very close approximation to the NPV of frequent payments.

¹⁰Remember that an annuity is simply the difference between a perpetuity received today and a perpetuity received in year t. A continuous stream of C dollars a year in perpetuity is worth C/r, where r is the continuously compounded rate. Our annuity, then, is worth

Since r is the continuously compounded rate, C/r received in year t is worth (C/r) × (1/ert) today. Our annuity formula is therefore

sometimes written as

Part 1 Value

Valuing Bonds

Investment in new plant and equipment requires money—often a lot of money. Sometimes firms can retain and accumulate earnings to cover the cost of investment, but often they need to raise extra cash from investors. If they choose not to sell additional shares of stock, the cash has to come from borrowing. If cash is needed for only a short while, firms may borrow from a bank. If they need cash for long-term investments, they generally issue bonds, which are simply long-term loans.

Companies are not the only bond issuers. Municipalities also raise money by selling bonds. So do national governments. There is always some risk that a company or municipality will not be able to come up with the cash to repay its bonds, but investors in government bonds can generally be confident that the promised payments will be made in full and on time.

We start our analysis of the bond market by looking at the valuation of government bonds and at the interest rate that the government pays when it borrows. Do not confuse this interest rate with the cost of capital for a corporation. The projects that companies undertake are almost invariably risky and investors demand higher prospective returns from these projects than from safe government bonds. (In Chapter 7 we start to look at the additional returns that investors demand from risky assets.)

The markets for government bonds are huge. In February 2012, investors held $10.6 trillion of U.S. government securities, and U.S. government agencies held a further $4.8 trillion. The bond markets are also sophisticated. Bond traders make massive trades motivated by tiny price discrepancies. This book is not for professional bond traders, but if you are to be involved in managing the company’s debt, you will have to get beyond the simple mechanics of bond valuation. Financial managers need to understand the bond pages in the financial press and know what bond dealers mean when they quote spot rates or yields to maturity. They realize why short-term rates are usually lower (but sometimes higher) than long-term rates and why the longest-term bond prices are most sensitive to fluctuations in interest rates. They can distinguish real (inflation-adjusted) interest rates and nominal (money) rates and anticipate how future inflation can affect interest rates. We cover all these topics in this chapter.

Companies can’t borrow at the same low interest rates as governments. The interest rates on government bonds are benchmarks for all interest rates, however. When government interest rates go up or down, corporate rates follow more or less proportionally. Therefore, financial managers had better understand how the government rates are determined and what happens when they change.

Corporate bonds are more complex securities than government bonds. A corporation may not be able to come up with the money to pay its debts, so investors have to worry more about default risk. Corporate bonds are also less liquid than government bonds: they are not as easy to buy or sell, particularly in large quantities or on short notice. These complications affect the “spread” of corporate bond rates over interest rates on government bonds of similar maturities.

This chapter only introduces corporate debt. We take a more detailed look in Chapters 23 and 24.

 3-1   Using the Present Value Formula to Value Bonds

If you own a bond, you are entitled to a fixed set of cash payoffs. Every year until the bond matures, you collect regular interest payments. At maturity, when you get the final interest payment, you also get back the face value of the bond, which is called the bond’s principal.

A Short Trip to Paris to Value a Government Bond

Why are we going to Paris, apart from the cafés, restaurants, and sophisticated nightlife? Because we want to start with the simplest type of bond, one that makes payments just once a year.

French government bonds, known as OATs (short for Obligations Assimilables du Trésor), pay interest and principal in euros (€). Suppose that in October 2011 you decide to buy €100 face value of the 5% OAT maturing in October 2016. Each December until the bond matures you are entitled to an interest payment of .05 × 100 = €5.00. This amount is the bond’s coupon.¹ When the bond matures in 2016, the government pays you the final €5.00 interest, plus the principal payment of €100. Your first coupon payment is in one year’s time, in October 2012. So the cash payments from the bond are as follows:

What is the present value of these payments? It depends on the opportunity cost of capital, which in this case equals the rate of return offered by other government debt issues denominated in euros. In October 2011, other medium-term French government bonds offered a return of about 2.4%. That is what you were giving up when you bought the 5.0% OATs. Therefore, to value the 5.0% OATs, you must discount the cash flows at 2.4%:

Bond prices are usually expressed as a percentage of face value. Thus the price of your 5.0% OAT was quoted as 112.11%.

You may have noticed a shortcut way to value this bond. Your OAT amounts to a package of two investments. The first investment gets the five annual coupon payments of €5.00 each. The second gets the €100 face value at maturity. You can use the annuity formula from Chapter 2 to value the coupon payments and then add on the present value of the final payment.

Thus the bond can be valued as a package of an annuity (the coupon payments) and a single, final payment (the repayment of principal).²

We just used the 2.4% interest rate to calculate the present value of the OAT. Now we turn the valuation around: If the price of the OAT is 112.11%, what is the interest rate? What return do investors get if they buy the bond and hold it to maturity? To answer this question, you need to find the value of the variable y that solves the following equation:

The rate of return y is called the bond’s yield to maturity. In this case, we already know that the present value of the bond is €112.11 at a 2.4% discount rate, so the yield to maturity must be 2.4%. If you buy the bond at 112.11% and hold it to maturity, you will earn a return of 2.4% per year.

Why is the yield to maturity less than the 5.0% coupon payment? Because you are paying €112.11 for a bond with a face value of only €100. You lose the difference of €12.11 if you hold the bond to maturity. On the other hand, you get five annual cash payments of €5.00. (The immediate, current yield on your investment is 5.00/112.11 = .0446, or 4.46%.) The yield to maturity blends the return from the coupon payments with the declining value of the bond over its remaining life.

Let us generalize. A bond, such as our OAT, that is priced above its face value is said to sell at a premium. Investors who buy a bond at a premium face a capital loss over the life of the bond, so the yield to maturity on these bonds is always less than the current yield. A bond that is priced below face value sells at a discount. Investors in discount bonds face a capital gain over the life of the bond, so the yield to maturity on a discount bond is greater than the current yield.

BEYOND THE PAGE

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Try It! Bond prices and approaching maturity

brealey.mhhe.com/c03

The only general procedure for calculating the yield to maturity is trial and error. You guess at an interest rate and calculate the present value of the bond’s payments. If the present value is greater than the actual price, your discount rate must have been too low, and you need to try a higher rate. The more practical solution is to use a spreadsheet program or a specially programmed calculator to calculate the yield. At the end of this chapter, you will find a box that lists the Excel function for calculating yield to maturity plus several other useful functions for bond analysts.

On to the United States: Semiannual Coupons and Bond Prices

Just like the French government, the U.S. Treasury raises money by regular auctions of new bond issues. Some of these issues do not mature for 20 or 30 years; others, known as notes, mature in 10 years or less. The Treasury also issues short-term debt maturing in a year or less. These short-term securities are known as Treasury bills. Treasury bonds, notes, and bills are traded in the fixed-income market.

Let’s look at an example of a U.S. government bond. In 1985 the Treasury issued 11.25% notes maturing in 2015. These bonds are called “the 11.25s of 2015.” Treasury bonds and notes have face values of $1,000, so if you own the 11.25s of 2015, the Treasury will give you back $1,000 at maturity. You can also look forward to a regular coupon but, in contrast to our French bond, coupons on Treasury bonds and notes are paid semiannually.³ Thus, the 11.25s of 2015 provide a coupon payment of 11.25/2 = 5.625% of face value every six months.

   TABLE 3.1 Treasury bond quotes, February 2012.

Source: The Wall Street Journal website, www.wsj.com.

You can’t buy Treasury bonds, notes, or bills on the stock exchange. They are traded by a network of bond dealers, who quote prices at which they are prepared to buy and sell. For example, suppose that in 2012 you decide to buy the 11.25s of 2015. You phone a broker who checks the current price on her screen. If you are happy to go ahead with the purchase, your broker contacts a bond dealer and the trade is done.

The prices at which you can buy or sell Treasury notes and bonds are shown each day in the financial press and on the web. The small sample of prices in Table 3.1 is taken from the The Wall Street Journal’s web page. Look at the entry for our 11.25s of February 2015. The asked price 133.14 is the price you need to pay to buy the bond from a dealer. This means that the 11.25% bond costs 133.14% of face value. The face value of the bond is $1,000, so each bond costs $1,331.40.⁴

The final column in the table shows the yield to maturity. Because interest is semiannual, yields on U.S. bonds are usually quoted as semiannually compounded yields. Thus, if you buy the 11.25% bond at the asked price and hold it to maturity, you earn a semiannually compounded return of .17%. This means that every six months you earn a return of .17/2 = .085%.

You can now repeat the present value calculations that we did for the French government bond. You just need to recognize that bonds in the U.S. have a face value of $1,000, that their coupons are paid semiannually, and that the quoted yield is a semiannually compounded rate.

Here are the cash payments from the 11.25s of 2015:

If investors demand a return of .085% every six months, then the present value of these cash flows is

Each bond is worth $1,331.40, or 133.14% of face value.

Again we could turn the valuation around: given the price, what’s the yield to maturity? Try it, and you’ll find (no surprise) that the yield to maturity is y = .00085. This is the semiannual rate of return that you can earn over the six remaining half-year periods until the note matures. Take care to remember that the yield is reported as an annual rate, calculated as 2 × .00085 = .0017, or .17%. If you see a reported yield to maturity of R%, you have to remember to use y = R/2% as the semiannual rate for discounting cash flows received every six months.

 3-2   How Bond Prices Vary with Interest Rates

Figure 3.1 plots the yield to maturity on 10-year U.S. Treasury bonds⁵ from 1900 to 2011. Notice how much the rate fluctuates. For example, interest rates climbed sharply after 1979 when Paul Volcker, the new chairman of the Fed, instituted a policy of tight money to rein in inflation. Within two years the interest rate on 10-year government bonds rose from 9% to a midyear peak of 15.8%. Contrast this with 2008, when investors fled to the safety of U.S. government bonds. By the end of that year long-term Treasury bonds offered a measly 2.2% rate of interest.

   FIGURE 3.1 The interest rate on 10-year U.S. Treasury bonds.

   FIGURE 3.2 Plot of bond prices as a function of the interest rate. The price of long-term bonds is more sensitive to changes in the interest rate than is the price of short-term bonds.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

As interest rates change, so do bond prices. For example, suppose that investors demanded a semiannual return of 4% on the 11.25s of 2015, rather than the .085% semiannual return we used above. In that case the price would be

The higher interest rate results in a lower price.

Bond prices and interest rates must move in opposite directions. The yield to maturity, our measure of the interest rate on a bond, is defined as the discount rate that explains the bond price. When bond prices fall, interest rates (that is, yields to maturity) must rise. When interest rates rise, bond prices must fall. We recall a hapless TV pundit who intoned, “The recent decline in long-term interest rates suggests that long-term bond prices may rise over the next week or two.” Of course the bond prices had already gone up. We are confident that you won’t make the pundit’s mistake.

The solid brown line in Figure 3.2 shows the value of our 11.25% bond for different interest rates. As the yield to maturity falls, the bond price increases. When the annual yield is equal to the bond’s annual coupon rate (11.25%), the bond sells for exactly its face value. When the yield is higher than 11.25%, the bond sells at a discount to face value. When the yield is lower than 11.25%, the bond sells at a premium.

Bond investors cross their fingers that market interest rates will fall, so that the price of their securities will rise. If they are unlucky and interest rates jump up, the value of their investment declines.

EXAMPLE 3.1 • Changes in Interest Rates and Bond Returns

On May 15, 2008, the U.S. Treasury sold $9 billion of 4.375% bonds maturing in February 2038. The bonds were issued at a price of 96.38% and offered a yield to maturity of 4.60%. This was the return to anyone buying at the issue price and holding the bonds to maturity. In the months following the issue, the financial crisis reached its peak. Lehman Brothers filed for bankruptcy with assets of $691 billion, and the government poured money into rescuing Fannie Mae, Freddie Mac, AIG, and a host of banks. As investors rushed to the safety of Treasury bonds, prices soared. By mid-December the price of the 4.375s of 2038 had reached 138.05% of face value and the yield had fallen to 2.5%. Anyone fortunate enough to have bought the bond at the issue price would have made a capital gain of $1,380.50 – $963.80 = $416.70. In addition, on August 15 the bond made its first coupon payment of $21.875 (this is the semiannual payment on the 4.375% coupon bond with a face value of $1,000). Our lucky investor would therefore have earned a seven-month rate of return of 45.5%:

Suddenly, government bonds did not seem quite so boring as before.

A change in interest rates has only a modest impact on the value of near-term cash flows but a much greater impact on the value of distant cash flows. Thus the price of long-term bonds is affected more by changing interest rates than the price of short-term bonds. For example, compare the two curves in Figure 3.2. The brown line shows how the price of the three-year 11.25% bond varies with the interest rate. The blue line shows how the price of a 30-year 11.25% bond varies. You can see that the 30-year bond is much more sensitive to interest rate fluctuations than the three-year note.

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Try It! Figure 3.2:
How changes in interest rates affect
long- and short-term bonds

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Duration and Volatility

Changes in interest rates have a greater impact on the prices of long-term bonds than on those of short-term bonds. But what do we mean by “long-term” and “short-term”? A coupon bond that matures in year 30 makes payments in each of years 1 through 30. It’s misleading to describe the bond as a 30-year bond; the average time to each cash payment is less than 30 years.

EXAMPLE 3.2 • Which Is the Longer-Term Bond?

Table 3.2 calculates the prices of two seven-year bonds. We assume annual coupon payments and a yield to maturity of 4% per year. Take a look at the time pattern of each bond’s cash payments and review how the prices are calculated:

Which of these two bonds is the longer-term investment? They both have the same final maturity, of course. But the timing of the bonds’ cash payments is not the same. In the case of the 3s, the average time to each cash flow is longer, because a higher proportion of the cash flows occurs at maturity, when the face value is paid off.

Suppose now that the yield to maturity on each bond falls to 3%. Which bond would you most like to own? The 3s, of course. Since they have the longer effective maturity, they should benefit most from a fall in yields. Table 3.3 confirms that this is indeed the case:

The 9s have the shorter average maturity, and therefore a shift in interest rates has a more muted effect on the price. That much is clear. However, it would be useful to have a precise measure of the average maturity, one that could be used to predict the exposure of each bond’s price to fluctuations in interest rates. There is such a measure, and it is called duration or Macaulay duration after its founder.

   TABLE 3.2 A comparison of the cash flows and prices of two Treasuries. Price is calculated assuming annual coupon payments and a yield to maturity of 4%.

Note: Both securities mature at the end of year 7.

   TABLE 3.3 The effect of a 1% fall in yield on the prices of two seven-year Treasuries.

Duration is the weighted average of the times to each of the cash payments. The times are the future years 1, 2, 3, etc., extending to the final maturity date, which we call T. The weight for each year is the present value of the cash flow received at that time divided by the total present value of the bond.

Table 3.4 shows how to compute duration for the 9% seven-year Treasuries, assuming annual payments. First, we value each of the coupon payments of $90 and the final payment of coupon plus face value of $1,090. Of course the present values of these payments add up to the bond price of $1,300.10. Then we calculate the fraction of the price accounted for by each cash flow and multiply each fraction by the year of the cash flow. The results sum across to a duration of 5.69 years.

   TABLE 3.4 Calculating the duration of the 9% seven-year bonds. The yield to maturity is 4% a year.

We leave it to you to calculate durations for the 3% bonds in Table 3.2. You will find that duration increases to 6.40 years.

We mentioned that investors and financial managers track duration because it measures how bond prices change when interest rates change. For this purpose it’s best to use modified duration or volatility, which is just duration divided by one plus the yield to maturity:

Modified duration measures the percentage change in bond price for a 1 percentage-point change in yield.⁶ Let’s try out this formula for our seven-year 9% bond in Table 3.3. The bond’s modified duration is duration/(1 + yield) = 5.69/1.04 = 5.47. This means that a 1% change in the yield to maturity should change the bond price by 5.47%.

Let’s check that prediction. Suppose the yield to maturity either increases or declines by .5%:

The total difference between price at yields of 4.5% and 3.5% is 2.687 + 2.784 = 5.47%. Thus a 1% change in interest rates means a 5.47% change in bond price, just as predicted.⁷

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Try It! More on duration

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The modified duration for the 3% bond in Table 3.3 is 6.40/1.04 = 6.15%. In other words, a 1% change in yield to maturity results in a 6.15% change in the bond’s price.

You can see why duration (or modified duration) is a handy measure of interest-rate risk.⁸ For example, in Chapter 26 we will look at how financial managers use the measure to protect the pension plan against unexpected changes in interest rates.

 3-3   The Term Structure of Interest Rates

When we explained in Chapter 2 how to calculate present values, we used the same discount rate to calculate the value of each period’s cash flow. A single yield to maturity y can also be used to discount all future cash payments from a bond. For many purposes, using a single discount rate is a perfectly acceptable approximation, but there are also occasions when you need to recognize that short-term interest rates are different from long-term rates.

The relationship between short- and long-term interest rates is called the term structure of interest rates. Look, for example, at Figure 3.3, which shows the term structure in two different years. Notice that in the later year the term structure sloped downward; long-term interest rates were lower than short-term rates. In the earlier year the pattern was reversed and long-term bonds offered a much higher interest rate than short-term bonds. You now need to learn how to measure the term structure and understand why long- and short-term rates differ.

   FIGURE 3.3 Short- and long-term interest rates do not always move in parallel. Between September 1992 and April 2000 U.S. short-term rates rose sharply while long-term rates declined.

Consider a simple loan that pays $1 at the end of one year. To find the present value of this loan you need to discount the cash flow by the one-year rate of interest, r1:

This rate, r1, is called the one-year spot rate. To find the present value of a loan that pays $1 at the end of two years, you need to discount by the two-year spot rate, r2:

The first year’s cash flow is discounted at today’s one-year spot rate and the second year’s flow is discounted at today’s two-year spot rate. The series of spot rates r1, r2, . . ., rt, . . . traces out the term structure of interest rates.

Now suppose you have to value $1 paid at the end of years 1 and 2. If the spot rates are different, say r1 = 3% and r2 = 4%, then we need two discount rates to calculate present value:

Once we know that PV = 1.895, we can go on to calculate a single discount rate that would give the right answer. That is, we could calculate the yield to maturity by solving for y in the following equation:

This gives a yield to maturity of 3.66%. Once we have the yield, we could use it to value other two-year annuities. But we can’t get the yield to maturity until we know the price. The price is determined by the spot interest rates for dates 1 and 2. Spot rates come first. Yields to maturity come later, after bond prices are set. That is why professionals identify spot interest rates and discount each cash flow at the spot rate for the date when the cash flow is received.

Spot Rates, Bond Prices, and the Law of One Price

The law of one price states that the same commodity must sell at the same price in a well-functioning market. Therefore, all safe cash payments delivered on the same date must be discounted at the same spot rate.

Table 3.5 illustrates how the law of one price applies to government bonds. It lists three government bonds, which we assume make annual coupon payments. All the bonds have the same coupon but they have different maturities. The shortest (bond A) matures in two years and the longest (bond C) in four.

   TABLE 3.5 The law of one price applied to government bonds.

Spot rates and discount factors are given at the top of each column. The law of one price says that investors place the same value on a risk-free dollar regardless of whether it is provided by bond A, B, or C. You can check that the law holds in the table.

Each bond is priced by adding the present values of each of its cash flows. Once total PV is calculated, we have the bond price. Only then can the yield to maturity be calculated.

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Try It! Table 3.5:
Spot rates, forward rates, and arbitrage

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Notice how the yield to maturity increases as bond maturity increases. The yields increase with maturity because the term structure of spot rates is upward-sloping. Yields to maturity are complex averages of spot rates. For example, you can see that the yield on the four-year bond (5.81%) lies between the one- and four-year spot rates (3% and 6%).

Financial managers who want a quick, summary measure of interest rates bypass spot interest rates and look in the financial press at yields to maturity. They may refer to the yield curve, which plots yields to maturity, instead of referring to the term structure, which plots spot rates. They may use the yield to maturity on one bond to value another bond with roughly the same coupon and maturity. They may speak with a broad brush and say, “Ampersand Bank will charge us 6% on a three-year loan,” referring to a 6% yield to maturity.

Throughout this book, we too use the yield to maturity to summarize the return required by bond investors. But you also need to understand the measure’s limitations when spot rates are not equal.

Measuring the Term Structure

You can think of the spot rate, rt, as the rate of interest on a bond that makes a single payment at time t. Such simple bonds do exist. They are known as stripped bonds, or strips. On request the U.S. Treasury will split a normal coupon bond into a package of mini-bonds, each of which makes just one cash payment. Our 11.25% bonds of 2015 could be exchanged for six semiannual coupon strips, each paying $56.25, and a principal strip paying $1,000. In February 2012 this package of coupon strips would have cost $280.29 and the principal strip would have cost $1,046.12, making a total cost of $1,326.41, just a little more than it cost to buy one 11.25% bond. That should be no surprise. Because the two investments provide identical cash payments, they must sell for very close to the same price.

   FIGURE 3.4 Spot rates on U.S. Treasury strips, February 2012.

We can use the prices of strips to measure the term structure of interest rates. For example, in February 2012 a 10-year strip cost $808.82. In return, investors could look forward to a single payment of $1,000 in February 2022. Thus investors were prepared to pay $.80882 for the promise of $1 at the end of 10 years. The 10-year discount factor was DF10 = 1/(1 + r10)10 = .80882, and the 10-year spot rate was r10 = (1/.80882).10 – 1 = .0214, or 2.14%. In Figure 3.4 we use the prices of strips with different maturities to plot the term structure of spot rates from 1 to 29 years. You can see that in 2012 investors required a much higher interest rate for lending for 29 years rather than for 1.

Why the Discount Factor Declines as Futurity Increases—and a Digression on Money Machines

In Chapter 2 we saw that the longer you have to wait for your money, the less is its present value. In other words, the two-year discount factor DF2 = 1/(1 + r2)2 is less than the one-year discount factor DF1 = 1/(1 + r1). But is this necessarily the case when there can be a different spot interest rate for each period?

Suppose that the one-year spot rate of interest is r1 = 20%, and the two-year spot rate is r2 = 7%. In this case the one-year discount factor is DF1 = 1/1.20 = .833 and the two-year discount factor is DF2 = 1/1.072 = .873. Apparently a dollar received the day after tomorrow is not necessarily worth less than a dollar received tomorrow.

But there is something wrong with this example. Anyone who could borrow and invest at these interest rates could become a millionaire overnight. Let us see how such a “money machine” would work. Suppose the first person to spot the opportunity is Hermione Kraft. Ms. Kraft first buys a one-year Treasury strip for .833 × $1,000 = $833. Now she notices that there is a way to earn an immediate surefire profit on this investment. She reasons as follows. Next year the strip will pay off $1,000 that can be reinvested for a further year. Although she does not know what interest rates will be at that time, she does know that she can always put the money in a checking account and be certain of having $1,000 at the end of year 2. Her next step, therefore, is to go to her bank and borrow the present value of this $1,000. At 7% interest the present value is PV = 1000/(1.07)2 = $873.

So Ms. Kraft borrows $873, invests $830, and walks away with a profit of $43. If that does not sound like very much, notice that by borrowing more and investing more she can make much larger profits. For example, if she borrows $21,778,584 and invests $20,778,584, she would become a millionaire.⁹

Of course this story is completely fanciful. Such an opportunity would not last long in well-functioning capital markets. Any bank that allowed you to borrow for two years at 7% when the one-year interest rate was 20% would soon be wiped out by a rush of small investors hoping to become millionaires and a rush of millionaires hoping to become billionaires. There are, however, two lessons to our story. The first is that a dollar tomorrow cannot be worth less than a dollar the day after tomorrow. In other words, the value of a dollar received at the end of one year (DF1) cannot be less than the value of a dollar received at the end of two years (DF2). There must be some extra gain from lending for two periods rather than one: (1 + r2)2 cannot be less than 1 + r1.

Our second lesson is a more general one and can be summed up by this precept: “There is no such thing as a surefire money machine.” The technical term for money machine is arbitrage. In well-functioning markets, where the costs of buying and selling are low, arbitrage opportunities are eliminated almost instantaneously by investors who try to take advantage of them.

Later in the book we invoke the absence of arbitrage opportunities to prove several useful properties about security prices. That is, we make statements like, “The prices of securities X and Y must be in the following relationship—otherwise there would be potential arbitrage profits and capital markets would not be in equilibrium.”

 3-4   Explaining the Term Structure

The term structure that we showed in Figure 3.4 was upward-sloping. In 2012 short-term interest rates in many countries were much lower than long-term rates. Why then didn’t everyone rush to buy long-term bonds? Who were the (foolish?) investors who put their money into the short end of the term structure?

Suppose that you held a portfolio of one-year bonds in 2012. Here are three possible reasons why you might decide to hold on to them, despite their low rate of return:

1.  You believe that short-term interest rates will be higher in the future.

2.  You worry about the greater exposure of long-term bonds to changes in interest rates.

3.  You worry about the risk of higher future inflation.

We review each of these reasons now.

Expectations Theory of the Term Structure

Recall that you own a portfolio of one-year bonds. A year from now, when the bonds mature, you can reinvest the proceeds for another one-year period and enjoy whatever interest rate the bond market offers then. The interest rate for the second year may be high enough to offset the first year’s low return. You often see an upward-sloping term structure when future interest rates are expected to rise.

EXAMPLE 3.3 • Expectations and the Term Structure

Suppose that the one-year interest rate, r1, is 5%, and the two-year rate, r2, is 7%. If you invest $100 for one year, your investment grows to 100 × 1.05 = $105; if you invest for two years, it grows to 100 × 1.072 = $114.49. The extra return that you earn for that second year is 1.072/1.05 – 1 = .090, or 9.0%.¹⁰

Would you be happy to earn that extra 9% for investing for two years rather than one? The answer depends on how you expect interest rates to change over the coming year. If you are confident that in 12 months’ time one-year bonds will yield more than 9.0%, you would do better to invest in a one-year bond and, when that matured, reinvest the cash for the next year at the higher rate. If you forecast that the future one-year rate is exactly 9.0%, then you will be indifferent between buying a two-year bond or investing for one year and then rolling the investment forward at next year’s short-term interest rate.

If everyone is thinking as you just did, then the two-year interest rate has to adjust so that everyone is equally happy to invest for one year or two. Thus the two-year rate will incorporate both today’s one-year rate and the consensus forecast of next year’s one-year rate.

We have just illustrated (in Example 3.3) the expectations theory of the term structure. It states that in equilibrium investment in a series of short-maturity bonds must offer the same expected return as an investment in a single long-maturity bond. Only if that is the case would investors be prepared to hold both short- and long-maturity bonds.

The expectations theory implies that the only reason for an upward-sloping term structure is that investors expect short-term interest rates to rise; the only reason for a declining term structure is that investors expect short-term rates to fall.

If short-term interest rates are significantly lower than long-term rates, it is tempting to borrow short-term rather than long-term. The expectations theory implies that such naïve strategies won’t work. If short-term rates are lower than long-term rates, then investors must be expecting interest rates to rise. When the term structure is upward-sloping, you are likely to make money by borrowing short only if investors are overestimating future increases in interest rates.

Even at a casual glance the expectations theory does not seem to be the complete explanation of term structure. For example, if we look back over the period 1900–2011, we find that the return on long-term U.S. Treasury bonds was on average 1.4 percentage points higher than the return on short-term Treasury bills. It is similar for Germany; it is 1.8% for Japan and 1.1% for the UK. Perhaps in these countries short-term interest rates stayed lower than investors expected, but it seems more likely that investors wanted some extra return for holding long bonds and that on average they got it. If so, the expectations theory is only a first step.

These days the expectations theory has few strict adherents. Nevertheless, most economists believe that expectations about future interest rates have an important effect on the term structure. For example, you often hear market commentators remark that the six-month interest rate is higher than the three-month rate and conclude that the market is expecting the Federal Reserve Board to raise interest rates.

Introducing Risk

What does the expectations theory leave out? The most obvious answer is “risk.” If you are confident about the future level of interest rates, you will simply choose the strategy that offers the highest return. But, if you are not sure of your forecasts, you may well opt for a less risky strategy even if it means giving up some return.

Remember that the prices of long-duration bonds are more volatile than prices of short-duration bonds. A sharp increase in interest rates can knock 30% or 40% off the price of long-term bonds.

For some investors, this extra volatility of long-duration bonds may not be a concern. For example, pension funds and life insurance companies have fixed long-term liabilities, and may prefer to lock in future returns by investing in long-term bonds. However, the volatility of long-term bonds does create extra risk for investors who do not have such long-term obligations. These investors will be prepared to hold long bonds only if they offer the compensation of a higher return. In this case the term structure will be upward-sloping more often than not. Of course, if interest rates are expected to fall, the term structure could be downward-sloping and still reward investors for lending long. But the additional reward for risk offered by long bonds would result in a less dramatic downward slope.

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Arbitrage models of term structure

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Inflation and Term Structure

Suppose you are saving for your retirement 20 years from now. Which of the following strategies is more risky? Invest in a succession of one-year Treasuries, rolled over annually, or invest once in 20-year strips? The answer depends on how confident you are about future inflation.

If you buy the 20-year strips, you know exactly how much money you will have at year 20, but you don’t know what that money will buy. Inflation may seem benign now, but who knows what it will be in 10 or 15 years? This uncertainty about inflation may make it uncomfortably risky for you to lock in one 20-year interest rate by buying the strips. This was a problem facing investors in 2009, when no one could be sure whether the country was facing the prospect of prolonged deflation or whether the high levels of government borrowing would prompt rapid inflation.

You can reduce exposure to inflation risk by investing short-term and rolling over the investment. You do not know future short-term interest rates, but you do know that future interest rates will adapt to inflation. If inflation takes off, you will probably be able to roll over your investment at higher interest rates.

If inflation is an important source of risk for long-term investors, borrowers must offer some extra incentive if they want investors to lend long. That is why we often see a steeply upward-sloping term structure when inflation is particularly uncertain.

 3-5   Real and Nominal Rates of Interest

It is now time to review more carefully the relation between inflation and interest rates. Suppose you invest $1,000 in a one-year bond that makes a single payment of $1,100 at the end of the year. Your cash flow is certain, but the government makes no promises about what that money will buy. If the prices of goods and services increase by more than 10%, you will lose ground in terms of purchasing power.

Several indexes are used to track the general level of prices. The best known is the Consumer Price Index (CPI), which measures the number of dollars that it takes to pay for a typical family’s purchases. The change in the CPI from one year to the next measures the rate of inflation.

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The German hyperinflation

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Figure 3.5 shows the rate of inflation in the U.S. since 1900. Inflation touched a peak at the end of World War I, when it reached 21%. However, this figure pales into insignificance compared with the hyperinflation in Zimbabwe in 2008. Prices there rose so fast that a Z$50 trillion bill was barely enough to buy a loaf of bread.

   FIGURE 3.5 Annual rates of inflation in the United States from 1900–2011.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

   FIGURE 3.6 Average rates of inflation in 18 countries from 1900–2011.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

Prices can fall as well as rise. The U.S. experienced severe deflation in the Great Depression, when prices fell by 24% in three years. More recently, Japan has experienced falling prices for more than a decade.

The average U.S. inflation rate from 1900 to 2011 was 3.1%. As you can see from Figure 3.6, among major economies the U.S. has been almost top of the class in holding inflation in check. Countries torn by war have generally experienced much higher inflation. For example, in Italy and Japan, inflation since 1900 has averaged over 10% a year.

Economists and financial managers refer to current, or nominal, dollars versus constant, or real, dollars. For example, the nominal cash flow from your one-year bond is $1,100. But if prices rise over the year by 6%, then each dollar will buy you 6% less next year than it does today. So at the end of the year $1,100 has the same purchasing power as 1,100/1.06 = $1,037.74 today. The nominal payoff on the bond is $1,100, but the real payoff is only $1,037.74.

The formula for converting nominal cash flows in a future period t to real cash flows today is

For example, suppose you invest in a 20-year Treasury strip, but inflation over the 20 years averages 6% per year. The strip pays $1,000 in year 20, but the real value of that payoff is only 1,000/1.0620 = $311.80. In this example, the purchasing power of $1 today declines to just over $.31 after 20 years.

These examples show you how to get from nominal to real cash flows. The journey from nominal to real interest rates is similar. When a bond dealer says that your bond yields 10%, she is quoting a nominal interest rate. That rate tells you how rapidly your money will grow, say over one year:

However, with an expected inflation rate of 6%, you are only 3.774% better off at the end of the year than at the start:

Thus, we could say, “The bond offers a 10% nominal rate of return,” or “It offers a 3.774% expected real rate of return.”

The formula for calculating the real rate of return is:

In our example, 1 + rreal = 1.10/1.06 = 1.03774. A common rule of thumb states that rreal = rnominal – inflation rate. In our example this gives rreal = .10 – .06 = .04, or 4%. This is not a bad approximation to the true real interest rate of 3.774%. But when inflation is high, it pays to use the full formula.

Indexed Bonds and the Real Rate of Interest

Most bonds promise you a fixed nominal rate of interest. The real interest rate that you receive is uncertain and depends on inflation. If the inflation rate turns out to be higher than you expected, the real return on your bonds will be lower.

You can nail down a real return, however. You do so by buying an indexed bond that makes cash payments linked to inflation. Indexed bonds have been around in many other countries for decades, but they were almost unknown in the United States until 1997, when the U.S. Treasury began to issue inflation-indexed bonds known as TIPS (Treasury Inflation-Protected Securities).¹¹

The real cash flows on TIPS are fixed, but the nominal cash flows (interest and principal) increase as the CPI increases.¹² For example, suppose that the U.S. Treasury issues 3% 20-year TIPS at a price equal to its face value of $1,000. If during the first year the CPI rises by 10%, then the coupon payment on the bond increases by 10% from $30 to 30 × 1.10 = $33. The amount that you will be paid at maturity also increases to $1,000 × 1.10 = $1,100. The purchasing power of the coupon and face value remain constant at $33/1.10 = $30 and $1,100/1.10 = $1,000. Thus, an investor who buys the bond at the issue price earns a real interest rate of 3%.

Long-term TIPS offered a yield of about .2% in February 2012.¹³ This is a real yield to maturity. It measures the extra goods and services your investment will allow you to buy. The .2% yield on TIPS was about 1.5% less than the nominal yield on ordinary Treasury bonds. If the annual inflation rate turns out to be higher than 1.5%, investors will earn a higher return by holding long-term TIPS; if the inflation rate turns out to be less than 1.5%, they would have been better off with nominal bonds.

What Determines the Real Rate of Interest?

The real rate of interest depends on people’s willingness to save (the supply of capital)¹⁴ and the opportunities for productive investment by governments and businesses (the demand for capital). For example, suppose that investment opportunities generally improve. Firms have more good projects, so they are willing to invest more than previously at the current real interest rate. Therefore, the rate has to rise to induce individuals to save the additional amount that firms want to invest.¹⁵ Conversely, if investment opportunities deteriorate, there will be a fall in the real interest rate.

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When yields were negative

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Short- and medium-term real interest rates are affected by the monetary policy of central banks. For example, sometimes central banks keep short-term nominal interest rates low despite significant inflation. The resulting real rates can be negative. Nominal interest rates usually cannot be negative, however, because investors can simply hold cash. Cash always pays zero interest, which is better than negative interest.

Real interest rates change but they usually do so gradually. We can see this by looking at the UK, where the government has issued indexed bonds since 1982. The green line in Figure 3.7 shows that the real yield to maturity on these bonds has fluctuated within a relatively narrow range, while the yield on nominal government bonds (the brown line) has declined dramatically.

Inflation and Nominal Interest Rates

How does the inflation outlook affect the nominal rate of interest? Here is how economist Irving Fisher answered the question. Suppose that consumers are equally happy with 100 apples today or 103 apples in a year’s time. In this case the real or “apple” interest rate is 3%. If the price of apples is constant at (say) $1 each, then we will be equally happy to receive $100 today or $103 at the end of the year. That extra $3 will allow us to buy 3% more apples at the end of the year than we could buy today.

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The yield on TIPs

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   FIGURE 3.7 The green line shows the real yield on long-term indexed bonds issued by the UK government. The brown line shows the yield on long-term nominal bonds. Notice that the real yield has been much more stable than the nominal yield.

But suppose now that the apple price is expected to increase by 5% to $1.05 each. In that case we would not be happy to give up $100 today for the promise of $103 next year. To buy 103 apples in a year’s time, we will need to receive 1.05 × $103 = $108.15. In other words, the nominal rate of interest must increase by the expected rate of inflation to 8.15%.

This is Fisher’s theory: A change in the expected inflation rate causes the same proportionate change in the nominal interest rate; it has no effect on the required real interest rate. The formula relating the nominal interest rate and expected inflation is

where r real is the real interest rate that consumers require and i is the expected inflation rate. In our example, the prospect of inflation causes 1 + r nominal to rise to 1.03 × 1.05 = 1.0815.

Not all economists would agree with Fisher that the real rate of interest is unaffected by the inflation rate. For example, if changes in prices are associated with changes in the level of industrial activity, then in inflationary conditions I might want more or less than 103 apples in a year’s time to compensate me for the loss of 100 today.

We wish we could show you the past behavior of interest rates and expected inflation. Instead we have done the next best thing and plotted in Figure 3.8 the return on Treasury bills (short-term government debt) against actual inflation for the United States, UK, and Germany. Notice that since 1953 the return on Treasury bills has generally been a little above the rate of inflation. Investors in each country earned an average real return of between 1% and 2% during this period.

Look now at the relationship between the rate of inflation and the Treasury bill rate. Figure 3.8 shows that investors have for the most part demanded a higher rate of interest when inflation was high. So it looks as if Fisher’s theory provides a useful rule of thumb for financial managers. If the expected inflation rate changes, it is a good bet that there will be a corresponding change in the interest rate. In other words, a strategy of rolling over short-term investments affords some protection against uncertain inflation.

 3-6   The Risk of Default

Corporate Bonds and Default Risk

Look at Table 3.6, which shows the yields to maturity on a sample of corporate bonds. Notice that the bonds all mature in 2017, but their yields to maturity differ dramatically. With a yield of over 25%, the bonds of Caesars Entertainment appeared to offer a mouth-watering rate of return. However, the company had been operating at a loss and had borrowed to the hilt. Investors foresaw that there was a good chance that the company would go bankrupt and that they would not get their money back. Thus the payments promised to the bondholders represent a best-case scenario: The firm will never pay more than the promised cash flows, but in hard times, it may pay less. This risk applies in some measure to all corporate bonds, but investors were much more confident that Johnson & Johnson would be able to service its debt and this is reflected in the low yield on its bonds.

   FIGURE 3.8 The return on Treasury bills and the rate of inflation in the UK, U.S., and Germany, 1953–2011.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

BEYOND THE PAGE

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Country interest rates and inflation

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   TABLE 3.6 Prices and yields of a sample of corporate bonds, January 2011.

Source: Bond transactions reported on FINRA’s TRACE service: cxa.marketwatch.com/finra/BondCenter/Default.aspx.

The safety of most corporate bonds can be judged from bond ratings provided by Moody’s, Standard & Poor’s (S&P), and Fitch. Table 3.7 lists the possible bond ratings in declining order of quality. For example, the bonds that receive the highest Standard & Poor’s rating are known as AAA (or “triple A”) bonds. Then come AA (double A), A, BBB bonds, and so on. Bonds rated BBB and above are called investment grade, while those with a rating of BB or below are referred to as speculative grade, high-yield, or junk bonds. Notice that the bonds in the first four rows of Table 3.7 are all investment-grade bonds; the rest are junk bonds.

BEYOND THE PAGE

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Bond rating definitions

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   TABLE 3.7 Key to bond ratings. The highest-quality bonds rated Baa/BBB or above are investment grade.

It is rare for highly rated bonds to default. However, when an investment-grade bond does go under, the shock waves are felt in all major financial centers. For example, in May 2001 WorldCom sold $11.8 billion of bonds with an investment-grade rating. About one year later, WorldCom filed for bankruptcy, and its bondholders lost more than 80% of their investment. For those bondholders, the agencies that had assigned investment-grade ratings were not the flavor of the month.

Because of the risk of default, yields on corporate bonds are higher than those of government bonds. For example, Figure 3.9 shows the yield spread of corporate bonds against U.S. Treasuries. Notice that the spreads widen as safety falls off. Notice also how spreads vary over time. They widened dramatically, for example, during the credit crunch of 2007 to 2009.¹⁶

   FIGURE 3.9 Yield spreads between corporate and 10-year Treasury bonds.

Sovereign Bonds and Default Risk

BEYOND THE PAGE

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Some sovereign defaults

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When investors buy corporate bonds or a bank lends to a company, they worry about the possibility of default and spend considerable time and effort assessing differences in credit risk. In Chapters 23 and 24 we will look much more closely at the pricing of corporate debt. By contrast, when the U.S. government issues dollar bonds, investors can generally be confident that those bonds will be repaid in full and on time. Of course, bondholders don’t know what that money will be worth. Governments have a nasty habit of reducing the real value of their debts by inflationary policies.

Although sovereign debt is generally less risky than corporate debt, we should not leave you with the impression that it is always safe even in money terms. Indeed even in the United States investors in government bonds have had their scary moments. Countries do occasionally default on their debts and, when they do so, the effects are sometimes catastrophic. We will look briefly at three circumstances in which countries may default.

Foreign Currency Debt Most government bond defaults have occurred when a foreign government borrows dollars. In these cases investors worry that in some future crisis the government may run out of taxing capacity and may not be able to come up with enough dollars to repay the debt. This worry shows up in bond prices and yields to maturity. For example, in 2001 the Argentinian government defaulted on $95 billion of debt. As the prospect of default loomed, the price of Argentinian bonds slumped, and the promised yield climbed to more than 40 percentage points above the yield on U.S. Treasuries. Argentina has plenty of company. Since 1970 there have been over 100 occasions that sovereign governments have defaulted on their foreign currency bonds.¹⁷

FINANCE IN PRACTICE

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Russian Roulette

  In 1997 Russia enjoyed its first year of positive economic growth since the fall of the Soviet Union.The country ran a trade surplus and inflation fell to 11% from 131% two years earlier. A significant inflow of foreign capital into the country reflected investors’ increased optimism, but it also left Russia and its banks vulnerable to any reversal of views.

Russia’s fragile economy was then hit by a double whammy. Starting in December 1997 the price of oil started to fall, and by the summer of 2008 it had halved. In addition, the currency crisis in Asia in 1997 led speculators to worry that the rouble might also need to be devalued.

As the political and economic situation deteriorated, President Yeltsin abruptly fired his entire government. Investor confidence in the economy and the government’s ability to manage the situation collapsed. By August, Russia’s central bank had spent an estimated $27 billion of reserves to counter speculative attacks on the currency. The yield on rouble bonds had soared to 200%, stock prices had fallen by more than 75% since the start of the year, and inflation had reached over 80%. It was no longer feasible for the government both to defend the rouble and service its domestic debt. Either it had to devalue or default or both. It chose the third option, floating the rouble and defaulting on a massive $39 billion of domestic debt.

Own Currency Debt If a government borrows in its own currency, there is less likelihood of default. After all, the government can always print the money needed to repay the bonds. Very occasionally, governments have chosen to default on their domestic debt rather than create the money to pay it off. As the nearby box explains, Russia in 1998 chose to default on its domestic ruble debt rather than simply printing more money.

Eurozone Debt The 17 countries in the eurozone do not even have the option of printing money to service their domestic debts; they have given up control over their own money supply to the European Central Bank. This was to pose a major problem for the Greek government, which had amassed a massive €330 billion (or about $440 billion) of debt. In May 2010 other eurozone governments and the International Monetary Fund (IMF) rushed to Greece’s aid, but investors were unconvinced that their assistance would be sufficient. By November 2011 the yield on 10-year Greek government debt had climbed to nearly 27%. In November after extensive meetings involving the IMF and other eurozone members, a further bail-out package was agreed upon. In return for this new funding, investors in Greek bonds were obliged to accept a write-down of some $100 billion in the value of their bonds. It was the largest ever sovereign default. As worries spread to the debts of several other eurozone countries, Ireland, Portugal, and Cyprus’s bonds were down-rated to junk level. Investors joked that, instead of offering a risk-free return, eurozone government bonds just offered a return-free risk.

USEFUL SPREADSHEET FUNCTIONS

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Valuing Bonds

   Spreadsheet programs such as Excel provide built-in functions to solve for a variety of bond valuation problems. You can find these functions by pressing fx on the Excel toolbar. If you then click on the function that you wish to use, Excel will ask you for the inputs that it needs. At the bottom left of the function box there is a Help facility with an example of how the function is used.

Here is a list of useful functions for valuing bonds, together with some points to remember when entering data:

•  PRICE: The price of a bond given its yield to maturity.

•  YLD: The yield to maturity of a bond given its price.

•  DURATION: The duration of a bond.

•  MDURATION: The modified duration (or volatility) of a bond.

   Note:

• You can enter all the inputs in these functions directly as numbers or as the addresses of cells that contain the numbers.

•  You must enter the yield and coupon as decimal values, for example, for 3% you would enter .03.

•  Settlement is the date that payment for the security is made. Maturity is the maturity date. You can enter these dates directly using the Excel date function; for example, you would enter 15 Feb 2009 as DATE(2009,02,15). Alternatively, you can enter these dates in a cell and then enter the cell address in the function.

•  In the functions for PRICE and YLD you need to scroll down in the function box to enter the frequency of coupon payments. Enter 1 for annual payments or 2 for semiannual.

•  The functions for PRICE and YLD ask for an entry for “basis.” We suggest you leave this blank. (See the Help facility for an explanation.)

SPREADSHEET QUESTIONS

The following questions provide an opportunity to practice each of these functions.

1.  (PRICE) In February 2009, Treasury 8.5s of 2020 yielded 3.2976%. What was their price? If the yield rose to 4%, what would happen to the price?

2.  (YLD) On the same day Treasury 3.5s of 2018 were priced at 107.46875%. What was their yield to maturity? Suppose that the price was 110.0%. What would happen to the yield?

3.  (DURATION) What was the duration of the Treasury 8.5s? How would duration change if the yield rose to 4%? Can you explain why?

4.  (MDURATION) What was the modified duration of the Treasury 8.5s? How would modified duration differ if the coupon were only 7.5%?

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SUMMARY

Bonds are simply long-term loans. If you own a bond, you are entitled to a regular interest (or coupon) payment and at maturity you get back the bond’s face value (or principal). In the U.S., coupons are normally paid every six months, but in other countries they may be paid annually.

The value of any bond is equal to its cash payments discounted at the spot rates of interest. For example, the present value of a 10-year bond with a 5% coupon paid annually equals

This calculation uses a different spot rate of interest for each period. A plot of spot rates by maturity shows the term structure of interest rates.

Spot interest rates are most conveniently calculated from the prices of strips, which are bonds that make a single payment of face value at maturity, with zero coupons along the way. The price of a strip maturing in a future date t reveals the discount factor and spot rate for cash flows at that date. All other safe cash payments on that date are valued at that same spot rate.

Investors and financial managers use the yield to maturity on a bond to summarize its prospective return. To calculate the yield to maturity on the 10-year 5s, you need to solve for y in the following equation:

The yield to maturity discounts all cash payments at the same rate, even if spot rates differ. Notice that the yield to maturity for a bond can’t be calculated until you know the bond’s price or present value.

A bond’s maturity tells you the date of its final payment, but it is also useful to know the average time to each payment. This is called the bond’s duration. Duration is important because there is a direct relationship between the duration of a bond and the exposure of its price to changes in interest rates. A change in interest rates has a greater effect on the price of long-duration bonds.

The term structure of interest rates is upward-sloping more often than not. This means that long-term spot rates are higher than short-term spot rates. But it does not mean that investing long is more profitable than investing short. The expectations theory of the term structure tells us that bonds are priced so that an investor who holds a succession of short bonds can expect the same return as another investor who holds a long bond. The expectations theory predicts an upward-sloping term structure only when future short-term interest rates are expected to rise.

The expectations theory cannot be a complete explanation of term structure if investors are worried about risk. Long bonds may be a safe haven for investors with long-term fixed liabilities. But other investors may not like the extra volatility of long-term bonds or may be concerned that a sudden burst of inflation may largely wipe out the real value of these bonds. These investors will be prepared to hold long-term bonds only if they offer the compensation of a higher rate of interest.

Bonds promise fixed nominal cash payments, but the real interest rate that they provide depends on inflation. The best-known theory about the effect of inflation on interest rates was suggested by Irving Fisher. He argued that the nominal, or money, rate of interest is equal to the required real rate plus the expected rate of inflation. If the expected inflation rate increases by 1%, so too will the money rate of interest. During the past 50 years Fisher’s simple theory has not done a bad job of explaining changes in short-term interest rates.

When you buy a U.S. Treasury bond, you can be fairly confident that you will get your money back. When you lend to a company, you face the risk that it will go belly-up and will not be able to repay its bonds. Defaults are rare for companies with investment-grade bond ratings, but investors worry nevertheless. Companies need to compensate investors for default risk by promising to pay higher rates of interest.

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FURTHER READING

Two good general texts on fixed income markets are:

F. J. Fabozzi and S. V. Mann, Handbook of Fixed Income Markets, 8th ed. (New York: McGraw-Hill, 2011).

S. Sundaresan, Fixed Income Markets and Their Derivatives, 3rd ed. (San Diego, CA: Academic Press, 2009).

Schaefer’s paper is a good review of duration and how it is used to hedge fixed liabilities:

A. M. Schaefer, “Immunisation and Duration: A Review of Theory, Performance and Application,” in The Revolution in Corporate Finance, ed. J. M. Stern and D. H. Chew, Jr. (Oxford: Basil Blackwell, 1986).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Prices and yields A 10-year bond is issued with a face value of $1,000, paying interest of $60 a year. If market yields increase shortly after the T-bond is issued, what happens to the bond’s

a.  Coupon rate?

b.  Price?

c.  Yield to maturity?

2.  Prices and yields The following statements are true. Explain why.

a.  If a bond’s coupon rate is higher than its yield to maturity, then the bond will sell for more than face value.

b.  If a bond’s coupon rate is lower than its yield to maturity, then the bond’s price will increase over its remaining maturity.

3.  Prices and yields In February 2012 Treasury 6¼s of 2030 offered a semiannually compounded yield of 2.70%. Recognizing that coupons are paid semiannually, calculate the bond’s price.

4.  Prices and yields Here are the prices of three bonds with 10-year maturities:

If coupons are paid annually, which bond offered the highest yield to maturity? Which had the lowest? Which bonds had the longest and shortest durations?

5.  Prices and yields Construct some simple examples to illustrate your answers to the following:

a.  If interest rates rise, do bond prices rise or fall?

b.  If the bond yield is greater than the coupon, is the price of the bond greater or less than 100?

c.  If the price of a bond exceeds 100, is the yield greater or less than the coupon?

d.  Do high-coupon bonds sell at higher or lower prices than low-coupon bonds?

e.  If interest rates change, does the price of high-coupon bonds change proportionately more than that of low-coupon bonds?

6.  Spot interest rates and yields Which comes first in the market for government bonds:

a.  Spot interest rates or yields to maturity?

b.  Bond prices or yields to maturity?

7.  Spot interest rates and yields Look again at Table 3.5. Suppose that spot interest rates all change to 4%—a “flat” term structure of interest rates.

a.  What is the new yield to maturity for each bond in the table?

b.  Recalculate the price of bond A.

8.  Spot interest rates and yields

a.  What is the formula for the value of a two-year, 5% bond in terms of spot rates?

b.  What is the formula for its value in terms of yield to maturity?

c.  If the two-year spot rate is higher than the one-year rate, is the yield to maturity greater or less than the two-year spot rate?

9.  Measuring term structure The following table shows the prices of a sample of U.S. Treasury strips in February 2012. Each strip makes a single payment of $1,000 at maturity.

a.  Calculate the annually compounded, spot interest rate for each year.

b.  Is the term structure upward- or downward-sloping or flat?

c.  Would you expect the yield on a coupon bond maturing in February 2017 to be higher or lower than the yield on the 2014 strip?

10.  Bond returns and yields

a.  An 8%, five-year bond yields 6%. If the yield remains unchanged, what will be its price one year hence? Assume annual coupon payments.

b.  What is the total return to an investor who held the bond over this year?

c.  What can you deduce about the relationship between the bond return over a particular period and the yields to maturity at the start and end of that period?

11.  Duration True or false? Explain.

a.  Longer-maturity bonds necessarily have longer durations.

b.  The longer a bond’s duration, the lower its volatility.

c.  Other things equal, the lower the bond coupon, the higher its volatility.

d.  If interest rates rise, bond durations rise also.

12.  Duration Calculate the durations and volatilities of securities A, B, and C. Their cash flows are shown below. The interest rate is 8%.

13.  Term-structure theories The one-year spot interest rate is r1 = 5% and the two-year rate is r2 = 6%. If the expectations theory is correct, what is the expected one-year interest rate in one year’s time?

14.  Real interest rates The two-year interest rate is 10% and the expected annual inflation rate is 5%.

a.  What is the expected real interest rate?

b.  If the expected rate of inflation suddenly rises to 7%, what does Fisher’s theory say about how the real interest rate will change? What about the nominal rate?

INTERMEDIATE

15.  Prices and yields A 10-year German government bond (bund) has a face value of €100 and a coupon rate of 5% paid annually. Assume that the interest rate (in euros) is equal to 6% per year. What is the bond’s PV?

16.  Prices and yields A 10-year Japanese government bond (JGB) with a face value of ¥50,000 pays a coupon of 5.5% (2.75% of face value every six months). The semiannually compounded interest rate is 5.2% (a six-month discount rate of 5.2/2 = 2.6%).

a.  What is the present value of the bond?

b.  Generate a graph or table showing how the bond’s present value changes for semiannually compounded interest rates between 1% and 15%.

17.  Prices and yields A six-year French government bond (OAT) makes annual coupon payments of 5% and offers a yield of 3% annually compounded. Suppose that one year later the bond still yields 3%. What return has the bondholder earned over the 12-month period? Now suppose that the bond yields 2% at the end of the year. What return would the bondholder earn in this case?

18.  Spot interest rates and yields A 6% six-year bond yields 12% and a 10% six-year bond yields 8%. Calculate the six-year spot rate. Assume annual coupon payments. (Hint: What would be your cash flows if you bought 1.2 10% bonds?)

19.  Spot interest rates and yields Is the yield on high-coupon bonds more likely to be higher than that on low-coupon bonds when the term structure is upward-sloping or when it is downward-sloping? Explain.

20.  Spot interest rates and yields You have estimated spot rates as follows:

r1 = 5.00%, r2 = 5.40%, r3 = 5.70%, r4 = 5.90%, r5 = 6.00%.

a.  What are the discount factors for each date (that is, the present value of $1 paid in year t)?

b.  Calculate the PV of the following bonds assuming annual coupons: (i) 5%, two-year bond; (ii) 5%, five-year bond; and (iii) 10%, five-year bond.

c.  Explain intuitively why the yield to maturity on the 10% bond is less than that on the 5% bond.

d.  What should be the yield to maturity on a five-year zero-coupon bond?

e.  Show that the correct yield to maturity on a five-year annuity is 5.75%.

f.  Explain intuitively why the yield on the five-year bonds described in part (c) must lie between the yield on a five-year zero-coupon bond and a five-year annuity.

21.  Duration Calculate durations and modified durations for the 3% bonds in Table 3.2. You can follow the procedure set out in Table 3.4 for the 9% coupon bonds. Confirm that modified duration predicts the impact of a 1% change in interest rates on the bond prices.

22.  Duration Find the spreadsheet for Table 3.4. on this book’s website, www.mcgraw-hill.co.uk/textbooks/brealey. Show how duration and volatility change if (a) the bond’s coupon is 8% of face value and (b) the bond’s yield is 6%. Explain your finding.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

23.  Duration The formula for the duration of a perpetual bond that makes an equal payment each year in perpetuity is (1 + yield)/yield. If each bond yields 5%, which has the longer duration—a perpetual bond or a 15-year zero-coupon bond? What if the yield is 10%?

24.  Prices and yields Look up prices of 10 government bonds with different coupons and different maturities. Calculate how their prices would change if their yields to maturity increased by 1 percentage point. Are long- or short-term bonds most affected by the change in yields? Are high- or low-coupon bonds most affected?

25.  Spot interest rates and yields Look again at Table 3.5. Suppose the spot interest rates change to the following downward-sloping term structure: r1 = 4.6%, r2 = 4.4%, r3 = 4.2%, and r4 = 4.0%. Recalculate discount factors, bond prices, and yields to maturity for each of the bonds listed in the table.

26.  Spot interest rates and yields Look at the spot interest rates shown in Problem 25. Suppose that someone told you that the five-year spot interest rate was 2.5%. Why would you not believe him? How could you make money if he was right? What is the minimum sensible value for the five-year spot rate?

27.  Term-structure theories Look again at the spot interest rates shown in Problem 25. What can you deduce about the one-year spot interest rate in three years if . . .

a.  The expectations theory of term structure is right?

b.  Investing in long-term bonds carries additional risks?

28.  Nominal and real returns Suppose that you buy a two-year 8% bond at its face value.

a.  What will be your nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your real return?

b.  Now suppose that the bond is a TIPS. What will be your real and nominal returns?

29.  Bond ratings A bond’s credit rating provides a guide to its price. As we write this in early 2012, Aaa bonds yield 5.3% and Baa bonds yield 5.9%. If some bad news causes a 10% five-year bond to be unexpectedly downrated from Aaa to Baa, what would be the effect on the bond price? (Assume annual coupons.)

30.  Prices and yields If a bond’s yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this with a simple example of a four-year bond selling at a premium to face value. Now do the same for a four-year bond selling at a discount. For convenience, assume annual coupon payments.

CHALLENGE

31.  Prices and yields Write a spreadsheet program to construct a series of bond tables that show the present value of a bond given the coupon rate, maturity, and yield to maturity. Assume that coupon payments are semiannual and yields are compounded semiannually.

32.  Price and spot interest rates Find the arbitrage opportunity (opportunities?). Assume for simplicity that coupons are paid annually. In each case the face value of the bond is $1,000.

33.  Duration The duration of a bond that makes an equal payment each year in perpetuity is (1 + yield)/yield. Prove it.

34.  Duration What is the duration of a common stock whose dividends are expected to grow at a constant rate in perpetuity?

35.  Prices and spot interest rates

a.  What spot rates are embedded in the following government bonds? The price of one-year strips is 93.46%. Assume for simplicity that bonds make only annual payments. (Hint: Can you devise a mixture of long and short positions in these bonds that gives a cash payoff only in year 2? In year 3?)

b.  A three-year bond with a 4% coupon is selling at 95.00%. Is there a profit opportunity here? If so, how would you take advantage of it?

36.  Prices and spot interest rates Look one more time at Table 3.5.

a.  Suppose you knew the bond prices but not the spot interest rates. Explain how you would calculate the spot rates. (Hint: You have four unknown spot rates, so you need four equations.)

b.  Suppose that you could buy bond C in large quantities at $1,040 rather than at its equilibrium price of $1,076.20. Show how you could make a zillion dollars without taking on any risk.

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FINANCE ON THE WEB

The websites of The Wall Street Journal (www.wsj.com) and the Financial Times (www.ft.com) are wonderful sources of market data. You should become familiar with them.

1.  Use www.wsj.com to answer the following questions:

a.  Find the prices of coupon strips. Use these prices to plot the term structure. If the expectations theory is correct, what is the expected one-year interest rate three years hence?

b.  Find a three- or four-year bond and construct a package of coupon and principal strips that provides the same cash flows. The law of one price predicts that the cost of the package should be very close to that of the bond. Is it?

c.  Find a long-term Treasury bond with a low coupon and calculate its duration. Now find another bond with a similar maturity and a higher coupon. Which has the longer duration?

d.  Look up the yields on 10-year nominal Treasury bonds and on TIPS. If you are confident that inflation will average 2% a year, which bond will provide the higher real return?

2.  Bond transactions are reported on FINRA’s TRACE service, which was the source of the data for Table 3.6. Use the Advanced Search facility in TRACE to find bond prices for Johnson & Johnson (JNJ), Walmart (WMT), Disney (DIS), SunTrust Banks (STI), and U.S. Steel (X). If possible, exclude callable issues that the company can buy back. Have the bond ratings changed? What has happened to the yields of these companies’ bonds? (You will find that bonds issued by the same company may have very different yields, so you will need to use your best judgment to answer this second question.)

___________

¹Bonds used to come with coupons attached, which had to be clipped off and presented to the issuer to obtain the interest payments. This is still the case with bearer bonds, where the only evidence of indebtedness is the bond itself. In many parts of the world bearer bonds are still issued and are popular with investors who would rather remain anonymous. The alternative is registered bonds, where the identity of the bond’s owner is recorded and the coupon payments are sent automatically. OATs are registered bonds.

²You could also value a four-year annuity of €5.00 plus a final payment of €105.00.

³The frequency of interest payments varies from country to country. For example, most euro bonds pay interest annually, while most bonds in the UK, Canada, and Japan pay interest semiannually.

⁴The quoted bond price is known as the flat (or clean) price. The price that the bond buyer actually pays (sometimes called the full or dirty price) is equal to the flat price plus the interest that the seller has already earned on the bond since the last interest payment. The precise method for calculating this accrued interest varies from one type of bond to another. Always use the flat price to calculate the yield.

⁵From this point forward, we will just say “bonds,” and not distinguish notes from bonds unless we are referring to a specific security. Note also that bonds with long maturities end up with short maturities when they approach the final payment date. Thus you will encounter 30-year bonds trading 20 years later at the same prices as new 10-year notes (assuming equal coupons).

⁶In other words, the derivative of the bond price with respect to a change in yield to maturity is dPV/dy = – duration/(1 + y) = – modified duration.

⁷If you look back at Figure 3.2, you will see that the plot of price against yield is not a straight line. This means that modified duration is a good predictor of the effect of interest rate changes only for small moves in interest rates.

⁸For simplicity, we assumed that the two Treasury bonds paid annual coupons. Calculating Macaulay duration for a bond with semiannual coupons is no different except that there are twice as many cash flows. To calculate modified duration with semiannual coupons you need to divide Macaulay duration by the yield every six months.

⁹We exaggerate Ms. Kraft’s profits. There are always costs to financial transactions, though they may be very small. For example, Ms. Kraft could use her investment in the one-year strip as security for the bank loan, but the bank would need to charge more than 7% on the loan to cover its costs.

¹⁰The extra return for lending for one more year is termed the forward rate of interest. In our example the forward rate is 9.0%. In Ms. Kraft’s arbitrage example, the forward interest rate was negative. In real life, forward interest rates can’t be negative. At the lowest they are zero.

¹¹Indexed bonds were not completely unknown in the United States before 1997. For example, in 1780 American Revolutionary soldiers were compensated with indexed bonds that paid the value of “five bushels of corn, 68 pounds and four-seventh parts of a pound of beef, ten pounds of sheep’s wool, and sixteen pounds of sole leather.”

¹²The reverse happens if there is deflation. In this case the coupon payment and principal amount are adjusted downward. However, the U.S. government guarantees that when the bond matures it will not pay less than its original nominal face value.

¹³The yield on short-term TIPs was negative. You were actually losing in real terms.

¹⁴Some of this saving is done indirectly. For example, if you hold 100 shares of IBM stock, and IBM retains and reinvests earnings of $1.00 a share, IBM is saving $100 on your behalf. The government may also oblige you to save by raising taxes to invest in roads, hospitals, etc.

¹⁵We assume that investors save more as interest rates rise. It doesn’t have to be that way. Suppose that 20 years hence you will need $50,000 in today’s dollars for your children’s college tuition. How much will you have to set aside today to cover this obligation? The answer is the present value of a real expenditure of $50,000 after 20 years, or 50,000/(1 + real interest rate)20. The higher the real interest rate, the lower the present value and the less you have to set aside.

¹⁶Corporate bonds are also less liquid than Treasuries: they are more difficult and expensive to trade, particularly in large quantities or on short notice. Many investors value liquidity and will demand a higher interest rate on a less liquid bond. Lack of liquidity accounts for some of the spread between yields on corporate and Treasury bonds.

¹⁷Occasionally, defaults have been a case of “won’t pay” rather than “can’t pay.” For example, in 2008 Ecuador’s president announced that his country would disavow $3.9 billion of “illegal” debts contracted by earlier regimes. In dealing with international lenders, he said, “We are up against real monsters.”

Part 1 Value

The Value of Common Stocks

We should warn you that being a financial expert has its occupational hazards. One is being cornered at cocktail parties by people who are eager to explain their system for making creamy profits by investing in common stocks. One of the few good things about a financial crisis is that these bores tend to disappear, at least temporarily.

We may exaggerate the perils of the trade. The point is that there is no easy way to ensure superior investment performance. Later in the book we show that in well-functioning capital markets it is impossible to predict changes in security prices. Therefore, in this chapter, when we use the concept of present value to price common stocks, we are not promising you a key to investment success; we simply believe that the idea can help you to understand why some investments are priced higher than others.

Why should you care? If you want to know the value of a firm’s stock, why can’t you look up the stock price on the Internet? Unfortunately, that is not always possible. For example, you may be the founder of a successful business. You currently own all the shares but are thinking of going public by selling off shares to other investors. You and your advisers need to estimate the price at which those shares can be sold.

There is also another, deeper reason why managers need to understand how shares are valued. If a firm acts in its shareholders’ interest, it should accept those investments that increase the value of their stake in the firm. But in order to do this, it is necessary to understand what determines the shares’ value.

We begin with a look at how stocks are traded. Then we explain the basic principles of share valuation and the use of discounted-cash-flow (DCF) models to estimate expected rates of return. Later in the chapter we show how DCF models can be used to value entire businesses rather than individual shares.

We will also explain the fundamental difference between growth and income stocks. A growth stock doesn’t just grow; its future investments are also expected to earn rates of return that are higher than the cost of capital. It’s the combination of growth and superior returns that generates high price–earnings ratios for growth stocks.

Still another warning: Everybody knows that common stocks are risky and that some are more risky than others. Therefore, investors will not commit funds to stocks unless the expected rates of return are commensurate with the risks. But we say next to nothing in this chapter about the linkages between risk and expected return. A more careful treatment of risk starts in Chapter 7.

 4-1   How Common Stocks Are Traded

General Electric (GE) has about 10.6 billion shares outstanding. Shareholders include large pension funds and insurance companies that each own several million shares, as well as individuals who own a handful of shares. If you owned one GE share, you would own .00000001% of the company and have a claim on the same tiny fraction of GE’s profits. Of course, the more shares you own, the larger your “share” of the company.

If GE wishes to raise new capital, it can do so either by borrowing or by selling new shares to investors. Sales of shares to raise new capital are said to occur in the primary market. But most trades in GE take place on the stock exchange, where investors buy and sell existing GE shares. Stock exchanges are really markets for secondhand shares, but they prefer to describe themselves as secondary markets, which sounds more important.

The two principal U.S. stock exchanges are the New York Stock Exchange and Nasdaq. Both compete vigorously for business and just as vigorously tout the advantages of their trading systems. The volume of business that they handle is immense. For example, on an average day the NYSE trades around 2 billion shares in some 2,300 companies.

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Major world stock exchanges

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In addition to the NYSE and Nasdaq, there are computer networks called electronic communication networks (ECNs) that connect traders with each other. Large U.S. companies may also arrange for their shares to be traded on foreign exchanges, such as the London exchange or the Euronext exchange in Paris. At the same time many foreign companies are listed on the U.S. exchanges. For example, the NYSE trades shares in Sony, Royal Dutch Shell, Canadian Pacific, Tata Motors, Deutsche Bank, Brasil Telecom, China Eastern Airlines, and 500 other companies.

Suppose that Ms. Jones, a longtime GE shareholder, no longer wishes to hold her shares in the company. She can sell them via the NYSE to Mr. Brown, who wants to increase his stake in the firm. The transaction merely transfers partial ownership of the firm from one investor to another. No new shares are created, and GE will neither care nor know that the trade has taken place.

Ms. Jones and Mr. Brown do not trade the GE shares themselves. Instead, their orders must go through a brokerage firm. Ms. Jones, who is anxious to sell, might give her broker a market order to sell stock at the best available price. On the other hand, Mr. Brown might state a price limit at which he is willing to buy GE stock. If his limit order cannot be executed immediately, it is recorded in the exchange’s limit order book until it can be executed.

When they transact on the NYSE, Brown and Jones are participating in a huge auction market in which the exchange’s designated market makers match up the orders of thousands of investors. Most major exchanges around the world, such as the Tokyo Stock Exchange, the London Stock Exchange, and the Deutsche Börse, are also auction markets, but the auctioneer in these cases is a computer.¹ This means that there is no stock exchange floor to show on the evening news and no one needs to ring a bell to start trading.

Nasdaq is not an auction market. All trades on Nasdaq take place between the investor and one of a group of professional dealers who are prepared to buy and sell stock. Dealer markets are common for other financial instruments. For example, most bonds are traded in dealer markets.

Trading Results for GE

You can track trades in GE or other public corporations on the Internet. For example, if you go to finance.yahoo.com, enter the ticker symbol GE, and ask to “Get Quotes,” you will see results like the table on the next page.²

GE’s closing price on January 27, 2012, was $19.03, down $.04 or .21% from the previous day’s close. GE traded in a range of $18.92 to 19.13, and between $14.02 and $21.65 over the prior 52 weeks. Trading volume was 32,617,690 shares, well below the three-month average of 60,699,500 shares per day. GE’s market cap (shorthand for market capitalization) was $201.07 billion.

GE’s earnings per share (EPS) over the previous 12 months were $1.24 (“ttm” stands for “trailing 12 months”). The ratio of stock price to EPS (the P/E ratio) was 15.4. Notice that this P/E ratio uses past EPS. P/E ratios using forecasted EPS are generally more useful. Security analysts forecasted an increase in GE’s EPS to 1.54 per share for 2012, which gives a forward P/E of 12.4.³

GE paid a cash dividend of $.68 per share per year, so its dividend yield (the ratio of dividend to price) was 3.60%.

Buying stocks is a risky occupation. GE stock traded at over $40 in 2007. By January 2012, the unfortunate investor who bought in at $40 lost more than half of his investment. Of course, you don’t come across such people at cocktail parties; they either keep quiet or aren’t invited.

Most of the trading on the NYSE and Nasdaq is in ordinary common stocks, but other securities are traded also, including preferred shares, which we cover in Chapter 14, and warrants, which we cover in Chapter 21. Investors can also choose from hundreds of exchange-traded funds (ETFs), which are portfolios of stocks that can be bought or sold in a single trade. With a few exceptions ETFs are not actively managed. Many simply aim to track a well-known market index such as the Dow Jones Industrial Average or the S&P 500. Others track specific industries or commodities. (We discuss ETFs more fully in Chapter 14.) You can also buy shares in closed-end mutual funds⁴ that invest in portfolios of securities. These include country funds, for example, the Mexico and Chile funds, that invest in portfolios of stocks in specific countries. Unlike ETFs, most closed-end funds are actively managed and seek to “beat the market.”

 4-2   How Common Stocks Are Valued

Finding the value of GE stock may sound like a simple problem. Each quarter, the company publishes a balance sheet, which lists the value of the firm’s assets and liabilities. At the end of September 2011 the book value of all GE’s assets—plant and machinery, inventories of materials, cash in the bank, and so on—was $738 billion. GE’s liabilities—money that it owes the banks, taxes that are due to be paid, and the like—amounted to $613 billion. The difference between the value of the assets and the liabilities was $125 billion. This was the book value of GE’s equity.

Book value is a reassuringly definite number. Each year KPMG, one of America’s largest accounting firms, gives its opinion that GE’s financial statements present fairly in all material respects the company’s financial position, in conformity with U.S. generally accepted accounting principles (commonly called GAAP). However, the book value of GE’s assets measures only their original (or “historical”) cost less an allowance for depreciation. This may not be a good guide to what those assets are worth today.

One can go on and on about the deficiencies of book value as a measure of market value. Book values are historical costs that do not incorporate inflation. (Countries with high or volatile inflation often require inflation-adjusted book values, however.) Book values usually exclude intangible assets such as trademarks and patents. Also accountants simply add up the book values of individual assets, and thus do not capture going-concern value. Going-concern value is created when a collection of assets is organized into a healthy operating business.

Book values can nevertheless be a useful benchmark. If a financial analyst says, “Holstein Oil sells for two times book value,” she is effectively saying that Holstein has doubled its shareholders’ past investments in the company.

Book values may also be useful clues about liquidation value. Liquidation value is what investors get when a failed company is shut down and its assets are sold off. Book values of “hard” assets like land, buildings, vehicles, and machinery can indicate possible liquidation values.

Intangible “soft” assets can be important even in liquidation, however. Eastman Kodak provides a good recent example. Kodak, which was one of the Nifty Fifty growth stocks of the 1960s, suffered a long decline and finally filed for bankruptcy in January 2012. What was its most valuable asset in bankruptcy? Its portfolio of patents, which was put up for sale. The present value of the patents was estimated, perhaps optimistically, at $3 billion.

Valuation by Comparables

When financial analysts need to value a business, they often start by identifying a sample of similar firms as potential comparables. They then examine how much investors in the comparable companies are prepared to pay per dollar of earnings or book assets. They see what the business would be worth if it traded at the comparables’ price–earnings or price-to-book-value ratios. This valuation approach is called valuation by comparables.

Table 4.1 tries out this valuation method for four companies and industries.⁵ Let’s start with Dow Chemical. In late January 2012 Dow’s stock was trading at about $33. Forecasted earnings per share (EPS) for 2012 were $2.62, giving a P/E ratio of 12.6. Dow’s market–book ratio (price divided by book value per share) was P/B = 2.0.

   TABLE 4.1 Stock price, price–earnings (P/E), and market–book (P/B) in January 2012. Selected companies are compared to potential comparables.

P/Es and P/Bs for several of Dow’s competitors are reported on the right-hand side of the table. Notice that Dow’s P/E is higher than the P/Es of these comparables. If you didn’t know Dow’s stock price, you could get an estimate by multiplying Dow’s forecasted EPS by the average P/E for the comparables. The estimate would be somewhat low (at 2.62 × 10.7 = 28.03), but nevertheless helpful. On the other hand, Dow’s P/B is much lower than for the comparables. In this case, the wide range of P/Bs for the comparables would give you a hint that P/B ratios are treacherous for this industry.

Look now at the Union Pacific railroad and the four comparables in Table 4.1. In this case the P/B ratios are similar for the comparables, though a little lower than for Union Pacific (an average of 2.7 versus 3.0). The average P/E for the comparables is a little higher (15.1 versus 14.1). Thus valuation by comparables would not give you exactly the right price for Union Pacific, but you would be close.

The ratios for Johnson & Johnson (J&J) and Apache illustrate the difficulties with valuation by comparables. That method would undervalue J&J, because both its P/E and P/B ratios are higher than for the four other pharmaceutical companies shown on the right-hand side of the table. Investors clearly saw extra value in J&J stock versus its competitors. On the other hand, investors valued Apache at lower P/E and P/B ratios than the four competitors shown in the table, which suggests some dark clouds ahead for Apache.

The difficulties in applying the valuation by comparables method for J&J and Apache do not invalidate the method. Maybe Table 4.1 doesn’t show the best comparables.⁶ A financial manager or analyst would have to dig deeper to understand Apache’s industry, the business of exploring for and producing oil and natural gas.

Of course investors did not need valuation by comparables to value Apache or the other companies in Table 4.1. They are all public companies with actively traded shares. Table 4.1 just illustrates how to compare stock prices based on P/E or P/B ratios.

Valuation by comparables is most useful when you don’t have a stock price. For example, Kinder Morgan announced in January 2012 that it was taking offers for the oil and gas exploration business of its El Paso subsidiary. The subsidiary was not a public company. Preliminary estimates put its value at $7 billion. It’s a safe bet that Kinder Morgan and its advisers were burning the midnight oil, doing their best to identify the best comparables for El Paso and checking what El Paso would be worth if it traded at the comparables’ P/E and P/B ratios.

But Kinder Morgan would have to be cautious. As Table 4.1 shows, these ratios can vary widely even within the same industry. To understand why this is so, we need to look more carefully at what determines a stock’s market value. We start by connecting stock prices to the cash flows that stockholders receive from the company in the form of cash dividends. This will lead us to a discounted cash flow (DCF) model of stock prices.

Stock Prices and Dividends

Not all companies pay dividends. Rapidly growing companies typically reinvest earnings instead of paying out cash. But most mature, profitable companies do pay regular cash dividends.

Think back to Chapter 3, where we explained how bonds are valued. The market value of a bond equals the discounted present value (PV) of the cash flows (interest and principal payments) that the bond will pay out over its lifetime. Let’s import and apply this idea to common stocks. The future cash flows to the owner of a share of common stock are the future dividends per share that the company will pay out. Thus the logic of discounted cash flow suggests

At first glance this statement may seem surprising. Investors hope for capital gains as well as dividends. That is, they hope to sell stocks for more than they paid for them. Why doesn’t the PV of a stock depend on capital gains? As we now explain, there is no inconsistency.

Today’s Price If you own a share of common stock, your cash payoff comes in two forms: (1) cash dividends and (2) capital gains or losses. Suppose that the current price of a share is P0, that the expected price at the end of a year is P1, and that the expected dividend per share is DIV1. The rate of return that investors expect from this share over the next year is defined as the expected dividend per share DIV1 plus the expected price appreciation per share P1 – P0, all divided by the price at the start of the year P0:

Suppose Fledgling Electronics stock is selling for $100 a share (P0 = 100). Investors expect a $5 cash dividend over the next year (DIV1 = 5). They also expect the stock to sell for $110 a year hence (P1 = 110). Then the expected return to the stockholders is 15%:

On the other hand, if you are given investors’ forecasts of dividend and price and the expected return offered by other equally risky stocks, you can predict today’s price:

For Fledgling Electronics DIV1 = 5 and P1 = 110. If r, the expected return for Fledgling is 15%, then today’s price should be $100:

What exactly is the discount rate, r, in this calculation? It’s called the market capitalization rate or cost of equity capital, which are just alternative names for the opportunity cost of capital, defined as the expected return on other securities with the same risks as Fledgling shares.

Many stocks will be safer than Fledgling, and many riskier. But among the thousands of traded stocks there will be a group with essentially the same risks. Call this group Fledgling’s risk class. Then all stocks in this risk class have to be priced to offer the same expected rate of return.

Let’s suppose that the other securities in Fledgling’s risk class all offer the same 15% expected return. Then $100 per share has to be the right price for Fledgling stock. In fact it is the only possible price. What if Fledgling’s price were above P0 = $100? In this case investors would shift their capital to the other securities and in the process would force down the price of Fledgling stock. If P0 were less than $100, the process would reverse. Investors would rush to buy, forcing the price up to $100. Therefore at each point in time all securities in an equivalent risk class are priced to offer the same expected return. This is a condition for equilibrium in well-functioning capital markets. It is also common sense.

Next Year’s Price? We have managed to explain today’s stock price P0 in terms of the dividend DIV1 and the expected price next year P1. Future stock prices are not easy things to forecast directly. But think about what determines next year’s price. If our price formula holds now, it ought to hold then as well:

That is, a year from now investors will be looking out at dividends in year 2 and price at the end of year 2. Thus we can forecast P1 by forecasting DIV2 and P2, and we can express P0 in terms of DIV1, DIV2, and P2:

Take Fledgling Electronics. A plausible explanation for why investors expect its stock price to rise by the end of the first year is that they expect higher dividends and still more capital gains in the second. For example, suppose that they are looking today for dividends of $5.50 in year 2 and a subsequent price of $121. That implies a price at the end of year 1 of

Today’s price can then be computed either from our original formula

or from our expanded formula

We have succeeded in relating today’s price to the forecasted dividends for two years (DIV1 and DIV2) plus the forecasted price at the end of the second year (P2). You will not be surprised to learn that we could go on to replace P2 by (DIV3 + P3)/(1 + r) and relate today’s price to the forecasted dividends for three years (DIV1, DIV2, and DIV3) plus the forecasted price at the end of the third year (P3). In fact we can look as far out into the future as we like, removing Ps as we go. Let us call this final period H. This gives us a general stock price formula:

The expression indicates the sum of the discounted dividends from year 1 to year H.

Table 4.2 continues the Fledgling Electronics example for various time horizons, assuming that the dividends are expected to increase at a steady 10% compound rate. The expected price Pt increases at the same rate each year. Each line in the table represents an application of our general formula for a different value of H. Figure 4.1 is a graph of the table. Each column shows the present value of the dividends up to the time horizon and the present value of the price at the horizon. As the horizon recedes, the dividend stream accounts for an increasing proportion of present value, but the total present value of dividends plus terminal price always equals $100.

   TABLE 4.2 Applying the stock valuation formula to Fledgling Electronics.

Assumptions:

1. Dividends increase at 10% per year, compounded.

2. Capitalization rate is 15%.

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Try It! Figure 4.1: Value and the investor’s horizon

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How far out could we look? In principle, the horizon period H could be infinitely distant. Common stocks do not expire of old age. Barring such corporate hazards as bankruptcy or acquisition, they are immortal. As H approaches infinity, the present value of the terminal price ought to approach zero, as it does in the final column of Figure 4.1. We can, therefore, forget about the terminal price entirely and express today’s price as the present value of a perpetual stream of cash dividends. This is usually written as

   FIGURE 4.1 As your horizon recedes, the present value of the future price (shaded area) declines but the present value of the stream of dividends (unshaded area) increases. The total present value (future price and dividends) remains the same.

where ∞ indicates infinity. This formula is the DCF or dividend discount model of stock prices. It’s another present value formula.⁷ We discount the cash flows in this case the dividend stream—by the return that can be earned in the capital market on securities of equivalent risk. Some find the DCF formula implausible because it seems to ignore capital gains. But we know that the formula was derived from the assumption that price in any period is determined by expected dividends and capital gains over the next period.

Notice that it is not correct to say that the value of a share is equal to the sum of the discounted stream of earnings per share. Earnings are generally larger than dividends because part of those earnings is reinvested in new plant, equipment, and working capital. Discounting earnings would recognize the rewards of that investment (higher future earnings and dividends) but not the sacrifice (a lower dividend today). The correct formulation states that share value is equal to the discounted stream of dividends per share. Share price is connected to future earnings per share but by a different formula, which we cover later in this chapter.

Although mature companies generally pay cash dividends, thousands of companies do not. For example, Google has never paid a dividend, yet it is a successful company with a market capitalization in early 2012 of $190 billion. How can this value be reconciled with the dividend discount model?

Why would a successful company decide not to pay cash dividends? There are two reasons at least. First, a growing company may maximize value by investing all its earnings rather than paying out any. The shareholders are better off with this policy, provided that the investments offer an expected rate of return higher than shareholders could get by investing on their own. In other words, shareholder value is maximized if the firm invests in projects that can earn more than the opportunity cost of capital. If such projects are plentiful, shareholders will be prepared to forgo immediate dividends. They will be happy to wait and receive deferred dividends.⁸

The dividend discount model is still logically correct for growth companies, but difficult to use when cash dividends are far in the future. In this case, most analysts switch to valuation by comparables or to earnings-based formulas, which we cover in Section 4-4.

Second, a company may pay out cash not as dividends but by repurchasing shares from stockholders. We cover the choice between dividends and repurchases in Chapter 16, where we also explain why repurchases do not invalidate the dividend discount model.⁹

Nevertheless the dividend discount model can be difficult to deploy if repurchases are irregular and unpredictable. In these cases, it can be better to start by calculating the present value of the total free cash flow available for dividends and repurchases. Discounting free cash flow gives the present value of the company as a whole. Dividing by the current number of shares outstanding gives present value per share. We cover this valuation method in Section 4-5.

The next section considers simplified versions of the dividend discount model.

 4-3   Estimating the Cost of Equity Capital

In Chapter 2 we encountered some simplified versions of the basic present value formula. Let us see whether they offer any insights into stock values. Suppose, for example, that we forecast a constant growth rate for a company’s dividends. This does not preclude year-to-year deviations from the trend: It means only that expected dividends grow at a constant rate. Such an investment would be just another example of the growing perpetuity that we valued in Chapter 2. To find its present value we must divide the first year’s cash payment by the difference between the discount rate and the growth rate:

Remember that we can use this formula only when g, the anticipated growth rate, is less than r, the discount rate. As g approaches r, the stock price becomes infinite. Obviously r must be greater than g if growth really is perpetual.

Our growing perpetuity formula explains P0 in terms of next year’s expected dividend DIV1, the projected growth trend g, and the expected rate of return on other securities of comparable risk r. Alternatively, the formula can be turned around to obtain an estimate of r from DIV1, P0, and g:

The expected return equals the dividend yield (DIV1/P0) plus the expected rate of growth in dividends (g).

These two formulas are much easier to work with than the general statement that “price equals the present value of expected future dividends.”¹⁰ Here is a practical example.

Using the DCF Model to Set Gas and Electricity Prices

In the United States the prices charged by local electric and gas utilities are regulated by state commissions. The regulators try to keep consumer prices down but are supposed to allow the utilities to earn a fair rate of return. But what is fair? It is usually interpreted as r, the market capitalization rate for the firm’s common stock. In other words the fair rate of return on equity for a public utility ought to be the cost of equity, that is, the rate offered by securities that have the same risk as the utility’s common stock.¹¹

Small variations in estimates of this return can have large effects on the prices charged to the customers and on the firm’s profits. So both utilities and regulators work hard to estimate the cost of equity accurately. They’ve noticed that most utilities are mature, stable companies that pay regular dividends. Such companies should be tailor-made for application of the constant-growth DCF formula.

Suppose you wished to estimate the cost of equity for Northwest Natural Gas, a local natural gas distribution company. Its stock was selling for $47.30 per share at the start of 2012. Dividend payments for the next year were expected to be $1.86 a share. Thus it was a simple matter to calculate the first half of the DCF formula:

The hard part is estimating g, the expected rate of dividend growth. One option is to consult the views of security analysts who study the prospects for each company. Analysts are rarely prepared to stick their necks out by forecasting dividends to kingdom come, but they often forecast growth rates over the next five years, and these estimates may provide an indication of the expected long-run growth path. In the case of Northwest, analysts in 2012 were forecasting an annual growth of 4.6%.¹² This, together with the dividend yield, gave an estimate of the cost of equity capital:

An alternative approach to estimating long-run growth starts with the payout ratio, the ratio of dividends to earnings per share (EPS). For Northwest, this ratio averaged about 60%. In other words, each year the company was plowing back into the business about 40% of earnings per share:

Also, Northwest’s ratio of earnings per share to book equity per share was about 11%. This is its return on equity, or ROE:

If Northwest earns 11% of book equity and reinvests 40% of income, then book equity will increase by .40 × .11 = .044, or 4.4%. Earnings and dividends per share will also increase by 4.4%:

That gives a second estimate of the market capitalization rate:

Although these estimates of Northwest’s cost of equity seem reasonable, there are obvious dangers in analyzing any single firm’s stock with the constant-growth DCF formula. First, the underlying assumption of regular future growth is at best an approximation. Second, even if it is an acceptable approximation, errors inevitably creep into the estimate of g.

Remember, Northwest’s cost of equity is not its personal property. In well-functioning capital markets investors capitalize the dividends of all securities in Northwest’s risk class at exactly the same rate. But any estimate of r for a single common stock is “noisy” and subject to error. Good practice does not put too much weight on single-company estimates of the cost of equity. It collects samples of similar companies, estimates r for each, and takes an average. The average gives a more reliable benchmark for decision making.

The next-to-last column of Table 4.3 gives DCF cost-of-equity estimates for Northwest and seven other gas distribution companies. These are all stable, mature companies for which the constant-growth DCF formula ought to work. Notice the variation in the cost-of-equity estimates. Some of the variation may reflect differences in the risk, but some is just noise. The average estimate is 9.5%.

   TABLE 4.3 Cost-of-equity estimates for local gas distribution companies at the start of 2012. The long-term growth rate is based on security analysts’ forecasts. In the multistage DCF model, growth after five years is assumed to adjust gradually to the estimated long-term growth rate of Gross Domestic Product (GDP).

a Annualized last quarterly dividend.

b Long-term GDP growth forecasted at 4.7%.

Source: The Brattle Group, Inc.

Estimates of this kind are only as good as the long-term forecasts on which they are based. For example, several studies have observed that security analysts are subject to behavioral biases and their forecasts tend to be over-optimistic. If so, such DCF estimates of the cost of equity should be regarded as upper estimates of the true figure.

Dangers Lurk in Constant-Growth Formulas

The simple constant-growth DCF formula is an extremely useful rule of thumb, but no more than that. Naive trust in the formula has led many financial analysts to silly conclusions.

We have stressed the difficulty of estimating r by analysis of one stock only. Try to use a large sample of equivalent-risk securities. Even that may not work, but at least it gives the analyst a fighting chance, because the inevitable errors in estimating r for a single security tend to balance out across a broad sample.

Also, resist the temptation to apply the formula to firms having high current rates of growth. Such growth can rarely be sustained indefinitely, but the constant-growth DCF formula assumes it can. This erroneous assumption leads to an overestimate of r.

Example The U.S. Surface Transportation Board (STB) tracks the “revenue adequacy” of U.S. railroads by comparing the railroads’ returns on book equity with estimates of the cost of the equity. To estimate the cost of equity, the STB traditionally used the constant-growth formula. It measured g by stock analysts’ forecasts of long-term earnings growth. The formula assumes that earnings and dividends grow at a constant rate forever, but the analysts’ “long-term” forecasts looked out five years at most. As the railroads’ profitability improved, the analysts became more and more optimistic. By 2009, their forecasts for growth averaged 12.5% per year. The average dividend yield was 2.6%, so the constant-growth model estimated the industry-average cost of capital at 2.6 + 12.5 = 15.1%.

So the STB said, in effect, “Wait a minute: railroad earnings and dividends can’t grow at 12.5% forever. The constant-growth formula no longer works for railroads. We’ve got to find a more accurate method.” The STB switched to a two-stage growth model, which we now discuss.

DCF Models with Two Stages of Growth Consider Growth-Tech, Inc., a firm with DIV1 = $.50 and P0 = $50. The firm has plowed back 80% of earnings and has had a return on equity (ROE) of 25%. This means that in the past

The temptation is to assume that the future long-term growth rate g also equals .20. This would imply

But this is silly. No firm can continue growing at 20% per year forever, except possibly under extreme inflationary conditions. Eventually, profitability will fall and the firm will respond by investing less.

In real life the return on equity will decline gradually over time, but for simplicity let’s assume it suddenly drops to 16% at year 3 and the firm responds by plowing back only 50% of earnings. Then g drops to .50 × .16 = .08.

Table 4.4 shows what’s going on. Growth-Tech starts year 1 with book equity of $10.00 per share. It earns $2.50, pays out 50 cents as dividends, and plows back $2. Thus it starts year 2 with book equity of $10 + 2 = $12. After another year at the same ROE and payout, it starts year 3 with equity of $14.40. However, ROE drops to .16, and the firm earns only $2.30. Dividends go up to $1.15, because the payout ratio increases, but the firm has only $1.15 to plow back. Therefore subsequent growth in earnings and dividends drops to 8%.

   TABLE 4.4 Forecasted earnings and dividends for Growth-Tech. Note the changes in year 3: ROE and earnings drop, but payout ratio increases, causing a big jump in dividends. However, subsequent growth in earnings and dividends falls to 8% per year. Note that the increase in equity equals the earnings not paid out as dividends.

Now we can use our general DCF formula:

Investors in year 3 will view Growth-Tech as offering 8% per year dividend growth. So we can use the constant-growth formula to calculate P3:

We have to use trial and error to find the value of r that makes P0 equal $50. It turns out that the r implicit in these more realistic forecasts is approximately .099, quite a difference from our “constant-growth” estimate of .21.

Our present value calculations for Growth-Tech used a two-stage DCF valuation model. In the first stage (years 1 and 2), Growth-Tech is highly profitable (ROE = 25%), and it plows back 80% of earnings. Book equity, earnings, and dividends increase by 20% per year. In the second stage, starting in year 3, profitability and plowback decline, and earnings settle into long-term growth at 8%. Dividends jump up to $1.15 in year 3, and then also grow at 8%.

Growth rates can vary for many reasons. Sometimes growth is high in the short run not because the firm is unusually profitable, but because it is recovering from an episode of low profitability. Table 4.5 displays projected earnings and dividends for Phoenix Corp., which is gradually regaining financial health after a near meltdown. The company’s equity is growing at a moderate 4%. ROE in year 1 is only 4%, however, so Phoenix has to reinvest all its earnings, leaving no cash for dividends. As profitability increases in years 2 and 3, an increasing dividend can be paid. Finally, starting in year 4, Phoenix settles into steady-state growth, with equity, earnings, and dividends all increasing at 4% per year.

Assume the cost of equity is 10%. Then Phoenix shares should be worth $9.13 per share:

You could go on to valuation models with three or more stages. For example, the far right column of Table 4.3 presents multistage DCF estimates of the cost of equity for our local gas distribution companies. In this case the long-term growth rates reported in the table do not continue forever. After five years, each company’s growth rate gradually adjusts to an estimated long-term growth rate for Gross Domestic Product (GDP).

We must leave you with two more warnings about DCF formulas for valuing common stocks or estimating the cost of equity. First, it’s almost always worthwhile to lay out a simple spreadsheet, like Table 4.4 or 4.5, to ensure that your dividend projections are consistent with the company’s earnings and required investments. Second, be careful about using DCF valuation formulas to test whether the market is correct in its assessment of a stock’s value. If your estimate of the value is different from that of the market, it is probably because you have used poor dividend forecasts. Remember what we said at the beginning of this chapter about simple ways of making money on the stock market: there aren’t any.

   TABLE 4.5 Forecasted earnings and dividends for Phoenix Corp. The company can initiate and increase dividends as profitability (ROE) recovers. Note that the increase in book equity equals the earnings not paid out as dividends.

 4-4   The Link Between Stock Price and Earnings per Share

Investors separate growth stocks from income stocks. They buy growth stocks primarily for the expectation of capital gains, and they are interested in the future growth of earnings rather than in next year’s dividends. They buy income stocks primarily for the cash dividends. Let us see whether these distinctions make sense.

Imagine first the case of a company that does not grow at all. It does not plow back any earnings and simply produces a constant stream of dividends. Its stock would resemble the perpetual bond described in Chapter 2. Remember that the return on a perpetuity is equal to the yearly cash flow divided by the present value. So the expected return on our share would be equal to the yearly dividend divided by the share price (i.e., the dividend yield). Since all the earnings are paid out as dividends, the expected return is also equal to the earnings per share divided by the share price (i.e., the earnings–price ratio). For example, if the dividend is $10 a share and the stock price is $100, we have¹³

The price equals

The expected return for growing firms can also equal the earnings–price ratio. The key is whether earnings are reinvested to provide a return equal to the market capitalization rate. For example, suppose our monotonous company suddenly hears of an opportunity to invest $10 a share next year. This would mean no dividend at t = 1. However, the company expects that in each subsequent year the project would earn $1 per share, and therefore the dividend could be increased to $11 a share.

Let us assume that this investment opportunity has about the same risk as the existing business. Then we can discount its cash flow at the 10% rate to find its net present value at year 1:

Thus the investment opportunity will make no contribution to the company’s value. Its prospective return is equal to the opportunity cost of capital.

What effect will the decision to undertake the project have on the company’s share price? Clearly none. The reduction in value caused by the nil dividend in year 1 is exactly offset by the increase in value caused by the extra dividends in later years. Therefore, once again the market capitalization rate equals the earnings–price ratio:

Table 4.6 repeats our example for different assumptions about the cash flow generated by the new project. Note that the earnings–price ratio, measured in terms of EPS1, next year’s expected earnings, equals the market capitalization rate (r) only when the new project’s NPV = 0. This is an extremely important point—managers frequently make poor financial decisions because they confuse earnings–price ratios with the market capitalization rate.

   TABLE 4.6 Effect on stock price of investing an additional $10 in year 1 at different rates of return. Notice that the earnings–price ratio overestimates r when the project has negative NPV and underestimates it when the project has positive NPV.

a Project costs $10.00 (EPS₁). NPV = –10 + C/r, where r = .10.

b NPV is calculated at year 1. To find the impact on P₀, discount for one year at r = .10.

In general, we can think of stock price as the capitalized value of average earnings under a no-growth policy, plus PVGO, the net present value of growth opportunities:

The earnings–price ratio, therefore, equals

It will underestimate r if PVGO is positive and overestimate it if PVGO is negative. The latter case is less likely, since firms are rarely forced to take projects with negative net present values.

Calculating the Present Value of Growth Opportunities for Fledgling Electronics

In our last example both dividends and earnings were expected to grow, but this growth made no net contribution to the stock price. The stock was in this sense an “income stock.” Be careful not to equate firm performance with the growth in earnings per share. A company that reinvests earnings at below the market capitalization rate r may increase earnings but will certainly reduce the share value.

Now let us turn to that well-known growth stock, Fledgling Electronics. You may remember that Fledgling’s market capitalization rate, r, is 15%. The company is expected to pay a dividend of $5 in the first year, and thereafter the dividend is predicted to increase indefinitely by 10% a year. We can use the simplified constant-growth formula to work out Fledgling’s price:

Suppose that Fledgling has earnings per share of EPS1 = $8.33. Its payout ratio is then

In other words, the company is plowing back 1 – .6, or 40% of earnings. Suppose also that Fledgling’s ratio of earnings to book equity is ROE = .25. This explains the growth rate of 10%:

The capitalized value of Fledgling’s earnings per share if it had a no-growth policy would be

But we know that the value of Fledgling stock is $100. The difference of $44.44 must be the amount that investors are paying for growth opportunities. Let’s see if we can explain that figure.

Each year Fledgling plows back 40% of its earnings into new assets. In the first year Fledgling invests $3.33 at a permanent 25% return on equity. Thus the cash generated by this investment is .25 × 3.33 = $.83 per year starting at t = 2. The net present value of the investment as of t = 1 is

Everything is the same in year 2 except that Fledgling will invest $3.67, 10% more than in year 1 (remember g = .10). Therefore at t = 2 an investment is made with a net present value of

Thus the payoff to the owners of Fledgling Electronics stock can be represented as the sum of (1) a level stream of earnings, which could be paid out as cash dividends if the firm did not grow, and (2) a set of tickets, one for each future year, representing the opportunity to make investments having positive NPVs. We know that the first component of the value of the share is

The first ticket is worth $2.22 in t = 1, the second is worth $2.22 × 1.10 = $2.44 in t = 2, the third is worth $2.44 × 1.10 = $2.69 in t = 3. These are the forecasted cash values of the tickets. We know how to value a stream of future cash values that grows at 10% per year: Use the constant-growth DCF formula, replacing the forecasted dividends with forecasted ticket values:

Now everything checks:

Why is Fledgling Electronics a growth stock? Not because it is expanding at 10% per year. It is a growth stock because the net present value of its future investments accounts for a significant fraction (about 44%) of the stock’s price.

Today’s stock price reflects investor expectations about the earning power of the firm’s current and future assets. Take Google, for example. Google has never paid a dividend. It plows back all its earnings into its business. In January 2012, its stock sold for $580 per share at a forward P/E of about 14. EPS forecasted for 2012 were $42.30.

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Valuing Google

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Suppose that Google did not grow, and that future EPS were expected to stay constant at $42.30. In this case Google could pay a constant dividend of $42.30 per share. If the cost of equity is, say, 12%, market value would be PV = 42.30/.12 = $353 per share, $227 less than the actual stock price of $580. So it appears that investors were valuing Google’s future investment opportunities at $227 per share, almost 40% of the stock price. Google is a growth stock because that large fraction of its market value comes from the expected NPV of its future investments.

 4-5   Valuing a Business by Discounted Cash Flow

Investors buy or sell shares of common stock. Companies often buy or sell entire businesses or major stakes in businesses. For example, we have noted Kinder Morgan’s plans to sell its El Paso exploration and production subsidiary. Both Kinder Morgan and potential bidders were doing their best to value that business by discounted cash flow.

DCF models work just as well for entire businesses as for shares of common stock. It doesn’t matter whether you forecast dividends per share or the total free cash flow of a business. Value today always equals future cash flow discounted at the opportunity cost of capital.

Valuing the Concatenator Business

Rumor has it that Establishment Industries is interested in buying your company’s concatenator manufacturing operation. Your company is willing to sell if it can get the full value of this rapidly growing business. The problem is to figure out what its true present value is.

Table 4.7 gives a forecast of free cash flow (FCF) for the concatenator business. Free cash flow is the amount of cash that a firm can pay out to investors after paying for all investments necessary for growth. As we will see, free cash flow can be negative for rapidly growing businesses.

   TABLE 4.7 Forecasts of free cash flow in $ millions for the concatenator division, with input assumptions in boldface type. Free cash flow is zero for periods 1 to 3 because investment absorbs all of net income. Free cash flow turns positive when growth slows down after period 3.

Notes:

1. Starting asset value is $10 million. Assets grow at 12% to start, then at 9%, and finally at 6% in perpetuity. Profitability is assumed constant at 12%.

2. Free cash flow equals earnings minus net investment. Net investment equals total capital outlays minus depreciation. We assume that investment for replacement of existing assets is covered by depreciation and that net investment is devoted to growth. Earnings are also net of depreciation.

Table 4.7 is similar to Table 4.4, which forecasted earnings and dividends per share for Growth-Tech, based on assumptions about Growth-Tech’s equity per share, return on equity, and the growth of its business. For the concatenator business, we also have assumptions about assets, profitability—in this case, after-tax operating earnings relative to assets—and growth. Growth starts out at a rapid 12% per year, then falls in two steps to a moderate 6% rate for the long run. The growth rate determines the net additional investment required to expand assets, and the profitability rate determines the earnings thrown off by the business.

Free cash flow, the fourth line in Table 4.7, is equal to the firm’s earnings less any new investment expenditures. Free cash flow is zero in years 1 to 3, even though the parent company is investing over $3 million during this period.

Are the early zeros for free cash flow a bad sign? No: Free cash flow is zero because the business is growing rapidly, not because it is unprofitable. Rapid growth is good news, not bad, because the business is earning 12%, 2 percentage points over the 10% cost of capital. If the business could grow at 20%, Establishment Industries and its stockholders would be happier still, although growth at 20% would mean still higher investment and negative free cash flow.

Valuation Format

The value of a business is usually computed as the discounted value of free cash flows out to a valuation horizon (H), plus the forecasted value of the business at the horizon, also discounted back to present value. That is,

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Try It! Table 4.7:
Valuing the concatenator division

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Of course, the concatenator business will continue after the horizon, but it’s not practical to forecast free cash flow year by year to infinity. PVH stands in for free cash flow in periods H + 1, H + 2, etc.

Valuation horizons are often chosen arbitrarily. Sometimes the boss tells everybody to use 10 years because that’s a round number. We will try year 6, because growth of the concatenator business seems to settle down to a long-run trend after year 7.

Estimating Horizon Value

There are several common formulas or rules of thumb for estimating horizon value. First, let us try the constant-growth DCF formula. This requires free cash flow for year 7, which we have from Table 4.7; a long-run growth rate, which appears to be 6%; and a discount rate, which some high-priced consultant has told us is 10%. Therefore,

The PV of the near-term free cash flows is $.9 million. Thus the present value of the concatenator division is

Now, are we done? Well, the mechanics of this calculation are perfect. But doesn’t it make you just a little nervous to find that 94% of the value of the business rests on the horizon value? Moreover, a little checking shows that the horizon value can change dramatically in response to apparently minor changes in assumptions. For example, if the long-run growth rate is 7% rather than 6%, the value of the business increases from $16.3 to $19.2 million.¹⁴

In other words, it’s easy for a discounted-cash-flow business valuation to be mechanically perfect and practically wrong. Smart financial managers try to check their results by calculating horizon value in different ways. Let’s try valuation by comparables, using P/E and market–book ratios.

Horizon Value Based on P/E Ratios Suppose you can observe stock prices for mature manufacturing companies whose scale, risk, and growth prospects today roughly match those projected for the concatenator business in year 6. Suppose further that these companies tend to sell at price–earnings ratios of about 11. Then you could reasonably guess that the price–earnings ratio of a mature concatenator operation will likewise be 11. That implies:

Horizon Value Based on Market–Book Ratios Suppose also that the market–book ratios of the sample of mature manufacturing companies tend to cluster around 1.5. If the concatenator business market–book ratio is 1.5 in year 6,

It’s easy to poke holes in these last two calculations. Book value, for example, is often a poor measure of the true value of a company’s assets. It can fall far behind actual asset values when there is rapid inflation, and it often entirely misses important intangible assets, such as your patents for concatenator design. Earnings may also be biased by inflation and a long list of arbitrary accounting choices. Finally, you never know when you have found a sample of truly similar companies to use as comparables.

But remember, the purpose of discounted cash flow is to estimate market value—to estimate what investors would pay for a stock or business. When you can observe what they actually pay for similar companies, that’s valuable evidence. Try to figure out a way to use it. One way to use it is through valuation by comparables, based on price–earnings or market–book ratios. Valuation rules of thumb, artfully employed, sometimes beat a complex discounted-cash-flow calculation hands down.

A Further Reality Check

Here is another approach to valuing a business. It is based on what you have learned about price–earnings ratios and the present value of growth opportunities.

Suppose the valuation horizon is set not by looking for the first year of stable growth, but by asking when the industry is likely to settle into competitive equilibrium. You might go to the operating manager most familiar with the concatenator business and ask:

Sooner or later you and your competitors will be on an equal footing when it comes to major new investments. You may still be earning a superior return on your core business, but you will find that introductions of new products or attempts to expand sales of existing products trigger intense resistance from competitors who are just about as smart and efficient as you are. Give a realistic assessment of when that time will come.

“That time” is the horizon after which PVGO, the net present value of subsequent growth opportunities, is zero. After all, PVGO is positive only when investments can be expected to earn more than the cost of capital. When your competition catches up, that happy prospect disappears.

We know that present value in any period equals the capitalized value of next period’s earnings, plus PVGO:

But what if PVGO = 0? At the horizon period H, then,

In other words, when the competition catches up, the price–earnings ratio equals 1/r, because PVGO disappears.¹⁵

Suppose that competition is expected to catch up in period 7. Then we can calculate the horizon value at period 6 as the present value of a level stream of earnings starting in period 7 and continuing indefinitely. The resulting value for the concatenator business is:

We now have four estimates of what Establishment Industries ought to pay for the concatenator business. The estimates reflect four different methods of estimating horizon value. There is no best method, although we like the last method, which sets the horizon date at the point when management expects PVGO to disappear. The last method forces managers to remember that sooner or later competition catches up.

Our calculated values for the concatenator business range from $13.2 to $16.3 million, a difference of about $3 million. The width of the range may be disquieting, but it is not unusual. Discounted-cash-flow formulas only estimate market value, and the estimates change as forecasts and assumptions change. Managers cannot know market value for sure until an actual transaction takes place.

Free Cash Flow, Dividends, and Repurchases

We assumed that the concatenator business was a division of Establishment Industries, not a freestanding corporation. But suppose it was a separate corporation with 1 million shares outstanding. How would we calculate price per share? Simple: Calculate the PV of the business and divide by 1 million. If we decide that the business is worth $16.3 million, the price per share is $16.30.

If the concatenator business were a public Concatenator Corp., with no other assets and operations, it could pay out its free cash flow as dividends. Dividends per share would be the free cash flow shown in Table 4.7 divided by 1 million shares: zero in periods 1 to 3, then $.42 per share in period 4, $.46 per share in period 5, etc.

We mentioned stock repurchases as an alternative to cash dividends. If repurchases are important, it’s often simpler to value total free cash flow than dividends per share. Suppose Concatenator Corp. decides not to pay cash dividends. Instead it will pay out all free cash flow by repurchasing shares. The market capitalization of the company should not change, because shareholders as a group will still receive all free cash flow.

Perhaps the following intuition will help. Suppose you own all of the 1 million Concatenator shares. Do you care whether you get free cash flow as dividends or by selling shares back to the firm? Your cash flows in each future period will always equal the free cash flows shown in Table 4.7. Your DCF valuation of the company will therefore depend on the free cash flows, not on how they are distributed.

Chapter 16 covers the choice between cash dividends and repurchases (including tax issues and other complications). But you can see why it’s attractive to value a company as a whole by forecasting and discounting free cash flow. You don’t have to ask how free cash flow will be paid out. You don’t have to forecast repurchases.

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SUMMARY

In this chapter we have used our newfound knowledge of present values to examine the market price of common stocks. The value of a stock is equal to the stream of cash payments discounted at the rate of return that investors expect to receive on other securities with equivalent risks.

Common stocks do not have a fixed maturity; their cash payments consist of an indefinite stream of dividends. Therefore, the present value of a share of common stock is

However, we did not just assume that investors purchase common stocks solely for dividends. In fact, we began with the assumption that investors have relatively short horizons and invest for both dividends and capital gains. Our fundamental valuation formula is, therefore,

This is a condition of market equilibrium. If it did not hold, the share would be overpriced or underpriced, and investors would rush to sell or buy it. The flood of sellers or buyers would force the price to adjust so that the fundamental valuation formula holds.

We also made use of the formula for a growing perpetuity presented in Chapter 2. If dividends are expected to grow forever at a constant rate of g, then

It is often helpful to twist this formula around and use it to estimate the market capitalization rate r, given P0 and estimates of DIV1 and g:

Remember, however, that this formula rests on a very strict assumption: constant dividend growth in perpetuity. This may be an acceptable assumption for mature, low-risk firms, but for many firms, near-term growth is unsustainably high. In that case, you may wish to use a two-stage DCF formula, where near-term dividends are forecasted and valued, and the constant-growth DCF formula is used to forecast the value of the shares at the start of the long run. The near-term dividends and the future share value are then discounted to present value.

The general DCF formula can be transformed into a statement about earnings and growth opportunities:

The ratio EPS1/r is the present value of the earnings per share that the firm would generate under a no-growth policy. PVGO is the net present value of the investments that the firm will make in order to grow. A growth stock is one for which PVGO is large relative to the present value of EPS, assuming no growth. Most growth stocks are stocks of rapidly expanding firms, but expansion alone does not create a high PVGO. What matters is the profitability of the new investments.

The same formulas that we used to value common shares can also be used to value entire businesses. In that case, we discount not dividends per share but the entire free cash flow generated by the business. Usually a two-stage DCF model is deployed. Free cash flows are forecasted out to a horizon and discounted to present value. Then a horizon value is forecasted, discounted, and added to the value of the free cash flows. The sum is the value of the business.

Valuing a business is simple in principle but not so easy in practice. Forecasting reasonable horizon values is particularly difficult. The usual assumption is moderate long-run growth after the horizon, which allows use of the growing-perpetuity DCF formula at the horizon. Horizon values can also be calculated by assuming “normal” price–earnings or market-to-book ratios at the horizon date.

The dividend discount models derived in this chapter work best for mature firms that pay regular cash dividends. The models also work when companies pay out cash by share repurchases as well as dividends. That said, it is also true that the dividend discount model is difficult to use if the company pays no dividends at all or if the split of payout between cash dividends and repurchases is unpredictable. In that case, it is easier to get price per share by forecasting and valuing the company’s total free cash flow and then dividing by the current number of shares outstanding.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  True/false True or false?

a.  All stocks in an equivalent-risk class are priced to offer the same expected rate of return.

b.  The value of a share equals the PV of future dividends per share.

2.  Dividend discount model Respond briefly to the following statement:

“You say stock price equals the present value of future dividends? That’s crazy! All the investors I know are looking for capital gains.”

3.  Dividend discount model Company X is expected to pay an end-of-year dividend of $5 a share. After the dividend its stock is expected to sell at $110. If the market capitalization rate is 8%, what is the current stock price?

4.  Dividend discount model Company Y does not plow back any earnings and is expected to produce a level dividend stream of $5 a share. If the current stock price is $40, what is the market capitalization rate?

5.  Dividend discount model Company Z’s earnings and dividends per share are expected to grow indefinitely by 5% a year. If next year’s dividend is $10 and the market capitalization rate is 8%, what is the current stock price?

6.  Dividend discount model Company Z-prime is like Z in all respects save one: Its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. What is Z-prime’s stock price? Assume next year’s EPS is $15.

7.  Dividend discount model If company Z (see Problem 5) were to distribute all its earnings, it could maintain a level dividend stream of $15 a share. How much is the market actually paying per share for growth opportunities?

8.  Dividend discount model Consider three investors:

a.  Mr. Single invests for one year.

b.  Ms. Double invests for two years.

c.  Mrs. Triple invests for three years.

Assume each invests in company Z (see Problem 5). Show that each expects to earn a rate of return of 8% per year.

9.  True/false True or false? Explain.

a.  The value of a share equals the discounted stream of future earnings per share.

b.  The value of a share equals the PV of earnings per share assuming the firm does not grow, plus the NPV of future growth opportunities.

10.  Free cash flow Under what conditions does r, a stock’s market capitalization rate, equal its earnings–price ratio EPS1/P0?

11.  Free cash flow What do financial managers mean by “free cash flow”? How is free cash flow calculated? Briefly explain.

12.  Horizon value What is meant by the “horizon value” of a business? How can it be estimated?

13.  Horizon value Suppose the horizon date is set at a time when the firm will run out of positive-NPV investment opportunities. How would you calculate the horizon value? (Hint: What is the P/EPS ratio when PVGO = 0?)

INTERMEDIATE

14.  Stock quotes and ratios Go to finance.yahoo.com and get trading quotes for IBM.

a.  What is the latest IBM stock price and market cap?

b.  What is IBM’s dividend payment and dividend yield?

c.  What is IBM’s trailing P/E ratio?

d.  Calculate IBM’s forward P/E ratio using the EPS forecasted by analysts for the next year.

e.  What is IBM’s price–book (P/B) ratio?

15.  Stock quotes and P/E ratios Look up Intel (INTC), Dell Computer (DELL), Oracle (ORCL), and Hewlett Packard (HPQ). Rank the companies forward P/E ratios from highest to lowest. What are the possible reasons for the different ratios? Which of these companies appears to have the most valuable growth opportunities?

16.  Valuation by comparables Look up P/E and P/B ratios for Entergy (ticker symbol ETR), using Yahoo! Finance or another Internet source. Calculate the same ratios for the following potential comparables: Constellation (CEG), Exelon (EXC), FPL Group (FPL), and Progress Energy (PGN). Set out the ratios in the same format as Table 4.1. Are the ratios for these electric companies tightly grouped or scattered? If you didn’t know Entergy’s stock price, would the comparables give a good estimate?

17.  P/E ratios and the dividend discount model Look up General Mills (GIS), Kellogg (K), Campbell Soup (CPB), and Kraft Foods (KFT).

a.  What are the current P/E and P/B ratios for these food companies? What are the dividend and dividend yield for each company?

b.  What are the growth rates of EPS and dividends for each company over the last five years? What EPS growth rates are forecasted by analysts? Do these growth rates appear to be on a steady trend that could be projected for the long run?

c.  Would you be confident in applying the constant-growth DCF model to measure these companies’ costs of equity? Why or why not?

18.  Dividend discount model Consider the following three stocks:

a.  Stock A is expected to provide a dividend of $10 a share forever.

b.  Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4% a year forever.

c.  Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i.e., until year 6) and zero thereafter.

If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%?

19.  Constant-growth DCF model Pharmecology is about to pay a dividend of $1.35 per share. It’s a mature company, but future EPS and dividends are expected to grow with inflation, which is forecasted at 2.75% per year.

a.  What is Pharmecology’s current stock price? The nominal cost of capital is 9.5%.

b.  Redo part (a) using forecasted real dividends and a real discount rate.

20.  Two-stage DCF model Company Q’s current return on equity (ROE) is 14%. It pays out one-half of earnings as cash dividends (payout ratio = .5). Current book value per share is $50. Book value per share will grow as Q reinvests earnings.

Assume that the ROE and payout ratio stay constant for the next four years. After that, competition forces ROE down to 11.5% and the payout ratio increases to 0.8. The cost of capital is 11.5%.

a.  What are Q’s EPS and dividends next year? How will EPS and dividends grow in years 2, 3, 4, 5, and subsequent years?

b.  What is Q’s stock worth per share? How does that value depend on the payout ratio and growth rate after year 4?

21.  Earnings and dividends Each of the following formulas for determining shareholders’ required rate of return can be right or wrong depending on the circumstances:

For each formula construct a simple numerical example showing that the formula can give wrong answers and explain why the error occurs. Then construct another simple numerical example for which the formula gives the right answer.

22.  PVGO Alpha Corp’s earnings and dividends are growing at 15% per year. Beta Corp’s earnings and dividends are growing at 8% per year. The companies’ assets, earnings, and dividends per share are now (at date 0) exactly the same. Yet PVGO accounts for a greater fraction of Beta Corp’s stock price. How is this possible? (Hint: There is more than one possible explanation.)

23.  DCF model and PVGO Look again at the financial forecasts for Growth-Tech given in Table 4.4. This time assume you know that the opportunity cost of capital is r = .12 (discard the .099 figure calculated in the text). Assume you do not know Growth-Tech’s stock value. Otherwise follow the assumptions given in the text.

a.  Calculate the value of Growth-Tech stock.

b.  What part of that value reflects the discounted value of P3, the price forecasted for year 3?

c.  What part of P3 reflects the present value of growth opportunities (PVGO) after year 3?

d.  Suppose that competition will catch up with Growth-Tech by year 4, so that it can earn only its cost of capital on any investments made in year 4 or subsequently. What is Growth-Tech stock worth now under this assumption? (Make additional assumptions if necessary.)

24.  DCF and free cash flow Compost Science, Inc. (CSI), is in the business of converting Boston’s sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 10% book return on equity. At the end of the year CSI is expected to pay a $4 dividend. It has been reinvesting 40% of earnings and growing at 4% a year.

a.  Suppose CSI continues on this growth trend. What is the expected long-run rate of return from purchasing the stock at $100? What part of the $100 price is attributable to the present value of growth opportunities?

b.  Now the MDC announces a plan for CSI to treat Cambridge sewage. CSI’s plant will, therefore, be expanded gradually over five years. This means that CSI will have to reinvest 80% of its earnings for five years. Starting in year 6, however, it will again be able to pay out 60% of earnings. What will be CSI’s stock price once this announcement is made and its consequences for CSI are known?

25.  DCF and free cash flow Permian Partners (PP) produces from aging oil fields in west Texas. Production is 1.8 million barrels per year in 2013, but production is declining at 7% per year for the foreseeable future. Costs of production, transportation, and administration add up to $25 per barrel. The average oil price was $65 per barrel in 2013.

PP has 7 million shares outstanding. The cost of capital is 9%. All of PP’s net income is distributed as dividends. For simplicity, assume that the company will stay in business forever and that costs per barrel are constant at $25. Also, ignore taxes.

a.  What is the PV of a PP share? Assume that oil prices are expected to fall to $60 per barrel in 2014, $55 per barrel in 2015, and $50 per barrel in 2016. After 2016, assume a long-term trend of oil-price increases at 5% per year.

b.  What is PP’s EPS/P ratio and why is it not equal to the 9% cost of capital?

26.  DCF and free cash flow Construct a new version of Table 4.7, assuming that competition drives down profitability (on existing assets as well as new investment) to 11.5% in year 6, 11% in year 7, 10.5% in year 8, and 8% in year 9 and all later years. What is the value of the concatenator business?

27.  Valuing free cash flow Mexican Motors’ market cap is 200 billion pesos. Next year’s free cash flow is 8.5 billion pesos. Security analysts are forecasting that free cash flow will grow by 7.5% per year for the next five years.

a.  Assume that the 7.5% growth rate is expected to continue forever. What rate of return are investors expecting?

b.  Mexican Motors has generally earned about 12% on book equity (ROE = 12%) and reinvested 50% of earnings. The remaining 50% of earnings has gone to free cash flow. Suppose the company maintains the same ROE and investment rate for the long run. What is the implication for the growth rate of earnings and free cash flow? For the cost of equity? Should you revise your answer to part (a) of this question?

28.  Valuing free cash flow Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2016 are as follows.

Phoenix’s recovery will be complete by 2021, and there will be no further growth in free cash flow.

a.  Calculate the PV of free cash flow, assuming a cost of equity of 9%.

b.  Assume that Phoenix has 12 million shares outstanding. What is the price per share?

c.  What is Phoenix’s P/E ratio? How do you expect that P/E ratio to change from 2017 to 2021?

d.  Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2017 to 2021.

29.  Stock quotes and ratios Look up the common stock listings in a recent issue of the Financial Times and check out several companies from the following list:

What are (a) the latest stock prices, (b) the annual dividends and dividend yields and (c) price-earnings ratios (P/Es)? What are the possible reasons for the differences in P/Es?

30.  Constant-growth DCF Model Clover, an Irish insurance exchange, has just paid an annual dividend of €2.70 per share. Future EPS and dividends are expected to grow at 2.3% per year. The nominal cost of capital is 9%.

a.  What is Clover’s current stock price (ex dividend)?

b.  Redo part (a) using forecasted real dividends and a real discount rate. Your answers to parts (a) and (b) should be identical.

CHALLENGE

31.  Constant-growth DCF formula The constant-growth DCF formula:

is sometimes written as:

where BVPS is book equity value per share, b is the plowback ratio, and ROE is the ratio of earnings per share to BVPS. Use this equation to show how the price-to-book ratio varies as ROE changes. What is price-to-book when ROE = r?

32.  DCF valuation Portfolio managers are frequently paid a proportion of the funds under management. Suppose you manage a $100 million equity portfolio offering a dividend yield (DIV1/P0) of 5%. Dividends and portfolio value are expected to grow at a constant rate. Your annual fee for managing this portfolio is .5% of portfolio value and is calculated at the end of each year. Assuming that you will continue to manage the portfolio from now to eternity, what is the present value of the management contract? How would the contract value change if you invested in stocks with a 4% yield?

33.  Valuing free cash flow Construct a new version of Table 4.7, assuming that the concatenator division grows at 20%, 12%, and 6%, instead of 12%, 9%, and 6%. You will get negative early free cash flows.

a.  Recalculate the PV of free cash flow. What does your revised PV say about the division’s PVGO?

b.  Suppose the division is the public corporation Concatco, with no other resources. Thus it will have to issue stock to cover the negative free cash flows. Does the need to issue shares change your valuation? Explain. (Hint: Suppose first that Concatco’s existing stockholders buy all of the newly issued shares. What is the value of the company to these stockholders? Now suppose instead that all the shares are issued to new stockholders, so that existing stockholders don’t have to contribute any cash. Does the value of the company to the existing stockholders change, assuming that the new shares are sold at a fair price?)

34.  DCF valuation and PVGO Delhi Big-Box Stores is solidly profitable and growing rapidly. At the same time it faces a relatively high opportunity cost of capital, which the CFO estimates at 14%. Construct a table in the same format as Table 4.7. Assume a starting asset value of R10 billion, initial ROE of 20%, and an initial growth rate of assets and earnings of 15% per year. But after year 5, the forecasted growth rate of assets falls to 10%.

a.  Calculate the value of the company and its PVGO.

b.  Why do you think Delhi’s CFO is forecasting a decline in ROE to the 14% cost of capital. Is such a decline normal in competitive markets?

c.  How does the company value and PVGO change if ROE is 14% in all future years?

● ● ● ● ●

FINANCE ON THE WEB

The major stock exchanges have wonderful websites. Start with the NYSE (www.nyse.com) and Nasdaq (www.nasdaq.com). Make sure you know how trading takes place on these exchanges.

MINI-CASE ● ● ● ● ●

Bok Sports

Ten years ago, in Johannesburg, Joost van Hees founded a small mail-order company selling high-quality sports equipment. Since those early days Bok Sports has grown steadily and been consistently profitable. The company has issued 2 million shares, all of which are owned by Joost van Hees and his five children.

For some months Joost has been wondering whether the time has come to take the company public. This would allow him to cash in on part of his investment and would make it easier for the firm to raise capital should it wish to expand in the future.

But how much are the shares worth? Joost’s first instinct is to look at the firm’s balance sheet, which shows that the book value of the equity is R263.4 million, or R131.7 per share. A share price of R131.7 would put the stock on a P/E ratio of 6.6. That is quite a bit lower than the 13.1 P/E ratio of Bok’s larger rival, Wenner Corporation.

Joost suspects that book value is not necessarily a good guide to a share’s market value. He thinks of his daughter Jenny, who works in an investment bank. She would undoubtedly know what the shares are worth.

Before speaking to her, Joost jots down some basic data on the company’s profitability. After recovering from its early losses, the company has earned a return that is higher than its estimated 10% cost of capital. Joost is fairly confident that the company could continue to grow fairly steadily for the next six to eight years. In fact he feels that the company’s growth has been somewhat held back in the last few years by the demands from two of the children for the company to make large dividend payments. Perhaps, if the company went public, it could hold back on dividends and plow more money back into the business.

There are some clouds on the horizon. Competition is increasing and only that morning Wenner announced plans to form a mail-order division. Joost is worried that beyond the next six or so years it might become difficult to find worthwhile investment opportunities.

Joost realizes that Jenny will need to know much more about the prospects for the business before she can put a final figure on Bok’s value, but he hopes that the information is sufficient for her to give a preliminary indication of the value of the shares.

QUESTIONS

1.  Help Jenny to forecast dividend payments for Bok and to estimate the value of the stock. You do not need to provide a single figure. For example, you may wish to calculate two figures, one on the assumption that the opportunity for further profitable investment disappears after six years and another assuming it disappears after eight years.

2.  How much of your estimate of the value of Bok’s stock comes from the present value of growth opportunities?

___________

¹Trades are still made face to face on the floor of the NYSE, but computerized trading is taking over. In 2006 the NYSE merged with Archipelago, an electronic trading system, and transformed itself into a public corporation. The following year it merged with Euronext, an electronic trading system in Europe, and changed its name to NYSE Euronext.

²Other good sources of trading data are moneycentral.msn.com or the online edition of The Wall Street Journal at www.wsj.com (look for the “Market” and then “Market Data” tabs).

³Yahoo! Finance provides extensive information and statistics on traded companies, including summaries of analyst forecasts. For example, you can click on “Key Statistics” or “Analyst Estimates” under “More on GE.”

⁴Closed-end mutual funds issue shares that are traded on stock exchanges. Open-end funds are not traded on exchanges. Investors in open-end funds transact directly with the fund. The fund issues new shares to investors and redeems shares from investors who want to withdraw money from the fund.

⁵Be extra careful when averaging P/Es. Watch out for companies with earnings close to zero or negative. One company with zero earnings and therefore an infinite P/E makes any average meaningless. Often it’s safer to use median P/Es rather than averages.

⁶Or maybe the table would work better with different financial ratios. For example, analysts may use the ratio of earnings before interest and taxes (EBIT) to enterprise value, defined as the sum of outstanding debt and the market capitalization of equity. This ratio is less sensitive to differences in debt financing policy. In Chapter 19 we discuss valuation when financing comes from a mix of debt and equity. We discuss other financial ratios in Chapter 28.

⁷Notice that this DCF formula uses a single discount rate for all future cash flows. This implicitly assumes that the company is all-equity-financed or that the fractions of debt and equity will stay constant. Chapters 17 through 19 discuss how the cost of equity changes when debt ratios change.

⁸The deferred payout may come all at once if the company is taken over by another. The selling price per share is equivalent to a bumper dividend.

⁹Notice that we have derived the dividend discount model using dividends per share. Paying out cash for repurchases rather than cash dividends reduces the number of shares outstanding and increases future earnings and dividends per share. The more shares repurchased, the faster the growth of earnings and dividends per shares. Thus repurchases benefit shareholders who do not sell as well as those who do sell. We show some examples in Chapter 16.

¹⁰These formulas were first developed in 1938 by Williams and were rediscovered by Gordon and Shapiro. See J. B. Williams, The Theory of Investment Value (Cambridge, MA: Harvard University Press, 1938); and M. J. Gordon and E. Shapiro, “Capital Equipment Analysis: The Required Rate of Profit,” Management Science 3 (October 1956), pp. 102–110.

¹¹This is the accepted interpretation of the U.S. Supreme Court’s directive in 1944 that “the returns to the equity owner [of a regulated business] should be commensurate with returns on investments in other enterprises having corresponding risks.” Federal Power Commission v. Hope Natural Gas Company, 302 U.S. 591 at 603.

¹²In this calculation we’re assuming that earnings and dividends are forecasted to grow forever at the same rate g. We show how to relax this assumption later in this chapter. The growth rate was based on the average earnings growth forecasted by Value Line and IBES. IBES compiles and averages forecasts made by security analysts. Value Line publishes its own analysts’ forecasts.

¹³Notice that we use next year’s EPS for E/P and P/E ratios. Thus we are using forward, not trailing, P/E.

¹⁴If long-run growth is 7% instead of 6%, an extra 1% of asset value will have to be plowed back into the concatenator business, reducing free cash flow from $1.09 million to $.97 million. The PV of cash flows from dates 1 to 6 stays at $.9 million.

¹⁵In other words, we can calculate horizon value as if earnings will not grow after the horizon date, because growth will add no value. But what does “no growth” mean? Suppose that the concatenator business maintains its assets and earnings in real (inflation-adjusted) terms. Then nominal earnings will grow at the inflation rate. This takes us back to the constant-growth formula: earnings in period H + 1 should be valued by dividing by r – g, where g in this case equals the inflation rate.

We have simplified the concatenator example. In real-life valuations, with big bucks involved, be careful to track growth from inflation as well as growth from investment. For guidance see M. Bradley and G. Jarrell, “Expected Inflation and the Constant-Growth Valuation Model,” Journal of Applied Corporate Finance 20 (Spring 2008), pp. 66–78.

Part 1 Value

Net Present Value and Other Investment Criteria

Acompany’s shareholders prefer to be rich rather than poor. Therefore, they want the firm to invest in every project that is worth more than it costs. The difference between a project’s value and its cost is its net present value (NPV). Companies can best help their shareholders by investing in all projects with a positive NPV and rejecting those with a negative NPV.

We start this chapter with a review of the net present value rule. We then turn to some other measures that companies may look at when making investment decisions. The first two of these measures, the project’s payback period and its book rate of return, are little better than rules of thumb, easy to calculate and easy to communicate. Although there is a place for rules of thumb in this world, an engineer needs something more accurate when designing a 100-story building, and a financial manager needs more than a rule of thumb when making a substantial capital investment decision.

Instead of calculating a project’s NPV, companies often compare the expected rate of return from investing in the project with the return that shareholders could earn on equivalent-risk investments in the capital market. The company accepts those projects that provide a higher return than shareholders could earn for themselves. If used correctly, this rate of return rule should always identify projects that increase firm value. However, we shall see that the rule sets several traps for the unwary.

We conclude the chapter by showing how to cope with situations when the firm has only limited capital. This raises two problems. One is computational. In simple cases we just choose those projects that give the highest NPV per dollar invested, but more elaborate techniques are sometimes needed to sort through the possible alternatives. The other problem is to decide whether capital rationing really exists and whether it invalidates the net present value rule. Guess what? NPV, properly interpreted, wins out in the end.

 5-1   A Review of the Basics

Vegetron’s chief financial officer (CFO) is wondering how to analyze a proposed $1 million investment in a new venture called project X. He asks what you think.

Your response should be as follows: “First, forecast the cash flows generated by project X over its economic life. Second, determine the appropriate opportunity cost of capital (r). This should reflect both the time value of money and the risk involved in project X. Third, use this opportunity cost of capital to discount the project’s future cash flows. The sum of the discounted cash flows is called present value (PV). Fourth, calculate net present value (NPV) by subtracting the $1 million investment from PV. If we call the cash flows C0, C1, and so on, then

We should invest in project X if its NPV is greater than zero.”

However, Vegetron’s CFO is unmoved by your sagacity. He asks why NPV is so important.

Your reply: “Let us look at what is best for Vegetron stockholders.” They want you to make their Vegetron shares as valuable as possible.

“Right now Vegetron’s total market value (price per share times the number of shares outstanding) is $10 million. That includes $1 million cash we can invest in project X.” The value of Vegetron’s other assets and opportunities must therefore be $9 million. We have to decide whether it is better to keep the $1 million cash and reject project X or to spend the cash and accept the project. Let us call the value of the new project PV. Then the choice is as follows:

“Clearly project X is worthwhile if its present value, PV, is greater than $1 million, that is, if net present value is positive.”

CFO: “How do I know that the PV of project X will actually show up in Vegetron’s market value?”

Your reply: “Suppose we set up a new, independent firm X, whose only asset is project X.” What would be the market value of firm X?

“Investors would forecast the dividends that firm X would pay and discount those dividends by the expected rate of return of securities having similar risks.” We know that stock prices are equal to the present value of forecasted dividends.

“Since project X is the only asset, the dividend payments we would expect firm X to pay are exactly the cash flows we have forecasted for project X.” Moreover, the rate investors would use to discount firm X’s dividends is exactly the rate we should use to discount project X’s cash flows.

“I agree that firm X is entirely hypothetical.” But if project X is accepted, investors holding Vegetron stock will really hold a portfolio of project X and the firm’s other assets. We know the other assets are worth $9 million considered as a separate venture. Since asset values add up, we can easily figure out the portfolio value once we calculate the value of project X as a separate venture.

“By calculating the present value of project X, we are replicating the process by which the common stock of firm X would be valued in capital markets.”

CFO: “The one thing I don’t understand is where the discount rate comes from.”

Your reply: “I agree that the discount rate is difficult to measure precisely.” But it is easy to see what we are trying to measure. The discount rate is the opportunity cost of investing in the project rather than in the capital market. In other words, instead of accepting a project, the firm can always return the cash to the shareholders and let them invest it in financial assets.

“You can see the trade-off (Figure 5.1). The opportunity cost of taking the project is the return shareholders could have earned had they invested the funds on their own. When we discount the project’s cash flows by the expected rate of return on financial assets, we are measuring how much investors would be prepared to pay for your project.”

   FIGURE 5.1 The firm can either keep and reinvest cash or return it to investors. (Arrows represent possible cash flows or transfers.) If cash is reinvested, the opportunity cost is the expected rate of return that shareholders could have obtained by investing in financial assets.

“But which financial assets?” Vegetron’s CFO queries. “The fact that investors expect only 12% on IBM stock does not mean that we should purchase Fly-by-Night Electronics if it offers 13%.”

Your reply: “The opportunity-cost concept makes sense only if assets of equivalent risk are compared. In general, you should identify financial assets that have the same risk as your project, estimate the expected rate of return on these assets, and use this rate as the opportunity cost.”

Net Present Value’s Competitors

When you advised the CFO to calculate the project’s NPV, you were in good company. These days 75% of firms always, or almost always, calculate net present value when deciding on investment projects. However, as you can see from Figure 5.2, NPV is not the only investment criterion that companies use, and firms often look at more than one measure of a project’s attractiveness.

   FIGURE 5.2 Survey evidence on the percentage of CFOs who always, or almost always, use a particular technique for evaluating investment projects.

Source: Reprinted from J. R. Graham and C. R. Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187–243, © 2001 with permission from Elsevier Science.

About three-quarters of firms calculate the project’s internal rate of return (or IRR); that is roughly the same proportion as use NPV. The IRR rule is a close relative of NPV and, when used properly, it will give the same answer. You therefore need to understand the IRR rule and how to take care when using it.

A large part of this chapter is concerned with explaining the IRR rule, but first we look at two other measures of a project’s attractiveness—the project’s payback and its book rate of return. As we will explain, both measures have obvious defects. Few companies rely on them to make their investment decisions, but they do use them as supplementary measures that may help to distinguish the marginal project from the no-brainer.

Later in the chapter we also come across one further investment measure, the profitability index. Figure 5.2 shows that it is not often used, but you will find that there are circumstances in which this measure has some special advantages.

Three Points to Remember about NPV

As we look at these alternative criteria, it is worth keeping in mind the following key features of the net present value rule. First, the NPV rule recognizes that a dollar today is worth more than a dollar tomorrow, because the dollar today can be invested to start earning interest immediately. Any investment rule that does not recognize the time value of money cannot be sensible. Second, net present value depends solely on the forecasted cash flows from the project and the opportunity cost of capital. Any investment rule that is affected by the manager’s tastes, the company’s choice of accounting method, the profitability of the company’s existing business, or the profitability of other independent projects will lead to inferior decisions. Third, because present values are all measured in today’s dollars, you can add them up. Therefore, if you have two projects A and B, the net present value of the combined investment is

This adding-up property has important implications. Suppose project B has a negative NPV. If you tack it onto project A, the joint project (A + B) must have a lower NPV than A on its own. Therefore, you are unlikely to be misled into accepting a poor project (B) just because it is packaged with a good one (A). As we shall see, the alternative measures do not have this property. If you are not careful, you may be tricked into deciding that a package of a good and a bad project is better than the good project on its own.

NPV Depends on Cash Flow, Not on Book Returns

Net present value depends only on the project’s cash flows and the opportunity cost of capital. But when companies report to shareholders, they do not simply show the cash flows. They also report book—that is, accounting—income and book assets.

Financial managers sometimes use these numbers to calculate a book (or accounting) rate of return on a proposed investment. In other words, they look at the prospective book income as a proportion of the book value of the assets that the firm is proposing to acquire:

Cash flows and book income are often very different. For example, the accountant labels some cash outflows as capital investments and others as operating expenses. The operating expenses are, of course, deducted immediately from each year’s income. The capital expenditures are put on the firm’s balance sheet and then depreciated. The annual depreciation charge is deducted from each year’s income. Thus the book rate of return depends on which items the accountant treats as capital investments and how rapidly they are depreciated.¹

Now the merits of an investment project do not depend on how accountants classify the cash flows² and few companies these days make investment decisions just on the basis of the book rate of return. But managers know that the company’s shareholders pay considerable attention to book measures of profitability and naturally they think (and worry) about how major projects would affect the company’s book return. Those projects that would reduce the company’s book return may be scrutinized more carefully by senior management.

You can see the dangers here. The company’s book rate of return may not be a good measure of true profitability. It is also an average across all of the firm’s activities. The average profitability of past investments is not usually the right hurdle for new investments. Think of a firm that has been exceptionally lucky and successful. Say its average book return is 24%, double shareholders’ 12% opportunity cost of capital. Should it demand that all new investments offer 24% or better? Clearly not: That would mean passing up many positive-NPV opportunities with rates of return between 12 and 24%.

We will come back to the book rate of return in Chapters 12 and 28, when we look more closely at accounting measures of financial performance.

 5-2   Payback

We suspect that you have often heard conversations that go something like this: “We are spending $6 a week, or around $300 a year, at the laundromat. If we bought a washing machine for $800, it would pay for itself within three years. That’s well worth it.” You have just encountered the payback rule.

A project’s payback period is found by counting the number of years it takes before the cumulative cash flow equals the initial investment. For the washing machine the payback period was just under three years. The payback rule states that a project should be accepted if its payback period is less than some specified cutoff period. For example, if the cutoff period is four years, the washing machine makes the grade; if the cutoff is two years, it doesn’t.

EXAMPLE 5.1 • The Payback Rule

Consider the following three projects:

Project A involves an initial investment of $2,000 (C0 = –2,000) followed by cash inflows during the next three years. Suppose the opportunity cost of capital is 10%. Then project A has an NPV of +$2,624:

Project B also requires an initial investment of $2,000 but produces a cash inflow of $500 in year 1 and $1,800 in year 2. At a 10% opportunity cost of capital project B has an NPV of –$58:

The third project, C, involves the same initial outlay as the other two projects but its first-period cash flow is larger. It has an NPV of +$50.

The net present value rule tells us to accept projects A and C but to reject project B.

Now look at how rapidly each project pays back its initial investment. With project A you take three years to recover the $2,000 investment; with projects B and C you take only two years. If the firm used the payback rule with a cutoff period of two years, it would accept only projects B and C; if it used the payback rule with a cutoff period of three or more years, it would accept all three projects. Therefore, regardless of the choice of cutoff period, the payback rule gives different answers from the net present value rule.

You can see why payback can give misleading answers as illustrated in Example 5.1:

1.  The payback rule ignores all cash flows after the cutoff date. If the cutoff date is two years, the payback rule rejects project A regardless of the size of the cash inflow in year 3.

2.  The payback rule gives equal weight to all cash flows before the cutoff date. The payback rule says that projects B and C are equally attractive, but because C’s cash inflows occur earlier, C has the higher net present value at any discount rate.

To use the payback rule, a firm must decide on an appropriate cutoff date. If it uses the same cutoff regardless of project life, it will tend to accept many poor short-lived projects and reject many good long-lived ones.

We have had little good to say about the payback rule. So why do many companies continue to use it? Senior managers don’t truly believe that all cash flows after the payback period are irrelevant. We suggest three explanations. First, payback may be used because it is the simplest way to communicate an idea of project profitability. Investment decisions require discussion and negotiation among people from all parts of the firm, and it is important to have a measure that everyone can understand. Second, managers of larger corporations may opt for projects with short paybacks because they believe that quicker profits mean quicker promotion. That takes us back to Chapter 1 where we discussed the need to align the objectives of managers with those of shareholders. Finally, owners of family firms with limited access to capital may worry about their future ability to raise capital. These worries may lead them to favor rapid payback projects even though a longer-term venture may have a higher NPV.

Discounted Payback

Occasionally companies discount the cash flows before they compute the payback period. The discounted cash flows for our three projects are as follows:

The discounted payback rule asks, How many years does the project have to last in order for it to make sense in terms of net present value? You can see that the value of the cash inflows from project B never exceeds the initial outlay and would always be rejected under the discounted payback rule. Thus the discounted payback rule will never accept a negative-NPV project. On the other hand, it still takes no account of cash flows after the cutoff date, so that good long-term projects such as A continue to risk rejection.

Rather than automatically rejecting any project with a long discounted payback period, many managers simply use the measure as a warning signal. These managers don’t unthinkingly reject a project with a long discounted-payback period. Instead they check that the proposer is not unduly optimistic about the project’s ability to generate cash flows into the distant future. They satisfy themselves that the equipment has a long life and that competitors will not enter the market and eat into the project’s cash flows.

 5-3   Internal (or Discounted-Cash-Flow) Rate of Return

Whereas payback and return on book are ad hoc measures, internal rate of return has a much more respectable ancestry and is recommended in many finance texts. If, therefore, we dwell more on its deficiencies, it is not because they are more numerous but because they are less obvious.

In Chapter 2 we noted that the net present value rule could also be expressed in terms of rate of return, which would lead to the following rule: “Accept investment opportunities offering rates of return in excess of their opportunity costs of capital.” That statement, properly interpreted, is absolutely correct. However, interpretation is not always easy for long-lived investment projects.

There is no ambiguity in defining the true rate of return of an investment that generates a single payoff after one period:

Alternatively, we could write down the NPV of the investment and find the discount rate that makes NPV = 0.

implies

Of course C1 is the payoff and –C0 is the required investment, and so our two equations say exactly the same thing. The discount rate that makes NPV = 0 is also the rate of return.

How do we calculate return when the project produces cash flows in several periods? Answer: we use the same definition that we just developed for one-period projects—the project rate of return is the discount rate that gives a zero NPV. This discount rate is known as the discounted-cash-flow (DCF) rate of return or internal rate of return (IRR). The internal rate of return is used frequently in finance. It can be a handy measure, but, as we shall see, it can also be a misleading measure. You should, therefore, know how to calculate it and how to use it properly.

Calculating the IRR

The internal rate of return is defined as the rate of discount that makes NPV = 0. So to find the IRR for an investment project lasting T years, we must solve for IRR in the following expression:

Actual calculation of IRR usually involves trial and error. For example, consider a project that produces the following flows:

The internal rate of return is IRR in the equation

Let us arbitrarily try a zero discount rate. In this case NPV is not zero but +$2,000:

The NPV is positive; therefore, the IRR must be greater than zero. The next step might be to try a discount rate of 50%. In this case net present value is –$889:

The NPV is negative; therefore, the IRR must be less than 50%. In Figure 5.3 we have plotted the net present values implied by a range of discount rates. From this we can see that a discount rate of 28% gives the desired net present value of zero. Therefore IRR is 28%.

   FIGURE 5.3 This project costs $4,000 and then produces cash inflows of $2,000 in year 1 and $4,000 in year 2. Its internal rate of return (IRR) is 28%, the rate of discount at which NPV is zero.

The easiest way to calculate IRR, if you have to do it by hand, is to plot three or four combinations of NPV and discount rate on a graph like Figure 5.3, connect the points with a smooth line, and read off the discount rate at which NPV = 0. It is of course quicker and more accurate to use a computer spreadsheet or a specially programmed calculator, and in practice this is what financial managers do. The Useful Spreadsheet Functions box near the end of the chapter presents Excel functions for doing so.

Some people confuse the internal rate of return and the opportunity cost of capital because both appear as discount rates in the NPV formula. The internal rate of return is a profitability measure that depends solely on the amount and timing of the project cash flows. The opportunity cost of capital is a standard of profitability that we use to calculate how much the project is worth. The opportunity cost of capital is established in capital markets. It is the expected rate of return offered by other assets with the same risk as the project being evaluated.

The IRR Rule

The internal rate of return rule is to accept an investment project if the opportunity cost of capital is less than the internal rate of return. You can see the reasoning behind this idea if you look again at Figure 5.3. If the opportunity cost of capital is less than the 28% IRR, then the project has a positive NPV when discounted at the opportunity cost of capital. If it is equal to the IRR, the project has a zero NPV. And if it is greater than the IRR, the project has a negative NPV. Therefore, when we compare the opportunity cost of capital with the IRR on our project, we are effectively asking whether our project has a positive NPV. This is true not only for our example. The rule will give the same answer as the net present value rule whenever the NPV of a project is a smoothly declining function of the discount rate.

Many firms use internal rate of return as a criterion in preference to net present value. We think that this is a pity. Although, properly stated, the two criteria are formally equivalent, the internal rate of return rule contains several pitfalls.

Pitfall 1—Lending or Borrowing?

Not all cash-flow streams have NPVs that decline as the discount rate increases. Consider the following projects A and B:

Each project has an IRR of 50%. (In other words, –1,000 + 1,500/1.50 = 0 and + 1,000 – 1,500/1.50 = 0.)

Does this mean that they are equally attractive? Clearly not, for in the case of A, where we are initially paying out $1,000, we are lending money at 50%; in the case of B, where we are initially receiving $1,000, we are borrowing money at 50%. When we lend money, we want a high rate of return; when we borrow money, we want a low rate of return.

If you plot a graph like Figure 5.3 for project B, you will find that NPV increases as the discount rate increases. Obviously the internal rate of return rule, as we stated it above, won’t work in this case; we have to look for an IRR less than the opportunity cost of capital.

Pitfall 2—Multiple Rates of Return

Helmsley Iron is proposing to develop a new strip mine in Western Australia. The mine involves an initial investment of A$30 billion and is expected to produce a cash inflow of A$10 billion a year for the next nine years. At the end of that time the company will incur A$65 billion of cleanup costs. Thus the cash flows from the project are:

Helmsley calculates the project’s IRR and its NPV as follows:

Note that there are two discount rates that make NPV = 0. That is, each of the following statements holds:

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Try It! Figure 5.4:
Helmsley’s multiple IRRs

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In other words, the investment has an IRR of both 3.50 and 19.54%. Figure 5.4 shows how this comes about. As the discount rate increases, NPV initially rises and then declines. The reason for this is the double change in the sign of the cash-flow stream. There can be as many internal rates of return for a project as there are changes in the sign of the cash flows.³

   FIGURE 5.4 Helmsley Iron’s mine has two internal rates of return. NPV = 0 when the discount rate is +3.50% and when it is + 19.54%.

Decommissioning and clean-up costs can sometimes be huge. Phillips Petroleum has estimated that it will need to spend $1 billion to remove its Norwegian offshore oil platforms. It can cost over $300 million to decommission a nuclear power plant. These are obvious instances where cash flows go from positive to negative, but you can probably think of a number of other cases where the company needs to plan for later expenditures. Ships periodically need to go into dry dock for a refit, hotels may receive a major face-lift, machine parts may need replacement, and so on.

Whenever the cash-flow stream is expected to change sign more than once, the company typically sees more than one IRR.

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A project with no IRR

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As if this is not difficult enough, there are also cases in which no internal rate of return exists. For example, project C has a positive net present value at all discount rates:

A number of adaptations of the IRR rule have been devised for such cases. Not only are they inadequate, but they also are unnecessary, for the simple solution is to use net present value.⁴

Pitfall 3—Mutually Exclusive Projects

Firms often have to choose from among several alternative ways of doing the same job or using the same facility. In other words, they need to choose from among mutually exclusive projects. Here too the IRR rule can be misleading.

Consider projects D and E:

Perhaps project D is a manually controlled machine tool and project E is the same tool with the addition of computer control. Both are good investments, but E has the higher NPV and is, therefore, better. However, the IRR rule seems to indicate that if you have to choose, you should go for D since it has the higher IRR. If you follow the IRR rule, you have the satisfaction of earning a 100% rate of return; if you follow the NPV rule, you are $11,818 richer.

You can salvage the IRR rule in these cases by looking at the internal rate of return on the incremental flows. Here is how to do it: First, consider the smaller project (D in our example). It has an IRR of 100%, which is well in excess of the 10% opportunity cost of capital.

You know, therefore, that D is acceptable. You now ask yourself whether it is worth making the additional $10,000 investment in E. The incremental flows from undertaking E rather than D are as follows:

The IRR on the incremental investment is 50%, which is also well in excess of the 10% opportunity cost of capital. So you should prefer project E to project D.⁵

Unless you look at the incremental expenditure, IRR is unreliable in ranking projects of different scale. It is also unreliable in ranking projects that offer different patterns of cash flow over time. For example, suppose the firm can take project F or project G but not both:

Project F has a higher IRR, but project G, which is a perpetuity, has the higher NPV. Figure 5.5 shows why the two rules give different answers. The green line gives the net present value of project F at different rates of discount. Since a discount rate of 33% produces a net present value of zero, this is the internal rate of return for project F. Similarly, the red line shows the net present value of project G at different discount rates. The IRR of project G is 20%. (We assume project G’s cash flows continue indefinitely.) Note, however, that project G has a higher NPV as long as the opportunity cost of capital is less than 15.6%.

   FIGURE 5.5 The IRR of project F exceeds that of project G, but the NPV of project F is higher only if the discount rate is greater than 15.6%.

The reason that IRR is misleading is that the total cash inflow of project G is larger but tends to occur later. Therefore, when the discount rate is low, G has the higher NPV; when the discount rate is high, F has the higher NPV. (You can see from Figure 5.5 that the two projects have the same NPV when the discount rate is 15.6%.) The internal rates of return on the two projects tell us that at a discount rate of 20% G has a zero NPV (IRR = 20%) and F has a positive NPV. Thus if the opportunity cost of capital were 20%, investors would place a higher value on the shorter-lived project F. But in our example the opportunity cost of capital is not 20% but 10%. So investors will pay a relatively high price for the longer-lived project. At a 10% cost of capital, an investment in G has an NPV of $9,000 and an investment in F has an NPV of only $3,592.⁶

This is a favorite example of ours. We have gotten many businesspeople’s reactions to it. When asked to choose between F and G, many choose F. The reason seems to be the rapid payback generated by project F. In other words, they believe that if they take F, they will also be able to use the rapid cash inflows to make other investments in the future, whereas if they take G, they won’t have money enough for these investments. In other words they implicitly assume that it is a shortage of capital that forces the choice between F and G. When this implicit assumption is brought out, they usually admit that G is better if there is no capital shortage.

But the introduction of capital constraints raises two further questions. The first stems from the fact that most of the executives preferring F to G work for firms that would have no difficulty raising more capital. Why would a manager at IBM, say, choose F on the grounds of limited capital? IBM can raise plenty of capital for future projects regardless of whether F or G is chosen; therefore these future opportunities should not affect the choice between F and G. The answer seems to be that large firms usually impose capital budgets on divisions and subdivisions as a part of the firm’s planning and control system. Since the system is complicated and cumbersome, the budgets are not easily altered, and so they are perceived as real constraints by middle management.

The second question is this. If there is a capital constraint, either real or self-imposed, should IRR be used to rank projects? The answer is no. The problem in this case is to find the package of investment projects that satisfies the capital constraint and has the largest net present value. The IRR rule will not identify this package. As we will show in the next section, the only practical and general way to do so is to use the technique of linear programming.

When we have to choose between projects F and G, it is easiest to compare the net present values. But if your heart is set on the IRR rule, you can use it as long as you look at the internal rate of return on the incremental flows. The procedure is exactly the same as we showed above. First, you check that project F has a satisfactory IRR. Then you look at the return on the incremental cash flows from G.

The IRR on the incremental cash flows from G is 15.6%. Since this is greater than the opportunity cost of capital, you should undertake G rather than F.⁷

Pitfall 4—What Happens When There Is More than One Opportunity Cost of Capital?

We have simplified our discussion of capital budgeting by assuming that the opportunity cost of capital is the same for all the cash flows, C1, C2, C3, etc. Remember our most general formula for calculating net present value:

In other words, we discount C1 at the opportunity cost of capital for one year, C2 at the opportunity cost of capital for two years, and so on. The IRR rule tells us to accept a project if the IRR is greater than the opportunity cost of capital. But what do we do when we have several opportunity costs? Do we compare IRR with r1, r2, r3, . . .? Actually we would have to compute a complex weighted average of these rates to obtain a number comparable to IRR.

What does this mean for capital budgeting? It means trouble for the IRR rule whenever there is more than one opportunity cost of capital. Many firms use the IRR, thereby implicitly assuming that there is no difference between short-term and long-term discount rates. They do this for the same reason that we have so far finessed the issue: simplicity.⁸

The Verdict on IRR

We have given four examples of things that can go wrong with IRR. We spent much less space on payback or return on book. Does this mean that IRR is worse than the other two measures? Quite the contrary. There is little point in dwelling on the deficiencies of payback or return on book. They are clearly ad hoc measures that often lead to silly conclusions. The IRR rule has a much more respectable ancestry. It is less easy to use than NPV, but, used properly, it gives the same answer.

Nowadays few large corporations use the payback period or return on book as their primary measure of project attractiveness. Most use discounted cash flow or “DCF,” and for many companies DCF means IRR, not NPV. For “normal” investment projects with an initial cash outflow followed by a series of cash inflows, there is no difficulty in using the internal rate of return to make a simple accept/reject decision. However, we think that financial managers need to worry more about Pitfall 3. Financial managers never see all possible projects. Most projects are proposed by operating managers. A company that instructs nonfinancial managers to look first at project IRRs prompts a search for those projects with the highest IRRs rather than the highest NPVs. It also encourages managers to modify projects so that their IRRs are higher. Where do you typically find the highest IRRs? In short-lived projects requiring little up-front investment. Such projects may not add much to the value of the firm.

We don’t know why so many companies pay such close attention to the internal rate of return, but we suspect that it may reflect the fact that management does not trust the forecasts it receives. Suppose that two plant managers approach you with proposals for two new investments. Both have a positive NPV of $1,400 at the company’s 8% cost of capital, but you nevertheless decide to accept project A and reject B. Are you being irrational?

The cash flows for the two projects and their NPVs are set out in the table below. You can see that, although both proposals have the same NPV, project A involves an investment of $9,000, while B requires an investment of $9 million. Investing $9,000 to make $1,400 is clearly an attractive proposition, and this shows up in A’s IRR of nearly 16%. Investing $9 million to make $1,400 might also be worth doing if you could be sure of the plant manager’s forecasts, but there is almost no room for error in project B. You could spend time and money checking the cash-flow forecasts, but is it really worth the effort? Most managers would look at the IRR and decide that, if the cost of capital is 8%, a project that offers a return of 8.01% is not worth the worrying time.

Alternatively, management may conclude that project A is a clear winner that is worth undertaking right away, but in the case of project B it may make sense to wait and see whether the decision looks more clear-cut in a year’s time.⁹ Management postpones the decision on projects such as B by setting a hurdle rate for the IRR that is higher than the cost of capital.

 5-4   Choosing Capital Investments When Resources Are Limited

Our entire discussion of methods of capital budgeting has rested on the proposition that the wealth of a firm’s shareholders is highest if the firm accepts every project that has a positive net present value. Suppose, however, that there are limitations on the investment program that prevent the company from undertaking all such projects. Economists call this capital rationing. When capital is rationed, we need a method of selecting the package of projects that is within the company’s resources yet gives the highest possible net present value.

An Easy Problem in Capital Rationing

Let us start with a simple example. The Swiss company, Euler Lösungen, has the following opportunities:

At a 10% cost of capital, all three projects are attractive, but suppose that Euler is limited to spending 10 million francs. In that case, it can invest either in project A or in projects B and C, but it cannot invest in all three. Although individually B and C have lower net present values than project A, when taken together they have the higher net present value. Here one cannot choose between projects solely on the basis of net present values. When funds are limited, the company needs to concentrate on getting the biggest bang for its buck. In other words, it must pick the projects that offer the highest net present value per dollar of initial outlay. This ratio is known as the profitability index:¹⁰

For the three projects the profitability index is calculated as follows:¹¹

Project B has the highest profitability index and C has the next highest. Therefore, if the budget limit is 10 million francs, Euler should accept these two projects.¹²

Unfortunately, there are some limitations to this simple ranking method. One of the most serious is that it breaks down whenever more than one resource is rationed.¹³ For example, suppose that Euler can raise only 10 million francs for investment in each of years 0 and 1 and that the menu of possible projects is expanded to include an investment next year in project D:

One strategy is to accept projects B and C; however, if Euler does this, it cannot also accept D, which costs more than the budget limit for period 1. An alternative is to accept project A in period 0. Although this has a lower net present value than the combination of B and C, it provides a 30 million franc positive cash flow in period 1. When this is added to the 10 million franc budget, the company can also afford to undertake D next year. A and D have lower profitability indexes than B and C, but they have a higher total net present value.

The reason that ranking on the profitability index fails in this example is that resources are constrained in each of two periods. In fact, this ranking method is inadequate whenever there is any other constraint on the choice of projects. This means that it cannot cope with cases in which two projects are mutually exclusive or in which one project is dependent on another.

For example, suppose that you have a long menu of possible projects starting this year and next. There is a limit on how much you can invest in each year. Perhaps also you can’t undertake both project alpha and beta (they both require the same piece of land), and you can’t invest in project gamma unless you also invest in delta (gamma is simply an add-on to delta). You need to find the package of projects that satisfies all these constraints and gives the highest NPV.

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Capital rationing models

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One way to tackle such a problem is to work through all possible combinations of projects. For each combination you first check whether the projects satisfy the constraints and then calculate the net present value. But it is smarter to recognize that linear programming (LP) techniques are specially designed to search through such possible combinations.

Uses of Capital Rationing Models

Linear programming models seem tailor-made for solving capital budgeting problems when resources are limited. Why then are they not universally accepted either in theory or in practice? One reason is that these models can turn out to be very complex. Second, as with any sophisticated long-range planning tool, there is the general problem of getting good data. It is just not worth applying costly, sophisticated methods to poor data. Furthermore, these models are based on the assumption that all future investment opportunities are known. In reality, the discovery of investment ideas is an unfolding process.

Our most serious misgivings center on the basic assumption that capital is limited. When we come to discuss company financing, we shall see that most large corporations do not face capital rationing and can raise large sums of money on fair terms. Why then do many company presidents tell their subordinates that capital is limited? If they are right, the capital market is seriously imperfect. What then are they doing maximizing NPV?¹⁴ We might be tempted to suppose that if capital is not rationed, they do not need to use linear programming and, if it is rationed, then surely they ought not to use it. But that would be too quick a judgment. Let us look at this problem more deliberately.

USEFUL SPREADSHEET FUNCTIONS

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Internal Rate of Return

  Spreadsheet programs such as Excel provide built-in functions to solve for internal rates of return. You can find these functions by pressing fx on the Excel toolbar. If you then click on the function that you wish to use, Excel will guide you through the inputs that are required. At the bottom left of the function box there is a Help facility with an example of how the function is used.

Here is a list of useful functions for calculating internal rates of return, together with some points to remember when entering data:

•  IRR: Internal rate of return on a series of regularly spaced cash flows.

•  XIRR: The same as IRR, but for irregularly spaced flows.

Note the following:

•  For these functions, you must enter the addresses of the cells that contain the input values.

•  The IRR functions calculate only one IRR even when there are multiple IRRs.

Spreadsheet Questions

The following questions provide an opportunity to practice each of the above functions:

1.  (IRR) Check the IRRs on projects F and G in Section 5-3.

2.  (IRR) What is the IRR of a project with the following cash flows:

3.  (IRR) Now use the function to calculate the IRR on Helmsley Iron’s mining project in Section 5-3. There are really two IRRs to this project (why?). How many IRRs does the function calculate?

4.  (XIRR) What is the IRR of a project with the following cash flows:

(All other cash flows are 0.)

Soft Rationing Many firms’ capital constraints are “soft.” They reflect no imperfections in capital markets. Instead they are provisional limits adopted by management as an aid to financial control.

Some ambitious divisional managers habitually overstate their investment opportunities. Rather than trying to distinguish which projects really are worthwhile, headquarters may find it simpler to impose an upper limit on divisional expenditures and thereby force the divisions to set their own priorities. In such instances budget limits are a rough but effective way of dealing with biased cash-flow forecasts. In other cases management may believe that very rapid corporate growth could impose intolerable strains on management and the organization. Since it is difficult to quantify such constraints explicitly, the budget limit may be used as a proxy.

Because such budget limits have nothing to do with any inefficiency in the capital market, there is no contradiction in using an LP model in the division to maximize net present value subject to the budget constraint. On the other hand, there is not much point in elaborate selection procedures if the cash-flow forecasts of the division are seriously biased.

Even if capital is not rationed, other resources may be. The availability of management time, skilled labor, or even other capital equipment often constitutes an important constraint on a company’s growth.

Hard Rationing Soft rationing should never cost the firm anything. If capital constraints become tight enough to hurt—in the sense that projects with significant positive NPVs are passed up—then the firm raises more money and loosens the constraint. But what if it can’t raise more money—what if it faces hard rationing?

Hard rationing implies market imperfections, but that does not necessarily mean we have to throw away net present value as a criterion for capital budgeting. It depends on the nature of the imperfection.

Arizona Aquaculture, Inc. (AAI), borrows as much as the banks will lend it, yet it still has good investment opportunities. This is not hard rationing so long as AAI can issue stock. But perhaps it can’t. Perhaps the founder and majority shareholder vetoes the idea from fear of losing control of the firm. Perhaps a stock issue would bring costly red tape or legal complications.¹⁵

This does not invalidate the NPV rule. AAI’s shareholders can borrow or lend, sell their shares, or buy more. They have free access to security markets. The type of portfolio they hold is independent of AAI’s financing or investment decisions. The only way AAI can help its shareholders is to make them richer. Thus AAI should invest its available cash in the package of projects having the largest aggregate net present value.

A barrier between the firm and capital markets does not undermine net present value so long as the barrier is the only market imperfection. The important thing is that the firm’s shareholders have free access to well-functioning capital markets.

The net present value rule is undermined when imperfections restrict shareholders’ portfolio choice. Suppose that Nevada Aquaculture, Inc. (NAI), is solely owned by its founder, Alexander Turbot. Mr. Turbot has no cash or credit remaining, but he is convinced that expansion of his operation is a high-NPV investment. He has tried to sell stock but has found that prospective investors, skeptical of prospects for fish farming in the desert, offer him much less than he thinks his firm is worth. For Mr. Turbot capital markets hardly exist. It makes little sense for him to discount prospective cash flows at a market opportunity cost of capital.

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SUMMARY

If you are going to persuade your company to use the net present value rule, you must be prepared to explain why other rules may not lead to correct decisions. That is why we have examined three alternative investment criteria in this chapter.

Some firms look at the book rate of return on the project. In this case the company decides which cash payments are capital expenditures and picks the appropriate rate to depreciate these expenditures. It then calculates the ratio of book income to the book value of the investment. Few companies nowadays base their investment decision simply on the book rate of return, but shareholders pay attention to book measures of firm profitability and some managers therefore look with a jaundiced eye on projects that would damage the company’s book rate of return.

Some companies use the payback method to make investment decisions. In other words, they accept only those projects that recover their initial investment within some specified period. Payback is an ad hoc rule. It ignores the timing of cash flows within the payback period, and it ignores subsequent cash flows entirely. It therefore takes no account of the opportunity cost of capital.

The internal rate of return (IRR) is defined as the rate of discount at which a project would have zero NPV. It is a handy measure and widely used in finance; you should therefore know how to calculate it. The IRR rule states that companies should accept any investment offering an IRR in excess of the opportunity cost of capital. The IRR rule is, like net present value, a technique based on discounted cash flows. It will therefore give the correct answer if properly used. The problem is that it is easily misapplied. There are four things to look out for:

1.  Lending or borrowing? If a project offers positive cash flows followed by negative flows, NPV can rise as the discount rate is increased. You should accept such projects if their IRR is less than the opportunity cost of capital.

2.  Multiple rates of return. If there is more than one change in the sign of the cash flows, the project may have several IRRs or no IRR at all.

3.  Mutually exclusive projects. The IRR rule may give the wrong ranking of mutually exclusive projects that differ in economic life or in scale of required investment. If you insist on using IRR to rank mutually exclusive projects, you must examine the IRR on each incremental investment.

4.  The cost of capital for near-term cash flows may be different from the cost for distant cash flows. The IRR rule requires you to compare the project’s IRR with the opportunity cost of capital. But sometimes there is an opportunity cost of capital for one-year cash flows, a different cost of capital for two-year cash flows, and so on. In these cases there is no simple yardstick for evaluating the IRR of a project.

In developing the NPV rule, we assumed that the company can maximize shareholder wealth by accepting every project that is worth more than it costs. But, if capital is strictly limited, then it may not be possible to take every project with a positive NPV. If capital is rationed in only one period, then the firm should follow a simple rule: Calculate each project’s profitability index, which is the project’s net present value per dollar of investment. Then pick the projects with the highest profitability indexes until you run out of capital. Unfortunately, this procedure fails when capital is rationed in more than one period or when there are other constraints on project choice. The only general solution is linear programming.

Hard capital rationing always reflects a market imperfection—a barrier between the firm and capital markets. If that barrier also implies that the firm’s shareholders lack free access to a well-functioning capital market, the very foundations of net present value crumble. Fortunately, hard rationing is rare for corporations in the United States. Many firms do use soft capital rationing, however. That is, they set up self-imposed limits as a means of financial planning and control.

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FURTHER READING

For a survey of capital budgeting procedures, see:

J. Graham and C. Harvey, “How CFOs Make Capital Budgeting and Capital Structure Decisions,” Journal of Applied Corporate Finance 15 (spring 2002), pp. 8–23.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Payback

a.  What is the payback period on each of the following projects?

b.  Given that you wish to use the payback rule with a cutoff period of two years, which projects would you accept?

c.  If you use a cutoff period of three years, which projects would you accept?

d.  If the opportunity cost of capital is 10%, which projects have positive NPVs?

e.  “If a firm uses a single cutoff period for all projects, it is likely to accept too many short-lived projects.” True or false?

f.  If the firm uses the discounted-payback rule, will it accept any negative-NPV projects? Will it turn down positive-NPV projects? Explain.

2.  IRR Write down the equation defining a project’s internal rate of return (IRR). In practice how is IRR calculated?

3.  IRR

a.  Calculate the net present value of the following project for discount rates of 0, 50, and 100%:

b.  What is the IRR of the project?

4.  IRR rule You have the chance to participate in a project that produces the following cash flows:

The internal rate of return is 13%. If the opportunity cost of capital is 10%, would you accept the offer?

5.  IRR rule Consider a project with the following cash flows:

a.  How many internal rates of return does this project have?

b.  Which of the following numbers is the project IRR:

(i) –50%; (ii) –12%; (iii) +5%; (iv) +50%?

c.  The opportunity cost of capital is 20%. Is this an attractive project? Briefly explain.

6.  IRR rule Consider projects Alpha and Beta:

The opportunity cost of capital is 8%.

Suppose you can undertake Alpha or Beta, but not both. Use the IRR rule to make the choice. (Hint: What’s the incremental investment in Alpha?)

7.  Capital rationing Suppose you have the following investment opportunities, but only $90,000 available for investment. Which projects should you take?

INTERMEDIATE

8.  Payback Consider the following projects:

a.  If the opportunity cost of capital is 10%, which projects have a positive NPV?

b.  Calculate the payback period for each project.

c.  Which project(s) would a firm using the payback rule accept if the cutoff period were three years?

d.  Calculate the discounted payback period for each project.

e.  Which project(s) would a firm using the discounted payback rule accept if the cutoff period were three years?

9.  Payback and IRR rules Respond to the following comments:

a.  “I like the IRR rule. I can use it to rank projects without having to specify a discount rate.”

b.  “I like the payback rule. As long as the minimum payback period is short, the rule makes sure that the company takes no borderline projects. That reduces risk.”

10.  IRR Calculate the IRR (or IRRs) for the following project:

For what range of discount rates does the project have positive NPV?

11.  IRR rule Consider the following two mutually exclusive projects:

a.  Calculate the NPV of each project for discount rates of 0%, 10%, and 20%. Plot these on a graph with NPV on the vertical axis and discount rate on the horizontal axis.

b.  What is the approximate IRR for each project?

c.  In what circumstances should the company accept project A?

d.  Calculate the NPV of the incremental investment (B – A) for discount rates of 0%, 10%, and 20%. Plot these on your graph. Show that the circumstances in which you would accept A are also those in which the IRR on the incremental investment is less than the opportunity cost of capital.

12.  IRR rule Mr. Cyrus Clops, the president of Giant Enterprises, has to make a choice between two possible investments:

The opportunity cost of capital is 9%. Mr. Clops is tempted to take B, which has the higher IRR.

a.  Explain to Mr. Clops why this is not the correct procedure.

b.  Show him how to adapt the IRR rule to choose the best project.

c.  Show him that this project also has the higher NPV.

13.  IRR rule The Korean shipbuilding company, Mipo Yards, has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of 250 million won at the end of each of the next two years. At the end of the third year the company will receive payment of 650 million won. The company can speed up construction by working an extra shift. In this case there will be a cash outlay of 550 million won at the end of the first year followed by a cash payment of 650 million won at the end of the second year. Use the IRR rule to show the (approximate) range of opportunity costs of capital at which the company should work the extra shift.

14.  Profitability index Look again at projects D and E in Section 5-3. Assume that the projects are mutually exclusive and that the opportunity cost of capital is 10%.

a.  Calculate the profitability index for each project.

b.  Show how the profitability-index rule can be used to select the superior project.

15.  Capital rationing Borghia Pharmaceuticals has $1 million allocated for capital expenditures. Which of the following projects should the company accept to stay within the $1 million budget? How much does the budget limit cost the company in terms of its market value? The opportunity cost of capital for each project is 11%.

CHALLENGE

16.  NPV and IRR rules Some people believe firmly, even passionately, that ranking projects on IRR is OK if each project’s cash flows can be reinvested at the project’s IRR. They also say that the NPV rule “assumes that cash flows are reinvested at the opportunity cost of capital.” Think carefully about these statements. Are they true? Are they helpful?

17.  Modified IRR Look again at the project cash flows in Problem 10. Calculate the modified IRR as defined in Footnote 4 in Section 5-3. Assume the cost of capital is 12%.

Now try the following variation on the MIRR concept. Figure out the fraction x such that x times C1 and C2 has the same present value as (minus) C3.

Define the modified project IRR as the solution of

Now you have two MIRRs. Which is more meaningful? If you can’t decide, what do you conclude about the usefulness of MIRRs?

18.  Capital rationing Consider the following capital rationing problem:

Set up this problem as a linear program and solve it.

You can allow partial investments, that is, 0 ≤ x ≤ 1. Calculate and interpret the shadow prices¹⁶ on the capital constraints.

19.  Payback rule Aviation Week and Space Technology (July 31, 2006, p. 19) explained why Finnair decided to add winglets to its seven Boeing 757–200s: “The high cost of fuel means that the installation will pay for itself after two years . . . . Fuel burn will be reduced 4–5%, the carrier estimates, and 200 nautical miles will be added to the range.” Was this a case where the payback rule worked? Was there any need for an NPV calculation? Could Finnair have generated additional useful information by calculating the NPV of this investment? Discuss.

MINI-CASE ● ● ● ● ●

Vegetron’s CFO Calls Again

(The first episode of this story was presented in Section 5-1.)

Later that afternoon, Vegetron’s CFO bursts into your office in a state of anxious confusion. The problem, he explains, is a last-minute proposal for a change in the design of the fermentation tanks that Vegetron will build to extract hydrated zirconium from a stockpile of powdered ore. The CFO has brought a printout (Table 5.1) of the forecasted revenues, costs, income, and book rates of return for the standard, low-temperature design. Vegetron’s engineers have just proposed an alternative high-temperature design that will extract most of the hydrated zirconium over a shorter period, five instead of seven years. The forecasts for the high-temperature method are given in Table 5.2.¹⁷

   TABLE 5.1 Income statement and book rates of return for low-temperature extraction of hydrated zirconium ($ thousands).

aRounded. Straight-line depreciation over seven years is 400/7 = 57.14, or $57,140 per year.

bCapital investment is $400,000 in year 0.

   TABLE 5.2 Income statement and book rates of return for high-temperature extraction of hydrated zirconium ($ thousands).

aStraight-line depreciation over five years is 400/5 = 80, or $80,000 per year.

bCapital investment is $400,000 in year 0.

CFO: Why do these engineers always have a bright idea at the last minute? But you’ve got to admit the high-temperature process looks good. We’ll get a faster payback, and the rate of return beats Vegetron’s 9% cost of capital in every year except the first. Let’s see, income is $30,000 per year. Average investment is half the $400,000 capital outlay, or $200,000, so the average rate of return is 30,000/200,000, or 15%—a lot better than the 9% hurdle rate. The average rate of return for the low-temperature process is not that good, only 28,000/200,000, or 14%. Of course we might get a higher rate of return for the low-temperature proposal if we depreciated the investment faster—do you think we should try that?

You: Let’s not fixate on book accounting numbers. Book income is not the same as cash flow to Vegetron or its investors. Book rates of return don’t measure the true rate of return.

CFO: But people use accounting numbers all the time. We have to publish them in our annual report to investors.

You: Accounting numbers have many valid uses, but they’re not a sound basis for capital investment decisions. Accounting changes can have big effects on book income or rate of return, even when cash flows are unchanged.

Here’s an example. Suppose the accountant depreciates the capital investment for the low-temperature process over six years rather than seven. Then income for years 1 to 6 goes down, because depreciation is higher. Income for year 7 goes up because the depreciation for that year becomes zero. But there is no effect on year-to-year cash flows, because depreciation is not a cash outlay. It is simply the accountant’s device for spreading out the “recovery” of the up-front capital outlay over the life of the project.

CFO: So how do we get cash flows?

You: In these cases it’s easy. Depreciation is the only noncash entry in your spreadsheets (Tables 5.1 and 5.2), so we can just leave it out of the calculation. Cash flow equals revenue minus operating costs. For the high-temperature process, annual cash flow is:

CFO: In effect you’re adding back depreciation, because depreciation is a noncash accounting expense.

You: Right. You could also do it that way:

CFO: Of course. I remember all this now, but book returns seem important when someone shoves them in front of your nose.

You: It’s not clear which project is better. The high-temperature process appears to be less efficient. It has higher operating costs and generates less total revenue over the life of the project, but of course it generates more cash flow in years 1 to 5.

CFO: Maybe the processes are equally good from a financial point of view. If so we’ll stick with the low-temperature process rather than switching at the last minute.

You: We’ll have to lay out the cash flows and calculate NPV for each process.

CFO: OK, do that. I’ll be back in a half hour—and I also want to see each project’s true, DCF rate of return.

QUESTIONS

1.  Are the book rates of return reported in Tables 5.1 and 5.2 useful inputs for the capital investment decision?

2.  Calculate NPV and IRR for each process. What is your recommendation? Be ready to explain to the CFO.

___________

¹This chapter’s mini-case contains simple illustrations of how book rates of return are calculated and of the difference between accounting income and project cash flow. Read the case if you wish to refresh your understanding of these topics. Better still, do the case calculations.

²Of course, the depreciation method used for tax purposes does have cash consequences that should be taken into account in calculating NPV. We cover depreciation and taxes in the next chapter.

³By Descartes’s “rule of signs” there can be as many different solutions to a polynomial as there are changes of sign.

⁴Companies sometimes get around the problem of multiple rates of return by discounting the later cash flows back at the cost of capital until there remains only one change in the sign of the cash flows. A modified internal rate of return (MIRR) can then be calculated on this revised series. In our example, the MIRR is calculated as follows:

1.  Calculate the present value in year 5 of all the subsequent cash flows:

2.  Add to the year 5 cash flow the present value of subsequent cash flows:

3.  Since there is now only one change in the sign of the cash flows, the revised series has a unique rate of return, which is 13.7%:

Since the MIRR of 13.7% is greater than the cost of capital (and the initial cash flow is negative), the project has a positive NPV when valued at the cost of capital.

Of course, it would be much easier in such cases to abandon the IRR rule and just calculate project NPV.

⁵You may, however, find that you have jumped out of the frying pan into the fire. The series of incremental cash flows may involve several changes in sign. In this case there are likely to be multiple IRRs and you will be forced to use the NPV rule after all.

⁶It is often suggested that the choice between the net present value rule and the internal rate of return rule should depend on the probable reinvestment rate. This is wrong. The prospective return on another independent investment should never be allowed to influence the investment decision.

⁷Because F and G had the same 10% cost of capital, we could choose between the two projects by asking whether the IRR on the incremental cash flows was greater or less than 10%. But suppose that F and G had different risks and therefore different costs of capital. In that case there would be no simple yardstick for assessing whether the IRR on the incremental cash flows was adequate.

⁸In Chapter 9 we look at some other cases in which it would be misleading to use the same discount rate for both short-term and long-term cash flows.

⁹In Chapter 22 we discuss when it may pay a company to delay undertaking a positive-NPV project. We will see that when projects are “deep-in-the-money” (project A), it generally pays to invest right away and capture the cash flows. However, in the case of projects that are “close-to-the-money” (project B) it makes more sense to wait and see.

¹⁰If a project requires outlays in two or more periods, the denominator should be the present value of the outlays. A few companies do not discount the benefits or costs before calculating the profitability index. The less said about these companies the better.

¹¹Sometimes the profitability index is defined as the ratio of the present value to initial outlay, that is, as PV/investment. This measure is also known as the benefit–cost ratio. To calculate the benefit–cost ratio, simply add 1.0 to each profitability index. Project rankings are unchanged.

¹²If a project has a positive profitability index, it must also have a positive NPV. Therefore, firms sometimes use the profitability index to select projects when capital is not limited. However, like the IRR, the profitability index can be misleading when used to choose between mutually exclusive projects. For example, suppose Euler is forced to choose between (1) investing 100 francs in a project whose payoffs have a present value of 200 francs or (2) investing 1 million francs in a project whose payoffs have a present value of 1.5 million francs. The first investment has the higher profitability index; the second makes you richer.

¹³It may also break down if it causes some money to be left over. It might be better to spend all the available funds even if this involves accepting a project with a slightly lower profitability index.

¹⁴Don’t forget that in the Appendix to Chapter 1 we had to assume perfect capital markets to derive the NPV rule.

¹⁵A majority owner who is “locked in” and has much personal wealth tied up in AAI may be effectively cut off from capital markets. The NPV rule may not make sense to such an owner, though it will to the other shareholders.

¹⁶A shadow price is the marginal change in the objective for a marginal change in the constraint.

¹⁷For simplicity we have ignored taxes. There will be plenty about taxes in Chapter 6.

Part 1 Value

Making Investment Decisions with the Net Present Value Rule

In 2012 Volkswagen announced plans to invest €14 billion in new manufacturing facilities in China. The first factory was to be built in Urumqi and would be capable of producing up to 50,000 cars a year.

How does a company such as Volkswagen decide to go ahead with such a massive investment? We know the answer in principle. The company needs to forecast the project’s cash flows and discount them at the opportunity cost of capital to arrive at the project’s NPV. A project with a positive NPV increases shareholder value.

But those cash flow forecasts do not arrive on a silver platter. For example, Volkswagen’s managers would have needed answers to a number of basic questions. How soon can the company launch the new models? How many cars are likely to be sold each year and at what price? How much does the firm need to invest in the new production facilities, and what is the likely production cost? How long will the model stay in production, and what happens to the plant and equipment at the end of that time?

These predictions need to be pulled together to produce a single set of cash-flow forecasts. That requires careful tracking of taxes, changes in working capital, inflation, and the end-of-project salvage values of plant, property, and equipment. The financial manager must also ferret out hidden cash flows and take care to reject accounting entries that look like cash flows but truly are not.

Our first task in this chapter is to look at how to develop a set of project cash flows. We will then work through a realistic and comprehensive example of a capital investment analysis.

We conclude the chapter by looking at how the financial manager should apply the present value rule when choosing between investment in plant and equipment with different economic lives. For example, suppose you must decide between machine Y with a 5-year useful life and Z with a 10-year life. The present value of Y’s lifetime investment and operating costs is naturally less than Z’s because Z will last twice as long. Does that necessarily make Y the better choice? Of course not. You will find that, when you are faced with this type of problem, the trick is to transform the present value of the cash flow into an equivalent annual flow, that is, the total cash per year from buying and operating the asset.

 6-1   Applying the Net Present Value Rule

Many projects require a heavy initial outlay on new production facilities. But often the largest investments involve the acquisition of intangible assets. For example, U.S. banks invest about $10 billion annually in new IT projects. Much of this expenditure goes to intangibles such as system design, programming, testing, and training. Think also of the huge expenditure by pharmaceutical companies on research and development (R&D). Merck, one of the largest pharmaceutical companies, spent $11 billion on R&D in 2010. The R&D cost of bringing one new prescription drug to market has been estimated at $800 million.

Expenditures on intangible assets such as IT and R&D are investments just like expenditures on new plant and equipment. In each case the company is spending money today in the expectation that it will generate a stream of future profits. Ideally, firms should apply the same criteria to all capital investments, regardless of whether they involve a tangible or intangible asset.

We have seen that an investment in any asset creates wealth if the discounted value of the future cash flows exceeds the up-front cost. But up to this point we have glossed over the problem of what to discount. When you are faced with this problem, you should stick to four general rules:

1.  Only cash flow is relevant.

2.  Always estimate cash flows on an incremental basis.

3.  Be consistent in your treatment of inflation.

4.  Separate investment and financing decisions.

We discuss each of these rules in turn.

Rule 1: Only Cash Flow Is Relevant

The first and most important point: Net present value depends on future cash flow. Cash flow is simply the difference between cash received and cash paid out. Many people nevertheless confuse cash flow with accounting income. Accounting income is intended to show how well the company is performing. Therefore, accountants start with “dollars in” and “dollars out,” but to obtain accounting income they adjust these inputs in two principal ways.

Capital Expenses When calculating expenditures, the accountant deducts current expenses but does not deduct capital expenses. There is a good reason for this. If the firm lays out a large amount of money on a big capital project, you do not conclude that the firm is performing poorly, even though a lot of cash is going out the door. Therefore, instead of deducting capital expenditure as it occurs, the accountant depreciates the outlay over several years.

That makes sense when judging firm performance, but it will get you into trouble when working out net present value. For example, suppose that you are analyzing an investment proposal. It costs $2,000 and is expected to provide a cash flow of $1,500 in the first year and $500 in the second. If the capital expenditure is depreciated over the two years, accounting income is $500 in year 1 and – $500 in year 2:

Suppose you were given this forecast income and naïvely discounted it at 10%. NPV would appear positive:

This has to be nonsense. The project is obviously a loser. You are laying out $2,000 today and simply getting it back later. At any positive discount rate the project has a negative NPV. The message is clear: When calculating NPV, record capital expenditures when they occur, not later when they show up as depreciation. To go from accounting income to cash flow, you need to add back depreciation (which is not a cash outflow) and subtract capital expenditure (which is a cash payment).

Working Capital When measuring income, accountants try to show profit as it is earned, rather than when the company and its customers get around to paying their bills.

For example, consider a company that spends $60 to produce goods in period 1. It sells these goods in period 2 for $100, but its customers do not pay their bills until period 3. The following diagram shows the firm’s cash flows. In period 1 there is a cash outflow of $60. Then, when customers pay their bills in period 3, there is an inflow of $100.

It would be misleading to say that the firm was running at a loss in period 1 (when cash flow was negative) or that it was extremely profitable in period 3 (when cash flow was positive). Therefore, the accountant looks at when the sale was made (period 2 in our example) and gathers together all the revenues and expenses associated with that sale. In the case of our company, the accountant would show for period 2

Of course, the accountant cannot ignore the actual timing of the cash expenditures and payments. So the $60 cash outlay in the first period will be treated not as an expense but as an investment in inventories. Subsequently, in period 2, when the goods are taken out of inventory and sold, the accountant shows a $60 reduction in inventories.

The accountant also does not ignore the fact that the firm has to wait to collect on its bills. When the sale is made in period 2, the accountant will record accounts receivable of $100 to show that the company’s customers owe $100 in unpaid bills. Later, when the customers pay those bills in period 3, accounts receivable are reduced by that $100.

To go from the figure for income to the actual cash flows, you need to add back these changes in inventories and receivables:

Net working capital (often referred to simply as working capital) is the difference between a company’s short-term assets and liabilities. Accounts receivable and inventories of raw materials and finished goods are the principal short-term assets. The principal short-term liabilities are accounts payable (bills that you have not paid) and taxes that have been incurred but not yet paid.¹ Most projects entail an investment in working capital, which should be recognized in your cash-flow forecasts.² By the same token, when the project comes to an end, you can usually recover some of the investment. This results in a cash inflow. (In our simple example the company made an investment in working capital of $60 in period 1 and $40 in period 2. It made a disinvestment of $100 in period 3, when the customers paid their bills.)

Working capital is a common source of confusion in capital investment calculations. Here are the most common mistakes:

1.  Forgetting about working capital entirely. We hope that you do not fall into that trap.

2.  Forgetting that working capital may change during the life of the project. Imagine that you sell $100,000 of goods a year and customers pay on average six months late. You therefore have $50,000 of unpaid bills. Now you increase prices by 10%, so revenues increase to $110,000. If customers continue to pay six months late, unpaid bills increase to $55,000, and so you need to make an additional investment in working capital of $5,000.

3.  Forgetting that working capital is recovered at the end of the project. When the project comes to an end, inventories are run down, any unpaid bills are (you hope) paid off, and you recover your investment in working capital. This generates a cash inflow.

Rule 2: Estimate Cash Flows on an Incremental Basis

The value of a project depends on all the additional cash flows that follow from project acceptance. Here are some things to watch for when you are deciding which cash flows to include:

Remember to Include Taxes Taxes are an expense just like wages and raw materials. Therefore, cash flows should be estimated on an after-tax basis. Some firms do not deduct tax payments. They try to offset this mistake by discounting the cash flows at a rate that is higher than the cost of capital. Unfortunately, there is no reliable formula for making such adjustments to the discount rate.

Do Not Confuse Average with Incremental Payoffs Most managers naturally hesitate to throw good money after bad. For example, they are reluctant to invest more money in a losing division. But occasionally you will encounter turnaround opportunities in which the incremental NPV from investing in a loser is strongly positive.

Conversely, it does not always make sense to throw good money after good. A division with an outstanding past profitability record may have run out of good opportunities. You would not pay a large sum for a 20-year-old horse, sentiment aside, regardless of how many races that horse had won or how many champions it had sired.

Here is another example illustrating the difference between average and incremental returns: Suppose that a railroad bridge is in urgent need of repair. With the bridge the railroad can continue to operate; without the bridge it can’t. In this case the payoff from the repair work consists of all the benefits of operating the railroad. The incremental NPV of such an investment may be enormous. Of course, these benefits should be net of all other costs and all subsequent repairs; otherwise the company may be misled into rebuilding an unprofitable railroad piece by piece.

Include All Incidental Effects It is important to consider a project’s effects on the remainder of the firm’s business. For example, suppose Sony proposes to launch PlayStation 4, a new version of its video game console. Demand for the new product will almost certainly cut into sales of Sony’s existing consoles. This incidental effect needs to be factored into the incremental cash flows. Of course, Sony may reason that it needs to go ahead with the new product because its existing product line is likely to come under increasing threat from competitors. So, even if it decides not to produce the new PlayStation, there is no guarantee that sales of the existing consoles will continue at their present level. Sooner or later they will decline.

Sometimes a new project will help the firm’s existing business. Suppose that you are the financial manager of an airline that is considering opening a new short-haul route from Peoria, Illinois, to Chicago’s O’Hare Airport. When considered in isolation, the new route may have a negative NPV. But once you allow for the additional business that the new route brings to your other traffic out of O’Hare, it may be a very worthwhile investment.

Forecast Sales Today and Recognize After-Sales Cash Flows to Come Later Financial managers should forecast all incremental cash flows generated by an investment. Sometimes these incremental cash flows last for decades. When GE commits to the design and production of a new jet engine, the cash inflows come first from the sale of engines and then from service and spare parts. A jet engine will be in use for 30 years. Over that period revenues from service and spare parts will be roughly seven times the engine’s purchase price.

Many manufacturing companies depend on the revenues that come after their products are sold. The consulting firm Accenture estimates that services and parts typically account for about 25% of revenues and 50% of profits for auto companies.³

Include Opportunity Costs The cost of a resource may be relevant to the investment decision even when no cash changes hands. For example, suppose a new manufacturing operation uses land that could otherwise be sold for $100,000. This resource is not free: It has an opportunity cost, which is the cash it could generate for the company if the project were rejected and the resource were sold or put to some other productive use.

This example prompts us to warn you against judging projects on the basis of “before versus after.” The proper comparison is “with or without.” A manager comparing before versus after might not assign any value to the land because the firm owns it both before and after:

The proper comparison, with or without, is as follows:

Comparing the two possible “afters,” we see that the firm gives up $100,000 by undertaking the project. This reasoning still holds if the land will not be sold but is worth $100,000 to the firm in some other use.

Sometimes opportunity costs may be very difficult to estimate; however, where the resource can be freely traded, its opportunity cost is simply equal to the market price. Consider a widely used aircraft such as the Boeing 737. Second-hand 737s are regularly traded, and their prices are quoted on the web. So, if an airline needs to know the opportunity cost of continuing to use one of its 737s, it just needs to look up the market price of a comparable plane. The opportunity cost of using the plane is equal to the cost of buying an equivalent aircraft to replace it.

Forget Sunk Costs Sunk costs are like spilled milk: They are past and irreversible outflows. Because sunk costs are bygones, they cannot be affected by the decision to accept or reject the project, and so they should be ignored.

Take the case of the James Webb Space Telescope. It was originally supposed to launch in 2011 and cost $1.6 billion. But the project became progressively more expensive and further behind schedule. An independent review board reported that the giant telescope could end up costing up to $6.5 billion and wouldn’t launch until 2015 at the earliest. As Congress debated whether to cancel the program, supporters of the project argued that it would be foolish to abandon a project on which so much had already been spent. Others countered that it would be even more foolish to continue with a project that had proved so costly. Both groups were guilty of the sunk-cost fallacy; the money that had already been spent by NASA was irrecoverable and, therefore, irrelevant to the decision to terminate the project.

Beware of Allocated Overhead Costs We have already mentioned that the accountant’s objective is not always the same as the investment analyst’s. A case in point is the allocation of overhead costs. Overheads include such items as supervisory salaries, rent, heat, and light. These overheads may not be related to any particular project, but they have to be paid for somehow. Therefore, when the accountant assigns costs to the firm’s projects, a charge for overhead is usually made. Now our principle of incremental cash flows says that in investment appraisal we should include only the extra expenses that would result from the project. A project may generate extra overhead expenses; then again, it may not. We should be cautious about assuming that the accountant’s allocation of overheads represents the true extra expenses that would be incurred.

Remember Salvage Value When the project comes to an end, you may be able to sell the plant and equipment or redeploy the assets elsewhere in the business. If the equipment is sold, you must pay tax on the difference between the sale price and the book value of the asset. The salvage value (net of any taxes) represents a positive cash flow to the firm.

Some projects have significant shut-down costs, in which case the final cash flows may be negative. For example, the mining company, FCX, has earmarked over $400 million to cover the future reclamation and closure costs of its New Mexico mines.

Rule 3: Treat Inflation Consistently

As we pointed out in Chapter 3, interest rates are usually quoted in nominal rather than real terms. For example, if you buy an 8% Treasury bond, the government promises to pay you $80 interest each year, but it does not promise what that $80 will buy. Investors take inflation into account when they decide what is an acceptable rate of interest.

If the discount rate is stated in nominal terms, then consistency requires that cash flows should also be estimated in nominal terms, taking account of trends in selling price, labor and materials costs, etc. This calls for more than simply applying a single assumed inflation rate to all components of cash flow. Labor costs per hour of work, for example, normally increase at a faster rate than the consumer price index because of improvements in productivity. Tax savings from depreciation do not increase with inflation; they are constant in nominal terms because tax law in the United States allows only the original cost of assets to be depreciated.

Of course, there is nothing wrong with discounting real cash flows at a real discount rate. In fact this is standard procedure in countries with high and volatile inflation. Here is a simple example showing that real and nominal discounting, properly applied, always give the same present value.

Suppose your firm usually forecasts cash flows in nominal terms and discounts at a 15% nominal rate. In this particular case, however, you are given project cash flows in real terms, that is, current dollars:

It would be inconsistent to discount these real cash flows at the 15% nominal rate. You have two alternatives: Either restate the cash flows in nominal terms and discount at 15%, or restate the discount rate in real terms and use it to discount the real cash flows.

Assume that inflation is projected at 10% a year. Then the cash flow for year 1, which is $35,000 in current dollars, will be 35,000 × 1.10 = $38,500 in year-1 dollars. Similarly the cash flow for year 2 will be 50,000 × (1.10)2 = $60,500 in year-2 dollars, and so on. If we discount these nominal cash flows at the 15% nominal discount rate, we have

Instead of converting the cash-flow forecasts into nominal terms, we could convert the discount rate into real terms by using the following relationship:

In our example this gives

If we now discount the real cash flows by the real discount rate, we have an NPV of $5,500, just as before:

The message of all this is quite simple. Discount nominal cash flows at a nominal discount rate. Discount real cash flows at a real rate. Never mix real cash flows with nominal discount rates or nominal flows with real rates.

Rule 4: Separate Investment and Financing Decisions

Suppose you finance a project partly with debt. How should you treat the proceeds from the debt issue and the interest and principal payments on the debt? Answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and principal payments on the debt as cash outflows. Regardless of the actual financing, you should view the project as if it were all-equity-financed, treating all cash outflows required for the project as coming from stockholders and all cash inflows as going to them.

This procedure focuses exclusively on the project cash flows, not the cash flows associated with alternative financing schemes. It, therefore, allows you to separate the analysis of the investment decision from that of the financing decision. First, you ask whether the project has a positive net present value, assuming all-equity financing. Then, if the project is viable, you can undertake a separate analysis of the best financing strategy. We explain in Chapter 19 how to recognize the effect of financing choices on project values.

 6-2   Example—IM&C’s Fertilizer Project

As the newly appointed financial manager of International Mulch and Compost Company (IM&C), you are about to analyze a proposal for marketing guano as a garden fertilizer. (IM&C’s planned advertising campaign features a rustic gentleman who steps out of a vegetable patch singing, “All my troubles have guano way.”)⁴

BEYOND THE PAGE

● ● ● ● ●

Try It! The guano spreadsheets

brealey.mhhe.com/c06

You are given the forecasts shown in Table 6.1. The project requires an investment of $10 million in plant and machinery (line 1). This machinery can be dismantled and sold for net proceeds estimated at $1.949 million in year 7 (line 1, column 7). This amount is your forecast of the plant’s salvage value.

Whoever prepared Table 6.1 depreciated the capital investment over six years to an arbitrary salvage value of $500,000, which is less than your forecast of salvage value. Straight-line depreciation was assumed. Under this method annual depreciation equals a constant proportion of the initial investment less salvage value ($9.5 million). If we call the depreciable life T, then the straight-line depreciation in year t is

Lines 6 through 12 in Table 6.1 show a simplified income statement for the guano project.⁵ This will be our starting point for estimating cash flow. All the entries in the table are nominal amounts. In other words, IM&C’s managers have taken into account the likely effect of inflation on prices and costs.

   TABLE 6.1 IM&C’s guano project—projections ($ thousands) reflecting inflation and assuming straight-line depreciation.

a Salvage value.

b We have departed from the usual income-statement format by not including depreciation in cost of goods sold.

Instead, we break out depreciation separately (see line 9).

c Start-up costs in years 0 and 1, and general and administrative costs in years 1 to 6.

d The difference between the salvage value and the ending book value of $500 is a taxable profit.

Table 6.2 derives cash-flow forecasts from the investment and income data given in Table 6.1. The project’s net cash flow is the sum of three elements:

   TABLE 6.2 IM&C’s guano project—initial cash-flow analysis assuming straight-line depreciation ($ thousands).

a Salvage value of $1,949 less tax of $507 on the difference between salvage value and ending book value.

Each of these items is shown in the table. Row 1 shows the initial capital investment and the estimated salvage value of the equipment when the project comes to an end. If, as you expect, the salvage value is higher than the depreciated value of the machinery, you will have to pay tax on the difference. So the salvage value in row 1 is shown after payment of this tax. Row 2 of the table shows the changes in working capital, and the remaining rows calculate the project’s operating cash flows.

Notice that in calculating the operating cash flows we did not deduct depreciation. Depreciation is an accounting entry. It affects the tax that the company pays, but the firm does not send anyone a check for depreciation. The operating cash flow is simply the dollars coming in less the dollars going out:⁶

For example, in year 6 of the guano project:

IM&C estimates the nominal opportunity cost of capital for projects of this type as 20%. When all cash flows are added up and discounted, the guano project is seen to offer a net present value of about $3.5 million:

Separating Investment and Financing Decisions

Notice that following our earlier Rule 4, we took no notice of how the guano project is financed. We did not deduct any debt proceeds from the initial investment, and we did not deduct interest and principal payments from the cash inflows. Common practice is to forecast cash flows as if the project is all-equity financed and to estimate separately any additional value resulting from the financing decision.

Investments in Working Capital

Now here is an important point. You can see from line 2 of Table 6.2 that working capital increases in the early and middle years of the project. Working capital summarizes the net investment in short-term assets associated with a firm, business, or project. Its most important components are inventory, accounts receivable, and accounts payable. The guano project’s requirements for working capital in year 2 might be as follows:

Why does working capital increase? There are several possibilities:

1.  Sales recorded on the income statement overstate actual cash receipts from guano shipments because sales are increasing and customers are slow to pay their bills. Therefore, accounts receivable increase.

2.  It takes several months for processed guano to age properly. Thus, as projected sales increase, larger inventories have to be held in the aging sheds.

3.  An offsetting effect occurs if payments for materials and services used in guano production are delayed. In this case accounts payable will increase.

The additional investment in working capital from year 2 to 3 might be

A more detailed cash-flow forecast for year 3 would look like Table 6.3.

There is an alternative to worrying about changes in working capital. You can estimate cash flow directly by counting the dollars coming in from customers and deducting the dollars going out to suppliers. You would also deduct all cash spent on production, including cash spent for goods held in inventory. In other words,

   TABLE 6.3 Details of cash-flow forecast for IM&C’s guano project in year 3 ($ thousands).

1.  If you replace each year’s sales with that year’s cash payments received from customers, you don’t have to worry about accounts receivable.

2.  If you replace cost of goods sold with cash payments for labor, materials, and other costs of production, you don’t have to keep track of inventory or accounts payable.

However, you would still have to construct a projected income statement to estimate taxes.

A Further Note on Depreciation

Depreciation is a noncash expense; it is important only because it reduces taxable income. It provides an annual tax shield equal to the product of depreciation and the marginal tax rate:

The present value of the tax shields ($554,000 for six years) is $1,842,000 at a 20% discount rate.

Now if IM&C could just get those tax shields sooner, they would be worth more, right? Fortunately tax law allows corporations to do just that: It allows accelerated depreciation.

BEYOND THE PAGE

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MACRS classes

brealey.mhhe.com/c06

The current rules for tax depreciation in the United States were set by the Tax Reform Act of 1986, which established a Modified Accelerated Cost Recovery System (MACRS). Table 6.4 summarizes the tax depreciation schedules. Note that there are six schedules, one for each recovery period class. Most industrial equipment falls into the five- and seven-year classes. To keep things simple, we assume that all the guano project’s investment goes into five-year assets. Thus, IM&C can write off 20% of its depreciable investment in year 1, as soon as the assets are placed in service, then 32% of depreciable investment in year 2, and so on. Here are the tax shields for the guano project:

   TABLE 6.4 Tax depreciation allowed under the modified accelerated cost recovery system (MACRS) (figures in percent of depreciable investment).

Notes:

1. Tax depreciation is lower in the first and last years because assets are assumed to be in service for only six months.

2. Real property is depreciated straight-line over 27.5 years for residential property and 39 years for nonresidential property.

The present value of these tax shields is $2,174,000, about $331,000 higher than under the straight-line method.

Table 6.5 recalculates the guano project’s impact on IM&C’s future tax bills, and Table 6.6 shows revised after-tax cash flows and present value. This time we have incorporated realistic assumptions about taxes as well as inflation. We arrive at a higher NPV than in Table 6.2, because that table ignored the additional present value of accelerated depreciation.

   TABLE 6.5 Tax payments on IM&C’s guano project ($ thousands).

a From Table 6.1.

b Salvage value is zero, for tax purposes, after all tax depreciation has been taken. Thus, IM&C will have to pay tax on the full salvage value of $1,949.

c A negative tax payment means a cash inflow, assuming IM&C can use the tax loss on its guano project to shield income from other projects.

There is one possible additional problem lurking in the woodwork behind Table 6.5: In the United States there is an alternative minimum tax, which can limit or defer the tax shields of accelerated depreciation or other tax preference items. Because the alternative minimum tax can be a motive for leasing, we discuss it in Chapter 25, rather than here. But make a mental note not to sign off on a capital budgeting analysis without checking whether your company is subject to the alternative minimum tax.

   TABLE 6.6 IM&C’s guano project—revised cash-flow analysis ($ thousands).

a From Table 6.1.

b From Table 6.5.

A Final Comment on Taxes

All large U.S. corporations keep two separate sets of books, one for stockholders and one for the Internal Revenue Service. It is common to use straight-line depreciation on the stockholder books and accelerated depreciation on the tax books. The IRS doesn’t object to this, and it makes the firm’s reported earnings higher than if accelerated depreciation were used everywhere. There are many other differences between tax books and shareholder books.⁷

The financial analyst must be careful to remember which set of books he or she is looking at. In capital budgeting only the tax books are relevant, but to an outside analyst only the shareholder books are available.

Project Analysis

Let us review. Several pages ago, you embarked on an analysis of IM&C’s guano project. You started with a simplified statement of assets and income for the project that you used to develop a series of cash-flow forecasts. Then you remembered accelerated depreciation and had to recalculate cash flows and NPV.

You were lucky to get away with just two NPV calculations. In real situations, it often takes several tries to purge all inconsistencies and mistakes. Then you may want to analyze some alternatives. For example, should you go for a larger or smaller project? Would it be better to market the fertilizer through wholesalers or directly to the consumer? Should you build 90,000-square-foot aging sheds for the guano in northern South Dakota rather than the planned 100,000-square-foot sheds in southern North Dakota? In each case your choice should be the one offering the highest NPV. Sometimes the alternatives are not immediately obvious. For example, perhaps the plan calls for two costly high-speed packing lines. But, if demand for guano is seasonal, it may pay to install just one high-speed line to cope with the base demand and two slower but cheaper lines simply to cope with the summer rush. You won’t know the answer until you have compared NPVs.

You will also need to ask some “what if” questions. How would NPV be affected if inflation rages out of control? What if technical problems delay start-up? What if gardeners prefer chemical fertilizers to your natural product? Managers employ a variety of techniques to develop a better understanding of how such unpleasant surprises could damage NPV. For example, they might undertake a sensitivity analysis, in which they look at how far the project could be knocked off course by bad news about one of the variables. Or they might construct different scenarios and estimate the effect of each on NPV. Another technique, known as break-even analysis, is to explore how far sales could fall short of forecast before the project went into the red.

In Chapter 10 we practice using each of these “what if” techniques. You will find that project analysis is much more than one or two NPV calculations.⁸

Calculating NPV in Other Countries and Currencies

Our guano project was undertaken in the United States by a U.S. company. But the principles of capital investment are the same worldwide. For example, suppose that you are the financial manager of the German company, K.G.R. Ökologische Naturdüngemittel GmbH (KGR), that is faced with a similar opportunity to make a €10 million investment in Germany. What changes?

1.  KGR must also produce a set of cash-flow forecasts, but in this case the project cash flows are stated in euros, the eurozone currency.

2.  In developing these forecasts, the company needs to recognize that prices and costs will be influenced by the German inflation rate.

3.  Profits from KGR’s project are liable to the German rate of corporate tax.

4.  KGR must use the German system of depreciation allowances. In common with many other countries, Germany allows firms to choose between two methods of depreciation—the straight-line system and the declining-balance system. KGR opts for the declining-balance method and writes off 30% of the depreciated value of the equipment each year (the maximum allowed under current German tax rules). Thus, in the first year KGR writes off .30 × 10 = €3 million and the written-down value of the equipment falls to 10 – 3 = €7 million. In year 2, KGR writes off .30 × 7 = €2.1 million and the written-down value is further reduced to 7 – 2.1 = €4.9 million. In year 4 KGR observes that depreciation would be higher if it could switch to straight-line depreciation and write off the balance of €3.43 million over the remaining three years of the equipment’s life. Fortunately, German tax law allows it to do this. Therefore, KGR’s depreciation allowance each year is calculated as follows:

Notice that KGR’s depreciation deduction declines for the first few years and then flattens out. That is also the case with the U.S. MACRS system of depreciation. In fact, MACRS is just another example of the declining-balance method with a later switch to straight-line.⁹

 6-3   Using the NPV Rule to Choose among Projects

Almost all real-world investment decisions entail either-or choices. Such choices are said to be mutually exclusive. We came across an example of mutually exclusive investments in Chapter 2. There we looked at whether it was better to build an office block for immediate sale or to rent it out and sell it at the end of two years. To decide between these alternatives, we calculated the NPV of each and chose the one with the higher NPV.

That is the correct procedure as long as the choice between the two projects does not affect any future decisions that you might wish to make. But sometimes the choices that you make today will have an impact on future opportunities. When that is so, choosing between competing projects is trickier. Here are four important, but often challenging, problems:

• The investment timing problem. Should you invest now or wait and think about it again next year? (Here, today’s investment is competing with possible future investments.)

• The choice between long- and short-lived equipment. Should the company save money today by installing cheaper machinery that will not last as long? (Here, today’s decision would accelerate a later investment in machine replacement.)

• The replacement problem. When should existing machinery be replaced? (Using it another year could delay investment in more modern equipment.)

• The cost of excess capacity. What is the cost of using equipment that is temporarily not needed? (Increasing use of the equipment may bring forward the date at which additional capacity is required.)

We will look at each of these problems in turn.

Problem 1: The Investment Timing Decision

The fact that a project has a positive NPV does not mean that it is best undertaken now. It might be even more valuable if undertaken in the future. The question of optimal timing is not difficult when the cash flows are certain. You must first examine alternative start dates (t) for the investment and calculate the net future value at each of these dates. Then, to find which of the alternatives would add most to the firm’s current value, you must discount these net future values back to the present:

For example, suppose you are CEO of a Russian company that owns a large tract of inaccessible timber in Arkhangelsk Oblast. To harvest it, you need to invest a substantial amount in access roads and other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices may rise as you wait, and the trees will keep growing, although at a gradually decreasing rate.

Let us suppose that the net present value of the harvest at different future dates is as follows:

As you can see, the longer you defer cutting the timber, the more money you will make. However, your concern is with the date that maximizes the net present value of your investment, that is, its contribution to the value of your firm today. You therefore need to discount the net future value of the harvest back to the present. Suppose the appropriate discount rate is 10%. Then, if you harvest the timber in year 1, it has a net present value of 585,000 roubles:

The net present value for other harvest dates is as follows:

The optimal point to harvest the timber is year 4 because this is the point that maximizes NPV.

Notice that before year 4, the net future value of the timber increases by more than 10% a year: The gain in value is greater than the cost of the capital tied up in the project. After year 4, the gain in value is still positive but less than the cost of capital. So delaying the harvest further just reduces shareholder wealth.¹⁰

The investment timing problem is much more complicated when you are unsure about future cash flows. We return to the problem of investment timing under uncertainty in Chapters 10 and 22.

Problem 2: The Choice between Long- and Short-Lived Equipment

Suppose the firm is forced to choose between two machines, A and B. The two machines are designed differently but have identical capacity and do exactly the same job. Machine A costs $15,000 and will last three years. It costs $4,000 per year to run. Machine B is an “economy” model, costing only $10,000, but it will last only two years and costs $6,000 per year to run.

Because the two machines produce exactly the same product, the only way to choose between them is on the basis of cost. The present value of each machine’s cost is as follows:

Should we take machine B, the one with the lower present value of costs? Not necessarily. All we have shown is that machine B offers two years of service for a lower total cost than three years of service from machine A. But is the annual cost of using B lower than that of A?

Suppose the financial manager agrees to buy machine A and pay for its operating costs out of her budget. She then charges the plant manager an annual amount for use of the machine. There will be three equal payments starting in year 1. The financial manager has to make sure that the present value of these payments equals the present value of the costs of each machine.

When the discount rate is 6%, the payment stream with such a present value turns out to be $10,610 a year. In other words, the cost of buying and operating machine A over its three-year life is equivalent to an annual charge of $10,610 a year for three years.

We calculated the equivalent annual cost by finding the three-year annuity with the same present value as A’s lifetime costs.

At a 6% cost of capital, the annuity factor is 2.673 for three years, so

A similar calculation for machine B gives an equivalent annual cost of $11,450:

Machine A is better, because its equivalent annual cost is less ($10,610 versus $11,450 for machine B).

Equivalent Annual Cash Flow, Inflation, and Technological Change When we calculated the equivalent annual costs of machines A and B, we implicitly assumed that inflation is zero. But, in practice, the cost of buying and operating the machines is likely to rise with inflation. If so, the nominal costs of operating the machines will rise, while the real costs will be constant. Therefore, when you compare the equivalent annual costs of two machines, we strongly recommend doing the calculations in real terms. Do not calculate equivalent annual cash flows as level nominal annuities. This procedure can give incorrect rankings of true equivalent annual flows at high inflation rates. See Challenge Problem 33 at the end of this chapter for an example.¹¹

There will also be circumstances in which even the real cash flows of buying and operating the two machines are not expected to be constant. For example, suppose that, thanks to technological improvements, new machines cost 20% less each year in real terms to buy and operate. In this case future owners of brand-new, lower-cost machines will be able to cut their (real) rental cost by 20%, and owners of old machines will be forced to match this reduction. Thus, we now need to ask: If the real level of rents declines by 20% a year, how much will it cost to rent each machine?

If the real rent for year 1 is rent1, then the real rent for year 2 is rent2 = 0.8 × rent1. Rent3 is 0.8 × rent2, or 0.64 × rent1. The owner of each machine must set the real rents sufficiently high to recover the present value of the costs. In the case of machine A:

For machine B:

The merits of the two machines are now reversed. Once we recognize that technology is expected to reduce the real costs of new machines, then it pays to buy the shorter-lived machine B rather than become locked into an aging technology with machine A in year 3.

You can imagine other complications. Perhaps machine C will arrive in year 1 with an even lower equivalent annual cost. You would then need to consider scrapping or selling machine B at year 1 (more on this decision below). The financial manager could not choose between machines A and B in year 0 without taking a detailed look at what each machine could be replaced with.

Comparing equivalent annual cash flows should never be a mechanical exercise; always think about the assumptions that are implicit in the comparison. Finally, remember why equivalent annual cash flows are necessary in the first place. It is because A and B will be replaced at different future dates. The choice between them therefore affects future investment decisions. If subsequent decisions are not affected by the initial choice (for example, because neither machine will be replaced), then we do not need to take future decisions into account.¹²

Equivalent Annual Cash Flow and Taxes We have not mentioned taxes. But you surely realized that machine A and B’s lifetime costs should be calculated after-tax, recognizing that operating costs are tax-deductible and that capital investment generates depreciation tax shields.

Problem 3: When to Replace an Old Machine

Our earlier comparison of machines A and B took the life of each machine as fixed. In practice, the point at which equipment is replaced reflects economics, not physical collapse. We must decide when to replace. The machine will rarely decide for us.

Here is a common problem. You are operating an elderly machine that is expected to produce a net cash inflow of $4,000 in the coming year and $4,000 next year. After that it will give up the ghost. You can replace it now with a new machine, which costs $15,000 but is much more efficient and will provide a cash inflow of $8,000 a year for three years. You want to know whether you should replace your equipment now or wait a year.

We can calculate the NPV of the new machine and also its equivalent annual cash flow, that is, the three-year annuity that has the same net present value:

In other words, the cash flows of the new machine are equivalent to an annuity of $2,387 per year. So we can equally well ask at what point we would want to replace our old machine with a new one producing $2,387 a year. When the question is put this way, the answer is obvious. As long as your old machine can generate a cash flow of $4,000 a year, who wants to put in its place a new one that generates only $2,387 a year?

It is a simple matter to incorporate salvage values into this calculation. Suppose that the current salvage value is $8,000 and next year’s value is $7,000. Let us see where you come out next year if you wait and then sell. On one hand, you gain $7,000, but you lose today’s salvage value plus a year’s return on that money. That is 8,000 × 1.06 = $8,480. Your net loss is 8,480 – 7,000 = $1,480, which only partly offsets the operating gain. You should not replace yet.

Remember that the logic of such comparisons requires that the new machine be the best of the available alternatives and that it in turn be replaced at the optimal point.

Problem 4: Cost of Excess Capacity

Any firm with a centralized information system (computer servers, storage, software, and telecommunication links) encounters many proposals for using it. Recently installed systems tend to have excess capacity, and since the immediate marginal costs of using them seem to be negligible, management often encourages new uses. Sooner or later, however, the load on a system increases to the point at which management must either terminate the uses it originally encouraged or invest in another system several years earlier than it had planned. Such problems can be avoided if a proper charge is made for the use of spare capacity.

Suppose we have a new investment project that requires heavy use of an existing information system. The effect of adopting the project is to bring the purchase date of a new, more capable system forward from year 4 to year 3. This new system has a life of five years, and at a discount rate of 6%, the present value of the cost of buying and operating it is $500,000.

We begin by converting the $500,000 present value of the cost of the new system to an equivalent annual cost of $118,700 for each of five years.¹³ Of course, when the new system in turn wears out, we will replace it with another. So we face the prospect of future information-system expenses of $118,700 a year. If we undertake the new project, the series of expenses begins in year 4; if we do not undertake it, the series begins in year 5. The new project, therefore, results in an additional cost of $118,700 in year 4. This has a present value of 118,700/(1.06)4, or about $94,000. This cost is properly charged against the new project.

When we recognize it, the NPV of the project may prove to be negative. If so, we still need to check whether it is worthwhile undertaking the project now and abandoning it later, when the excess capacity of the present system disappears.

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SUMMARY

By now present value calculations should be a matter of routine. However, forecasting project cash flows will never be routine. Here is a checklist that will help you to avoid mistakes:

1.  Discount cash flows, not profits.

a.  Remember that depreciation is not a cash flow (though it may affect tax payments).

b.  Concentrate on cash flows after taxes. Stay alert for differences between tax depreciation and depreciation used in reports to shareholders.

c.  Exclude debt interest or the cost of repaying a loan from the project cash flows. This enables you to separate the investment from the financing decision.

d.  Remember the investment in working capital. As sales increase, the firm may need to make additional investments in working capital, and as the project comes to an end, it will recover those investments.

e.  Beware of allocated overhead charges for heat, light, and so on. These may not reflect the incremental costs of the project.

2.  Estimate the project’s incremental cash flows—that is, the difference between the cash flows with the project and those without the project.

a.  Include all indirect effects of the project, such as its impact on the sales of the firm’s other products.

b.  Forget sunk costs.

c.  Include opportunity costs, such as the value of land that you would otherwise sell.

3.  Treat inflation consistently.

a.  If cash flows are forecasted in nominal terms, use a nominal discount rate.

b.  Discount real cash flows at a real rate.

4.  Separate investment and financing decisions by forecasting cash flows as if the project is all-equity financed

These principles of valuing capital investments are the same worldwide, but inputs and assumptions vary by country and currency. For example, cash flows from a project in Germany would be in euros, not dollars, and would be forecasted after German taxes.

When we assessed the guano project, we transformed the series of future cash flows into a single measure of their present value. Sometimes it is useful to reverse this calculation and to convert the present value into a stream of annual cash flows. For example, when choosing between two machines with unequal lives, you need to compare equivalent annual cash flows. Remember, though, to calculate equivalent annual cash flows in real terms and adjust for technological change if necessary.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Cash flows Which of the following should be treated as incremental cash flows when deciding whether to invest in a new manufacturing plant? The site is already owned by the company, but existing buildings would need to be demolished.

a.  The market value of the site and existing buildings

b.  Demolition costs and site clearance

c.  The cost of a new access road put in last year

d.  Lost earnings on other products due to executive time spent on the new facility

e.  A proportion of the cost of leasing the president’s jet airplane

f.  Future depreciation of the new plant

g.  The reduction in the corporation’s tax bill resulting from tax depreciation of the new plant

h.  The initial investment in inventories of raw materials

i.  Money already spent on engineering design of the new plant

2.  Real and nominal flows Mr. Art Deco will be paid $100,000 one year hence. This is a nominal flow, which he discounts at an 8% nominal discount rate:

The inflation rate is 4%.

Calculate the PV of Mr. Deco’s payment using the equivalent real cash flow and real discount rate. (You should get exactly the same answer as he did.)

3.  Cash flows True or false?

a.  A project’s depreciation tax shields depend on the actual future rate of inflation.

b.  Project cash flows should take account of interest paid on any borrowing undertaken to finance the project.

c.  In the U.S., income reported to the tax authorities must equal income reported to shareholders.

d.  Accelerated depreciation reduces near-term project cash flows and therefore reduces project NPV.

4.  Depreciation How does the PV of depreciation tax shields vary across the recovery-period classes shown in Table 6.4? Give a general answer; then check it by calculating the PVs of depreciation tax shields in the five-year and seven-year classes. The tax rate is 35% and the discount rate is 10%.

5.  Working capital The following table tracks the main components of working capital over the life of a four-year project.

Calculate net working capital and the cash inflows and outflows due to investment in working capital.

6.  Equivalent annual costs When appraising mutually exclusive investments in plant and equipment, financial managers calculate the investments’ equivalent annual costs and rank the investments on this basis. Why is this necessary? Why not just compare the investments’ NPVs? Explain briefly.

7.  Equivalent annual costs Air conditioning for a college dormitory will cost $1.5 million to install and $200,000 per year to operate. The system should last 25 years. The real cost of capital is 5%, and the college pays no taxes. What is the equivalent annual cost?

8.  Equivalent annual cash flows Machines A and B are mutually exclusive and are expected to produce the following real cash flows:

The real opportunity cost of capital is 10%.

a.  Calculate the NPV of each machine.

b.  Calculate the equivalent annual cash flow from each machine.

c.  Which machine should you buy?

9.  Replacement decisions Machine C was purchased five years ago for $200,000 and produces an annual real cash flow of $80,000. It has no salvage value but is expected to last another five years. The company can replace machine C with machine B (see Problem 8) either now or at the end of five years. Which should it do?

INTERMEDIATE

10.  Real and nominal flows Restate the net cash flows in Table 6.6 in real terms. Discount the restated cash flows at a real discount rate. Assume a 20% nominal rate and 10% expected inflation. NPV should be unchanged at +3,802, or $3,802,000.

11.  Real and nominal flows CSC is evaluating a new project to produce encapsulators. The initial investment in plant and equipment is €500,000. Sales of encapsulators in year 1 are forecasted at €200,000 and costs at €100,000. Both are expected to increase by 10% a year in line with inflation. Profits are taxed at 35%. Working capital in each year consists of inventories of raw materials and is forecasted at 20% of sales in the following year.

The project will last five years and the equipment at the end of this period will have no further value. For tax purposes the equipment can be depreciated straight-line over these five years. If the nominal discount rate is 15%, show that the net present value of the project is the same whether calculated using real cash flows or nominal flows.

12.  Opportunity costs In 1898 Simon North announced plans to construct a funeral home on land he owned and rented out as a storage area for railway carts. (A local newspaper commended Mr. North for not putting the cart before the hearse.) Rental income from the site barely covered real estate taxes, but the site was valued at $45,000. However, Mr. North had refused several offers for the land and planned to continue renting it out if for some reason the funeral home was not built. Therefore he did not include the value of the land as an outlay in his NPV analysis of the funeral home. Was this the correct procedure? Explain.

13.  Working capital Each of the following statements is true. Explain why they are consistent.

a.  When a company introduces a new product, or expands production of an existing product, investment in net working capital is usually an important cash outflow.

b.  Forecasting changes in net working capital is not necessary if the timing of all cash inflows and outflows is carefully specified.

14.  Depreciation Ms. T. Potts, the treasurer of Ideal China, has a problem. The company has just ordered a new kiln for $400,000. Of this sum, $50,000 is described by the supplier as an installation cost. Ms. Potts does not know whether the Internal Revenue Service (IRS) will permit the company to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $50,000 using the five-year MACRS tax depreciation schedule. How will the IRS’s decision affect the after-tax cost of the kiln? The tax rate is 35% and the opportunity cost of capital is 5%.

15.  Project NPV After spending $3 million on research, Better Mousetraps has developed a new trap. The project requires an initial investment in plant and equipment of $6 million. This investment will be depreciated straight-line over five years to a value of zero, but, when the project comes to an end in five years, the equipment can in fact be sold for $500,000. The firm believes that working capital at each date must be maintained at 10% of next year’s forecasted sales. Production costs are estimated at $1.50 per trap and the traps will be sold for $4 each. (There are no marketing expenses.) Sales forecasts are given in the following table. The firm pays tax at 35% and the required return on the project is 12%. What is the NPV?

16.  Project NPV and IRR A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,000 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Company B pays corporate taxes at a rate of 35% and can depreciate the investment for tax purposes using the five-year MACRS tax depreciation schedule. Suppose the opportunity cost of capital is 8%. Ignore inflation.

a.  Calculate project NPV for each company.

b.  What is the IRR of the after-tax cash flows for each company? What does comparison of the IRRs suggest is the effective corporate tax rate?

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

17.  Project analysis Go to the Excel spreadsheet versions of Tables 6.1, 6.5, and 6.6 at www.mcgraw-hill.co.uk/textbooks/brealey and answer the following questions.

a.  How does the guano project’s NPV change if IM&C is forced to use the seven-year MACRS tax depreciation schedule?

b.  New engineering estimates raise the possibility that capital investment will be more than $10 million, perhaps as much as $15 million. On the other hand, you believe that the 20% cost of capital is unrealistically high and that the true cost of capital is about 11%. Is the project still attractive under these alternative assumptions?

c.  Continue with the assumed $15 million capital investment and the 11% cost of capital. What if sales, cost of goods sold, and net working capital are each 10% higher in every year? Recalculate NPV. (Note: Enter the revised sales, cost, and working-capital forecasts in the spreadsheet for Table 6.1.)

18.  Project NPV A widget manufacturer currently produces 200,000 units a year. It buys widget lids from an outside supplier at a price of $2 a lid. The plant manager believes that it would be cheaper to make these lids rather than buy them. Direct production costs are estimated to be only $1.50 a lid. The necessary machinery would cost $150,000 and would last 10 years. This investment could be written off for tax purposes using the seven-year tax depreciation schedule. The plant manager estimates that the operation would require additional working capital of $30,000 but argues that this sum can be ignored since it is recoverable at the end of the 10 years. If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, would you support the plant manager’s proposal? State clearly any additional assumptions that you need to make.

19.  Cash flows Reliable Electric is considering a proposal to manufacture a new type of industrial electric motor that would replace most of its existing product line. A research breakthrough has given Reliable a two-year lead on its competitors. The project proposal is summarized in Table 6.7 below.

a.  Read the notes to the table carefully. Which entries make sense? Which do not? Why or why not?

b.  What additional information would you need to construct a version of Table 6.7 that makes sense?

c.  Construct such a table and recalculate NPV. Make additional assumptions as necessary.

20.  Project NPV Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $35,000. The object is to save on horse transporter rentals.

   TABLE 6.7 Cash flows and present value of Reliable Electric’s proposed investment ($ thousands). See Problem 19.

Notes:

1.  Capital expenditure: $8 million for new machinery and $2.4 million for a warehouse extension. The full cost of the extension has been charged to this project, although only about half of the space is currently needed. Since the new machinery will be housed in an existing factory building, no charge has been made for land and building.

2.  Research and development: $1.82 million spent in 2012. This figure was corrected for 10% inflation from the time of expenditure to date. Thus 1.82 × 1.1 = $2 million.

3.  Working capital: Initial investment in inventories.

4.  Revenue: These figures assume sales of 2,000 motors in 2014, 4,000 in 2015, and 10,000 per year from 2016 through 2023. The initial unit price of $4,000 is forecasted to remain constant in real terms.

5.  Operating costs: These include all direct and indirect costs. Indirect costs (heat, light, power, fringe benefits, etc.) are assumed to be 200% of direct labor costs. Operating costs per unit are forecasted to remain constant in real terms at $2,000.

6.  Overhead: Marketing and administrative costs, assumed equal to 10% of revenue.

7.  Depreciation: Straight-line for 10 years.

8.  Interest: Charged on capital expenditure and working capital at Reliable’s current borrowing rate of 15%.

9.  Income: Revenue less the sum of research and development, operating costs, overhead, depreciation, and interest.

10.  Tax: 35% of income. However, income is negative in 2013. This loss is carried forward and deducted from taxable income in 2011.

11.  Net cash flow: Assumed equal to income less tax.

12.  Net present value: NPV of net cash flow at a 15% discount rate.

Marsha had been renting a transporter every other week for $200 per day plus $1.00 per mile. Most of the trips are 80 or 100 miles in total. Marsha usually gives the driver a $40 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.45 per mile. Insurance costs for Marsha’s transporter are $1,200 per year.

The transporter will probably be worth $15,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Is the transporter a positive-NPV investment? Assume a nominal discount rate of 9% and a 3% forecasted inflation rate. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored.

21.  Project NPV United Pigpen is considering a proposal to manufacture high-protein hog feed. The project would make use of an existing warehouse, which is currently rented out to a neighboring firm. The next year’s rental charge on the warehouse is $100,000, and thereafter the rent is expected to grow in line with inflation at 4% a year. In addition to using the warehouse, the proposal envisages an investment in plant and equipment of $1.2 million. This could be depreciated for tax purposes straight-line over 10 years. However, Pigpen expects to terminate the project at the end of eight years and to resell the plant and equipment in year 8 for $400,000. Finally, the project requires an initial investment in working capital of $350,000. Thereafter, working capital is forecasted to be 10% of sales in each of years 1 through 7.

Year 1 sales of hog feed are expected to be $4.2 million, and thereafter sales are forecasted to grow by 5% a year, slightly faster than the inflation rate. Manufacturing costs are expected to be 90% of sales, and profits are subject to tax at 35%. The cost of capital is 12%. What is the NPV of Pigpen’s project?

22.  Project NPV Hindustan Motors has been producing its Ambassador car in India since 1948. As the company’s website explains, the Ambassador’s “dependability, spaciousness, and comfort factor have made it the most preferred car for generations of Indians.” Hindustan is now considering producing the car in China. This will involve an initial investment of RMB 4 billion.¹⁴ The plant will start production after one year. It is expected to last for five years and have a salvage value at the end of this period of RMB 500 million in real terms. The plant will produce 100,000 cars a year. The firm anticipates that in the first year it will be able to sell each car for RMB 65,000, and thereafter the price is expected to increase by 4% a year.

Raw materials for each car are forecasted to cost RMB 18,000 in the first year and these costs are predicted to increase by 3% annually. Total labor costs for the plant are expected to be RMB 1.1 billion in the first year and thereafter will increase by 7% a year. The land on which the plant is built can be rented for five years at a fixed cost of RMB 300 million a year payable at the beginning of each year. Hindustan’s discount rate for this type of project is 12% (nominal). The expected rate of inflation is 5%. The plant can be depreciated straight-line over the five-year period and profits will be taxed at 25%. Assume all cash flows occur at the end of each year except where otherwise stated. What is the NPV of the project plant?

23.  Taxes In the International Mulch and Compost example (Section 6-2), we assumed that losses on the project could be used to offset taxable profits elswhere in the corporation. Suppose that the losses had to be carried forward and offset against future taxable profits from the project. How would the project NPV change? What is the value of the company’s ability to use the tax deductions immediately?

24.  Equivalent annual cash flows As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $50,000. Its operating costs are $20,000 a year, but in five years the machine will require a $20,000 overhaul. Thereafter operating costs will be $30,000 until the machine is finally sold in year 10 for $5,000.

The older machine could be sold today for $25,000. If it is kept, it will need an immediate $20,000 overhaul. Thereafter operating costs will be $30,000 a year until the machine is finally sold in year 5 for $5,000.

Both machines are fully depreciated for tax purposes. The company pays tax at 35%. Cash flows have been forecasted in real terms. The real cost of capital is 12%. Which machine should United Automation sell? Explain the assumptions underlying your answer.

25.  Equivalent annual costs Low-energy lightbulbs typically cost $3.60, have a life of nine years, and use about $2.00 of electricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.60. On the other hand, they last only about a year and use about $7.00 of energy.¹⁵ If the real discount rate is 4%, which product is cheaper to use?

26.  Replacement decisions Hayden Inc. has a number of copiers that were bought four years ago for $20,000. Currently maintenance costs $2,000 a year, but the maintenance agreement expires at the end of two years and thereafter the annual maintenance charge will rise to $8,000. The machines have a current resale value of $8,000, but at the end of year 2 their value will have fallen to $3,500. By the end of year 6 the machines will be valueless and would be scrapped.

Hayden is considering replacing the copiers with new machines that would do essentially the same job. These machines cost $25,000, and the company can take out an eight-year maintenance contract for $1,000 a year. The machines will have no value by the end of the eight years and will be scrapped.

Both machines are depreciated by using seven-year MACRS, and the tax rate is 35%. Assume for simplicity that the inflation rate is zero. The real cost of capital is 7%. When should Hayden replace its copiers?

27.  Equivalent annual costs In the early 1990s, the California Air Resources Board (CARB) started planning its “Phase 2” requirements for reformulated gasoline (RFG). RFG is gasoline blended to tight specifications designed to reduce pollution from motor vehicles. CARB consulted with refiners, environmentalists, and other interested parties to design these specifications. As the outline for the Phase 2 requirements emerged, refiners realized that substantial capital investments would be required to upgrade California refineries.

Assume a refiner is contemplating an investment of $400 million to upgrade its Californian plant. The investment lasts for 25 years and does not change raw-material and operating costs. The real (inflation-adjusted) cost of capital is 7%. How much extra revenue would be needed each year to recover that cost?

28.  Equivalent annual costs Look at the last question where you calculated the equivalent annual cost of producing reformulated gasoline in California. Capital investment was $400 million. Suppose this amount can be depreciated for tax purposes on the 10-year MACRS schedule from Table 6.4. The marginal tax rate, including California taxes, is 39%, the cost of capital is 7%, and there is no inflation. The refinery improvements have an economic life of 25 years.

a.  Calculate the after-tax equivalent annual cost. (Hint: It’s easiest to use the PV of depreciation tax shields as an offset to the initial investment).

b.  How much extra would retail gasoline customers have to pay to cover this equivalent annual cost? (Note: Extra income from higher retail prices would be taxed.)

29.  Equivalent annual costs The Borstal Company has to choose between two machines that do the same job but have different lives. The two machines have the following costs:

These costs are expressed in real terms.

a.  Suppose you are Borstal’s financial manager. If you had to buy one or the other machine and rent it to the production manager for that machine’s economic life, what annual rental payment would you have to charge? Assume a 6% real discount rate and ignore taxes.

b.  Which machine should Borstal buy?

c.  Usually the rental payments you derived in part (a) are just hypothetical—a way of calculating and interpreting equivalent annual cost. Suppose you actually do buy one of the machines and rent it to the production manager. How much would you actually have to charge in each future year if there is steady 8% per year inflation? (Note: The rental payments calculated in part (a) are real cash flows. You would have to mark up those payments to cover inflation.)

30.  Equivalent annual costs Look again at your calculations for Problem 29 above. Suppose that technological change is expected to reduce costs by 10% per year. There will be new machines in year 1 that cost 10% less to buy and operate than A and B. In year 2 there will be a second crop of new machines incorporating a further 10% reduction, and so on. How does this change the equivalent annual costs of machines A and B?

31.  Equivalent annual costs The president’s executive jet is not fully utilized. You judge that its use by other officers would increase direct operating costs by only $20,000 a year and would save $100,000 a year in airline bills. On the other hand, you believe that with the increased use the company will need to replace the jet at the end of three years rather than four. A new jet costs $1.1 million and (at its current low rate of use) has a life of six years. Assume that the company does not pay taxes. All cash flows are forecasted in real terms. The real opportunity cost of capital is 8%. Should you try to persuade the president to allow other officers to use the plane?

32.  Tax Depreciation In countries such as Sweden and Norway, companies may depreciate capital investments at a constant rate for tax purposes. For example, a company investing 100 kroner could depreciate the investment by 30% to .70 × 100 = 70 kroner in year 1, by a further 30% to .70 × 70 = 49 kroner in year 2, to .70 × 49 = 34.3 kroner in year 3, and so on. What is the PV of depreciation tax shields if the tax rate is 25% and the interest rate 5%? How would the PV change if the company could write down only 20% in each year? Assume that the investment’s economic life is 10 years, and that all remaining undepreciated value is written off in year 10.

CHALLENGE

33.  Effective tax rates One measure of the effective tax rate is the difference between the IRRs of pretax and after-tax cash flows, divided by the pretax IRR. Consider, for example, an investment I generating a perpetual stream of pretax cash flows C. The pretax IRR is C/I, and the after-tax IRR is C(1 – TC)/I, where TC is the statutory tax rate. The effective rate, call it TE, is

In this case the effective rate equals the statutory rate.

a.  Calculate TE for the guano project in Section 6-2.

b.  How does the effective rate depend on the tax depreciation schedule? On the inflation rate?

c.  Consider a project where all of the up-front investment is treated as an expense for tax purposes. For example, R&D and marketing outlays are always expensed in the United States. They create no tax depreciation. What is the effective tax rate for such a project?

34.  Equivalent annual costs We warned that equivalent annual costs should be calculated in real terms. We did not fully explain why. This problem will show you.

Look back to the cash flows for machines A and B (in “Choosing between Long- and Short-Lived Equipment”). The present values of purchase and operating costs are 28.37 (over three years for A) and 21.00 (over two years for B). The real discount rate is 6% and the inflation rate is 5%.

a.  Calculate the three- and two-year level nominal annuities which have present values of 28.37 and 21.00. Explain why these annuities are not realistic estimates of equivalent annual costs. (Hint: In real life machinery rentals increase with inflation.)

b.  Suppose the inflation rate increases to 25%. The real interest rate stays at 6%. Recalculate the level nominal annuities. Note that the ranking of machines A and B appears to change. Why?

35.  Project NPV In December 2005 Mid-American Energy brought online one of the largest wind farms in the world. It cost an estimated $386 million and the 257 turbines have a total capacity of 360.5 megawatts (mW). Wind speeds fluctuate and most wind farms are expected to operate at an average of only 35% of their rated capacity. In this case, at an electricity price of $55 per megawatt-hour (mWh), the project will produce revenues in the first year of $60.8 million (i.e., .35 × 8,760 hours × 360.5 mW × $55 per mWh). A reasonable estimate of maintenance and other costs is about $18.9 million in the first year of operation. Thereafter, revenues and costs should increase with inflation by around 3% a year.

Conventional power stations can be depreciated using 20-year MACRS, and their profits are taxed at 35%. Suppose that the project will last 20 years and the cost of capital is 12%. To encourage renewable energy sources, the government offers several tax breaks for wind farms.

a.  How large a tax break (if any) was needed to make Mid-American’s investment a positive-NPV venture?

b.  Some wind farm operators assume a capacity factor of 30% rather than 35%. How would this lower capacity factor alter project NPV?

36.  Investment Timing You own an idle silver mine in Chile. You can reopen the mine now and extract the remaining silver by investing 200 million pesos and committing to extraction costs with PV = 200 million pesos. The PV of the silver is 500 million pesos. However, technological advances will reduce the PV of extraction costs by 12 million pesos per year, to 188 million pesos in year 1, 176 million pesos in year 2, etc. Prepare a forecast showing how NPV changes if the mine reopening is delayed to year 1, 2, 3, 4 or 5. Assume that the price of silver will appreciate at 4% per year. When should you invest if the cost of capital is 14%? What if the cost of capital is 20%?

MINI-CASE ● ● ● ● ●

New Economy Transport (A)

The New Economy Transport Company (NETCO) was formed in 1959 to carry cargo and passengers between ports in the Pacific Northwest and Alaska. By 2012 its fleet had grown to four vessels, including a small dry-cargo vessel, the Vital Spark.

The Vital Spark is 25 years old and badly in need of an overhaul. Peter Handy, the finance director, has just been presented with a proposal that would require the following expenditures:

Mr. Handy believes that all these outlays could be depreciated for tax purposes in the seven-year MACRS class.

NETCO’s chief engineer, McPhail, estimates the postoverhaul operating costs as follows:

These costs generally increase with inflation, which is forecasted at 2.5% a year.

The Vital Spark is carried on NETCO’s books at a net depreciated value of only $100,000, but could probably be sold “as is,” along with an extensive inventory of spare parts, for $200,000. The book value of the spare parts inventory is $40,000. Sale of the Vital Spark would generate an immediate tax liability on the difference between sale price and book value.

The chief engineer also suggests installation of a brand-new engine and control system, which would cost an extra $600,000.¹⁶ This additional equipment would not substantially improve the Vital Spark’s performance, but would result in the following reduced annual fuel, labor, and maintenance costs:

Overhaul of the Vital Spark would take it out of service for several months. The overhauled vessel would resume commercial service next year. Based on past experience, Mr. Handy believes that it would generate revenues of about $1.4 million next year, increasing with inflation thereafter.

But the Vital Spark cannot continue forever. Even if overhauled, its useful life is probably no more than 10 years, 12 years at the most. Its salvage value when finally taken out of service will be trivial.

NETCO is a conservatively financed firm in a mature business. It normally evaluates capital investments using an 11% cost of capital. This is a nominal, not a real, rate. NETCO’s tax rate is 35%.

QUESTION

1.  Calculate the NPV of the proposed overhaul of the Vital Spark, with and without the new engine and control system. To do the calculation, you will have to prepare a spreadsheet table showing all costs after taxes over the vessel’s remaining economic life. Take special care with your assumptions about depreciation tax shields and inflation.

New Economy Transport (B)

There is no question that the Vital Spark needs an overhaul soon. However, Mr. Handy feels it unwise to proceed without also considering the purchase of a new vessel. Cohn and Doyle, Inc., a Wisconsin shipyard, has approached NETCO with a design incorporating a Kort nozzle, extensively automated navigation and power control systems, and much more comfortable accommodations for the crew. Estimated annual operating costs of the new vessel are:

The crew would require additional training to handle the new vessel’s more complex and sophisticated equipment. Training would probably cost $50,000 next year.

The estimated operating costs for the new vessel assume that it would be operated in the same way as the Vital Spark. However, the new vessel should be able to handle a larger load on some routes, which could generate additional revenues, net of additional out-of-pocket costs, of as much as $100,000 per year. Moreover, a new vessel would have a useful service life of 20 years or more.

Cohn and Doyle offered the new vessel for a fixed price of $3,000,000, payable half immediately and half on delivery next year.

Mr. Handy stepped out on the foredeck of the Vital Spark as she chugged down the Cook Inlet. “A rusty old tub,” he muttered, “but she’s never let us down.” I’ll bet we could keep her going until next year while Cohn and Doyle are building her replacement. We could use up the spare parts to keep her going. We might even be able to sell or scrap her for book value when her replacement arrives.

“But how do I compare the NPV of a new ship with the old Vital Spark? Sure, I could run a 20-year NPV spreadsheet, but I don’t have a clue how the replacement will be used in 2027 or 2032. Maybe I could compare the overall cost of overhauling and operating the Vital Spark to the cost of buying and operating the proposed replacement.”

QUESTIONS

1.  Calculate and compare the equivalent annual costs of (a) overhauling and operating the Vital Spark for 12 more years, and (b) buying and operating the proposed replacement vessel for 20 years. What should Mr. Handy do if the replacement’s annual costs are the same or lower?

2.  Suppose the replacement’s equivalent annual costs are higher than the Vital Spark’s. What additional information should Mr. Handy seek in this case?

___________

¹If you delay paying your bills, your investment in net working capital is reduced. When you finally pay up, it is increased.

²Holdings of cash and marketable securities are also short-term assets and debt due within a year is a short-term liability. These are not relevant to your capital budgeting calculations.

³Accenture, “Refocusing on the After-Sales Market,” 2010.

⁴Sorry.

⁵We have departed from the usual income-statement format by separating depreciation from costs of goods sold.

⁶There are several alternative ways to calculate operating cash flow. For example, you can add depreciation back to the after-tax profit:

Thus, in year 6 of the guano project:

Another alternative is to calculate after-tax profit assuming no depreciation, and then to add back the tax saving provided by the depreciation allowance:

Thus, in year 6 of the guano project:

⁷This separation of tax accounts from shareholder accounts is not found worldwide. In Japan, for example, taxes reported to shareholders must equal taxes paid to the government; ditto for France and many other European countries.

⁸In the meantime you might like to get ahead of the game by viewing the spreadsheets for the guano project and seeing how NPV would change with a shortfall in sales or an unexpected rise in costs.

⁹Take, for example, the 10-year MACRS schedule. It allows the firm to deduct 20% of the written-down value of the asset annually. Since the IRS assumes that the asset is bought midyear, the firm deducts 10% of the investment in year 1 and writes down the value of the asset to 100 – 10 = 90% of its purchase cost. In the second year it deducts 20% of the written-down value, that is, .2 × 90 = 18% of purchase cost. The written-down value is now 90 – 18 = 72% of cost, and therefore in year 3 the MACRS deduction is .2 × 72 = 14.4% cost. By the end of year 6 the investment has been written down to 29.49% of cost, and the company switches to straight-line depreciation for the remaining 4.5 years of the asset’s life.

¹⁰Our timber-cutting example conveys the right idea about investment timing, but it misses an important practical point: The sooner you cut the first crop of trees, the sooner the second crop can start growing. Thus, the value of the second crop depends on when you cut the first. This more complex and realistic problem can be solved in one of two ways:

1.  Find the cutting dates that maximize the present value of a series of harvests, taking into account the different growth rates of young and old trees.

2.  Repeat our calculations, counting the future market value of cut-over land as part of the payoff to the first harvest. The value of cut-over land includes the present value of all subsequent harvests.

The second solution is far simpler if you can figure out what cut-over land will be worth.

¹¹If you actually rent out the machine to the plant manager, or anyone else, be careful to specify that the rental payments be “indexed” to inflation. If inflation runs on at 5% per year and rental payments do not increase proportionally, then the real value of the rental payments must decline and will not cover the full cost of buying and operating the machine.

¹²However, if neither machine will be replaced, then we have to consider the extra revenue generated by machine A in its third year, when it will be operating but B will not.

¹³The present value of $118,700 a year for five years discounted at 6% is $500,000.

¹⁴The Renminbi (RMB) is the Chinese currency.

¹⁵Source: www.energystar.gov

¹⁶This additional outlay would also qualify for tax depreciation in the seven-year MACRS class.

Part 2 Risk

Introduction to Risk and Return

We have managed to go through six chapters without directly addressing the problem of risk, but now the jig is up. We can no longer be satisfied with vague statements like “The opportunity cost of capital depends on the risk of the project.” We need to know how risk is defined, what the links are between risk and the opportunity cost of capital, and how the financial manager can cope with risk in practical situations.

In this chapter we concentrate on the first of these issues and leave the other two to Chapters 8 and 9. We start by summarizing more than 100 years of evidence on rates of return in capital markets. Then we take a first look at investment risks and show how they can be reduced by portfolio diversification. We introduce you to beta, the standard risk measure for individual securities.

The themes of this chapter, then, are portfolio risk, security risk, and diversification. For the most part, we take the view of the individual investor. But at the end of the chapter we turn the problem around and ask whether diversification makes sense as a corporate objective.

 7-1   Over a Century of Capital Market History in One Easy Lesson

Financial analysts are blessed with an enormous quantity of data. There are comprehensive databases of the prices of U.S. stocks, bonds, options, and commodities, as well as huge amounts of data for securities in other countries. We focus on a study by Dimson, Marsh, and Staunton that measures the historical performance of three portfolios of U.S. securities:¹

1.  A portfolio of Treasury bills, that is, U.S. government debt securities maturing in less than one year.²

2.  A portfolio of U.S. government bonds.

3.  A portfolio of U.S. common stocks.

These investments offer different degrees of risk. Treasury bills are about as safe an investment as you can make. There is no risk of default, and their short maturity means that the prices of Treasury bills are relatively stable. In fact, an investor who wishes to lend money for, say, three months can achieve a perfectly certain payoff by purchasing a Treasury bill maturing in three months. However, the investor cannot lock in a real rate of return: There is still some uncertainty about inflation.

   FIGURE 7.1 How an investment of $1 at the start of 1900 would have grown by the end of 2011, assuming reinvestment of all dividend and interest payments.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

   FIGURE 7.2 How an investment of $1 at the start of 1900 would have grown in real terms by the end of 2011, assuming reinvestment of all dividend and interest payments. Compare this plot with Figure 7.1, and note how inflation has eroded the purchasing power of returns to investors.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

By switching to long-term government bonds, the investor acquires an asset whose price fluctuates as interest rates vary. (Bond prices fall when interest rates rise and rise when interest rates fall.) An investor who shifts from bonds to common stocks shares in all the ups and downs of the issuing companies.

Figure 7.1 shows how your money would have grown if you had invested $1 at the start of 1900 and reinvested all dividend or interest income in each of the three portfolios.³ Figure 7.2 is identical except that it depicts the growth in the real value of the portfolio. We focus here on nominal values.

   TABLE 7.1 Average rates of return on U.S. Treasury bills, government bonds, and common stocks, 1900–2011 (figures in % per year).

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns, (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

Investment performance coincides with our intuitive risk ranking. A dollar invested in the safest investment, Treasury bills, would have grown to $74 by the end of 2011, barely enough to keep up with inflation. An investment in long-term Treasury bonds would have produced $245. Common stocks were in a class by themselves. An investor who placed a dollar in the stocks of large U.S. firms would have received $21,978.

We can also calculate the rate of return from these portfolios for each year from 1900 to 2011. This rate of return reflects both cash receipts—dividends or interest—and the capital gains or losses realized during the year. Averages of the 112 annual rates of return for each portfolio are shown in Table 7.1.

Since 1900 Treasury bills have provided the lowest average return—3.9% per year in nominal terms and 1.0% in real terms. In other words, the average rate of inflation over this period was about 3% per year. Common stocks were again the winners. Stocks of major corporations provided an average nominal return of 11.3%. By taking on the risk of common stocks, investors earned a risk premium of 11.3 – 3.9 = 7.3% over the return on Treasury bills.⁴

You may ask why we look back over such a long period to measure average rates of return. The reason is that annual rates of return for common stocks fluctuate so much that averages taken over short periods are meaningless. Our only hope of gaining insights from historical rates of return is to look at a very long period.⁵

Arithmetic Averages and Compound Annual Returns

Notice that the average returns shown in Table 7.1 are arithmetic averages. In other words, we simply added the 112 annual returns and divided by 112. The arithmetic average is higher than the compound annual return over the period. The 112-year compound annual return for common stocks was 9.3%.⁶

The proper uses of arithmetic and compound rates of return from past investments are often misunderstood. Therefore, we call a brief time-out for a clarifying example.

Suppose that the price of Big Oil’s common stock is $100. There is an equal chance that at the end of the year the stock will be worth $90, $110, or $130. Therefore, the return could be –10%, +10%, or +30% (we assume that Big Oil does not pay a dividend). The expected return is ⅓ (–10 + 10 + 30) = +10%.

If we run the process in reverse and discount the expected cash flow by the expected rate of return, we obtain the value of Big Oil’s stock:

The expected return of 10% is therefore the correct rate at which to discount the expected cash flow from Big Oil’s stock. It is also the opportunity cost of capital for investments that have the same degree of risk as Big Oil.

Now suppose that we observe the returns on Big Oil stock over a large number of years. If the odds are unchanged, the return will be –10% in a third of the years, +10% in a further third, and +30% in the remaining years. The arithmetic average of these yearly returns is

Thus the arithmetic average of the returns correctly measures the opportunity cost of capital for investments of similar risk to Big Oil stock.⁷

The average compound annual return⁸ on Big Oil stock would be

which is less than the opportunity cost of capital. Investors would not be willing to invest in a project that offered an 8.8% expected return if they could get an expected return of 10% in the capital markets. The net present value of such a project would be

Moral: If the cost of capital is estimated from historical returns or risk premiums, use arithmetic averages, not compound annual rates of return.⁹

Using Historical Evidence to Evaluate Today’s Cost of Capital

Suppose there is an investment project that you know—don’t ask how—has the same risk as Standard and Poor’s Composite Index. We will say that it has the same degree of risk as the market portfolio, although this is speaking somewhat loosely, because the index does not include all risky securities. What rate should you use to discount this project’s forecasted cash flows?

Clearly you should use the currently expected rate of return on the market portfolio; that is the return investors would forgo by investing in the proposed project. Let us call this market return rm. One way to estimate rm is to assume that the future will be like the past and that today’s investors expect to receive the same “normal” rates of return revealed by the averages shown in Table 7.1. In this case, you would set rm at 11.3%, the average of past market returns.

Unfortunately, this is not the way to do it; rm is not likely to be stable over time. Remember that it is the sum of the risk-free interest rate rf and a premium for risk. We know that rf varies. For example, in 1981 the interest rate on Treasury bills was about 15%. It is difficult to believe that investors in that year were content to hold common stocks offering an expected return of only 11.3%.

If you need to estimate the return that investors expect to receive, a more sensible procedure is to take the interest rate on Treasury bills and add 7.3%, the average risk premium shown in Table 7.1. For example, suppose that the current interest rate on Treasury bills is 2%. Adding on the average risk premium gives

The crucial assumption here is that there is a normal, stable risk premium on the market portfolio, so that the expected future risk premium can be measured by the average past risk premium.

Even with over 100 years of data, we can’t estimate the market risk premium exactly; nor can we be sure that investors today are demanding the same reward for risk that they were 50 or 100 years ago. All this leaves plenty of room for argument about what the risk premium really is.¹⁰

BEYOND THE PAGE

● ● ● ● ●

Market risk premium survey

brealey.mhhe.com/c07

Many financial managers and economists believe that long-run historical returns are the best measure available. Others have a gut instinct that investors don’t need such a large risk premium to persuade them to hold common stocks.¹¹ For example, surveys of chief financial officers commonly suggest that they expect a market risk premium that is several percentage points below the historical average.¹²

If you believe that the expected market risk premium is less than the historical average, you probably also believe that history has been unexpectedly kind to investors in the United States and that their good luck is unlikely to be repeated. Here are two reasons that history may overstate the risk premium that investors demand today.

Reason 1 Since 1900 the United States has been among the world’s most prosperous countries. Other economies have languished or been wracked by war or civil unrest. By focusing on equity returns in the United States, we may obtain a biased view of what investors expected. Perhaps the historical averages miss the possibility that the United States could have turned out to be one of these less-fortunate countries.¹³

Figure 7.3 sheds some light on this issue. It is taken from a comprehensive study by Dimson, Marsh, and Staunton of market returns in 19 countries and shows the average risk premium in each country between 1900 and 2011. There is no evidence here that U.S. investors have been particularly fortunate; the U.S. was just about average in terms of returns.

   FIGURE 7.3 Average market risk premiums (nominal return on stocks minus nominal return on bills), 1900–2011.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

In Figure 7.3 Danish stocks come bottom of the league; the average risk premium in Denmark was only 4.7%. The clear winner was Italy with a premium of 9.9%. Some of these differences between countries may reflect differences in risk. For example, Italian stocks have been particularly variable and investors may have required a higher return to compensate. But remember how difficult it is to make precise estimates of what investors expected. You probably would not be too far out if you concluded that the expected risk premium was the same in each country.¹⁴

Reason 2 Stock prices in the United States have for some years outpaced the growth in company dividends or earnings. For example, between 1950 and 2000 dividend yields in the United States fell from 7.2% to 1.1%. It seems unlikely that investors expected such a sharp decline in yields, in which case some part of the actual return during this period was unexpected.

Some believe that the low dividend yields at the turn of the century reflected optimism that the new economy would lead to a golden age of prosperity and surging profits, but others attribute the low yields to a reduction in the market risk premium. Perhaps the growth in mutual funds has made it easier for individuals to diversify away part of their risk, or perhaps pension funds and other financial institutions have found that they also could reduce their risk by investing part of their funds overseas. If these investors can eliminate more of their risk than in the past, they may be content with a lower return.

To see how a rise in stock prices can stem from a fall in the risk premium, suppose that a stock is expected to pay a dividend next year of $12 (DIV1 = 12). The stock yields 3% and the dividend is expected to grow indefinitely by 7% a year (g = .07). Therefore the total return that investors expect is r = 3 + 7 = 10%. We can find the stock’s value by plugging these numbers into the constant-growth formula that we used in Chapter 4 to value stocks:

Imagine that investors now revise downward their required return to r = 9%. The dividend yield falls to 2% and the value of the stock rises to

Thus a fall from 10% to 9% in the required return leads to a 50% rise in the stock price. If we include this price rise in our measures of past returns, we will be doubly wrong in our estimate of the risk premium. First, we will overestimate the return that investors required in the past. Second, we will fail to recognize that the return investors require in the future is lower than they needed in the past.

Dividend Yields and the Risk Premium

If there has been a downward shift in the return that investors have required, then past returns will provide an overestimate of the risk premium. We can’t wholly get around this difficulty, but we can get another clue to the risk premium by going back to the constant-growth model that we discussed in Chapter 4. If stock prices are expected to keep pace with the growth in dividends, then the expected market return is equal to the dividend yield plus the expected dividend growth—that is, r = DIV1/P0 + g. Dividend yields in the United States have averaged 4.3% since 1900, and the annual growth in dividends has averaged 4.7%. If this dividend growth is representative of what investors expected, then the expected market return over this period was DIV1/P0 + g = 4.3 + 4.7 = 9.0%, or 5.1% above the risk-free interest rate. This figure is 2.2% lower than the realized risk premium reported in Table 7.1.¹⁵

Dividend yields have averaged 4.3% since 1900, but, as you can see from Figure 7.4, they have fluctuated quite sharply. At the end of 1917, stocks were offering a yield of 9.0%; as we write this in early 2012, dividend yields are 2.15%, well below the long-term average. You sometimes hear financial managers suggest that when dividend yields are low, capital is relatively cheap. Is there any truth to this? Should companies be adjusting their cost of capital to reflect these fluctuations in yield?

Notice that there are only two possible reasons for the yield changes in Figure 7.4. One is that in some years investors were unusually optimistic or pessimistic about g, the future growth in dividends. The other is that r, the required return, was unusually high or low. Economists who have studied the behavior of dividend yields have concluded that very little of the variation is related to the subsequent rate of dividend growth. If they are right, the level of yields ought to be telling us something about the return that investors require.

   FIGURE 7.4 Dividend yields in the U.S. 1900–2011.

Source: R. J. Shiller, “Long Term Stock, Bond, Interest Rate and Consumption Data since 1871,” www.econ.yale.edu/-shiller/data.htm. Used with permission.

This in fact appears to be the case. A reduction in the dividend yield seems to herald a reduction in the risk premium that investors can expect over the following few years. So, when yields are relatively low, companies may be justified in shaving their estimate of required returns over the next year or so. However, changes in the dividend yield tell companies next to nothing about the expected risk premium over the next 10 or 20 years. It seems that, when estimating the discount rate for longer term investments, a firm can safely ignore year-to-year fluctuations in the dividend yield.

Out of this debate only one firm conclusion emerges: Do not trust anyone who claims to know what returns investors expect. History contains some clues, but ultimately we have to judge whether investors on average have received what they expected. Many financial economists rely on the evidence of history and therefore work with a risk premium of about 7%. The remainder generally use a somewhat lower figure. Brealey, Myers, and Allen have no official position on the issue, but we believe that a range of 5% to 8% is reasonable for the risk premium in the United States.

 7-2   Measuring Portfolio Risk

You now have a couple of benchmarks. You know the discount rate for safe projects, and you have an estimate of the rate for average-risk projects. But you don’t know yet how to estimate discount rates for assets that do not fit these simple cases. To do that, you have to learn (1) how to measure risk and (2) the relationship between risks borne and risk premiums demanded.

Figure 7.5 shows the 112 annual rates of return for U.S. common stocks. The fluctuations in year-to-year returns are remarkably wide. The highest annual return was 57.6% in 1933—a partial rebound from the stock market crash of 1929–1932. However, there were losses exceeding 25% in six years, the worst being the –43.9% return in 1931.

   FIGURE 7.5 The stock market has been a profitable but extremely variable investment.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

Another way of presenting these data is by a histogram or frequency distribution. This is done in Figure 7.6, where the variability of year-to-year returns shows up in the wide “spread” of outcomes.

   FIGURE 7.6 Histogram of the annual rates of return from the stock market in the United States, 1900–2011, showing the wide spread of returns from investment in common stocks.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns, (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

The standard statistical measures of spread are variance and standard deviation. The variance of the market return is the expected squared deviation from the expected return. In other words,

where is the actual return and rm is the expected return.¹⁶ The standard deviation is simply the square root of the variance:

Standard deviation is often denoted by σ and variance by σ2.

Here is a very simple example showing how variance and standard deviation are calculated. Suppose that you are offered the chance to play the following game. You start by investing $100. Then two coins are flipped. For each head that comes up you get back your starting balance plus 20%, and for each tail that comes up you get back your starting balance less 10%. Clearly there are four equally likely outcomes:

•  Head + head: You gain 40%.

•  Head + tail: You gain 10%.

•  Tail + head: You gain 10%.

•  Tail + tail: You lose 20%.

There is a chance of 1 in 4, or .25, that you will make 40%; a chance of 2 in 4, or .5, that you will make 10%; and a chance of 1 in 4, or .25, that you will lose 20%. The game’s expected return is, therefore, a weighted average of the possible outcomes:

Table 7.2 shows that the variance of the percentage returns is 450. Standard deviation is the square root of 450, or 21. This figure is in the same units as the rate of return, so we can say that the game’s variability is 21%.

   TABLE 7.2 The coin-tossing game: Calculating variance and standard deviation.

One way of defining uncertainty is to say that more things can happen than will happen. The risk of an asset can be completely expressed, as we did for the coin-tossing game, by writing all possible outcomes and the probability of each. In practice this is cumbersome and often impossible. Therefore we use variance or standard deviation to summarize the spread of possible outcomes.¹⁷

These measures are natural indexes of risk.¹⁸ If the outcome of the coin-tossing game had been certain, the standard deviation would have been zero. The actual standard deviation is positive because we don’t know what will happen.

Or think of a second game, the same as the first except that each head means a 35% gain and each tail means a 25% loss. Again, there are four equally likely outcomes:

•  Head + head: You gain 70%.

•  Head + tail: You gain 10%.

•  Tail + head: You gain 10%.

•  Tail + tail: You lose 50%.

For this game the expected return is 10%, the same as that of the first game. But its standard deviation is double that of the first game, 42% versus 21%. By this measure the second game is twice as risky as the first.

Measuring Variability

In principle, you could estimate the variability of any portfolio of stocks or bonds by the procedure just described. You would identify the possible outcomes, assign a probability to each outcome, and grind through the calculations. But where do the probabilities come from? You can’t look them up in the newspaper; newspapers seem to go out of their way to avoid definite statements about prospects for securities. We once saw an article headlined “Bond Prices Possibly Set to Move Sharply Either Way.” Stockbrokers are much the same. Yours may respond to your query about possible market outcomes with a statement like this:

The market currently appears to be undergoing a period of consolidation. For the intermediate term, we would take a constructive view, provided economic recovery continues. The market could be up 20% a year from now, perhaps more if inflation continues low. On the other hand, . . .

The Delphic oracle gave advice, but no probabilities.

Most financial analysts start by observing past variability. Of course, there is no risk in hindsight, but it is reasonable to assume that portfolios with histories of high variability also have the least predictable future performance.

The annual standard deviations and variances observed for our three portfolios over the period 1900–2011 were:¹⁹

As expected, Treasury bills were the least variable security, and common stocks were the most variable. Government bonds hold the middle ground.

You may find it interesting to compare the coin-tossing game and the stock market as alternative investments. The stock market generated an average annual return of 11.3% with a standard deviation of 20.0%. The game offers 10% and 21%, respectively—slightly lower return and about the same variability. Your gambling friends may have come up with a crude representation of the stock market.

Figure 7.7 compares the standard deviation of stock market returns in 19 countries over the same 112-year period. Canada occupies low field with a standard deviation of 17.2%, but most of the other countries cluster together with percentage standard deviations in the low 20s.

   FIGURE 7.7 The risk (standard deviation of annual returns) of markets around the world, 1900–2011.

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002), with updates provided by the authors.

Of course, there is no reason to suppose that the market’s variability should stay the same over more than a century. For example, Germany, Italy, and Japan now have much more stable economies and markets than they did in the years leading up to and including the Second World War.

Figure 7.8 does not suggest a long-term upward or downward trend in the volatility of the U.S. stock market.²⁰ Instead there have been periods of both calm and turbulence. In 2005, an unusually tranquil year, the standard deviation of returns was only 9%, less than half the long-term average. Four years later, in the financial crisis, the standard deviation had tripled at over 30%. By early 2012 it had dropped back to 18%.²¹

   FIGURE 7.8 Annualized standard deviation of the preceding 52 weekly changes in the Dow Jones Industrial Average, 1900–2011.

Market turbulence over shorter daily, weekly, or monthly periods can be amazingly high. On Black Monday, October 19, 1987, the U.S. market fell by 23% on a single day. The market standard deviation for the week surrounding Black Monday was equivalent to 89% per year. Fortunately volatility dropped back to normal levels within a few weeks after the crash.

How Diversification Reduces Risk

We can calculate our measures of variability equally well for individual securities and portfolios of securities. Of course, the level of variability over 100 years is less interesting for specific companies than for the market portfolio—it is a rare company that faces the same business risks today as it did a century ago.

Table 7.3 presents estimated standard deviations for 10 well-known common stocks for a recent two-year period.²² Do these standard deviations look high to you? They should. The market portfolio’s standard deviation was 19.5% during this period. Most of our individual stocks had higher volatility. Ford and Dow Chemical were more than twice as variable as the market portfolio.

   TABLE 7.3 Standard deviations for selected U.S. common stocks, December 2009–December 2011 (figures in percent per year).

Take a look also at Table 7.4, which shows the standard deviations of some well-known stocks from different countries and of the markets in which they trade. Some of these stocks are more variable than others, but you can see that once again the individual stocks for the most part are more variable than the market indexes.

   TABLE 7.4 Standard deviations for selected foreign stocks and market indexes, December 2009–December 2011 (figures in percent per year).

   FIGURE 7.9 Average risk (standard deviation) of portfolios containing different numbers of stocks. The stocks were selected randomly from stocks traded on the New York Exchange from 2006 through 2010. Notice that diversification reduces risk rapidly at first, then more slowly.

Note: The figure shows the average risk of randomly selected portfolios divided equally among N stocks. The group of stocks consists of all those continuously quoted on the NYSE, 2006–2010.

This raises an important question: The market portfolio is made up of individual stocks, so why doesn’t its variability reflect the average variability of its components? The answer is that diversification reduces variability.

Even a little diversification can provide a substantial reduction in variability. Suppose you calculate and compare the standard deviations between 2006 and 2010 of one-stock portfolios, two-stock portfolios, five-stock portfolios, etc. You can see from Figure 7.9 that diversification can cut the variability of returns about in half. Notice also that you can get most of this benefit with relatively few stocks: The improvement is much smaller when the number of securities is increased beyond, say, 20 or 30.²³

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Diversification works because prices of different stocks do not move exactly together. Statisticians make the same point when they say that stock price changes are less than perfectly correlated. Look, for example, at Figure 7.10, which plots the prices of Starbucks and Newmont Mining for the 104 weeks ending December 2011. As we showed in Table 7.3, during this period the standard deviation of returns was about 29% for Newmont and 26% for Starbucks. Although the two stocks enjoyed a fairly bumpy ride, they did not move in exact lockstep. Often a decline in the value of Newmont was offset by a rise in the price of Starbucks.²⁴ So, if you had split your portfolio between the two stocks, you could have reduced the monthly fluctuations in the value of your investment. You can see from the blue line in Figure 7.10 that if your portfolio had been evenly divided between Newmont and Starbucks, there would have been many more months when the return was just middling and far fewer cases of extreme returns. By diversifying between the two stocks, you would have reduced the standard deviation of the returns to under 23% a year.

   FIGURE 7.10 The value of a portfolio evenly divided between Newmont Mining and Starbucks was less volatile than either stock on its own. The assumed initial investment is $100.

The risk that potentially can be eliminated by diversification is called specific risk.²⁵ Specific risk stems from the fact that many of the perils that surround an individual company are peculiar to that company and perhaps its immediate competitors. But there is also some risk that you can’t avoid, regardless of how much you diversify. This risk is generally known as market risk.²⁶ Market risk stems from the fact that there are other economywide perils that threaten all businesses. That is why stocks have a tendency to move together. And that is why investors are exposed to market uncertainties, no matter how many stocks they hold.

In Figure 7.11 we have divided risk into its two parts—specific risk and market risk. If you have only a single stock, specific risk is very important; but once you have a portfolio of 20 or more stocks, diversification has done the bulk of its work. For a reasonably well-diversified portfolio, only market risk matters. Therefore, the predominant source of uncertainty for a diversified investor is that the market will rise or plummet, carrying the investor’s portfolio with it.

   FIGURE 7.11 Diversification eliminates specific risk. But there is some risk that diversification cannot  eliminate. This is called market risk.

 7-3   Calculating Portfolio Risk

We have given you an intuitive idea of how diversification reduces risk, but to understand fully the effect of diversification, you need to know how the risk of a portfolio depends on the risk of the individual shares.

Suppose that 60% of your portfolio is invested in Heinz and the remainder is invested in Exxon Mobil. You expect that over the coming year Heinz will give a return of 6% and Exxon, 10%. The expected return on your portfolio is simply a weighted average of the expected returns on the individual stocks:²⁷

Calculating the expected portfolio return is easy. The hard part is to work out the risk of your portfolio. In the past the standard deviation of returns was 14.6% for Heinz and 21.9% for Exxon. You believe that these figures are a good representation of the spread of possible future outcomes. At first you may be inclined to assume that the standard deviation of the portfolio is a weighted average of the standard deviations of the two stocks, that is, (.60 × 14.6) + (.40 × 21.9) = 17.5%. That would be correct only if the prices of the two stocks moved in perfect lockstep. In any other case, diversification reduces the risk below this figure.

The exact procedure for calculating the risk of a two-stock portfolio is given in Figure 7.12. You need to fill in four boxes. To complete the top-left box, you weight the variance of the returns on stock 1 by the square of the proportion invested in it . Similarly, to complete the bottom-right box, you weight the variance of the returns on stock 2 by the square of the proportion invested in stock 2 .

The entries in these diagonal boxes depend on the variances of stocks 1 and 2; the entries in the other two boxes depend on their covariance. As you might guess, the covariance is a measure of the degree to which the two stocks “covary.” The covariance can be expressed as the product of the correlation coefficient ρ12 and the two standard deviations:²⁸

For the most part stocks tend to move together. In this case the correlation coefficient ρ12 is positive, and therefore the covariance σ12 is also positive. If the prospects of the stocks were wholly unrelated, both the correlation coefficient and the covariance would be zero; and if the stocks tended to move in opposite directions, the correlation coefficient and the covariance would be negative. Just as you weighted the variances by the square of the proportion invested, so you must weight the covariance by the product of the two proportionate holdings x1 and x2.

Once you have completed these four boxes, you simply add the entries to obtain the portfolio variance:

The portfolio standard deviation is, of course, the square root of the variance.

   FIGURE 7.12 The variance of a two-stock portfolio is the sum of these four boxes. x1, x2 = proportions invested in stocks 1 and 2; variance of stock returns; covariance of returns = correlation between returns on stocks 1 and 2.

Now you can try putting in some figures for Heinz and Exxon. We said earlier that if the two stocks were perfectly correlated, the standard deviation of the portfolio would lie 40% of the way between the standard deviations of the two stocks. Let us check this out by filling in the boxes with ρ12 = +1.

The variance of your portfolio is the sum of these entries:

The standard deviation is or 40% of the way between 14.6 and 21.9.

Heinz and Exxon do not move in perfect lockstep. If recent experience is any guide, the correlation between the two stocks is about .49. If we go through the same exercise again with ρ12 = .49, we find

The standard deviation is . The risk is now less than 40% of the way between 14.6 and 21.9. In fact, it is not much more than the risk of investing in Heinz alone.

The greatest payoff to diversification comes when the two stocks are negatively correlated. Unfortunately, this almost never occurs with real stocks, but just for illustration, let us assume it for Heinz and Exxon. And as long as we are being unrealistic, we might as well go whole hog and assume perfect negative correlation (ρ12 = –1). In this case,

   FIGURE 7.13 To find the variance of an N-stock portfolio, we must add the entries in a matrix like this. The diagonal cells contain variance terms (x2σ2) and the off-diagonal cells contain covariance terms (xixjσij).

When there is perfect negative correlation, there is always a portfolio strategy (represented by a particular set of portfolio weights) that will completely eliminate risk.²⁹ It’s too bad perfect negative correlation doesn’t really occur between common stocks.

General Formula for Computing Portfolio Risk

The method for calculating portfolio risk can easily be extended to portfolios of three or more securities. We just have to fill in a larger number of boxes. Each of those down the diagonal—the red boxes in Figure 7.13—contains the variance weighted by the square of the proportion invested. Each of the other boxes contains the covariance between that pair of securities, weighted by the product of the proportions invested.³⁰

Limits to Diversification

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The market factor’s
importance, 1980–2011

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Did you notice in Figure 7.13 how much more important the covariances become as we add more securities to the portfolio? When there are just two securities, there are equal numbers of variance boxes and of covariance boxes. When there are many securities, the number of covariances is much larger than the number of variances. Thus the variability of a well-diversified portfolio reflects mainly the covariances.

Suppose we are dealing with portfolios in which equal investments are made in each of N stocks. The proportion invested in each stock is, therefore, 1/N. So in each variance box we have (1/N)2 times the variance, and in each covariance box we have (1/N)2 times the covariance. There are N variance boxes and N2 – N covariance boxes. Therefore,

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Correlations between markets

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Notice that as N increases, the portfolio variance steadily approaches the average covariance. If the average covariance were zero, it would be possible to eliminate all risk by holding a sufficient number of securities. Unfortunately common stocks move together, not independently. Thus most of the stocks that the investor can actually buy are tied together in a web of positive covariances that set the limit to the benefits of diversification. Now we can understand the precise meaning of the market risk portrayed in Figure 7.11. It is the average covariance that constitutes the bedrock of risk remaining after diversification has done its work.

 7-4   How Individual Securities Affect Portfolio Risk

We presented earlier some data on the variability of 10 individual U.S. securities. Ford had the highest standard deviation and Walmart had the lowest. If you had held Ford on its own, the spread of possible returns would have been three times greater than if you had held Walmart on its own. But that is not a very interesting fact. Wise investors don’t put all their eggs into just one basket: They reduce their risk by diversification. They are therefore interested in the effect that each stock will have on the risk of their portfolio.

This brings us to one of the principal themes of this chapter. The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio. Tattoo that statement on your forehead if you can’t remember it any other way. It is one of the most important ideas in this book.

Market Risk Is Measured by Beta

If you want to know the contribution of an individual security to the risk of a well-diversified portfolio, it is no good thinking about how risky that security is if held in isolation—you need to measure its market risk, and that boils down to measuring how sensitive it is to market movements. This sensitivity is called beta (β).

Stocks with betas greater than 1.0 tend to amplify the overall movements of the market. Stocks with betas between 0 and 1.0 tend to move in the same direction as the market, but not as far. Of course, the market is the portfolio of all stocks, so the “average” stock has a beta of 1.0. Table 7.5 reports betas for the 10 well-known common stocks we referred to earlier.

Over the two years from December 2009 to December 2011, Ford had a beta of 1.53. If the future resembles the past, this means that on average when the market rises an extra 1%, Ford’s stock price will rise by an extra 1.53%. When the market falls an extra 2%, Ford’s stock prices will fall an extra 2 × 1.53 = 3.06%. Thus a line fitted to a plot of Ford’s returns versus market returns has a slope of 1.53. See Figure 7.14.

Of course Ford’s stock returns are not perfectly correlated with market returns. The company is also subject to specific risk, so the actual returns will be scattered about the line in Figure 7.14. Sometimes Ford will head south while the market goes north, and vice versa.

   FIGURE 7.14 The return on Ford stock changes on average by 1.53% for each additional 1% change in the market return. Beta is therefore 1.53.

Of the 10 stocks in Table 7.5 Ford has one of the highest betas. Heinz is at the other extreme. A line fitted to a plot of Heinz’s returns versus market returns would be less steep: Its slope would be only .40. Notice that many of the stocks that have high standard deviations also have high betas. But that is not always so. For example, Newmont, which has a relatively high standard deviation, has joined the low-beta club in the right-hand column of Table 7.5. It seems that while Newmont is a risky investment if held on its own, it makes a relatively low contribution to the risk of a diversified portfolio.

   TABLE 7.5 Betas for selected U.S. common stocks, December 2009–December 2011.

Just as we can measure how the returns of a U.S. stock are affected by fluctuations in the U.S. market, so we can measure how stocks in other countries are affected by movements in their markets. Table 7.6 shows the betas for the sample of stocks from other countries. As in the case of our U.S. sample, the highest betas include the auto companies and banks.

Why Security Betas Determine Portfolio Risk

Let us review the two crucial points about security risk and portfolio risk:

•  Market risk accounts for most of the risk of a well-diversified portfolio.

•  The beta of an individual security measures its sensitivity to market movements.

It is easy to see where we are headed: In a portfolio context, a security’s risk is measured by beta. Perhaps we could just jump to that conclusion, but we would rather explain it. Here is an intuitive explanation. We provide a more technical one in footnote 32.

Where’s Bedrock? Look back to Figure 7.11, which shows how the standard deviation of portfolio return depends on the number of securities in the portfolio. With more securities, and therefore better diversification, portfolio risk declines until all specific risk is eliminated and only the bedrock of market risk remains.

   TABLE 7.6 Betas for selected foreign stocks, December 2009–December 2011 (beta is measured relative to the stock’s home market).

Where’s bedrock? It depends on the average beta of the securities selected.

Suppose we constructed a portfolio containing a large number of stocks—500, say—drawn randomly from the whole market. What would we get? The market itself, or a portfolio very close to it. The portfolio beta would be 1.0, and the correlation with the market would be 1.0. If the standard deviation of the market were 20% (roughly its average for 1900–2011), then the portfolio standard deviation would also be 20%. This is shown by the green line in Figure 7.15.

   FIGURE 7.15 The green line shows that a well diversified portfolio of randomly selected stocks ends up with β = 1 and a standard deviation equal to the market’s—in this case 20%. The upper red line shows that a well diversified portfolio with β = 1.5 has a standard deviation of about 30%—1.5 times that of the market. The lower brown line shows that a well-diversified portfolio with β = .5 has a standard deviation of about 10%—half that of the market.

But suppose we constructed the portfolio from a large group of stocks with an average beta of 1.5. Again we would end up with a 500-stock portfolio with virtually no specific risk—a portfolio that moves almost in lockstep with the market. However, this portfolio’s standard deviation would be 30%, 1.5 times that of the market.³¹ A well-diversified portfolio with a beta of 1.5 will amplify every market move by 50% and end up with 150% of the market’s risk. The upper red line in Figure 7.15 shows this case.

Of course, we could repeat the same experiment with stocks with a beta of .5 and end up with a well-diversified portfolio half as risky as the market. You can see this also in Figure 7.15.

The general point is this: The risk of a well-diversified portfolio is proportional to the portfolio beta, which equals the average beta of the securities included in the portfolio. This shows you how portfolio risk is driven by security betas.

Calculating Beta A statistician would define the beta of stock i as

where σim is the covariance between the stock returns and the market returns and is the variance of the returns on the market. It turns out that this ratio of covariance to variance measures a stock’s contribution to portfolio risk.³²

Here is a simple example of how to do the calculations. Columns 2 and 3 in Table 7.7 show the returns over a particular six-month period on the market and the stock of the Anchovy Queen restaurant chain. You can see that, although both investments provided an average return of 2%, Anchovy Queen’s stock was particularly sensitive to market movements, rising more when the market rises and falling more when the market falls.

   TABLE 7.7 Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of the variance to the covariance (i.e., ).

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Columns 4 and 5 show the deviations of each month’s return from the average. To calculate the market variance, we need to average the squared deviations of the market returns (column 6). And to calculate the covariance between the stock returns and the market, we need to average the product of the two deviations (column 7). Beta is the ratio of the covariance to the market variance, or 76/50.67 = 1.50. A diversified portfolio of stocks with the same beta as Anchovy Queen would be one-and-a-half times as volatile as the market.

 7-5   Diversification and Value Additivity

We have seen that diversification reduces risk and, therefore, makes sense for investors. But does it also make sense for the firm? Is a diversified firm more attractive to investors than an undiversified one? If it is, we have an extremely disturbing result. If diversification is an appropriate corporate objective, each project has to be analyzed as a potential addition to the firm’s portfolio of assets. The value of the diversified package would be greater than the sum of the parts. So present values would no longer add.

Diversification is undoubtedly a good thing, but that does not mean that firms should practice it. If investors were not able to hold a large number of securities, then they might want firms to diversify for them. But investors can diversify.³³ In many ways they can do so more easily than firms. Individuals can invest in the steel industry this week and pull out next week. A firm cannot do that. To be sure, the individual would have to pay brokerage fees on the purchase and sale of steel company shares, but think of the time and expense for a firm to acquire a steel company or to start up a new steel-making operation.

You can probably see where we are heading. If investors can diversify on their own account, they will not pay any extra for firms that diversify. And if they have a sufficiently wide choice of securities, they will not pay any less because they are unable to invest separately in each factory. Therefore, in countries like the United States, which have large and competitive capital markets, diversification does not add to a firm’s value or subtract from it. The total value is the sum of its parts.

This conclusion is important for corporate finance, because it justifies adding present values. The concept of value additivity is so important that we will give a formal definition of it. If the capital market establishes a value PV(A) for asset A and PV(B) for B, the market value of a firm that holds only these two assets is

A three-asset firm combining assets A, B, and C would be worth PV(ABC) = PV(A) + PV(B) + PV(C), and so on for any number of assets.

We have relied on intuitive arguments for value additivity. But the concept is a general one that can be proved formally by several different routes.³⁴ The concept seems to be widely accepted, for thousands of managers add thousands of present values daily, usually without thinking about it.

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SUMMARY

Our review of capital market history showed that the returns to investors have varied according to the risks they have borne. At one extreme, very safe securities like U.S. Treasury bills have provided an average return over 112 years of only 3.9% a year. The riskiest securities that we looked at were common stocks. The stock market provided an average return of 11.3%, a premium of 7.3% over the safe rate of interest.

This gives us two benchmarks for the opportunity cost of capital. If we are evaluating a safe project, we discount at the current risk-free rate of interest. If we are evaluating a project of average risk, we discount at the expected return on the average common stock. Historical evidence suggests that this return is 7.3% above the risk-free rate, but many financial managers and economists opt for a lower figure. That still leaves us with a lot of assets that don’t fit these simple cases. Before we can deal with them, we need to learn how to measure risk.

Risk is best judged in a portfolio context. Most investors do not put all their eggs into one basket: They diversify. Thus the effective risk of any security cannot be judged by an examination of that security alone. Part of the uncertainty about the security’s return is diversified away when the security is grouped with others in a portfolio.

Risk in investment means that future returns are unpredictable. This spread of possible outcomes is usually measured by standard deviation. The standard deviation of the market portfolio, generally represented by the Standard and Poor’s Composite Index, is around 20% a year.

Most individual stocks have higher standard deviations than this, but much of their variability represents specific risk that can be eliminated by diversification. Diversification cannot eliminate market risk. Diversified portfolios are exposed to variation in the general level of the market.

A security’s contribution to the risk of a well-diversified portfolio depends on how the security is liable to be affected by a general market decline. This sensitivity to market movements is known as beta (β). Beta measures the amount that investors expect the stock price to change for each additional 1% change in the market. The average beta of all stocks is 1.0. A stock with a beta greater than 1 is unusually sensitive to market movements; a stock with a beta below 1 is unusually insensitive to market movements. The standard deviation of a well-diversified portfolio is proportional to its beta. Thus a diversified portfolio invested in stocks with a beta of 2.0 will have twice the risk of a diversified portfolio with a beta of 1.0.

One theme of this chapter is that diversification is a good thing for the investor. This does not imply that firms should diversify. Corporate diversification is redundant if investors can diversify on their own account. Since diversification does not affect the value of the firm, present values add even when risk is explicitly considered. Thanks to value additivity, the net present value rule for capital budgeting works even under uncertainty.

In this chapter we have introduced you to a number of formulas. They are reproduced in the endpapers to the book. You should take a look and check that you understand them.

Near the end of Chapter 9 we list some Excel functions that are useful for measuring the risk of stocks and portfolios.

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FURTHER READING

For international evidence on market returns since 1900, see:

E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002). More recent data is available in The Credit Suisse Global Investment Returns Yearbook at www.tinyurl.com/DMSyearbook.

The Ibbotson Yearbook is a valuable record of the performance of U.S. securities since 1926:

Ibbotson Stocks, Bonds, Bills, and Inflation 2011 Yearbook (Chicago, IL: Morningstar, Inc., 2012).

Useful books and reviews on the equity risk premium include:

B. Cornell, The Equity Risk Premium: The Long-Run Future of the Stock Market (New York: Wiley, 1999).

P. Fernandez, J. Aguirreamalloa, and L. C. Avendaño, “Market Risk Premium Used in 82 Countries in 2012: A Survey with 7,192 Answers,” June 13, 2012. Available at http://ssrn.com/abstract=2084213.

W. Goetzmann and R. Ibbotson, The Equity Risk Premium: Essays and Explorations (Oxford University Press, 2006).

R. Mehra (ed.), Handbook of Investments: Equity Risk Premium 1 (Amsterdam, North-Holland, 2007).

R. Mehra and E. C. Prescott, “The Equity Risk Premium in Prospect,” in Handbook of the Economics of Finance, eds. G. M. Constantinides, M. Harris, and R. M. Stulz (Amsterdam, North-Holland, 2003) Vol 1, Part 2, pp. 889–938.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Expected return and standard deviation A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100.

What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation of this rate of return.

2.  Standard deviation of returns The following table shows the nominal returns on the U.S. stocks and the rate of inflation.

a.  What was the standard deviation of the market returns?

b.  Calculate the average real return.

3.  Average returns and standard deviation During the boom years of 2003–2007, ace mutual fund manager Diana Sauros produced the following percentage rates of return. Rates of return on the market are given for comparison.

Calculate the average return and standard deviation of Ms. Sauros’s mutual fund. Did she do better or worse than the market by these measures?

4.  Portfolio risk True or false?

a.  Investors prefer diversified companies because they are less risky.

b.  If stocks were perfectly positively correlated, diversification would not reduce risk.

c.  Diversification over a large number of assets completely eliminates risk.

d.  Diversification works only when assets are uncorrelated.

e.  A stock with a low standard deviation always contributes less to portfolio risk than a stock with a higher standard deviation.

f.  The contribution of a stock to the risk of a well-diversified portfolio depends on its market risk.

g.  A well-diversified portfolio with a beta of 2.0 is twice as risky as the market portfolio.

h.  An undiversified portfolio with a beta of 2.0 is less than twice as risky as the market portfolio.

5.  Diversification In which of the following situations would you get the largest reduction in risk by spreading your investment across two stocks?

a.  The two shares are perfectly correlated.

b.  There is no correlation.

c.  There is modest negative correlation.

d.  There is perfect negative correlation.

6.  Portfolio risk To calculate the variance of a three-stock portfolio, you need to add nine boxes:

Use the same symbols that we used in this chapter; for example, x1 = proportion invested in stock 1 and σ12 = covariance between stocks 1 and 2. Now complete the nine boxes.

7.  Portfolio risk Suppose the standard deviation of the market return is 20%.

a.  What is the standard deviation of returns on a well-diversified portfolio with a beta of 1.3?

b.  What is the standard deviation of returns on a well-diversified portfolio with a beta of 0?

c.  A well-diversified portfolio has a standard deviation of 15%. What is its beta?

d.  A poorly diversified portfolio has a standard deviation of 20%. What can you say about its beta?

8.  Portfolio beta A portfolio contains equal investments in 10 stocks. Five have a beta of 1.2; the remainder have a beta of 1.4. What is the portfolio beta?

a.  1.3.

b.  Greater than 1.3 because the portfolio is not completely diversified.

c.  Less than 1.3 because diversification reduces beta.

9.  Beta What is the beta of each of the stocks shown in Table 7.8?

   TABLE 7.8 See Problem 9.

INTERMEDIATE

10.  Risk premiums Here are inflation rates and U.S. stock market and Treasury bill returns between 1929 and 1933:

a.  What was the real return on the stock market in each year?

b.  What was the average real return?

c.  What was the risk premium in each year?

d.  What was the average risk premium?

e.  What was the standard deviation of the risk premium?

11.  Stocks vs. bonds Each of the following statements is dangerous or misleading. Explain why.

a.  A long-term United States government bond is always absolutely safe.

b.  All investors should prefer stocks to bonds because stocks offer higher long-run rates of return.

c.  The best practical forecast of future rates of return on the stock market is a 5- or 10-year average of historical returns.

12.  Risk Hippique s.a., which owns a stable of racehorses, has just invested in a mysterious black stallion with great form but disputed bloodlines. Some experts in horseflesh predict the horse will win the coveted Prix de Bidet; others argue that it should be put out to grass. Is this a risky investment for Hippique shareholders? Explain.

13.  Risk and diversification Lonesome Gulch Mines has a standard deviation of 42% per year and a beta of +.10. Amalgamated Copper has a standard deviation of 31% a year and a beta of +.66. Explain why Lonesome Gulch is the safer investment for a diversified investor.

14.  Portfolio risk Hyacinth Macaw invests 60% of her funds in stock I and the balance in stock J. The standard deviation of returns on I is 10%, and on J it is 20%. Calculate the variance of portfolio returns, assuming

a.  The correlation between the returns is 1.0.

b.  The correlation is .5.

c.  The correlation is 0.

15.  Portfolio risk

a.  How many variance terms and how many covariance terms do you need to calculate the risk of a 100-share portfolio?

b.  Suppose all stocks had a standard deviation of 30% and a correlation with each other of .4. What is the standard deviation of the returns on a portfolio that has equal holdings in 50 stocks?

c.  What is the standard deviation of a fully diversified portfolio of such stocks?

16.  Portfolio risk Suppose that the standard deviation of returns from a typical share is about .40 (or 40%) a year. The correlation between the returns of each pair of shares is about .3.

a.  Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares.

b.  Use your estimates to draw a graph like Figure 7.11. How large is the underlying market risk that cannot be diversified away?

c.  Now repeat the problem, assuming that the correlation between each pair of stocks is zero.

17.  Portfolio risk Table 7.9 shows standard deviations and correlation coefficients for eight stocks from different countries. Calculate the variance of a portfolio with equal investments in each stock.

18.  Portfolio risk Your eccentric Aunt Claudia has left you $50,000 in BP shares plus $50,000 cash. Unfortunately her will requires that the BP stock not be sold for one year and the $50,000 cash must be entirely invested in one of the stocks shown in Table 7.9. What is the safest attainable portfolio under these restrictions?

19.  Beta There are few, if any, real companies with negative betas. But suppose you found one with β = –.25.

a.  How would you expect this stock’s rate of return to change if the overall market rose by an extra 5%? What if the market fell by an extra 5%?

b.  You have $1 million invested in a well-diversified portfolio of stocks. Now you receive an additional $20,000 bequest. Which of the following actions will yield the safest overall portfolio return?

i. Invest $20,000 in Treasury bills (which have β = 0).

ii. Invest $20,000 in stocks with β = 1.

iii. Invest $20,000 in the stock with β = –.25.

Explain your answer.

20.  Portfolio risk You can form a portfolio of two assets, A and B, whose returns have the following characteristics:

If you demand an expected return of 12%, what are the portfolio weights? What is the portfolio’s standard deviation?

   TABLE 7.9 Standard deviations of returns and correlation coefficients for a sample of eight stocks.

Note: Correlations and standard deviations are calculated using returns in each country’s own currency; in other words, they assume that the investor is protected against exchange risk.

21.  Interest rates and risk premiums Here are inflation rates, short-term interest rates and market returns for Australia from 2007–2011.

a.  What was the real rate of return on the Australian market in each year?

b.  What was the average real rate of return?

c.  What was the risk premium in each year?

d.  What was the average risk premium?

e.  What was the standard deviation of the risk premium?

CHALLENGE

22.  Portfolio risk Here are some historical data on the risk characteristics of Dell and McDonald’s:

Assume the standard deviation of the return on the market was 19.5%.

a.  The correlation coefficient of Dell’s return versus McDonald’s is .48. What is the standard deviation of a portfolio invested half in Dell and half in McDonald’s?

b.  What is the standard deviation of a portfolio invested one-third in Dell, one-third in McDonald’s, and one-third in risk-free Treasury bills?

c.  What is the standard deviation if the portfolio is split evenly between Dell and McDonald’s and is financed at 50% margin, that is, the investor puts up only 50% of the total amount and borrows the balance from the broker?

d.  What is the approximate standard deviation of a portfolio composed of 100 stocks with betas of 1.25 like Dell? How about 100 stocks like McDonald’s? (Hint: Part (d) should not require anything but the simplest arithmetic to answer.)

23.  Portfolio risk Suppose that Treasury bills offer a return of about 6% and the expected market risk premium is 8.5%. The standard deviation of Treasury-bill returns is zero and the standard deviation of market returns is 20%. Use the formula for portfolio risk to calculate the standard deviation of portfolios with different proportions in Treasury bills and the market. (Note: The covariance of two rates of return must be zero when the standard deviation of one return is zero.) Graph the expected returns and standard deviations.

24.  Beta Calculate the beta of each of the stocks in Table 7.9 relative to a portfolio with equal investments in each stock.

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FINANCE ON THE WEB

You can download data for questions 1 and 2 from finance.yahoo.com. Refer to the Useful Spreadsheet Functions box near the end of Chapter 9 for information on Excel functions.

1.  Download to a spreadsheet the last three years of monthly adjusted stock prices for Coca-Cola (KO), Citigroup (C), and Pfizer (PFE).

a.  Calculate the monthly returns.

b.  Calculate the monthly standard deviation of those returns (see Section 7-2). Use the Excel function STDEVP to check your answer. Find the annualized standard deviation by multiplying by the square root of 12.

c.  Use the Excel function CORREL to calculate the correlation coefficient between the monthly returns for each pair of stocks. Which pair provides the greatest gain from diversification?

d.  Calculate the standard deviation of returns for a portfolio with equal investments in the three stocks.

2.  Download to a spreadsheet the last five years of monthly adjusted stock prices for each of the companies in Table 7.5 and for the Standard & Poor’s Composite Index (S&P 500).

a.  Calculate the monthly returns.

b.  Calculate beta for each stock using the Excel function SLOPE, where the “y” range refers to the stock return (the dependent variable) and the “x” range is the market return (the independent variable).

c.  How have the betas changed from those reported in Table 7.5?

3.  A large mutual fund group such as Fidelity offers a variety of funds. They include sector funds that specialize in particular industries and index funds that simply invest in the market index. Log on to www.fidelity.com and find first the standard deviation of returns on the Fidelity Spartan 500 Index Fund, which replicates the S&P 500. Now find the standard deviations for different sector funds. Are they larger or smaller than the figure for the index fund? How do you interpret your findings?

___________

¹See E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Investment Returns (Princeton, NJ: Princeton University Press, 2002).

²Treasury bills were not issued before 1919. Before that date the interest rate used is the commercial paper rate.

³Portfolio values are plotted on a log scale. If they were not, the ending values for the common stock portfolio would run off the top of the page.

⁴Figures are rounded.

⁵We cannot be sure that this period is truly representative and that the average is not distorted by a few unusually high or low returns. The reliability of an estimate of the average is usually measured by its standard error. For example, the standard error of our estimate of the average risk premium on common stocks is 1.9%. There is a 95% chance that the true average is within plus or minus 2 standard errors of the 7.3% estimate. In other words, if you said that the true average was between 3.5 and 11.1%, you would have a 95% chance of being right. Technical note: The standard error of the average is equal to the standard deviation divided by the square root of the number of observations. In our case the standard deviation is 20.3%, and therefore the standard error is

⁶This was calculated from (1 + r)112 = 21,978, which implies r = .093. Technical note: For log normally distributed returns the annual compound return is equal to the arithmetic average return minus half the variance. For example, the annual standard deviation of returns on the U.S. market was about .20, or 20%. Variance was therefore .202, or .04. The compound annual return is about .04/2 = .02, or 2 percentage points less than the arithmetic average.

⁷You sometimes hear that the arithmetic average correctly measures the opportunity cost of capital for one-year cash flows, but not for more distant ones. Let us check. Suppose that you expect to receive a cash flow of $121 in year 2. We know that one year hence investors will value that cash flow by discounting at 10% (the arithmetic average of possible returns). In other words, at the end of the year they will be willing to pay PV1 = 121/1.10 = $110 for the expected cash flow. But we already know how to value an asset that pays off $110 in year 1—just discount at the 10% opportunity cost of capital. Thus PV0 = PV1/1.10 = 110/1.1 = $100. Our example demonstrates that the arithmetic average (10% in our example) provides a correct measure of the opportunity cost of capital regardless of the timing of the cash flow.

⁸The compound annual return is often referred to as the geometric average return.

⁹Our discussion above assumed that we knew that the returns of –10, +10, and +30% were equally likely. For an analysis of the effect of uncertainty about the expected return see I. A. Cooper, “Arithmetic Versus Geometric Mean Estimators: Setting Discount Rates for Capital Budgeting,” European Financial Management 2 (July 1996), pp. 157–167; and E. Jacquier, A. Kane, and A. J. Marcus, “Optimal Estimation of the Risk Premium for the Long Run and Asset Allocation: A Case of Compounded Estimation Risk,” Journal of Financial Econometrics 3 (2005), pp. 37–55. When future returns are forecasted to distant horizons, the historical arithmetic means are upward-biased. This bias would be small in most corporate-finance applications, however.

¹⁰Some of the disagreements simply reflect the fact that the risk premium is sometimes defined in different ways. Some measure the average difference between stock returns and the returns (or yields) on long-term bonds. Others measure the difference between the compound rate of return on stocks and the interest rate. As we explained above, this is not an appropriate measure of the cost of capital.

¹¹There is some theory behind this instinct. The high risk premium earned in the market seems to imply that investors are extremely risk-averse. If that is true, investors ought to cut back their consumption when stock prices fall and wealth decreases. But the evidence suggests that when stock prices fall, investors spend at nearly the same rate. This is difficult to reconcile with high risk aversion and a high market risk premium. There is an active research literature on this “equity premium puzzle.” See R. Mehra, “The Equity Premium Puzzle: A Review,” Foundations and Trends in Finance® 2 (2006), pp. 11–81, and R. Mehra, ed., Handbook of the Equity Risk Premium (Amsterdam: Elsevier Handbooks in Finance Series, 2008).

¹²It is difficult to interpret the responses to such surveys precisely. For example, one is conducted every quarter by Duke University and CFO magazine and reported on at www.cfosurvey.org. On average since inception CFOs have predicted a 10-year return on U.S. equities of 3.7% in excess of the return on 10-year Treasury bonds. However, respondents appear to have interpreted the question as asking for their forecast of the compound annual return. In this case the comparable expected (arithmetic average) premium over bills is probably 2 or 3 percentage points higher at about 6%. For a description of the survey data, see J. R. Graham and C. Harvey, “The Long-Run Equity Risk Premium,” Finance Research Letters 2 (2005), pp. 185–194.

¹³This possibility was suggested in P. Jorion and W. N. Goetzmann, “Global Stock Markets in the Twentieth Century,” Journal of Finance 54 (June 1999), pp. 953–980.

¹⁴We are concerned here with the difference between the nominal market return and the nominal interest rate. Sometimes you will see real risk premiums quoted—that is, the difference between the real market return and the real interest rate. If the inflation rate is i, then the real risk premium is (rm – rf)/(1 + i). For countries such as Italy that have experienced a high degree of inflation, this real risk premium may be significantly lower than the nominal premium.

¹⁵See E. F. Fama and K. R. French, “The Equity Premium,” Journal of Finance 57 (April 2002), pp. 637–659. Fama and French quote even lower estimates of the risk premium, particularly for the second half of the period. The difference partly reflects the fact that they define the risk premium as the difference between market returns and the commercial paper rate. Except for the years 1900–1918, the interest rates used in Table 7.1 are the rates on U.S. Treasury bills.

¹⁶One more technical point. When variance is estimated from a sample of observed returns, we add the squared deviations and divide by N – 1, where N is the number of observations. We divide by N – 1 rather than N to correct for what is called the loss of a degree of freedom. The formula is

where is the market return in period t and rm is the mean of the values of

¹⁷Which of the two we use is solely a matter of convenience. Since standard deviation is in the same units as the rate of return, it is generally more convenient to use standard deviation. However, when we are talking about the proportion of risk that is due to some factor, it is less confusing to work in terms of the variance.

¹⁸As we explain in Chapter 8, standard deviation and variance are the correct measures of risk if the returns are normally distributed.

¹⁹In discussing the riskiness of bonds, be careful to specify the time period and whether you are speaking in real or nominal terms. The nominal return on a long-term government bond is absolutely certain to an investor who holds on until maturity; in other words, it is risk-free if you forget about inflation. After all, the government can always print money to pay off its debts. However, the real return on Treasury securities is uncertain because no one knows how much each future dollar will buy.

The bond returns used to construct this table were measured annually. The returns reflect year-to-year changes in bond prices as well as interest received. The one-year returns on long-term bonds are risky in both real and nominal terms.

²⁰These estimates are derived from weekly rates of return. The weekly variance is converted to an annual variance by multiplying by 52. That is, the variance of the weekly return is one-fifty-second of the annual variance. The longer you hold a security or portfolio, the more risk you have to bear.

This conversion assumes that successive weekly returns are statistically independent. This is, in fact, a good assumption, as we will show in Chapter 13.

Because variance is approximately proportional to the length of time interval over which a security or portfolio return is measured, standard deviation is proportional to the square root of the interval.

²¹The standard deviation for 2012 is the VIX index of market volatility, published by the Chicago Board Options Exchange (CBOE). We explain the VIX index in Chapter 21. In the meantime, you may wish to check the current level of the VIX on finance.yahoo.com or at the CBOE website.

²²These standard deviations are also calculated from weekly data.

²³There is some evidence that stocks have become individually more risky but have moved less closely together. Consequently, the benefits of diversification have increased. See J. Y. Campbell, M. Lettau, B. C. Malkiel, and Y. Xu, “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk,” Journal of Finance 56 (February 2001), pp. 1–43.

²⁴Over this period the correlation between the returns on the two stocks was .31.

²⁵Specific risk may be called unsystematic risk, residual risk, unique risk, or diversifiable risk.

²⁶Market risk may be called systematic risk or undiversifiable risk.

²⁷Let’s check this. Suppose you invest $60 in Heinz and $40 in Exxon. The expected dollar return on your Heinz holding is .06 × 60 = $3.60, and on Exxon it is .10 × 40 = $4.00. The expected dollar return on your portfolio is 3.60 + 4.00 = $7.60. The portfolio rate of return is 7.60/100 = .076, or 7.6%.

²⁸Another way to define the covariance is as follows:

Note that any security’s covariance with itself is just its variance:

²⁹Since the standard deviation of Exxon is 1.5 times that of Heinz, you need to invest 1.5 times more in Heinz to eliminate risk in this two-stock portfolio.

³⁰The formal equivalent to “add up all the boxes” is

Notice that when i = j, σij is just the variance of stock i.

³¹A 500-stock portfolio with β = 1.5 would still have some specific risk because it would be unduly concentrated in high-beta industries. Its actual standard deviation would be a bit higher than 30%. If that worries you, relax; we will show you in Chapter 8 how you can construct a fully diversified portfolio with a beta of 1.5 by borrowing and investing in the market portfolio.

³²To understand why, skip back to Figure 7.13. Each row of boxes in Figure 7.13 represents the contribution of that particular security to the portfolio’s risk. For example, the contribution of stock 1 is

where xi is the proportion invested in stock i, and σij is the covariance between stocks i and j (note: σii is equal to the variance of stock i). In other words, the contribution of stock 1 to portfolio risk is equal to the relative size of the holding (x1) times the average covariance between stock 1 and all the stocks in the portfolio. We can write this more concisely by saying that the contribution of stock 1 to portfolio risk is equal to the holding size (x1) times the covariance between stock 1 and the entire portfolio (σ1p).

To find stock 1’s relative contribution to risk we simply divide by the portfolio variance to give . In other words, it is equal to the holding size (x1) times the beta of stock 1 relative to the portfolio .

We can calculate the beta of a stock relative to any portfolio by simply taking its covariance with the portfolio and dividing by the portfolio’s variance. If we wish to find a stock’s beta relative to the market portfolio we just calculate its covariance with the market portfolio and divide by the variance of the market:

³³One of the simplest ways for an individual to diversify is to buy shares in a mutual fund that holds a diversified portfolio.

³⁴You may wish to refer to the Appendix to Chapter 31, which discusses diversification and value additivity in the context of mergers.

Part 2 Risk

Portfolio Theory and the Capital Asset Pricing Model

In Chapter 7 we began to come to grips with the problem of measuring risk. Here is the story so far.

The stock market is risky because there is a spread of possible outcomes. The usual measure of this spread is the standard deviation or variance. The risk of any stock can be broken down into two parts. There is the specific or diversifiable risk that is peculiar to that stock, and there is the market risk that is associated with marketwide variations. Investors can eliminate specific risk by holding a well-diversified portfolio, but they cannot eliminate market risk. All the risk of a fully diversified portfolio is market risk.

A stock’s contribution to the risk of a fully diversified portfolio depends on its sensitivity to market changes. This sensitivity is generally known as beta. A security with a beta of 1.0 has average market risk—a well-diversified portfolio of such securities has the same standard deviation as the market index. A security with a beta of .5 has below-average market risk—a well-diversified portfolio of these securities tends to move half as far as the market moves and has half the market’s standard deviation.

In this chapter we build on this newfound knowledge. We present leading theories linking risk and return in a competitive economy, and we show how these theories can be used to estimate the returns required by investors in different stock-market investments. We start with the most widely used theory, the capital asset pricing model, which builds directly on the ideas developed in the last chapter. We will also look at another class of models, known as arbitrage pricing or factor models. Then in Chapter 9 we show how these ideas can help the financial manager cope with risk in practical capital budgeting situations.

 8-1   Harry Markowitz and the Birth of Portfolio Theory

Most of the ideas in Chapter 7 date back to an article written in 1952 by Harry Markowitz.¹ Markowitz drew attention to the common practice of portfolio diversification and showed exactly how an investor can reduce the standard deviation of portfolio returns by choosing stocks that do not move exactly together. But Markowitz did not stop there; he went on to work out the basic principles of portfolio construction. These principles are the foundation for much of what has been written about the relationship between risk and return.

We begin with Figure 8.1, which shows a histogram of the daily returns on IBM stock from 1991 to 2011. On this histogram we have superimposed a bell-shaped normal distribution. The result is typical: When measured over a short interval, the past rates of return on any stock conform fairly closely to a normal distribution.²

   FIGURE 8.1 Daily price changes for IBM are approximately normally distributed. This plot spans 1991 to 2011.

Normal distributions can be completely defined by two numbers. One is the average or expected return; the other is the variance or standard deviation. Now you can see why in Chapter 7 we discussed the calculation of expected return and standard deviation. They are not just arbitrary measures: if returns are normally distributed, expected return and standard deviation are the only two measures that an investor need consider.

Figure 8.2 pictures the distribution of possible returns from three investments. A and B offer an expected return of 10%, but A has the much wider spread of possible outcomes. Its standard deviation is 15%; the standard deviation of B is 7.5%. Most investors dislike uncertainty and would therefore prefer B to A.

   FIGURE 8.2 Investments A and B both have an expected return of 10%, but because investment A has the greater spread of possible returns, it is more risky than B. We can measure this spread by the standard deviation. Investment A has a standard deviation of 15%; B, 7.5%. Most investors would prefer B to A. Investments B and C both have the same standard deviation, but C offers a higher expected return. Most investors would prefer C to B.

BEYOND THE PAGE

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Utility theory

brealey.mhhe.com/c08

Now compare investments B and C. This time both have the same standard deviation, but the expected return is 20% from stock C and only 10% from stock B. Most investors like high expected return and would therefore prefer C to B.

Combining Stocks into Portfolios

Suppose that you are wondering whether to invest in the shares of Heinz or Exxon Mobil. You decide that Heinz offers an expected return of 6.0% and Exxon offers an expected return of 10.0%. After looking back at the past variability of the two stocks, you also decide that the standard deviation of returns is 14.6% for Heinz and 21.9% for Exxon. Exxon offers the higher expected return, but it is more risky.

Now there is no reason to restrict yourself to holding only one stock. For example, in Section 7-3 we analyzed what would happen if you invested 60% of your money in Heinz and 40% in Exxon. The expected return on this portfolio is 7.6%, simply a weighted average of the expected returns on the two holdings. What about the risk of such a portfolio? We know that thanks to diversification the portfolio risk is less than the average of the risks of the separate stocks. In fact, on the basis of past experience the standard deviation of this portfolio is 15.1%.³

The curved blue line in Figure 8.3 shows the expected return and risk that you could achieve by different combinations of the two stocks. Which of these combinations is best depends on your stomach. If you want to stake all on getting rich quickly, you should put all your money in Exxon. If you want a more peaceful life, you should invest most of your money in Heinz, but you should keep at least a small investment in Exxon.⁴

   FIGURE 8.3 The curved line illustrates how expected return and standard deviation change as you hold different combinations of two stocks. For example, if you invest 40% of your money in Exxon Mobil and the remainder in Heinz, your expected return is 7.6%, which is 40% of the way between the expected returns on the two stocks. The standard deviation is 15.1%, which is less than 40% of the way between the standard deviations of the two stocks. This is because diversification reduces risk.

We saw in Chapter 7 that the gain from diversification depends on how highly the stocks are correlated. Fortunately, on past experience there is only a modest correlation between the returns of Heinz and Exxon (ρ = +.49). If their stocks moved in exact lockstep (ρ = +1), there would be no gains at all from diversification. You can see this by the gold dotted line in Figure 8.3. The red dotted line in the figure shows a second extreme (and equally unrealistic) case in which the returns on the two stocks are perfectly negatively correlated (ρ = –1). If this were so, your portfolio would have no risk.

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Try It! Markowitz portfolio program

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In practice, you are not limited to investing in just two stocks. For example, you could decide to choose a portfolio from the 10 stocks listed in the first column of Table 8.1. After analyzing the prospects for each firm, you come up with forecasts of their returns. You are most optimistic about the outlook for Dow Chemical, and forecast that it will provide a return of 16.4%. At the other extreme, you predict a return of only 6% for Heinz. You use data for the past two years to estimate the risk of each stock and the correlation between the returns on each pair of stocks.⁵

   TABLE 8.1 Examples of efficient portfolios chosen from 10 stocks.

Note: Standard deviations and the correlations between stock returns were estimated from weekly returns, December 2009–December 2011. Efficient portfolios are calculated assuming that short sales are prohibited.

Now look at Figure 8.4. Each diamond marks the combination of risk and return offered by a different individual security.

   FIGURE 8.4 Each diamond shows the expected return and standard deviation of 1 of the 10 stocks in Table 8.1. There are many possible combinations of expected return and standard deviation from investing in a mixture of these stocks. If you like high expected returns and dislike high standard deviations, you will prefer portfolios along the red line. These are efficient portfolios. We have marked the three efficient portfolios described in Table 8.1 (A, B, and C).

By holding different proportions of the 10 securities, you can obtain an even wider selection of risk and return, but which combination is best? Well, what is your goal? Which direction do you want to go? The answer should be obvious: you want to go up (to increase expected return) and to the left (to reduce risk). Go as far as you can, and you will end up with one of the portfolios that lies along the red line. Markowitz called them efficient portfolios. They offer the highest expected return for any level of risk.

We will not calculate this set of efficient portfolios here, but you may be interested in how to do it. Think back to the capital rationing problem in Section 5-4. There we wanted to deploy a limited amount of capital investment in a mixture of projects to give the highest NPV. Here we want to deploy an investor’s funds to give the highest expected return for a given standard deviation. In principle, both problems can be solved by hunting and pecking—but only in principle. To solve the capital rationing problem, we can employ linear programming; to solve the portfolio problem, we would turn to a variant of linear programming known as quadratic programming. Given the expected return and standard deviation for each stock, as well as the correlation between each pair of stocks, we could use a standard quadratic computer program to calculate the set of efficient portfolios.

Three of these efficient portfolios are marked in Figure 8.4. Their compositions are summarized in Table 8.1. Portfolio A offers the highest expected return: It is invested entirely in one stock, Dow Chemical. Portfolio C offers the minimum risk; you can see from Table 8.1 that it has large holdings in Heinz and Walmart, which have the lowest standard deviations. However, the portfolio also has a small holding in Newmont even though it is individually quite risky. The reason? On past evidence the fortunes of gold-mining shares, such as Newmont, are relatively uncorrelated with those of other stocks and so provide additional diversification.

Table 8.1 also shows the compositions of a third efficient portfolio with intermediate levels of risk and expected return.

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Portfolio selection in practice

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Of course, large investment funds can choose from thousands of stocks and thereby achieve a wider choice of risk and return. This choice is represented in Figure 8.5 by the shaded, broken-egg-shaped area. The set of efficient portfolios is again marked by the red curved line.

   FIGURE 8.5 Lending and borrowing extend the range of investment possibilities. If you invest in portfolio S and lend or borrow at the risk-free interest rate, rf, you can achieve any point along the straight line from rf through S. This gives you a higher expected return for any level of risk than if you just invest in common stocks.

We Introduce Borrowing and Lending

Now we introduce yet another possibility. Suppose that you can also lend or borrow money at some risk-free rate of interest rf. If you invest some of your money in Treasury bills (i.e., lend money) and place the remainder in common stock portfolio S, you can obtain any combination of expected return and risk along the straight line joining rf and S in Figure 8.5. Since borrowing is merely negative lending, you can extend the range of possibilities to the right of S by borrowing funds at an interest rate of rf and investing them as well as your own money in portfolio S.

Let us put some numbers on this. Suppose that portfolio S has an expected return of 15% and a standard deviation of 16%. Treasury bills offer an interest rate (rf) of 5% and are risk-free (i.e., their standard deviation is zero). If you invest half your money in portfolio S and lend the remainder at 5%, the expected return on your investment is likewise halfway between the expected return on S and the interest rate on Treasury bills:

And the standard deviation is halfway between the standard deviation of S and the standard deviation of Treasury bills:⁶

Or suppose that you decide to go for the big time: You borrow at the Treasury bill rate an amount equal to your initial wealth, and you invest everything in portfolio S. You have twice your own money invested in S, but you have to pay interest on the loan. Therefore your expected return is

And the standard deviation of your investment is

You can see from Figure 8.5 that when you lend a portion of your money, you end up partway between rf and S; if you can borrow money at the risk-free rate, you can extend your possibilities beyond S. You can also see that regardless of the level of risk you choose, you can get the highest expected return by a mixture of portfolio S and borrowing or lending. S is the best efficient portfolio. There is no reason ever to hold, say, portfolio T.

If you have a graph of efficient portfolios, as in Figure 8.5, finding this best efficient portfolio is easy. Start on the vertical axis at rf and draw the steepest line you can to the curved red line of efficient portfolios. That line will be tangent to the red line. The efficient portfolio at the tangency point is better than all the others. Notice that it offers the highest ratio of risk premium to standard deviation. This ratio of the risk premium to the standard deviation is called the Sharpe ratio:

Investors track Sharpe ratios to measure the risk-adjusted performance of investment managers. (Take a look at the mini-case at the end of this chapter.)

We can now separate the investor’s job into two stages. First, the best portfolio of common stocks must be selected—S in our example. Second, this portfolio must be blended with borrowing or lending to obtain an exposure to risk that suits the particular investor’s taste. Each investor, therefore, should put money into just two benchmark investments—a risky portfolio S and a risk-free loan (borrowing or lending).

What does portfolio S look like? If you have better information than your rivals, you will want the portfolio to include relatively large investments in the stocks you think are undervalued. But in a competitive market you are unlikely to have a monopoly of good ideas. In that case there is no reason to hold a different portfolio of common stocks from anybody else. In other words, you might just as well hold the market portfolio. That is why many professional investors invest in a market-index portfolio and why most others hold well-diversified portfolios.

 8-2   The Relationship Between Risk and Return

In Chapter 7 we looked at the returns on selected investments. The least risky investment was U.S. Treasury bills. Since the return on Treasury bills is fixed, it is unaffected by what happens to the market. In other words, Treasury bills have a beta of 0. We also considered a much riskier investment, the market portfolio of common stocks. This has average market risk: its beta is 1.0.

Wise investors don’t take risks just for fun. They are playing with real money. Therefore, they require a higher return from the market portfolio than from Treasury bills. The difference between the return on the market and the interest rate is termed the market risk premium. Since 1900 the market risk premium (rm – rf) has averaged 7.3% a year.

In Figure 8.6 we have plotted the risk and expected return from Treasury bills and the market portfolio. You can see that Treasury bills have a beta of 0 and a risk premium of 0.⁷ The market portfolio has a beta of 1 and a risk premium of rm – rf. This gives us two benchmarks for the expected risk premium. But what is the expected risk premium when beta is not 0 or 1?

   FIGURE 8.6 The capital asset pricing model states that the expected risk premium on each investment is proportional to its beta. This means that each investment should lie on the sloping security market line connecting Treasury bills and the market portfolio.

In the mid-1960s three economists—William Sharpe, John Lintner, and Jack Treynor—produced an answer to this question.⁸ Their answer is known as the capital asset pricing model, or CAPM. The model’s message is both startling and simple. In a competitive market, the expected risk premium varies in direct proportion to beta. This means that in Figure 8.6 all investments must plot along the sloping line, known as the security market line. The expected risk premium on an investment with a beta of .5 is, therefore, half the expected risk premium on the market; the expected risk premium on an investment with a beta of 2 is twice the expected risk premium on the market. We can write this relationship as

Some Estimates of Expected Returns

Before we tell you where the formula comes from, let us use it to figure out what returns investors are looking for from particular stocks. To do this, we need three numbers: β, rf, and rm – rf. We gave you estimates of the betas of 10 stocks in Table 7.5. We will suppose that the interest rate on Treasury bills is about 2%.

How about the market risk premium? As we pointed out in the last chapter, we can’t measure rm – rf with precision. From past evidence it appears to be 7.3%, although many economists and financial managers would forecast a slightly lower figure. Let us use 7% in this example.

Table 8.2 puts these numbers together to give an estimate of the expected return on each stock. The stock with the highest beta in our sample is Dow Chemical. Our estimate of the expected return from Dow is 14.5%. The stock with the lowest beta is Heinz. Our estimate of its expected return is 4.78%, 2.78% more than the interest rate on Treasury bills. Notice that these expected returns are not the same as the hypothetical forecasts of return that we assumed in Table 8.1 to generate the efficient frontier.

   TABLE 8.2 These estimates of the returns expected by investors in January 2012 were based on the capital asset pricing model. We assumed 2% for the interest rate rf and 7% for the expected risk premium rm – rf.

You can also use the capital asset pricing model to find the discount rate for a new capital investment. For example, suppose that you are analyzing a proposal by Exxon to expand its business. At what rate should you discount the forecasted cash flows? According to Table 8.2, investors are looking for a return of 8.9% from businesses with the risk of Exxon. So the cost of capital for a further investment in the same business is 8.9%.⁹

In practice, choosing a discount rate is seldom so easy. (After all, you can’t expect to be paid a fat salary just for plugging numbers into a formula.) For example, you must learn how to adjust the expected return to remove the extra risk caused by company borrowing. Also you need to consider the difference between short- and long-term interest rates. As we write this in January 2012, the interest rate on Treasury bills is at a record low of .1% and well below long-term rates. It is possible that investors were content with the prospect of quite modest equity returns in the short run, but they almost certainly required higher long-run returns than the figures shown in Table 8.2. If that is so, a cost of capital based on short-term rates may be inappropriate for long-term capital investments. But these refinements can wait until later.

Review of the Capital Asset Pricing Model

Let us review the basic principles of portfolio selection:

1.   Investors like high expected return and low standard deviation. Common stock portfolios that offer the highest expected return for a given standard deviation are known as efficient portfolios.

2.   If the investor can lend or borrow at the risk-free rate of interest, one efficient portfolio is better than all the others: the portfolio that offers the highest ratio of risk premium to standard deviation (that is, portfolio S in Figure 8.5). A risk-averse investor will put part of his money in this efficient portfolio and part in the risk-free asset. A risk-tolerant investor may put all her money in this portfolio or she may borrow and put in even more.

3.   The composition of this best efficient portfolio depends on the investor’s assessments of expected returns, standard deviations, and correlations. But suppose everybody has the same information and the same assessments. If there is no superior information, each investor should hold the same portfolio as everybody else; in other words, everyone should hold the market portfolio.

Now let us go back to the risk of individual stocks:

4.   Do not look at the risk of a stock in isolation but at its contribution to portfolio risk. This contribution depends on the stock’s sensitivity to changes in the value of the portfolio.

5.   A stock’s sensitivity to changes in the value of the market portfolio is known as beta. Beta, therefore, measures the marginal contribution of a stock to the risk of the market portfolio.

Now if everyone holds the market portfolio, and if beta measures each security’s contribution to the market portfolio risk, then it is no surprise that the risk premium demanded by investors is proportional to beta. That is what the CAPM says.

What If a Stock Did Not Lie on the Security Market Line?

Imagine that you encounter stock A in Figure 8.7. Would you buy it? We hope not¹⁰—if you want an investment with a beta of .5, you could get a higher expected return by investing half your money in Treasury bills and half in the market portfolio. If everybody shares your view of the stock’s prospects, the price of A will have to fall until the expected return matches what you could get elsewhere.

   FIGURE 8.7 In equilibrium no stock can lie below the security market line. For example, instead of buying stock A, investors would prefer to lend part of their money and put the balance in the market portfolio. And instead of buying stock B, they would prefer to borrow and invest in the market portfolio.

What about stock B in Figure 8.7? Would you be tempted by its high return? You wouldn’t if you were smart. You could get a higher expected return for the same beta by borrowing 50 cents for every dollar of your own money and investing in the market portfolio. Again, if everybody agrees with your assessment, the price of stock B cannot hold. It will have to fall until the expected return on B is equal to the expected return on the combination of borrowing and investment in the market portfolio.¹¹

We have made our point. An investor can always obtain an expected risk premium of β(rm – rf) by holding a mixture of the market portfolio and a risk-free loan. So in well-functioning markets nobody will hold a stock that offers an expected risk premium of less than β(rm – rf). But what about the other possibility? Are there stocks that offer a higher expected risk premium? In other words, are there any that lie above the security market line in Figure 8.7? If we take all stocks together, we have the market portfolio. Therefore, we know that stocks on average lie on the line. Since none lies below the line, then there also can’t be any that lie above the line. Thus each and every stock must lie on the security market line and offer an expected risk premium of

 8-3   Validity and Role of the Capital Asset Pricing Model

Any economic model is a simplified statement of reality. We need to simplify in order to interpret what is going on around us. But we also need to know how much faith we can place in our model.

Let us begin with some matters about which there is broad agreement. First, few people quarrel with the idea that investors require some extra return for taking on risk. That is why common stocks have given on average a higher return than U.S. Treasury bills. Who would want to invest in risky common stocks if they offered only the same expected return as bills? We would not, and we suspect you would not either.

Second, investors do appear to be concerned principally with those risks that they cannot eliminate by diversification. If this were not so, we should find that stock prices increase whenever two companies merge to spread their risks. And we should find that investment companies which invest in the shares of other firms are more highly valued than the shares they hold. But we do not observe either phenomenon. Mergers undertaken just to spread risk do not increase stock prices, and investment companies are no more highly valued than the stocks they hold.

The capital asset pricing model captures these ideas in a simple way. That is why financial managers find it a convenient tool for coming to grips with the slippery notion of risk and why nearly three-quarters of them use it to estimate the cost of capital.¹² It is also why economists often use the capital asset pricing model to demonstrate important ideas in finance even when there are other ways to prove these ideas. But that does not mean that the capital asset pricing model is ultimate truth. We will see later that it has several unsatisfactory features, and we will look at some alternative theories. Nobody knows whether one of these alternative theories is eventually going to come out on top or whether there are other, better models of risk and return that have not yet seen the light of day.

Tests of the Capital Asset Pricing Model

Imagine that in 1931 ten investors gathered together in a Wall Street bar and agreed to establish investment trust funds for their children. Each investor decided to follow a different strategy. Investor 1 opted to buy the 10% of the New York Stock Exchange stocks with the lowest estimated betas; investor 2 chose the 10% with the next-lowest betas; and so on, up to investor 10, who proposed to buy the stocks with the highest betas. They also planned that at the end of each year they would reestimate the betas of all NYSE stocks and reconstitute their portfolios.¹³ And so they parted with much cordiality and good wishes.

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Figure 8.8: Returns and beta

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In time the 10 investors all passed away, but their children agreed to meet in early 2011 in the same bar to compare the performance of their portfolios. Figure 8.8 shows how they had fared. Investor 1’s portfolio turned out to be much less risky than the market; its beta was only .50. However, investor 1 also realized the lowest return, 10.0% above the risk-free rate of interest. At the other extreme, the beta of investor 10’s portfolio was 1.54, about three times that of investor 1’s portfolio. But investor 10 was rewarded with the highest return, averaging 16.1% a year above the interest rate. So over this 80-year period returns did indeed increase with beta.

   FIGURE 8.8 The capital asset pricing model states that the expected risk premium from any investment should lie on the security market line. The dots show the actual average risk premiums from portfolios with different betas. The high-beta portfolios generated higher average returns, just as predicted by the CAPM. But the high-beta portfolios plotted below the market line, and the low-beta portfolios plotted above. A line fitted to the 10 portfolio returns would be “flatter” than the market line.

Source: F. Black, “Beta and Return,” Journal of Portfolio Management 20 (Fall 1993), pp. 8–18. Used with permission of Institutional Investor, Inc., www.iijournals.com. All rights reserved. Updates courtesy of Adam Kolasinski.

As you can see from Figure 8.8, the market portfolio over the same 80-year period provided an average return of 12.3% above the interest rate¹⁴ and (of course) had a beta of 1.0. The CAPM predicts that the risk premium should increase in proportion to beta, so that the returns of each portfolio should lie on the upward-sloping security market line in Figure 8.8. Since the market provided a risk premium of 12.3%, investor 1’s portfolio, with a beta of .50, should have provided a risk premium of 6.1% and investor 10’s portfolio, with a beta of 1.54, should have given a premium of 18.9%. You can see that, while high-beta stocks performed better than low-beta stocks, the difference was not as great as the CAPM predicts.

Although Figure 8.8 provides broad support for the CAPM, critics have pointed out that the slope of the line has been particularly flat in recent years. For example, Figure 8.9 shows how our 10 investors fared between 1966 and 2010. Now it is less clear who is buying the drinks: returns are pretty much in line with the CAPM with the important exception of the two highest-risk portfolios. Investor 10, who rode the roller coaster of a high-beta portfolio, earned a return that was only marginally above that of the market. Of course, before 1966 the line was correspondingly steeper. This is also shown in Figure 8.9.

   FIGURE 8.9 The relationship between beta and actual average return has been weaker since the mid-1960s. Stocks with the highest betas have provided poor returns.

Source: F. Black, “Beta and Return,” Journal of Portfolio Management 20 (Fall 1993), pp. 8–18. Used with permission of Institutional Investor, Inc., www.iijournals.com. All rights reserved. Updates courtesy of Adam Kolasinski.

What is going on here? It is hard to say. Defenders of the capital asset pricing model emphasize that it is concerned with expected returns, whereas we can observe only actual returns. Actual stock returns reflect expectations, but they also embody lots of “noise”—the steady flow of surprises that conceal whether on average investors have received the returns they expected. This noise may make it impossible to judge whether the model holds better in one period than another.¹⁵ Perhaps the best that we can do is to focus on the longest period for which there is reasonable data. This would take us back to Figure 8.8, which suggests that expected returns do indeed increase with beta, though less rapidly than the simple version of the CAPM predicts.¹⁶

The CAPM has also come under fire on a second front: although return has not risen with beta in recent years, it has been related to other measures. For example, the red line in Figure 8.10 shows the cumulative difference between the returns on small-firm stocks and large-firm stocks. If you had bought the shares with the smallest market capitalizations and sold those with the largest capitalizations, this is how your wealth would have changed. You can see that small-cap stocks did not always do well, but over the long haul their owners have made substantially higher returns. Since the end of 1926 the average annual difference between the returns on the two groups of stocks has been 3.6%.

   FIGURE 8.10 The red line shows the cumulative difference between the returns on small-firm and large-firm stocks from 1926 to 2011. The green line shows the cumulative difference between the returns on high book-to-market-value stocks (i.e., value stocks) and low book-to-market-value stocks (i.e., growth stocks).

Source: Kenneth French’s website, mba.tuck.dartmouth.edu/pages/faculty/ken.french/ data_library.html. Used with permission.

Now look at the green line in Figure 8.10, which shows the cumulative difference between the returns on value stocks and growth stocks. Value stocks here are defined as those with high ratios of book value to market value. Growth stocks are those with low ratios of book to market. Notice that value stocks have provided a higher long-run return than growth stocks.¹⁷ Since 1926 the average annual difference between the returns on value and growth stocks has been 4.8%.

Figure 8.10 does not fit well with the CAPM, which predicts that beta is the only reason that expected returns differ. It seems that investors saw risks in “small-cap” stocks and value stocks that were not captured by beta.¹⁸ Take value stocks, for example. Many of these stocks may have sold below book value because the firms were in serious trouble; if the economy slowed unexpectedly, the firms might have collapsed altogether. Therefore, investors, whose jobs could also be on the line in a recession, may have regarded these stocks as particularly risky and demanded compensation in the form of higher expected returns. If that were the case, the simple version of the CAPM cannot be the whole truth.

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The momentum factor

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Again, it is hard to judge how seriously the CAPM is damaged by this finding. The relationship among stock returns and firm size and book-to-market ratio has been well documented. However, if you look long and hard at past returns, you are bound to find some strategy that just by chance would have worked in the past. This practice is known as “data-mining” or “data snooping.” Maybe the size and book-to-market effects are simply chance results that stem from data snooping. If so, they should have vanished once they were discovered. There is some evidence that this is the case. For example, if you look again at Figure 8.10, you will see that since the mid-1980s small-firm stocks have underperformed just about as often as they have overperformed.

There is no doubt that the evidence on the CAPM is less convincing than scholars once thought. But it will be hard to reject the CAPM beyond all reasonable doubt. Since data and statistics are unlikely to give final answers, the plausibility of the CAPM theory will have to be weighed along with the empirical “facts.”

Assumptions behind the Capital Asset Pricing Model

The capital asset pricing model rests on several assumptions that we did not fully spell out. For example, we assumed that investment in U.S. Treasury bills is risk-free. It is true that there is little chance of default, but bills do not guarantee a real return. There is still some uncertainty about inflation. Another assumption was that investors can borrow money at the same rate of interest at which they can lend. Generally borrowing rates are higher than lending rates.

It turns out that many of these assumptions are not crucial, and with a little pushing and pulling it is possible to modify the capital asset pricing model to handle them. The really important idea is that investors are content to invest their money in a limited number of benchmark portfolios. (In the basic CAPM these benchmarks are Treasury bills and the market portfolio.)

In these modified CAPMs expected return still depends on market risk, but the definition of market risk depends on the nature of the benchmark portfolios. In practice, none of these alternative capital asset pricing models is as widely used as the standard version.

 8-4   Some Alternative Theories

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The consumption CAPM

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The capital asset pricing model pictures investors as solely concerned with the level and uncertainty of their future wealth. But this could be too simplistic. For example, investors may become accustomed to a particular standard of living, so that poverty tomorrow may be particularly difficult to bear if you were wealthy yesterday. Behavioral psychologists have also observed that investors do not focus solely on the current value of their holdings, but look back at whether their investments are showing a profit. A gain, however small, may be an additional source of satisfaction. The capital asset pricing model does not allow for the possibility that investors may take account of the price at which they purchased stock and feel elated when their investment is in the black and depressed when it is in the red.¹⁹

Arbitrage Pricing Theory

The capital asset pricing theory begins with an analysis of how investors construct efficient portfolios. Stephen Ross’s arbitrage pricing theory, or APT, comes from a different family entirely. It does not ask which portfolios are efficient. Instead, it starts by assuming that each stock’s return depends partly on pervasive macroeconomic influences or “factors” and partly on “noise”—events that are unique to that company. Moreover, the return is assumed to obey the following simple relationship:

The theory does not say what the factors are: there could be an oil price factor, an interest-rate factor, and so on. The return on the market portfolio might serve as one factor, but then again it might not.

Some stocks will be more sensitive to a particular factor than other stocks. Exxon Mobil would be more sensitive to an oil factor than, say, Coca-Cola. If factor 1 picks up unexpected changes in oil prices, b1 will be higher for Exxon Mobil.

For any individual stock there are two sources of risk. First is the risk that stems from the pervasive macroeconomic factors. This cannot be eliminated by diversification. Second is the risk arising from possible events that are specific to the company. Diversification eliminates specific risk, and diversified investors can therefore ignore it when deciding whether to buy or sell a stock. The expected risk premium on a stock is affected by factor or macroeconomic risk; it is not affected by specific risk.

Arbitrage pricing theory states that the expected risk premium on a stock should depend on the expected risk premium associated with each factor and the stock’s sensitivity to each of the factors (b1, b2, b3, etc.). Thus the formula is²⁰

Notice that this formula makes two statements:

1.   If you plug in a value of zero for each of the b’s in the formula, the expected risk premium is zero. A diversified portfolio that is constructed to have zero sensitivity to each macroeconomic factor is essentially risk-free and therefore must be priced to offer the risk-free rate of interest. If the portfolio offered a higher return, investors could make a risk-free (or “arbitrage”) profit by borrowing to buy the portfolio. If it offered a lower return, you could make an arbitrage profit by running the strategy in reverse; in other words, you would sell the diversified zero-sensitivity portfolio and invest the proceeds in U.S. Treasury bills.

2.   A diversified portfolio that is constructed to have exposure to, say, factor 1, will offer a risk premium, which will vary in direct proportion to the portfolio’s sensitivity to that factor. For example, imagine that you construct two portfolios, A and B, that are affected only by factor 1. If portfolio A is twice as sensitive as portfolio B to factor 1, portfolio A must offer twice the risk premium. Therefore, if you divided your money equally between U.S. Treasury bills and portfolio A, your combined portfolio would have exactly the same sensitivity to factor 1 as portfolio B and would offer the same risk premium.

Suppose that the arbitrage pricing formula did not hold. For example, suppose that the combination of Treasury bills and portfolio A offered a higher return. In that case investors could make an arbitrage profit by selling portfolio B and investing the proceeds in the mixture of bills and portfolio A.

The arbitrage that we have described applies to well-diversified portfolios, where the specific risk has been diversified away. But if the arbitrage pricing relationship holds for all diversified portfolios, it must generally hold for the individual stocks. Each stock must offer an expected return commensurate with its contribution to portfolio risk. In the APT, this contribution depends on the sensitivity of the stock’s return to unexpected changes in the macroeconomic factors.

A Comparison of the Capital Asset Pricing Model and Arbitrage Pricing Theory

Like the capital asset pricing model, arbitrage pricing theory stresses that expected return depends on the risk stemming from economywide influences and is not affected by specific risk. You can think of the factors in arbitrage pricing as representing special portfolios of stocks that tend to be subject to a common influence. If the expected risk premium on each of these portfolios is proportional to the portfolio’s market beta, then the arbitrage pricing theory and the capital asset pricing model will give the same answer. In any other case they will not.

How do the two theories stack up? Arbitrage pricing has some attractive features. For example, the market portfolio that plays such a central role in the capital asset pricing model does not feature in arbitrage pricing theory.²¹ So we do not have to worry about the problem of measuring the market portfolio, and in principle we can test the arbitrage pricing theory even if we have data on only a sample of risky assets.

Unfortunately you win some and lose some. Arbitrage pricing theory does not tell us what the underlying factors are—unlike the capital asset pricing model, which collapses all macroeconomic risks into a well-defined single factor, the return on the market portfolio.

The Three-Factor Model

Look back at the equation for APT. To estimate expected returns, you first need to follow three steps:

Step 1: Identify a reasonably short list of macroeconomic factors that could affect stock returns.

Step 2: Estimate the expected risk premium on each of these factors (rfactor 1 – rf, etc.).

Step 3: Measure the sensitivity of each stock to the factors (b1, b2, etc.).

One way to shortcut this process is to take advantage of the research by Fama and French, which showed that stocks of small firms and those with a high book-to-market ratio have provided above-average returns. This could simply be a coincidence. But there is also some evidence that these factors are related to company profitability and therefore may be picking up risk factors that are left out of the simple CAPM.²²

If investors do demand an extra return for taking on exposure to these factors, then we have a measure of the expected return that looks very much like arbitrage pricing theory:

This is commonly known as the Fama–French three-factor model. Using it to estimate expected returns is the same as applying the arbitrage pricing theory. Here is an example.²³

Step 1: Identify the Factors Fama and French have already identified the three factors that appear to determine expected returns. The returns on each of these factors are

Step 2: Estimate the Risk Premium for Each Factor We will keep to our figure of 7% for the market risk premium. History may provide a guide to the risk premium for the other two factors. As we saw earlier, between 1926 and 2011 the difference between the annual returns on small and large capitalization stocks averaged 3.6% a year, while the difference between the returns on stocks with high and low book-to-market ratios averaged 4.8%.

Step 3: Estimate the Factor Sensitivities Some stocks are more sensitive than others to fluctuations in the returns on the three factors. You can see this from the first three columns of numbers in Table 8.3, which show some estimates of the factor sensitivities of 10 industry groups for the 60 months ending in July 2011. For example, an increase of 1% in the return on the book-to-market factor reduces the return on computer stocks by .52% but increases the return on construction stocks by .22%. In other words, when value stocks (high book-to-market) outperform growth stocks (low book-to-market), computer stocks tend to perform relatively badly and construction stocks do relatively well.

   TABLE 8.3 Estimates of expected equity returns for selected industries using the Fama–French three-factor model and the CAPM.

a The expected return equals the risk-free interest rate plus the factor sensitivities multiplied by the factor risk premiums, that is, rf + (bmarket × 7) + (bsize × 3.6) + (bbook-to-market × 4.8).

b Estimated as rf + β(rm – rf ), that is, rf + β × 7. Note that we used simple regression to estimate β in the CAPM formula. This beta may, therefore, be different from bmarket that we estimated from a multiple regression of stock returns on the three factors.

Once you have estimated the factor sensitivities, it is a simple matter to multiply each of them by the expected factor return and add up the results. For example, the expected risk premium on computer stocks is r – rf = (1.22 × 7) + (.45 × 3.6) – (.52 × 4.8) = 7.7%. To calculate the expected return we need to add on the risk-free interest rate, which we assume to be 2%. Thus the three-factor model suggests that expected return on computer stocks is 2 + 7.7 = 9.7%.

Compare this figure with the expected return estimate using the capital asset pricing model (the final column of Table 8.3). The three-factor model provides a slightly lower estimate of the expected return for computer stocks. Why? Largely because computer stocks are growth stocks with a low exposure (–.52) to the book-to-market factor. The three-factor model produces a lower expected return for growth stocks, but it produces a higher figure for value stocks such as those of banks and construction companies which have a high book-to-market ratio.

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SUMMARY

The basic principles of portfolio selection boil down to a commonsense statement that investors try to increase the expected return on their portfolios and to reduce the standard deviation of that return. A portfolio that gives the highest expected return for a given standard deviation, or the lowest standard deviation for a given expected return, is known as an efficient portfolio. To work out which portfolios are efficient, an investor must be able to state the expected return and standard deviation of each stock and the degree of correlation between each pair of stocks.

Investors who are restricted to holding common stocks should choose efficient portfolios that suit their attitudes to risk. But investors who can also borrow and lend at the risk-free rate of interest should choose the best common stock portfolio regardless of their attitudes to risk. Having done that, they can then set the risk of their overall portfolio by deciding what proportion of their money they are willing to invest in stocks. The best efficient portfolio offers the highest ratio of forecasted risk premium to portfolio standard deviation.

For an investor who has only the same opportunities and information as everybody else, the best stock portfolio is the same as the best stock portfolio for other investors. In other words, he or she should invest in a mixture of the market portfolio and a risk-free loan (i.e., borrowing or lending).

A stock’s marginal contribution to portfolio risk is measured by its sensitivity to changes in the value of the portfolio. The marginal contribution of a stock to the risk of the market portfolio is measured by beta. That is the fundamental idea behind the capital asset pricing model (CAPM), which concludes that each security’s expected risk premium should increase in proportion to its beta:

The capital asset pricing theory is the best-known model of risk and return. It is plausible and widely used but far from perfect. Actual returns are related to beta over the long run, but the relationship is not as strong as the CAPM predicts, and other factors seem to explain returns better since the mid-1960s. Stocks of small companies, and stocks with high book values relative to market prices, appear to have risks not captured by the CAPM.

The arbitrage pricing theory offers an alternative theory of risk and return. It states that the expected risk premium on a stock should depend on the stock’s exposure to several pervasive macroeconomic factors that affect stock returns:

Here b’s represent the individual security’s sensitivities to the factors, and rfactor – rf is the risk premium demanded by investors who are exposed to this factor.

Arbitrage pricing theory does not say what these factors are. It asks for economists to hunt for unknown game with their statistical toolkits. Fama and French have suggested three factors:

•   The return on the market portfolio less the risk-free rate of interest.

•   The difference between the return on small- and large-firm stocks.

•   The difference between the return on stocks with high book-to-market ratios and stocks with low book-to-market ratios.

In the Fama–French three-factor model, the expected return on each stock depends on its exposure to these three factors.

Each of these different models of risk and return has its fan club. However, all financial economists agree on two basic ideas: (1) Investors require extra expected return for taking on risk, and (2) they appear to be concerned predominantly with the risk that they cannot eliminate by diversification.

Near the end of Chapter 9 we list some Excel Functions that are useful for measuring the risk of stocks and portfolios.

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FURTHER READING

A number of textbooks on portfolio selection explain both Markowitz’s original theory and some ingenious simplified versions. See, for example,

E. J. Elton, M. J. Gruber, S. J. Brown, and W. N. Goetzmann: Modern Portfolio Theory and Investment Analysis, 7th ed. (New York: John Wiley & Sons, 2007).

The literature on the capital asset pricing model is enormous. There are dozens of published tests of the capital asset pricing model. Fischer Black’s paper is a very readable example. Discussions of the theory tend to be more uncompromising. Two excellent but advanced examples are Campbell’s survey paper and Cochrane’s book.

F. Black, “Beta and Return,” Journal of Portfolio Management 20 (Fall 1993), pp. 8–18.

J. Y. Campbell, “Asset Pricing at the Millennium,” Journal of Finance 55 (August 2000), pp. 1515–1567.

J. H. Cochrane, Asset Pricing, revised ed. (Princeton, NJ: Princeton University Press, 2004).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.   Portfolio risk and return Here are returns and standard deviations for four investments.

Calculate the standard deviations of the following portfolios.

a.  50% in Treasury bills, 50% in stock P.

b.  50% each in Q and R, assuming the shares have

•  perfect positive correlation.

•  perfect negative correlation.

•  no correlation.

c.  Plot a figure like Figure 8.3 for Q and R, assuming a correlation coefficient of .5.

d.  Stock Q has a lower return than R but a higher standard deviation. Does that mean that Q’s price is too high or that R’s price is too low?

2.   Portfolio risk and return For each of the following pairs of investments, state which would always be preferred by a rational investor (assuming that these are the only investments available to the investor):

3.   Sharpe ratio Use the long-term data on security returns in Sections 7-1 and 7-2 to calculate the historical level of the Sharpe ratio of the market portfolio.

4.   Efficient portfolios Figure 8.11 below purports to show the range of attainable combinations of expected return and standard deviation.

a.  Which diagram is incorrectly drawn and why?

b.  Which is the efficient set of portfolios?

c.  If rf is the rate of interest, mark with an X the optimal stock portfolio.

5.   Efficient portfolios

a.  Plot the following risky portfolios on a graph:

b.  Five of these portfolios are efficient, and three are not. Which are inefficient ones?

c.  Suppose you can also borrow and lend at an interest rate of 12%. Which of the above portfolios has the highest Sharpe ratio?

d.  Suppose you are prepared to tolerate a standard deviation of 25%. What is the maximum expected return that you can achieve if you cannot borrow or lend?

e.  What is your optimal strategy if you can borrow or lend at 12% and are prepared to tolerate a standard deviation of 25%? What is the maximum expected return that you can achieve with this risk?

6.   CAPM Suppose that the Treasury bill rate is 6% rather than 2%. Assume that the expected return on the market stays at 10%. Use the betas in Table 8.2.

   FIGURE 8.11 See Problem 4.

a.  Calculate the expected return from Pfizer.

b.  Find the highest expected return that is offered by one of these stocks.

c.  Find the lowest expected return that is offered by one of these stocks.

d.  Would Ford offer a higher or lower expected return if the interest rate were 6% rather than 2%? Assume that the expected market return stays at 10%.

e.  Would Walmart offer a higher or lower expected return if the interest rate were 8%?

7.   CAPM True or false?

a.  The CAPM implies that if you could find an investment with a negative beta, its expected return would be less than the interest rate.

b.  The expected return on an investment with a beta of 2.0 is twice as high as the expected return on the market.

c.  If a stock lies below the security market line, it is undervalued.

8.   APT Consider a three-factor APT model. The factors and associated risk premiums are

Calculate expected rates of return on the following stocks. The risk-free interest rate is 7%.

a.  A stock whose return is uncorrelated with all three factors.

b.  A stock with average exposure to each factor (i.e., with b = 1 for each).

c.  A pure-play energy stock with high exposure to the energy factor (b = 2) but zero exposure to the other two factors.

d.  An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b = – 1.5 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices rise.)

INTERMEDIATE

9.   True/false True or false? Explain or qualify as necessary.

a.  Investors demand higher expected rates of return on stocks with more variable rates of return.

b.  The CAPM predicts that a security with a beta of 0 will offer a zero expected return.

c.  An investor who puts $10,000 in Treasury bills and $20,000 in the market portfolio will have a beta of 2.0.

d.  Investors demand higher expected rates of return from stocks with returns that are highly exposed to macroeconomic risks.

e.  Investors demand higher expected rates of return from stocks with returns that are very sensitive to fluctuations in the stock market.

10.   Portfolio risk and return Look back at the calculation for Heinz and Exxon in Section 8-1. Recalculate the expected portfolio return and standard deviation for different values of x1 and x2, assuming the correlation coefficient ρ12 = 0. Plot the range of possible combinations of expected return and standard deviation as in Figure 8.3. Repeat the problem for ρ12 = +.25.

11.   Portfolio risk and return Mark Harrywitz proposes to invest in two shares, X and Y. He expects a return of 12% from X and 8% from Y. The standard deviation of returns is 8% for X and 5% for Y. The correlation coefficient between the returns is .2.

a.  Compute the expected return and standard deviation of the following portfolios:

b.  Sketch the set of portfolios composed of X and Y.

c.  Suppose that Mr. Harrywitz can also borrow or lend at an interest rate of 5%. Show on your sketch how this alters his opportunities. Given that he can borrow or lend, what proportions of the common stock portfolio should be invested in X and Y?

12.   Portfolio risk and return Ebenezer Scrooge has invested 60% of his money in share A and the remainder in share B. He assesses their prospects as follows:

a.  What are the expected return and standard deviation of returns on his portfolio?

b.  How would your answer change if the correlation coefficient were 0 or –.5?

c.  Is Mr. Scrooge’s portfolio better or worse than one invested entirely in share A, or is it not possible to say?

13.   Sharpe ratio Look back at Problem 3 in Chapter 7. The risk-free interest rate in each of these years was as follows:

a.  Calculate the average return and standard deviation of returns for Ms. Sauros’s portfolio and for the market. Use these figures to calculate the Sharpe ratio for the portfolio and the market. On this measure did Ms. Sauros perform better or worse than the market?

b.  Now calculate the average return that you could have earned over this period if you had held a combination of the market and a risk-free loan. Make sure that the combination has the same beta as Ms. Sauros’s portfolio. Would your average return on this portfolio have been higher or lower?

Explain your results.

14.   Portfolio beta Look back at Table 7.5 on page 179.

a.  What is the beta of a portfolio that has 40% invested in Ford and 60% in Pfizer?

b.  Would you invest in this portfolio if you had no superior information about the prospects for these stocks? Devise an alternative portfolio with the same expected return and less risk.

c.  Now repeat parts (a) and (b) with a portfolio that has 40% invested in Starbucks and 60% in Walmart.

15.   CAPM The Treasury bill rate is 4%, and the expected return on the market portfolio is 12%. Using the capital asset pricing model:

a.  Draw a graph similar to Figure 8.6 showing how the expected return varies with beta.

b.  What is the risk premium on the market?

c.  What is the required return on an investment with a beta of 1.5?

d.  If an investment with a beta of .8 offers an expected return of 9.8%, does it have a positive NPV?

e.  If the market expects a return of 11.2% from stock X, what is its beta?

16.   Portfolio risk and return Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9%, and the annual standard deviation is 10%.

Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund that closely tracks the Standard & Poor’s 500 Index. The index has an expected return of 14%, and its standard deviation is 16%.

a.  Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he thereby improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 6%.

b.  Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is +.1.

17.   Cost of capital Gianni Schicchi is evaluating an expansion of his business. The cash-flow forecasts for the project are as follows:

The firm’s existing assets have a beta of 1.4. The risk-free interest rate is 4% and the expected return on the market portfolio is 12%. What is the project’s NPV?

18.   APT Some true or false questions about the APT:

a.  The APT factors cannot reflect diversifiable risks.

b.  The market rate of return cannot be an APT factor.

c.  There is no theory that specifically identifies the APT factors.

d.  The APT model could be true but not very useful, for example, if the relevant factors change unpredictably.

19.   APT Consider the following simplified APT model:

Calculate the expected return for the following stocks. Assume rf = 5%.

20.   APT Look again at Problem 19. Consider a portfolio with equal investments in stocks P, P2, and P3.

a.  What are the factor risk exposures for the portfolio?

b.  What is the portfolio’s expected return?

21.   APT The following table shows the sensitivity of four stocks to the three Fama–French factors. Estimate the expected return on each stock assuming that the interest rate is 2%, the expected risk premium on the market is 7%, the expected risk premium on the size factor is 3.7%, and the expected risk premium on the book-to-market factor is 4.9%.

CHALLENGE

22.   Minimum-risk portfolio In footnote 4 we noted that the minimum-risk portfolio contained an investment of 84.9% in Heinz and 15.1% in Exxon Mobil. Prove it. (Hint: You need a little calculus to do so.)

23.   Efficient portfolios Look again at the set of the three efficient portfolios that we calculated in Section 8-1.

a.  If the interest rate is 10%, which of the four efficient portfolios should you hold?

b.  What is the beta of each holding relative to that portfolio? (Hint: Note that if a portfolio is efficient, the expected risk premium on each holding must be proportional to the beta of the stock relative to that portfolio.)

c.  How would your answers to (a) and (b) change if the interest rate were 5%?

24.   APT The following question illustrates the APT. Imagine that there are only two pervasive macroeconomic factors. Investments X, Y, and Z have the following sensitivities to these two factors:

We assume that the expected risk premium is 4% on factor 1 and 8% on factor 2. Treasury bills obviously offer zero risk premium.

a.  According to the APT, what is the risk premium on each of the three stocks?

b.  Suppose you buy $200 of X and $50 of Y and sell $150 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?

c.  Suppose you buy $80 of X and $60 of Y and sell $40 of Z. What is the sensitivity of your portfolio to each of the two factors? What is the expected risk premium?

d.  Finally, suppose you buy $160 of X and $20 of Y and sell $80 of Z. What is your portfolio’s sensitivity now to each of the two factors? And what is the expected risk premium?

e.  Suggest two possible ways that you could construct a fund that has a sensitivity of .5 to factor 1 only. (Hint: One portfolio contains an investment in Treasury bills.) Now compare the risk premiums on each of these two investments.

f.  Suppose that the APT did not hold and that X offered a risk premium of 8%, Y offered a premium of 14%, and Z offered a premium of 16%. Devise an investment that has zero sensitivity to each factor and that has a positive risk premium.

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FINANCE ON THE WEB

You can download data for the following questions from finance.yahoo.com.

The book’s website (www.mcgraw-hill.co.uk/textbooks/brealey) contains an Excel program for calculating the efficient frontier. (We are grateful to Darien Huang for providing us with a copy of this program.) Excel functions SLOPE, STDEV, COVAR, and CORREL are especially useful for answering the following questions.

1.   a.  Download up to 10 years of monthly returns for 10 different stocks and enter them into the Excel program. Enter some plausible figures for the expected return on each stock and find the set of efficient portfolios. Assume that you cannot borrow or lend.

b.  How does the possibility of short sales improve the choices open to the investor?

2.   Find a low-risk stock—Walmart or Kellogg would be a good candidate. Use monthly returns for the most recent three years to confirm that the beta is less than 1.0. Now estimate the annual standard deviation for the stock and the S&P index, and the correlation between the returns on the stock and the index. Forecast the expected return for the stock, assuming the CAPM holds, with a market return of 12% and a risk-free rate of 5%.

a.  Plot a graph like Figure 8.5 showing the combinations of risk and return from a portfolio invested in your low-risk stock and the market. Vary the fraction invested in the stock from 0 to 100%.

b.  Suppose that you can borrow or lend at 5%. Would you invest in some combination of your low-risk stock and the market, or would you simply invest in the market? Explain.

c.  Suppose that you forecasted a return on the stock that is 5 percentage points higher than the CAPM return used in part (b). Redo parts (a) and (b) with the higher forecasted return.

d.  Find a high-risk stock and redo parts (a) and (b).

3.   Recalculate the betas for the stocks in Table 8.2 using the latest 60 monthly returns. Recalculate expected rates of return from the CAPM formula, using a current risk-free rate and a market risk premium of 7%. How have the expected returns changed from Table 8.2?

MINI-CASE ● ● ● ● ●

John and Marsha on Portfolio Selection

The scene: John and Marsha hold hands in a cozy French restaurant in downtown Manhattan, several years before the mini-case in Chapter 9. Marsha is a futures-market trader. John manages a $125 million common-stock portfolio for a large pension fund. They have just ordered tournedos financiere for the main course and flan financiere for dessert. John reads the financial pages of The Wall Street Journal by candlelight.

John: Wow! Potato futures hit their daily limit. Let’s add an order of gratin dauphinoise. Did you manage to hedge the forward interest rate on that euro loan?

Marsha: John, please fold up that paper. (He does so reluctantly.) John, I love you. Will you marry me?

John: Oh, Marsha, I love you too, but . . . there’s something you must know about me—something I’ve never told anyone.

Marsha: (concerned) John, what is it?

John: I think I’m a closet indexer.

Marsha: What? Why?

John: My portfolio returns always seem to track the S&P 500 market index. Sometimes I do a little better, occasionally a little worse. But the correlation between my returns and the market returns is over 90%.

Marsha: What’s wrong with that? Your client wants a diversified portfolio of large-cap stocks. Of course your portfolio will follow the market.

John: Why doesn’t my client just buy an index fund? Why is he paying me? Am I really adding value by active management? I try, but I guess I’m just an . . . indexer.

Marsha: Oh, John, I know you’re adding value. You were a star security analyst.

John: It’s not easy to find stocks that are truly over- or undervalued. I have firm opinions about a few, of course.

Marsha: You were explaining why Pioneer Gypsum is a good buy. And you’re bullish on Global Mining.

John: Right, Pioneer. (Pulls handwritten notes from his coat pocket.) Stock price $87.50. I estimate the expected return as 11% with an annual standard deviation of 32%.

Marsha: Only 11%? You’re forecasting a market return of 12.5%.

John: Yes, I’m using a market risk premium of 7.5% and the risk-free interest rate is about 5%. That gives 12.5%. But Pioneer’s beta is only .65. I was going to buy 30,000 shares this morning, but I lost my nerve. I’ve got to stay diversified.

Marsha: Have you tried modern portfolio theory?

John: MPT? Not practical. Looks great in textbooks, where they show efficient frontiers with 5 or 10 stocks. But I choose from hundreds, maybe thousands, of stocks. Where do I get the inputs for 1,000 stocks? That’s a million variances and covariances!

Marsha: Actually only about 500,000, dear. The covariances above the diagonal are the same as the covariances below. But you’re right, most of the estimates would be out-of-date or just garbage.

John: To say nothing about the expected returns. Garbage in, garbage out.

Marsha: But John, you don’t need to solve for 1,000 portfolio weights. You only need a handful. Here’s the trick: Take your benchmark, the S&P 500, as security 1. That’s what you would end up with as an indexer. Then consider a few securities you really know something about. Pioneer could be security 2, for example. Global, security 3. And so on. Then you could put your wonderful financial mind to work.

John: I get it: active management means selling off some of the benchmark portfolio and investing the proceeds in specific stocks like Pioneer. But how do I decide whether Pioneer really improves the portfolio? Even if it does, how much should I buy?

Marsha: Just maximize the Sharpe ratio, dear.

John: I’ve got it! The answer is yes!

Marsha: What’s the question?

John: You asked me to marry you. The answer is yes. Where should we go on our honeymoon?

Marsha: How about Australia? I’d love to visit the Sydney Futures Exchange.

QUESTIONS

1.  Table 8.4 reproduces John’s notes on Pioneer Gypsum and Global Mining. Calculate the expected return, risk premium, and standard deviation of a portfolio invested partly in the market and partly in Pioneer. (You can calculate the necessary inputs from the betas and standard deviations given in the table.) Does adding Pioneer to the market benchmark improve the Sharpe ratio? How much should John invest in Pioneer and how much in the market?

2.  Repeat the analysis for Global Mining. What should John do in this case? Assume that Global accounts for .75% of the S&P index. (Assume a market standard deviation of 16%.)

   TABLE 8.4 John’s notes on Pioneer Gypsum and Global Mining.

___________

¹H. M. Markowitz, “Portfolio Selection,” Journal of Finance 7 (March 1952), pp. 77–91.

²If you were to measure returns over long intervals, the distribution would be skewed. For example, you would encounter returns greater than 100% but none less than –100%. The distribution of returns over periods of, say, one year would be better approximated by a lognormal distribution. The lognormal distribution, like the normal, is completely specified by its mean and standard deviation. You would also find that the distribution of price changes has a longer tail than the normal and lognormal distributions. Extreme events or “black swans” crop up with alarming frequency.

³We pointed out in Section 7-3 that the correlation between the returns of Heinz and Exxon has been about .49. The variance of a portfolio which is invested 60% in Heinz and 40% in Exxon is

The portfolio standard deviation is .

⁴The portfolio with the minimum risk has 84.9% in Heinz. We assume in Figure 8.3 that you may not take negative positions in either stock, that is, we rule out short sales.

⁵There are 45 different correlation coefficients, so we have not listed them in Table 8.1.

⁶If you want to check this, write down the formula for the standard deviation of a two-stock portfolio:

Now see what happens when security 2 is riskless, that is, when σ2 = 0.

⁷Remember that the risk premium is the difference between the investment’s expected return and the risk-free rate. For Treasury bills, the difference is zero.

⁸W. F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance 19 (September 1964), pp. 425–442; and J. Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Economics and Statistics 47 (February 1965), pp. 13–37. Treynor’s article has not been published.

⁹Remember that instead of investing in plant and machinery, the firm could return the money to the shareholders. The opportunity cost of investing is the return that shareholders could expect to earn by buying financial assets. This expected return depends on the market risk of the assets.

¹⁰Unless, of course, we were trying to sell it.

¹¹Of course, investing in A or B only would be stupid; you would hold an undiversified portfolio.

¹²See J. R. Graham and C. R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187–243. A number of the managers surveyed reported using more than one method to estimate the cost of capital. Seventy-three percent used the capital asset pricing model, while 39% stated they used the average historical stock return and 34% used the capital asset pricing model with some extra risk factors.

¹³Betas were estimated using returns over the previous 60 months.

¹⁴In Figure 8.8 the stocks in the “market portfolio” are weighted equally. Since the stocks of small firms have provided higher average returns than those of large firms, the risk premium on an equally weighted index is higher than on a value-weighted index. This is one reason for the difference between the 11.8% market risk premium in Figure 8.8 and the 7.3% premium reported in Table 7.1.

¹⁵A second problem with testing the model is that the market portfolio should contain all risky investments, including stocks, bonds, commodities, real estate—even human capital. Most market indexes contain only a sample of common stocks.

¹⁶We say “simple version” because Fischer Black has shown that if there are borrowing restrictions, there should still exist a positive relationship between expected return and beta, but the security market line would be less steep as a result. See F. Black, “Capital Market Equilibrium with Restricted Borrowing,” Journal of Business 45 (July 1972), pp. 444–455.

¹⁷Fama and French calculated the returns on portfolios designed to take advantage of the size effect and the book-to-market effect. See E. F. Fama and K. R. French, “The Cross-Section of Expected Stock Returns,” Journal of Financial Economics 47 (June 1992), pp. 427–465. When calculating the returns on these portfolios, Fama and French control for differences in firm size when comparing stocks with low and high book-to-market ratios. Similarly, they control for differences in the book-to-market ratio when comparing small- and large-firm stocks. For details of the methodology and updated returns on the size and book-to-market factors see Kenneth French’s website (mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html).

¹⁸An investor who bought small-company stocks and sold large-company stocks would have incurred some risk. Her portfolio would have had a beta of .28. This is not nearly large enough to explain the difference in returns. There is no simple relationship between the return on the value- and growth-stock portfolios and beta.

¹⁹We discuss aversion to loss again in Chapter 13. The implications for asset pricing are explored in S. Benartzi and R. Thaler, “Myopic Loss Aversion and the Equity Premium Puzzle,” Quarterly Journal of Economics 110 (1995), pp. 75–92; and in N. Barberis, M. Huang, and T. Santos, “Prospect Theory and Asset Prices,” Quarterly Journal of Economics 116 (2001), pp. 1–53.

²⁰There may be some macroeconomic factors that investors are simply not worried about. For example, some macroeconomists believe that money supply doesn’t matter and therefore investors are not worried about inflation. Such factors would not command a risk premium. They would drop out of the APT formula for expected return.

²¹Of course, the market portfolio may turn out to be one of the factors, but that is not a necessary implication of arbitrage pricing theory.

²²E. F. Fama and K. R. French, “Size and Book-to-Market Factors in Earnings and Returns,” Journal of Finance 50 (1995), pp. 131–155.

²³The three-factor model was first used to estimate the cost of capital for different industry groups by Fama and French. See E. F. Fama and K. R. French, “Industry Costs of Equity,” Journal of Financial Economics 43 (1997), pp. 153–193. Fama and French emphasize the imprecision in using either the CAPM or an APT-style model to estimate the returns that investors expect.

Part 2 Risk

Risk and the Cost of Capital

L ong before the development of modern theories linking risk and return, smart financial managers adjusted for risk in capital budgeting. They knew that risky projects are, other things equal, less valuable than safe ones—that is just common sense. Therefore they demanded higher rates of return from risky projects, or they based their decisions about risky projects on conservative forecasts of project cash flows.

Today most companies start with the company cost of capital as a benchmark risk-adjusted discount rate for new investments. The company cost of capital is the right discount rate only for investments that have the same risk as the company’s overall business. For riskier projects the opportunity cost of capital is greater than the company cost of capital. For safer projects it is less.

The company cost of capital is usually estimated as a weighted-average cost of capital, that is, as the average rate of return demanded by investors in the company’s debt and equity. The hardest part of estimating the weighted-average cost of capital is figuring out the cost of equity, that is, the expected rate of return to investors in the firm’s common stock. Many firms turn to the capital asset pricing model (CAPM) for an answer. The CAPM states that the expected rate of return equals the risk-free interest rate plus a risk premium that depends on beta and the market risk premium.

We explained the CAPM in the last chapter, but didn’t show you how to estimate betas. You can’t look up betas in a newspaper or see them clearly by tracking a few day-to-day changes in stock price. But you can get useful statistical estimates from the history of stock and market returns.

Now suppose you’re responsible for a specific investment project. How do you know if the project is average risk or above- or below-average risk? We suggest you check whether the project’s cash flows are more or less sensitive to the business cycle than the average project. Also check whether the project has higher or lower fixed operating costs (higher or lower operating leverage) and whether it requires large future investments.

Remember that a project’s cost of capital depends only on market risk. Diversifiable risk can affect project cash flows but does not increase the cost of capital. Also don’t be tempted to add arbitrary fudge factors to discount rates. Fudge factors are too often added to discount rates for projects in unstable parts of the world, for example.

Risk varies from project to project. Risk can also vary over time for a given project. For example, some projects are riskier in youth than in old age. But financial managers usually assume that project risk will be the same in every future period, and they use a single risk-adjusted discount rate for all future cash flows. We close the chapter by introducing certainty equivalents, which illustrate how risk can change over time.

 9-1   Company and Project Costs of Capital

The company cost of capital is defined as the expected return on a portfolio of all the company’s existing securities. It is the opportunity cost of capital for investment in the firm’s assets, and therefore the appropriate discount rate for the firm’s average-risk projects.

If the firm has no debt outstanding, then the company cost of capital is just the expected rate of return on the firm’s stock. Many large, successful companies pretty well fit this special case, including Johnson & Johnson (J&J). Johnson and Johnson’s common stock has a beta of about .5. Suppose that the risk-free interest rate is 2% and the market risk premium is 7%. Then the capital asset pricing model would imply an expected return of 5.5% from J&J’s stock:

If J&J is contemplating an expansion of its existing business, it would make sense to discount the forecasted cash flows at 5.5%.¹

The company cost of capital is not the correct discount rate if the new projects are more or less risky than the firm’s existing business. Each project should in principle be evaluated at its own opportunity cost of capital. This is a clear implication of the value-additivity principle introduced in Chapter 7. For a firm composed of assets A and B, the firm value is

Here PV(A) and PV(B) are valued just as if they were mini-firms in which stockholders could invest directly. Investors would value A by discounting its forecasted cash flows at a rate reflecting the risk of A. They would value B by discounting at a rate reflecting the risk of B. The two discount rates will, in general, be different. If the present value of an asset depended on the identity of the company that bought it, present values would not add up, and we know they do add up. (Consider a portfolio of $1 million invested in J&J and $1 million invested in Toyota. Would any reasonable investor say that the portfolio is worth anything more or less than $2 million?)

If the firm considers investing in a third project C, it should also value C as if C were a mini-firm. That is, the firm should discount the cash flows of C at the expected rate of return that investors would demand if they could make a separate investment in C. The opportunity cost of capital depends on the use to which that capital is put.

Perhaps we’re saying the obvious. Think of J&J: It is a massive health care and consumer products company, with $65 billion in sales in 2011. J&J has well-established consumer products, including Band-Aid® bandages, Tylenol®, and products for skin care and babies. It also invests heavily in much chancier ventures, such as biotech research and development (R&D). Do you think that a new production line for baby lotion has the same cost of capital as an investment in biotech R&D? We don’t, though we admit that estimating the cost of capital for biotech R&D could be challenging.

Suppose we measure the risk of each project by its beta. Then J&J should accept any project lying above the upward-sloping security market line that links expected return to risk in Figure 9.1. If the project is high-risk, J&J needs a higher prospective return than if the project is low-risk. That is different from the company cost of capital rule, which accepts any project regardless of its risk as long as it offers a higher return than the company’s cost of capital.

   FIGURE 9.1 A comparison between the company cost of capital rule and the required return from the capital asset pricing model. J&J’s company cost of capital is about 5.5%. This is the correct discount rate only if the project beta is .50. In general, the correct discount rate increases as project beta increases. J&J should accept projects with rates of return above the security market line relating required return to beta.

The rule tells J&J to accept any project above the horizontal cost of capital line in Figure 9.1, that is, any project offering a return of more than 5.5%.

It is clearly silly to suggest that J&J should demand the same rate of return from a very safe project as from a very risky one. If J&J used the company cost of capital rule, it would reject many good low-risk projects and accept many poor high-risk projects. It is also silly to suggest that just because another company has a still lower company cost of capital, it is justified in accepting projects that J&J would reject.

Perfect Pitch and the Cost of Capital

The true cost of capital depends on project risk, not on the company undertaking the project. So why is so much time spent estimating the company cost of capital?

There are two reasons. First, many (maybe most) projects can be treated as average risk, that is, neither more nor less risky than the average of the company’s other assets. For these projects the company cost of capital is the right discount rate. Second, the company cost of capital is a useful starting point for setting discount rates for unusually risky or safe projects. It is easier to add to, or subtract from, the company cost of capital than to estimate each project’s cost of capital from scratch.

There is a good musical analogy here. Most of us, lacking perfect pitch, need a well-defined reference point, like middle C, before we can sing on key. But anyone who can carry a tune gets relative pitches right. Businesspeople have good intuition about relative risks, at least in industries they are used to, but not about absolute risk or required rates of return. Therefore, they set a companywide cost of capital as a benchmark. This is not the right discount rate for everything the company does, but adjustments can be made for more or less risky ventures.

That said, we have to admit that many large companies use the company cost of capital not just as a benchmark, but also as an all-purpose discount rate for every project proposal. Measuring differences in risk is difficult to do objectively, and financial managers shy away from intracorporate squabbles. (You can imagine the bickering: “My projects are safer than yours! I want a lower discount rate!” “No they’re not! Your projects are riskier than a naked call option!”)²

When firms force the use of a single company cost of capital, risk adjustment shifts from the discount rate to project cash flows. Top management may demand extra-conservative cash-flow forecasts from extra-risky projects. They may refuse to sign off on an extra-risky project unless NPV, computed at the company cost of capital, is well above zero. Rough-and-ready risk adjustments are better than none at all.

Debt and the Company Cost of Capital

We defined the company cost of capital as “the expected return on a portfolio of all the company’s existing securities.” That portfolio usually includes debt as well as equity. Thus the cost of capital is estimated as a blend of the cost of debt (the interest rate) and the cost of equity (the expected rate of return demanded by investors in the firm’s common stock).

Suppose the company’s market-value balance sheet looks like this:

The values of debt and equity add up to overall firm value (D + E = V) and firm value V equals asset value. These figures are all market values, not book (accounting) values. The market value of equity is often much larger than the book value, so the market debt ratio D/V is often much lower than a debt ratio computed from the book balance sheet.

The 7.5% cost of debt is the opportunity cost of capital for the investors who hold the firm’s debt. The 15% cost of equity is the opportunity cost of capital for the investors who hold the firm’s shares. Neither measures the company cost of capital, that is, the opportunity cost of investing in the firm’s assets. The cost of debt is less than the company cost of capital, because debt is safer than the assets. The cost of equity is greater than the company cost of capital, because the equity of a firm that borrows is riskier than the assets. Equity is not a direct claim on the firm’s free cash flow. It is a residual claim that stands behind debt.

The company cost of capital is not equal to the cost of debt or to the cost of equity but is a blend of the two. Suppose you purchased a portfolio consisting of 100% of the firm’s debt and 100% of its equity. Then you would own 100% of its assets lock, stock, and barrel. You would not share the firm’s free cash flow with anyone; every dollar that the firm pays out would be paid to you.

The expected rate of return on your hypothetical portfolio is the company cost of capital. The expected rate of return is just a weighted average of the cost of debt (rD = 7.5%) and the cost of equity (rE = 15%). The weights are the relative market values of the firm’s debt and equity, that is, D/V = 30% and E/V = 70%.³

This blended measure of the company cost of capital is called the weighted-average cost of capital or WACC (pronounced “whack”). Calculating WACC is a bit more complicated than our example suggests, however. For example, interest is a tax-deductible expense for corporations, so the after-tax cost of debt is (1 – Tc)rD, where Tc is the marginal corporate tax rate. Suppose Tc = 35%. Then after-tax WACC is

We give another example of the after-tax WACC later in this chapter, and we cover the topic in much more detail in Chapter 19. But now we turn to the hardest part of calculating WACC, estimating the cost of equity.

 9-2   Measuring the Cost of Equity

To calculate the weighted-average cost of capital, you need an estimate of the cost of equity. You decide to use the capital asset pricing model (CAPM). Here you are in good company: as we saw in the last chapter, most large U.S. companies do use the CAPM to estimate the cost of equity, which is the expected rate of return on the firm’s common stock.⁴ The CAPM says that

Now you have to estimate beta. Let us see how that is done in practice.

Estimating Beta

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How to estimate beta

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In principle we are interested in the future beta of the company’s stock, but lacking a crystal ball, we turn first to historical evidence. For example, look at the scatter diagram at the top left of Figure 9.2. Each dot represents the return on Citigroup stock and the return on the market in a particular week. The plot starts in January 2010 and runs to December 2011, so there are 104 dots in all.

   FIGURE 9.2 We have used past returns to estimate the betas of three stocks for the periods January 2010 to December 2011 (left-hand diagrams) and January 2008 to December 2009 (right-hand diagrams). Beta is the slope of the fitted line. Notice that in both periods Citigroup had the highest beta and Campbell Soup the lowest. Standard errors are in parentheses below the betas. The standard error shows the range of possible error in the beta estimate. We also report the proportion of total risk that is due to market movements (R2).

The second diagram on the left shows a similar plot for the returns on Disney stock, and the third shows a plot for Campbell Soup. In each case we have fitted a line through the points. The slope of this line is an estimate of beta. It tells us how much on average the stock price changed when the market return was 1% higher or lower.

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Try It! Comparing beta estimates

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The right-hand diagrams show similar plots for the same three stocks during the subsequent period ending in December 2009. Betas do change. As you might expect, Citigroup’s beta leapt skyward during the financial crisis. You would have been well off target if you had blindly used its beta during the crisis period to predict its beta in more normal times. However, you could have been pretty confident that Campbell Soup’s beta was much less than Citigroup’s and that Disney’s beta was somewhere between the two.⁵

Only a small portion of each stock’s total risk comes from movements in the market. The rest is firm-specific, diversifiable risk, which shows up in the scatter of points around the fitted lines in Figure 9.2. R-squared (R2) measures the proportion of the total variance in the stock’s returns that can be explained by market movements. For example, from 2010 to 2011, the R2 for Campbell Soup was .22. In other words, 22% of Campbell Soup’s risk was market risk and 78% was diversifiable risk. The variance of the returns on Campbell Soup stock was 187.⁶ So we could say that the variance in stock returns that was due to the market was .22 × 187 = 41, and the variance of diversifiable returns was .78 × 187 = 146.

The estimates of beta shown in Figure 9.2 are just that. They are based on the stocks’ returns in 104 particular weeks. The noise in the returns can obscure the true beta.⁷ Therefore, statisticians calculate the standard error of the estimated beta to show the extent of possible mismeasurement. Then they set up a confidence interval of the estimated value plus or minus two standard errors. For example, the standard error of Campbell Soup’s estimated beta in the most recent period is about .06. Thus the confidence interval for Campbell Soup’s beta is .33 plus or minus 2 × .06. If you state that the true beta for Campbell Soup is between .21 and .45, you have a 95% chance of being right. Notice that we can be equally confident of our estimate of Disney’s beta, but much less confident of Citigroup’s.

Usually you will have more information (and thus more confidence) than this simple, and somewhat depressing, calculation suggests. For example, you know that Campbell Soup’s estimated beta was well below 1 in two successive two-year periods. Citigroup’s estimated beta was well above 1 in both periods. Nevertheless, there is always a large margin for error when estimating the beta for individual stocks.

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Try It! Beta estimates for U.S. stocks

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Fortunately, the estimation errors tend to cancel out when you estimate betas of portfolios.⁸ That is why financial managers often turn to industry betas. For example, Table 9.1 shows estimates of beta and the standard errors of these estimates for the common stocks of seven railroad companies. Three of the standard errors are .1 or above. However, the table also shows the estimated beta for a portfolio of all seven railroad stocks. Notice that the estimated industry beta is somewhat more reliable. This shows up in the lower standard error.

   TABLE 9.1 Estimates of betas and standard errors for a sample of railroad companies and for an equally weighted portfolio of these companies, based on weekly returns from January 2010 to December 2011. The portfolio beta is more reliable than the betas of the individual companies. Note the lower standard error for the portfolio.

The Expected Return on Union Pacific Corporation’s Common Stock

Suppose that in early 2012 you had been asked to estimate the company cost of capital of Union Pacific. Table 9.1 provides two clues about the true beta of Union Pacific’s stock: the direct estimate of 1.21 and the average estimate for the industry of 1.34. We will use the direct estimate of 1.21.⁹

The next issue is what value to use for the risk-free interest rate. By the first months of 2012, the U.S. Federal Reserve Board had pushed down Treasury bill rates to .02% in an attempt to stimulate the economy. The one-year interest rate was only a little higher, at .12%. Yields on longer-maturity U.S. Treasury bonds were higher still, at about 2.7% on 20-year bonds.

The CAPM is a short-term model. It works period by period and calls for a short-term interest rate. But could a .02% three-month risk-free rate give the right discount rate for cash flows 10 or 20 years in the future? Well, now that you mention it, probably not.

Financial managers muddle through this problem in one of two ways. The first way simply uses a long-term risk-free rate in the CAPM formula. If this short-cut is used, then the market risk premium must be restated as the average difference between market returns and returns on long-term Treasuries.¹⁰

The second way retains the usual definition of the market risk premium as the difference between market returns and returns on short-term Treasury bill rates. But now you have to forecast the expected return from holding Treasury bills over the life of the project. In Chapter 3 we observed that investors require a risk premium for holding long-term bonds rather than bills. Table 7.1 showed that over the past century this risk premium has averaged about 1.4%. So to get a rough but reasonable estimate of the expected long-term return from investing in Treasury bills, we need to subtract 1.4% from the current yield on long-term bonds. In our example

This is a plausible estimate of the expected average future return on Treasury bills. We therefore use this rate in our example.

Returning to our Union Pacific example, suppose you decide to use a market risk premium of 7%. Then the resulting estimate for Union Pacific’s cost of equity is about 9.7%:

Union Pacific’s After-Tax Weighted-Average Cost of Capital

Now you can calculate Union Pacific’s after-tax WACC in early 2012. The company’s cost of debt was about 4.8%. With a 35% corporate tax rate, the after-tax cost of debt was rD(1 – TC) = 4.8 × (1 – .35) = 3.1%. The ratio of debt to overall company value was D/V = 14.3%. Therefore

Union Pacific should set its overall cost of capital to 8.8%, assuming that its CFO agrees with our estimates.

Warning The cost of debt is always less than the cost of equity. The WACC formula blends the two costs. The formula is dangerous, however, because it suggests that the average cost of capital could be reduced by substituting cheap debt for expensive equity. It doesn’t work that way! As the debt ratio D/V increases, the cost of the remaining equity also increases, offsetting the apparent advantage of more cheap debt. We show how and why this offset happens in Chapter 17.

Debt does have a tax advantage, however, because interest is a tax-deductible expense. That is why we use the after-tax cost of debt in the after-tax WACC. We cover debt and taxes in much more detail in Chapters 18 and 19.

Union Pacific’s Asset Beta

The after-tax WACC depends on the average risk of the company’s assets, but it also depends on taxes and financing. It’s easier to think about project risk if you measure it directly. The direct measure is called the asset beta.

We calculate the asset beta as a blend of the separate betas of debt (βD) and equity (βE). For Union Pacific we have βE = 1.21, and we’ll assume βD = .3.¹¹ The weights are the fractions of debt and equity financing, D/V = .143 and E/V = .857:

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Try It! Asset betas

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Calculating an asset beta is similar to calculating a weighted-average cost of capital. The debt and equity weights D/V and E/V are the same. The logic is also the same: Suppose you purchased a portfolio consisting of 100% of the firm’s debt and 100% of its equity. Then you would own 100% of its assets lock, stock, and barrel, and the beta of your portfolio would equal the beta of the assets. The portfolio beta is of course just a weighted average of the betas of debt and equity.

This asset beta is an estimate of the average risk of Union Pacific’s railroad business. It is a useful benchmark, but it can take you only so far. Not all railroad investments are average risk. And if you are the first to use railroad-track networks as interplanetary transmission antennas, you will have no asset beta to start with.

How can you make informed judgments about costs of capital for projects or lines of business when you suspect that risk is not average? That is our next topic.

 9-3   Analyzing Project Risk

Suppose that a coal-mining corporation wants to assess the risk of investing in commercial real estate, for example, in a new company headquarters. The asset beta for coal mining is not helpful. You need to know the beta of real estate. Fortunately, portfolios of commercial real estate are traded. For example, you could estimate asset betas from returns on Real Estate Investment Trusts (REITs) specializing in commercial real estate.¹² The REITs would serve as traded comparables for the proposed office building. You could also turn to indexes of real estate prices and returns derived from sales and appraisals of commercial properties.¹³

A company that wants to set a cost of capital for one particular line of business typically looks for pure plays in that line of business. Pure-play companies are public firms that specialize in one activity. For example, suppose that J&J wants to set a cost of capital for its pharmaceutical business. It could estimate the average asset beta or cost of capital for pharmaceutical companies that have not diversified into consumer products like Band-Aid® bandages or baby powder.

Overall company costs of capital are almost useless for conglomerates. Conglomerates diversify into several unrelated industries, so they have to consider industry-specific costs of capital. They therefore look for pure plays in the relevant industries. Take Richard Branson’s Virgin Group as an example. The group combines many different companies, including airlines (Virgin Atlantic) and retail outlets for music, books, and movies (Virgin Megastores). Fortunately there are many examples of pure-play airlines and pure-play retail chains. The trick is picking the comparables with business risks that are most similar to Virgin’s companies.

Sometimes good comparables are not available or not a good match to a particular project. Then the financial manager has to exercise his or her judgment. Here we offer the following advice:

1.  Think about the determinants of asset betas. Often the characteristics of high- and low-beta assets can be observed when the beta itself cannot be.

2.  Don’t be fooled by diversifiable risk.

3.  Avoid fudge factors. Don’t give in to the temptation to add fudge factors to the discount rate to offset things that could go wrong with the proposed investment. Adjust cash-flow forecasts first.

What Determines Asset Betas?

Cyclicality Many people’s intuition associates risk with the variability of earnings or cash flow. But much of this variability reflects diversifiable risk. Lone prospectors searching for gold look forward to extremely uncertain future income, but whether they strike it rich is unlikely to depend on the performance of the market portfolio. Even if they do find gold, they do not bear much market risk. Therefore, an investment in gold prospecting has a high standard deviation but a relatively low beta.

What really counts is the strength of the relationship between the firm’s earnings and the aggregate earnings on all real assets. We can measure this either by the earnings beta or by the cash-flow beta. These are just like a real beta except that changes in earnings or cash flow are used in place of rates of return on securities. We would predict that firms with high earnings or cash-flow betas should also have high asset betas.

This means that cyclical firms—firms whose revenues and earnings are strongly dependent on the state of the business cycle—tend to be high-beta firms. Thus you should demand a higher rate of return from investments whose performance is strongly tied to the performance of the economy. Examples of cyclical businesses include airlines, luxury resorts and restaurants, construction, and steel. (Much of the demand for steel depends on construction and capital investment.) Examples of less-cyclical businesses include food and tobacco products and established consumer brands such as J&J’s baby products. MBA programs are another example, because spending a year or two at a business school is an easier choice when jobs are scarce. Applications to top MBA programs increase in recessions.

Operating Leverage A production facility with high fixed costs, relative to variable costs, is said to have high operating leverage. High operating leverage means a high asset beta. Let us see how this works.

The cash flows generated by an asset can be broken down into revenue, fixed costs, and variable costs:

Costs are variable if they depend on the rate of output. Examples are raw materials, sales commissions, and some labor and maintenance costs. Fixed costs are cash outflows that occur regardless of whether the asset is active or idle, for example, property taxes or the wages of workers under contract.

We can break down the asset’s present value in the same way:

Or equivalently

Those who receive the fixed costs are like debtholders in the project; they simply get a fixed payment. Those who receive the net cash flows from the asset are like holders of common stock; they get whatever is left after payment of the fixed costs.

We can now figure out how the asset’s beta is related to the betas of the values of revenue and costs. The beta of PV(revenue) is a weighted average of the betas of its component parts:

The fixed-cost beta should be about zero; whoever receives the fixed costs receives a fixed stream of cash flows. The betas of the revenues and variable costs should be approximately the same, because they respond to the same underlying variable, the rate of output. Therefore we can substitute βrevenue for βvariable cost and solve for the asset beta. Remember, we are assuming βfixed cost = 0. Also, PV(revenue) – PV(variable cost) = PV(asset) + PV(fixed cost).¹⁴

Thus, given the cyclicality of revenues (reflected in βrevenue), the asset beta is proportional to the ratio of the present value of fixed costs to the present value of the project.

Now you have a rule of thumb for judging the relative risks of alternative designs or technologies for producing the same project. Other things being equal, the alternative with the higher ratio of fixed costs to project value will have the higher project beta. Empirical tests confirm that companies with high operating leverage actually do have high betas.¹⁵

We have interpreted fixed costs as costs of production, but fixed costs can show up in other forms, for example, as future investment outlays. Suppose that an electric utility commits to build a large electricity-generating plant. The plant will take several years to build, and the cost is fixed. Our operating leverage formula still applies, but with PV(future investment) included in PV(fixed costs). The commitment to invest therefore increases the plant’s asset beta. Of course PV(future investment) decreases as the plant is constructed and disappears when the plant is up and running. Therefore the plant’s asset beta is only temporarily high during construction.

Other Sources of Risk So far we have focused on cash flows. Cash-flow risk is not the only risk. A project’s value is equal to the expected cash flows discounted at the risk-adjusted discount rate r. If either the risk-free rate or the market risk premium changes, then r will change and so will the project value. A project with very long-term cash flows is more exposed to such shifts in the discount rate than one with short-term cash flows. This project will, therefore, have a high beta even though it may not have high operating leverage and cyclicality.¹⁶

You cannot hope to estimate the relative risk of assets with any precision, but good managers examine any project from a variety of angles and look for clues as to its riskiness. They know that high market risk is a characteristic of cyclical ventures, of projects with high fixed costs and of projects that are sensitive to marketwide changes in the discount rate. They think about the major uncertainties affecting the economy and consider how projects are affected by these uncertainties.

Don’t Be Fooled by Diversifiable Risk

In this chapter we have defined risk as the asset beta for a firm, industry, or project. But in everyday usage, “risk” simply means “bad outcome.” People think of the risks of a project as a list of things that can go wrong. For example,

•  A geologist looking for oil worries about the risk of a dry hole.

•  A pharmaceutical-company scientist worries about the risk that a new drug will have unacceptable side effects.

•  A plant manager worries that new technology for a production line will fail to work, requiring expensive changes and repairs.

•  A telecom CFO worries about the risk that a communications satellite will be damaged by space debris. (This was the fate of an Iridium satellite in 2009, when it collided with Russia’s defunct Cosmos 2251. Both were blown to smithereens.)

Notice that these risks are all diversifiable. For example, the Iridium-Cosmos collision was definitely a zero-beta event. These hazards do not affect asset betas and should not affect the discount rate for the projects.

Sometimes financial managers increase discount rates in an attempt to offset these risks. This makes no sense. Diversifiable risks should not increase the cost of capital.

EXAMPLE 9.1 • Allowing for Possible Bad Outcomes

Project Z will produce just one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at a 10% company cost of capital:

But now you discover that the company’s engineers are behind schedule in developing the technology required for the project. They are confident it will work, but they admit to a small chance that it will not. You still see the most likely outcome as $1 million, but you also see some chance that project Z will generate zero cash flow next year.

Now the project’s prospects are clouded by your new worry about technology. It must be worth less than the $909,100 you calculated before that worry arose. But how much less? There is some discount rate (10% plus a fudge factor) that will give the right value, but we do not know what that adjusted discount rate is.

We suggest you reconsider your original $1 million forecast for project Z’s cash flow. Project cash flows are supposed to be unbiased forecasts that give due weight to all possible outcomes, favorable and unfavorable. Managers making unbiased forecasts are correct on average. Sometimes their forecasts will turn out high, other times low, but their errors will average out over many projects.

If you forecast a cash flow of $1 million for projects like Z, you will overestimate the average cash flow, because every now and then you will hit a zero. Those zeros should be “averaged in” to your forecasts.

For many projects, the most likely cash flow is also the unbiased forecast. If there are three possible outcomes with the probabilities shown below, the unbiased forecast is $1 million. (The unbiased forecast is the sum of the probability-weighted cash flows.)

This might describe the initial prospects of project Z. But if technological uncertainty introduces a 10% chance of a zero cash flow, the unbiased forecast could drop to $900,000:

The present value is

Managers often work out a range of possible outcomes for major projects, sometimes with explicit probabilities attached. We give more elaborate examples and further discussion in Chapter 10. But even when outcomes and probabilities are not explicitly written down, the manager can still consider the good and bad outcomes as well as the most likely one. When the bad outcomes outweigh the good, the cash-flow forecast should be reduced until balance is regained.

Step 1, then, is to do your best to make unbiased forecasts of a project’s cash flows. Unbiased forecasts incorporate all risks, including diversifiable risks as well as market risks. Step 2 is to consider whether diversified investors would regard the project as more or less risky than the average project. In this step only market risks are relevant.

Avoid Fudge Factors in Discount Rates

Think back to our example of project Z, where we reduced forecasted cash flows from $1 million to $900,000 to account for a possible failure of technology. The project’s PV was reduced from $909,100 to $818,000. You could have gotten the right answer by adding a fudge factor to the discount rate and discounting the original forecast of $1 million. But you have to think through the possible cash flows to get the fudge factor, and once you forecast the cash flows correctly, you don’t need the fudge factor.

Fudge factors in discount rates are dangerous because they displace clear thinking about future cash flows. Here is an example.

EXAMPLE 9.2 • Correcting for Optimistic Forecasts

Torsten Lindstedt, the CFO of Swedish Shipping is disturbed to find that cash-flow forecasts for its investment projects are almost always optimistic. On average they are 10% too high. He therefore decides to compensate by adding 10% to the company’s WACC, increasing it from 12% to 22%.¹⁷

Suppose the CFO is right about the 10% upward bias in cash-flow forecasts. Can he just add 10% to the discount rate?

   TABLE 9.2 The original cash-flow forecasts for the ZZ project (line 1) are too optimistic. The forecasts and PVs should be reduced by 10% (lines 3 and 4). But adding a 10% fudge factor to the discount rate reduces PVs by far more than 10% (line 6). The fudge factor overcorrects for bias and would penalize long-lived projects.

Project ZZ has level forecasted cash flows of 1,000 Swedish kronor per year lasting for 15 years. The first two lines of Table 9.2 show these forecasts and their PVs discounted at 12%. Lines 3 and 4 show the corrected forecasts, each reduced by 10%, and the corrected PVs, which are (no surprise) also reduced by 10% (line 5). Line 6 shows the PVs when the uncorrected forecasts are discounted at 22%. The final line 7 shows the percentage reduction in PVs at the 22% discount rate, compared to the unadjusted PVs in line 2.

Line 5 shows the correct adjustment for optimism (10%). Line 7 shows what happens when a 10% fudge factor is added to the discount rate. The effect on the first year’s cash flow is a PV “haircut” of about 8%, 2% less than the CFO expected. But later present values are knocked down by much more than 10%, because the fudge factor is compounded in the 22% discount rate. By years 10 and 15, the PV haircuts are 57% and 72%, far more than the 10% bias that the CFO started with.

Did the CFO really think that bias accumulated as shown in line 7 of Table 9.2? We doubt that he ever asked that question. If he was right in the first place, and the true bias is 10%, then adding a 10% fudge factor to the discount rate understates PV. The fudge factor also makes long-lived projects look much worse than quick-payback projects.¹⁸

Discount Rates for International Projects

In this chapter we have concentrated on domestic investments. In Chapter 27 we say more about investments made internationally. Here we simply warn against adding fudge factors to discount rates for projects in developing economies. Such fudge factors are too often seen in practice.

It’s true that markets are more volatile in developing economies, but much of that risk is diversifiable for investors in the U.S., Europe, and other developed countries. It’s also true that more things can go wrong for projects in developing economies, particularly in countries that are unstable politically. Expropriations happen. Sometimes governments default on their obligations to international investors. Thus it’s especially important to think through the downside risks and to give them weight in cash-flow forecasts.

Some international projects are at least partially protected from these downsides. For example, an opportunistic government would gain little or nothing by expropriating the local IBM affiliate, because the affiliate would have little value without the IBM brand name, products, and customer relationships. A privately owned toll road would be a more tempting target, because the toll road would be relatively easy for the local government to maintain and operate.

 9-4   Certainty Equivalents—Another Way to Adjust for Risk

BEYOND THE PAGE

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Certainty equivalents and the CAPM

brealey.mhhe.com/c09

In practical capital budgeting, a single risk-adjusted rate is used to discount all future cash flows. This assumes that project risk does not change over time, but remains constant year-in and year-out. We know that this cannot be strictly true, for the risks that companies are exposed to are constantly shifting. We are venturing here onto somewhat difficult ground, but there is a way to think about risk that can suggest a route through. It involves converting the expected cash flows to certainty equivalents. First we work through an example showing what certainty equivalents are. Then, as a reward for your investment, we use certainty equivalents to uncover what you are really assuming when you discount a series of future cash flows at a single risk-adjusted discount rate. We also value a project where risk changes over time and ordinary discounting fails. Your investment will be rewarded still more when we cover options in Chapters 20 and 21 and forward and futures pricing in Chapter 26. Option-pricing formulas discount certainty equivalents. Forward and futures prices are certainty equivalents.

Valuation by Certainty Equivalents

Think back to the simple real estate investment that we used in Chapter 2 to introduce the concept of present value. You are considering construction of an office building that you plan to sell after one year for $800,000. That cash flow is uncertain with the same risk as the market, so β = 1. The risk-free interest rate is rf = 7%, but you discount the $800,000 payoff at a risk-adjusted rate of r = 12%. This gives a present value of 800,000/1.12 = $714,286.

Suppose a real estate company now approaches and offers to fix the price at which it will buy the building from you at the end of the year. This guarantee would remove any uncertainty about the payoff on your investment. So you would accept a lower figure than the uncertain payoff of $800,000. But how much less? If the building has a present value of $714,286 and the interest rate is 7%, then

In other words, a certain cash flow of $764,286 has exactly the same present value as an expected but uncertain cash flow of $800,000. The cash flow of $764,286 is therefore known as the certainty-equivalent cash flow. To compensate for both the delayed payoff and the uncertainty in real estate prices, you need a return of 800,000 – 714,286 = $85,714. One part of this difference compensates for the time value of money. The other part ($800,000 – 764,286 = $35,714) is a markdown or haircut to compensate for the risk attached to the forecasted cash flow of $800,000.

Our example illustrates two ways to value a risky cash flow:

Method 1: Discount the risky cash flow at a risk-adjusted discount rate r that is greater than rf.¹⁹ The risk-adjusted discount rate adjusts for both time and risk. This is illustrated by the clockwise route in Figure 9.3.

Method 2: Find the certainty-equivalent cash flow and discount at the risk-free interest rate rf. When you use this method, you need to ask, What is the smallest certain payoff for which I would exchange the risky cash flow? This is called the certainty equivalent, denoted by CEQ. Since CEQ is the value equivalent of a safe cash flow, it is discounted at the risk-free rate. The certainty-equivalent method makes separate adjustments for risk and time. This is illustrated by the counterclockwise route in Figure 9.3.

   FIGURE 9.3 Two ways to calculate present value. “Haircut for risk” is financial slang referring to the reduction of the cash flow from its forecasted value to its certainty equivalent.

We now have two identical expressions for the PV of a cash flow at period 1:²⁰

For cash flows two, three, or t years away,

When to Use a Single Risk-Adjusted Discount Rate for Long-Lived Assets

We are now in a position to examine what is implied when a constant risk-adjusted discount rate is used to calculate a present value.

Consider two simple projects. Project A is expected to produce a cash flow of $100 million for each of three years. The risk-free interest rate is 6%, the market risk premium is 8%, and project A’s beta is .75. You therefore calculate A’s opportunity cost of capital as follows:

Discounting at 12% gives the following present value for each cash flow:

Now compare these figures with the cash flows of project B. Notice that B’s cash flows are lower than A’s; but B’s flows are safe, and therefore they are discounted at the risk-free interest rate. The present value of each year’s cash flow is identical for the two projects.

In year 1 project A has a risky cash flow of 100. This has the same PV as the safe cash flow of 94.6 from project B. Therefore 94.6 is the certainty equivalent of 100. Since the two cash flows have the same PV, investors must be willing to give up 100 – 94.6 = 5.4 in expected year-1 income in order to get rid of the uncertainty.

In year 2 project A has a risky cash flow of 100, and B has a safe cash flow of 89.6. Again both flows have the same PV. Thus, to eliminate the uncertainty in year 2, investors are prepared to give up 100 – 89.6 = 10.4 of future income. To eliminate uncertainty in year 3, they are willing to give up 100 – 84.8 = 15.2 of future income.

To value project A, you discounted each cash flow at the same risk-adjusted discount rate of 12%. Now you can see what is implied when you did that. By using a constant rate, you effectively made a larger deduction for risk from the later cash flows:

The second cash flow is riskier than the first because it is exposed to two years of market risk. The third cash flow is riskier still because it is exposed to three years of market risk. This increased risk is reflected in the certainty equivalents that decline by a constant proportion each period.

Therefore, use of a constant risk-adjusted discount rate for a stream of cash flows assumes that risk accumulates at a constant rate as you look farther out into the future.

A Common Mistake

You sometimes hear people say that because distant cash flows are riskier, they should be discounted at a higher rate than earlier cash flows. That is quite wrong: We have just seen that using the same risk-adjusted discount rate for each year’s cash flow implies a larger deduction for risk from the later cash flows. The reason is that the discount rate compensates for the risk borne per period. The more distant the cash flows, the greater the number of periods and the larger the total risk adjustment.

When You Cannot Use a Single Risk-Adjusted Discount Rate for Long-Lived Assets

Sometimes you will encounter problems where the use of a single risk-adjusted discount rate will get you into trouble. For example, later in the book we look at how options are valued. Because an option’s risk is continually changing, the certainty-equivalent method needs to be used.

Here is a disguised, simplified, and somewhat exaggerated version of an actual project proposal that one of the authors was asked to analyze. The scientists at Vegetron have come up with an electric mop, and the firm is ready to go ahead with pilot production and test marketing. The preliminary phase will take one year and cost $125,000. Management feels that there is only a 50% chance that pilot production and market tests will be successful. If they are, then Vegetron will build a $1 million plant that would generate an expected annual cash flow in perpetuity of $250,000 a year after taxes. If they are not successful, the project will have to be dropped.

The expected cash flows (in thousands of dollars) are

Management has little experience with consumer products and considers this a project of extremely high risk.²¹ Therefore management discounts the cash flows at 25%, rather than at Vegetron’s normal 10% standard:

This seems to show that the project is not worthwhile.

Management’s analysis is open to criticism if the first year’s experiment resolves a high proportion of the risk. If the test phase is a failure, then there is no risk at all—the project is certain to be worthless. If it is a success, there could well be only normal risk from then on. That means there is a 50% chance that in one year Vegetron will have the opportunity to invest in a project of normal risk, for which the normal discount rate of 10% would be appropriate. Thus the firm has a 50% chance to invest $1 million in a project with a net present value of $1.5 million:

USEFUL SPREADSHEET FUNCTIONS

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Estimating Stock and Market Risk

   Spreadsheets such as Excel have some built-in statistical functions that are useful for calculating risk measures. You can find these functions by clicking fx on the Excel toolbar. If you then click on the function that you wish to use, Excel will ask you for the inputs that it needs. At the bottom left of the function box there is a Help facility with an example of how the function is used.

Here is a list of useful functions for estimating stock and market risk. You can enter the inputs for all these functions as numbers or as the addresses of cells that contain the numbers.

1.  VARP and STDEVP: Calculate variance and standard deviation of a series of numbers, as shown in Section 7-2.

2.  VAR and STDEV: Footnote 16 on page 168 noted that when variance is estimated from a sample of observations (the usual case), a correction should be made for the loss of a degree of freedom. VAR and STDEV provide the corrected measures. For any large sample VAR and VARP will be similar.

3.  SLOPE: Useful for calculating the beta of a stock or portfolio.

4.  CORREL: Useful for calculating the correlation between the returns on any two investments.

5.  COVAR: Portfolio risk depends on the covariance between the returns on each pair of stocks. COVAR calculates the covariance.

6.  RSQ: R-squared is the square of the correlation coefficient and is useful for measuring the proportion of the variance of a stock’s returns that can be explained by the market.

7.  AVERAGE: Calculates the average of any series of numbers.

If, say, you need to know the standard error of your estimate of beta, you can obtain more detailed statistics by going to the Tools menu and clicking on Data Analysis and then on Regression.

SPREADSHEET QUESTIONS

The following questions provide opportunities to practice each of the Excel functions.

1.  (VAR and STDEV) Choose two well-known stocks and download the latest 61 months of adjusted prices from finance.yahoo.com. Calculate the monthly returns for each stock. Now find the variance and standard deviation of the returns for each stock by using VAR and STDEV. Annualize the variance by multiplying by 12 and the standard deviation by multiplying by the square root of 12.

2.  (AVERAGE, VAR, and STDEV) Now calculate the annualized variance and standard deviation for a portfolio that each month has equal holdings in the two stocks. Is the result more or less than the average of the standard deviations of the two stocks? Why?

3.  (SLOPE) Download the Standard & Poor’s index for the same period (its symbol is ˆGSPC). Find the beta of each stock and of the portfolio. (Note: You need to enter the stock returns as the Y-values and market returns as the X-values.) Is the beta of the portfolio more or less than the average of the betas of the two stocks?

4.  (CORREL) Calculate the correlation between the returns on the two stocks. Use this measure and your earlier estimates of each stock’s variance to calculate the variance of a portfolio that is evenly divided between the two stocks. (You may need to reread Section 7-3 to refresh your memory of how to do this.) Check that you get the same answer as when you calculated the portfolio variance directly.

5.  (COVAR) Repeat question 4, but now calculate the covariance directly, rather than from the correlations and variances.

6.  (RSQ) For each of the two stocks calculate the proportion of the variance explained by the market index. Do the results square with your intuition?

7.  Use the Regression facility under the Data Analysis menu to calculate the beta of each stock and of the portfolio (beta here is called the coefficient of the X-variable). Look at the standard error of the estimate in the cell to the right. How confident can you be of your estimates of the betas of each stock? How about your estimate of the portfolio beta?

Thus we could view the project as offering an expected payoff of .5(1,500) + .5(0) = 750, or $750,000, at t = 1 on a $125,000 investment at t = 0. Of course, the certainty equivalent of the payoff is less than $750,000, but the difference would have to be very large to justify rejecting the project. For example, if the certainty equivalent is half the forecasted cash flow (an extremely large cash flow haircut) and the risk-free rate is 7%, the project is worth $225,500:

This is not bad for a $125,000 investment—and quite a change from the negative-NPV that management got by discounting all future cash flows at 25%.

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SUMMARY

In Chapter 8 we set out the basic principles for valuing risky assets. This chapter shows you how to apply those principles when valuing capital investment projects.

Suppose the project has the same market risk as the company’s existing assets. In this case, the project cash flows can be discounted at the company cost of capital. The company cost of capital is the rate of return that investors require on a portfolio of all of the company’s outstanding debt and equity. It is usually calculated as an after-tax weighted-average cost of capital (after-tax WACC), that is, as the weighted average of the after-tax cost of debt and the cost of equity. The weights are the relative market values of debt and equity. The cost of debt is calculated after tax because interest is a tax-deductible expense.

The hardest part of calculating the after-tax WACC is estimation of the cost of equity. Most large, public corporations use the capital asset pricing model (CAPM) to do this. They generally estimate the firm’s equity beta from past rates of return for the firm’s common stock and for the market, and they check their estimate against the average beta of similar firms.

The after-tax WACC is the correct discount rate for projects that have the same market risk as the company’s existing business. Many firms, however, use the after-tax WACC as the discount rate for all projects. This is a dangerous procedure. If the procedure is followed strictly, the firm will accept too many high-risk projects and reject too many low-risk projects. It is project risk that counts: the true cost of capital depends on the use to which the capital is put.

Managers, therefore, need to understand why a particular project may have above- or below-average risk. You can often identify the characteristics of a high- or low-beta project even when the beta cannot be estimated directly. For example, you can figure out how much the project’s cash flows are affected by the performance of the entire economy. Cyclical projects are generally high-beta projects. You can also look at operating leverage. Fixed production costs increase beta.

Don’t be fooled by diversifiable risk. Diversifiable risks do not affect asset betas or the cost of capital, but the possibility of bad outcomes should be incorporated in the cash-flow forecasts. Also be careful not to offset worries about a project’s future performance by adding a fudge factor to the discount rate. Fudge factors don’t work, and they may seriously undervalue long-lived projects.

There is one more fence to jump. Most projects produce cash flows for several years. Firms generally use the same risk-adjusted rate to discount each of these cash flows. When they do this, they are implicitly assuming that cumulative risk increases at a constant rate as you look further into the future. That assumption is usually reasonable. It is precisely true when the project’s future beta will be constant, that is, when risk per period is constant.

But exceptions sometimes prove the rule. Be on the alert for projects where risk clearly does not increase steadily. In these cases, you should break the project into segments within which the same discount rate can be reasonably used. Or you should use the certainty-equivalent version of the DCF model, which allows separate risk adjustments to each period’s cash flow.

The nearby box (on page 236) provides useful spreadsheet functions for estimating stock and market risk.

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FURTHER READING

Michael Brennan provides a useful, but quite difficult, survey of the issues covered in this chapter:

M. J. Brennan, “Corporate Investment Policy,” Handbook of the Economics of Finance, Volume 1A, Corporate Finance, eds. G. M. Constantinides, M. Harris, and R. M. Stulz (Amsterdam: Elsevier BV, 2003).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Company cost of capital Suppose a firm uses its company cost of capital to evaluate all projects. Will it underestimate or overestimate the value of high-risk projects?

2.  WACC A company is 40% financed by risk-free debt. The interest rate is 10%, the expected market risk premium is 8%, and the beta of the company’s common stock is .5. What is the company cost of capital? What is the after-tax WACC, assuming that the company pays tax at a 35% rate?

3.  Measuring risk Look back to the top-right panel of Figure 9.2. What proportion of Citigroup’s returns was explained by market movements? What proportion of risk was diversifiable? How does the diversifiable risk show up in the plot? What is the range of possible errors in the estimated beta?

4.  Definitions Define the following terms:

a.  Cost of debt

b.  Cost of equity

c.  After-tax WACC

d.  Equity beta

e.  Asset beta

f.  Pure-play comparable

g.  Certainty equivalent

5.  Asset betas EZCUBE Corp. is 50% financed with long-term bonds and 50% with common equity. The debt securities have a beta of .15. The company’s equity beta is 1.25. What is EZCUBE’s asset beta?

6.  Diversifiable risk Many investment projects are exposed to diversifiable risks. What does “diversifiable” mean in this context? How should diversifiable risks be accounted for in project valuation? Should they be ignored completely?

7.  Fudge factors John Barleycorn estimates his firm’s after-tax WACC at only 8%. Nevertheless he sets a 15% companywide discount rate to offset the optimistic biases of project sponsors and to impose “discipline” on the capital-budgeting process. Suppose Mr. Barleycorn is correct about the project sponsors, who are in fact optimistic by 7% on average. Will the increase in the discount rate from 8% to 15% offset the bias?

8.  Asset betas Which of these projects is likely to have the higher asset beta, other things equal? Why?

a.  The sales force for project A is paid a fixed annual salary. Project B’s sales force is paid by commissions only.

b.  Project C is a first-class-only airline. Project D is a well-established line of breakfast cereals.

9.  True/false True or false?

a.  The company cost of capital is the correct discount rate for all projects, because the high risks of some projects are offset by the low risk of other projects.

b.  Distant cash flows are riskier than near-term cash flows. Therefore long-term projects require higher risk-adjusted discount rates.

c.  Adding fudge factors to discount rates undervalues long-lived projects compared with quick-payoff projects.

10.  Certainty equivalents A project has a forecasted cash flow of $110 in year 1 and $121 in year 2. The interest rate is 5%, the estimated risk premium on the market is 10%, and the project has a beta of .5. If you use a constant risk-adjusted discount rate, what is

a.  The PV of the project?

b.  The certainty-equivalent cash flow in year 1 and year 2?

c.  The ratio of the certainty-equivalent cash flows to the expected cash flows in years 1 and 2?

INTERMEDIATE

11.  Cost of capital The total market value of the common stock of Molino de Sanchez SA is €6 million, and the total value of its debt is €4 million. The treasurer estimates that the beta of the stock is currently 1.5 and that the expected risk premium on the market is 6%. The Treasury bill rate is 4%. Assume for simplicity that Molino’s debt is risk-free and the company does not pay tax.

a.  What is the required return on Molino stock?

b.  Estimate the company cost of capital.

c.  What is the discount rate for an expansion of the company’s present business?

d.  Suppose the company wants to diversify into the manufacture of rose-colored spectacles. The beta of unleveraged optical manufacturers is 1.2. Estimate the required return on Molino’s new venture.

12.  Cost of capital Nero Violins has the following capital structure:

a.  What is the firm’s asset beta? (Hint: What is the beta of a portfolio of all the firm’s securities?)

b.  Assume that the CAPM is correct. What discount rate should Nero set for investments that expand the scale of its operations without changing its asset beta? Assume a risk-free interest rate of 5% and a market risk premium of 6%.

13.  Measuring risk The following table shows estimates of the risk of two well-known Canadian stocks:

a.  What proportion of each stock’s risk was market risk, and what proportion was specific risk?

b.  What is the variance of Toronto Dominion? What is the specific variance?

c.  What is the confidence interval on Research in Motion’s beta?

d.  If the CAPM is correct, what is the expected return on Toronto Dominion? Assume a risk-free interest rate of 5% and an expected market return of 12%.

e.  Suppose that next year the market provides a zero return. Knowing this, what return would you expect from Toronto Dominion?

14.  Company cost of capital You are given the following information for Golden Fleece Financial:

Calculate Golden Fleece’s company cost of capital. Ignore taxes.

15.  Measuring risk Look again at Table 9.1. This time we will concentrate on Norfolk Southern.

a.  Calculate Norfolk Southern’s cost of equity from the CAPM using its own beta estimate and the industry beta estimate. How different are your answers? Assume a risk-free rate of 2% and a market risk premium of 7%.

b.  Can you be confident that Norfolk Southern’s true beta is not the industry average?

c.  Under what circumstances might you advise Norfolk Southern to calculate its cost of equity based on its own beta estimate?

16.  Asset betas What types of firms need to estimate industry asset betas? How would such a firm make the estimate? Describe the process step by step.

17.  WACC Binomial Tree Farm’s financing includes $5 million of bank loans. Its common equity is shown in Binomial’s Annual Report at $6.67 million. It has 500,000 shares of common stock outstanding, which trade on the Wichita Stock Exchange at $18 per share. What debt ratio should Binomial use to calculate its WACC or asset beta? Explain.

18.  Betas and operating leverage You run a perpetual encabulator machine, which generates revenues averaging $20 million per year. Raw material costs are 50% of revenues. These costs are variable—they are always proportional to revenues. There are no other operating costs. The cost of capital is 9%. Your firm’s long-term borrowing rate is 6%.

Now you are approached by Studebaker Capital Corp., which proposes a fixed-price contract to supply raw materials at $10 million per year for 10 years.

a.  What happens to the operating leverage and business risk of the encabulator machine if you agree to this fixed-price contract?

b.  Calculate the present value of the encabulator machine with and without the fixed-price contract.

19.  Political risk Mom and Pop Groceries has just dispatched a year’s supply of groceries to the government of the Central Antarctic Republic. Payment of $250,000 will be made one year hence after the shipment arrives by snow train. Unfortunately there is a good chance of a coup d’état, in which case the new government will not pay. Mom and Pop’s controller therefore decides to discount the payment at 40%, rather than at the company’s 12% cost of capital.

a.  What’s wrong with using a 40% rate to offset political risk?

b.  How much is the $250,000 payment really worth if the odds of a coup d’état are 25%?

20.  Fudge factors An oil company is drilling a series of new wells on the perimeter of a producing oil field. About 20% of the new wells will be dry holes. Even if a new well strikes oil, there is still uncertainty about the amount of oil produced: 40% of new wells that strike oil produce only 1,000 barrels a day; 60% produce 5,000 barrels per day.

a.  Forecast the annual cash revenues from a new perimeter well. Use a future oil price of $100 per barrel.

b.  A geologist proposes to discount the cash flows of the new wells at 30% to offset the risk of dry holes. The oil company’s normal cost of capital is 10%. Does this proposal make sense? Briefly explain why or why not.

21.  Certainty equivalents A project has the following forecasted cash flows:

The estimated project beta is 1.5. The market return rm is 16%, and the risk-free rate rf is 7%.

a.  Estimate the opportunity cost of capital and the project’s PV (using the same rate to discount each cash flow).

b.  What are the certainty-equivalent cash flows in each year?

c.  What is the ratio of the certainty-equivalent cash flow to the expected cash flow in each year?

d.  Explain why this ratio declines.

22.  Changing risk The McGregor Whisky Company is proposing to market diet scotch. The product will first be test-marketed for two years in Edinburgh at an initial cost of £500,000. This test launch is not expected to produce any profits but should reveal consumer preferences. There is a 60% chance that demand will be satisfactory. In this case McGregor will spend £5 million to launch the scotch nationwide and will receive an expected annual profit of £700,000 in perpetuity. If demand is not satisfactory, diet scotch will be withdrawn.

Once consumer preferences are known, the product will be subject to an average degree of risk, and, therefore, McGregor requires a return of 12% on its investment. However, the initial test-market phase is viewed as much riskier, and McGregor demands a return of 20% on this initial expenditure.

What is the NPV of the diet scotch project?

CHALLENGE

23.  Beta of costs Suppose you are valuing a future stream of high-risk (high-beta) cash outflows. High risk means a high discount rate. But the higher the discount rate, the less the present value. This seems to say that the higher the risk of cash outflows, the less you should worry about them! Can that be right? Should the sign of the cash flow affect the appropriate discount rate? Explain.

24.  Fudge factors An oil company executive is considering investing $10 million in one or both of two wells: well 1 is expected to produce oil worth $3 million a year for 10 years; well 2 is expected to produce $2 million for 15 years. These are real (inflation-adjusted) cash flows.

The beta for producing wells is .9. The market risk premium is 8%, the nominal risk-free interest rate is 6%, and expected inflation is 4%.

The two wells are intended to develop a previously discovered oil field. Unfortunately there is still a 20% chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the $10 million investment.

Ignore taxes and make further assumptions as necessary.

a.  What is the correct real discount rate for cash flows from developed wells?

b.  The oil company executive proposes to add 20 percentage points to the real discount rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate.

c.  What do you say the NPVs of the two wells are?

d.  Is there any single fudge factor that could be added to the discount rate for developed wells that would yield the correct NPV for both wells? Explain.

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FINANCE ON THE WEB

You can download data for the following questions from finance.yahoo.com.

1.  Look at the companies listed in Table 8.2. Calculate monthly rates of return for two successive five-year periods. Calculate betas for each subperiod using the Excel SLOPE function. How stable was each company’s beta? Suppose that you had used these betas to estimate expected rates of return from the CAPM. Would your estimates have changed significantly from period to period?

2.  Identify a sample of food companies. For example, you could try Campbell Soup (CPB), General Mills (GIS), Kellogg (K), Kraft Foods (KFT), and Sara Lee (SLE).

a.  Estimate beta and R2 for each company, using five years of monthly returns and Excel functions SLOPE and RSQ.

b.  Average the returns for each month to give the return on an equally weighted portfolio of the stocks. Then calculate the industry beta using these portfolio returns. How does the R2 of this portfolio compare with the average R2 of the individual stocks?

c.  Use the CAPM to calculate an average cost of equity (requity) for the food industry. Use current interest rates—take a look at the end of Section 9-2—and a reasonable estimate of the market risk premium.

MINI-CASE ● ● ● ● ●

The Jones Family, Incorporated

The Scene: Early evening in an ordinary family room in Manhattan. Modern furniture, with old copies of The Wall Street Journal and the Financial Times scattered around. Autographed photos of Alan Greenspan and George Soros are prominently displayed. A picture window reveals a distant view of lights on the Hudson River. John Jones sits at a computer terminal, glumly sipping a glass of chardonnay and putting on a carry trade in Japanese yen over the Internet. His wife Marsha enters.

Marsha: Hi, honey. Glad to be home. Lousy day on the trading floor, though. Dullsville. No volume. But I did manage to hedge next year’s production from our copper mine. I couldn’t get a good quote on the right package of futures contracts, so I arranged a commodity swap.

John doesn’t reply.

Marsha: John, what’s wrong? Have you been selling yen again? That’s been a losing trade for weeks.

John: Well, yes. I shouldn’t have gone to Goldman Sachs’s foreign exchange brunch. But I’ve got to get out of the house somehow. I’m cooped up here all day calculating covariances and efficient risk-return trade-offs while you’re out trading commodity futures. You get all the glamour and excitement.

Marsha: Don’t worry, dear, it will be over soon. We only recalculate our most efficient common stock portfolio once a quarter. Then you can go back to leveraged leases.

John: You trade, and I do all the worrying. Now there’s a rumor that our leasing company is going to get a hostile takeover bid. I knew the debt ratio was too low, and you forgot to put on the poison pill. And now you’ve made a negative-NPV investment!

Marsha: What investment?

John: That wildcat oil well. Another well in that old Sourdough field. It’s going to cost $5 million! Is there any oil down there?

Marsha: That Sourdough field has been good to us, John. Where do you think we got the capital for your yen trades? I bet we’ll find oil. Our geologists say there’s only a 30% chance of a dry hole.

John: Even if we hit oil, I bet we’ll only get 75 barrels of crude oil per day.

Marsha: That’s 75 barrels day in, day out. There are 365 days in a year, dear.

John and Marsha’s teenage son Johnny bursts into the room.

Johnny: Hi, Dad! Hi, Mom! Guess what? I’ve made the junior varsity derivatives team! That means I can go on the field trip to the Chicago Board Options Exchange. (Pauses.) What’s wrong?

John: Your mother has made another negative-NPV investment. A wildcat oil well, way up on the North Slope of Alaska.

Johnny: That’s OK, Dad. Mom told me about it. I was going to do an NPV calculation yesterday, but I had to finish calculating the junk-bond default probabilities for my corporate finance homework. (Grabs a financial calculator from his backpack.) Let’s see: 75 barrels a day times 365 days per year times $100 per barrel when delivered in Los Angeles . . . that’s $2.7 million per year.

John: That’s $2.7 million next year, assuming that we find any oil at all. The production will start declining by 5% every year. And we still have to pay $20 per barrel in pipeline and tanker charges to ship the oil from the North Slope to Los Angeles. We’ve got some serious operating leverage here.

Marsha: On the other hand, our energy consultants project increasing oil prices. If they increase with inflation, price per barrel should increase by roughly 2.5% per year. The wells ought to be able to keep pumping for at least 15 years.

Johnny: I’ll calculate NPV after I finish with the default probabilities. The interest rate is 6%. Is it OK if I work with the beta of .8 and our usual figure of 7% for the market risk premium?

Marsha: I guess so, Johnny. But I am concerned about the fixed shipping costs.

John: (Takes a deep breath and stands up.) Anyway, how about a nice family dinner? I’ve reserved our usual table at the Four Seasons.

   Everyone exits.

Announcer: Is the wildcat well really negative-NPV? Will John and Marsha have to fight a hostile takeover? Will Johnny’s derivatives team use Black–Scholes or the binomial method? Find out in the next episode of The Jones Family, Incorporated.

You may not aspire to the Jones family’s way of life, but you will learn about all their activities, from futures contracts to binomial option pricing, later in this book. Meanwhile, you may wish to replicate Johnny’s NPV analysis.

QUESTIONS

1.  Calculate the NPV of the wildcat oil well, taking account of the probability of a dry hole, the shipping costs, the decline in production, and the forecasted increase in oil prices. How long does production have to continue for the well to be a positive-NPV investment? Ignore taxes and other possible complications.

2.  Now consider operating leverage. How should the shipping costs be valued, assuming that output is known and the costs are fixed? How would your answer change if the shipping costs were proportional to output? Assume that unexpected fluctuations in output are zero-beta and diversifiable. (Hint: The Jones’s oil company has an excellent credit rating. Its long-term borrowing rate is only 7%.)

___________

¹We have simplified by treating J&J as all-equity-financed. J&J’s market-value debt ratio is very low, but not zero. We discuss debt financing and the weighted-average cost of capital below.

²A “naked” call option is an option purchased with no offsetting (hedging) position in the underlying stock or in other options. We discuss options in Chapter 20.

³Recall that the 30% and 70% weights in your hypothetical portfolio are based on market, not book, values. Now you can see why. If the portfolio were constructed with different book weights, say 50–50, then the portfolio returns could not equal the asset returns.

⁴The CAPM is not the last word on risk and return, of course, but the principles and procedures covered in this chapter work just as well with other models such as the Fama–French three-factor model. See Section 8-4.

⁵Notice that to estimate beta you must regress the returns on the stock on the market returns. You would get a very similar estimate if you simply used the percentage changes in the stock price and the market index. But sometimes people make the mistake of regressing the stock price level on the level of the index and obtain nonsense results.

⁶This is an annual figure; we annualized the monthly variance by multiplying by 12 (see footnote 18 in Chapter 7). The standard deviation was

⁷Estimates of beta may be distorted if there are extreme returns in one or two months. This is a potential problem in our estimates for 2008–2009, since you can see in Figure 9.2 that there was one week in October 2008 when the market fell by over 18%. The performance of each stock that month has an excessive effect on the estimated beta. In such cases statisticians may prefer to give less weight to the extreme observations or even to omit them entirely.

⁸If the observations are independent, the standard error of the estimated mean beta declines in proportion to the square root of the number of stocks in the portfolio.

⁹One reason that Union Pacific’s beta is less than that of the average railroad is that the company has below-average debt ratio. Chapter 19 explains how to adjust betas for differences in debt ratios.

¹⁰This approach gives a security market line with a higher intercept and a lower market risk premium. Using a “flatter” security market line is perhaps a better match to the historical evidence, which shows that the slope of average returns against beta is not as steeply upward-sloping as the CAPM predicts. See Figures 8.8 and 8.9.

¹¹Why is the debt beta positive? Two reasons: First, debt investors worry about the risk of default. Corporate bond prices fall, relative to Treasury-bond prices, when the economy goes from expansion to recession. The risk of default is therefore partly a macroeconomic and market risk. Second, all bonds are exposed to uncertainty about interest rates and inflation. Even Treasury bonds have positive betas when long-term interest rates and inflation are volatile and uncertain.

¹²REITs are investment funds that invest in real estate. You would have to be careful to identify REITs investing in commercial properties similar to the proposed office building. There are also REITs that invest in other types of real estate, including apartment buildings, shopping centers, and timberland.

¹³See Chapter 23 in D. Geltner, N. G. Miller, J. Clayton, and P. Eichholtz, Commercial Real Estate Analysis and Investments, 2nd ed. (South-Western College Publishing, 2006).

¹⁴In Chapter 10 we describe an accounting measure of the degree of operating leverage (DOL), defined as DOL = 1 + fixed costs/profits. DOL measures the percentage change in profits for a 1% change in revenue. We have derived here a version of DOL expressed in PVs and betas.

¹⁵See B. Lev, “On the Association between Operating Leverage and Risk,” Journal of Financial and Quantitative Analysis 9 (September 1974), pp. 627–642; and G. N. Mandelker and S. G. Rhee, “The Impact of the Degrees of Operating and Financial Leverage on Systematic Risk of Common Stock,” Journal of Financial and Quantitative Analysis 19 (March 1984), pp. 45–57.

¹⁶See J. Y. Campbell and J. Mei, “Where Do Betas Come From? Asset Price Dynamics and the Sources of Systematic Risk,” Review of Financial Studies 6 (Fall 1993), pp. 567–592. Cornell discusses the effect of duration on project risk in B. Cornell, “Risk, Duration and Capital Budgeting: New Evidence on Some Old Questions,” Journal of Business 72 (April 1999), pp. 183–200.

¹⁷The CFO is ignoring Brealey, Myers, and Allen’s Second Law, which we cover in the next chapter.

¹⁸The optimistic bias could be worse for distant than near cash flows. If so, the CFO should make the time-pattern of bias explicit and adjust the cash-flow forecasts accordingly.

¹⁹The discount rate r can be less than rf for assets with negative betas. But actual betas are almost always positive.

²⁰CEQ1 can be calculated directly from the capital asset pricing model. The certainty-equivalent form of the CAPM states that the certainty-equivalent value of the cash flow C1 is C1 – λ is the covariance between the uncertain cash flow, and the return on the market, . Lambda, λ, is a measure of the market price of risk. It is defined as . For example, if rm – rf = .08 and the standard deviation of market returns is σm = .20, then lambda = .08/.20² = 2.

²¹We will assume that they mean high market risk and that the difference between 25% and 10% is not a fudge factor introduced to offset optimistic cash-flow forecasts.

Part 3 Best Practices in Capital Budgeting

Project Analysis

Having read our earlier chapters on capital budgeting, you may have concluded that the choice of which projects to accept or reject is a simple one. You just need to draw up a set of cash-flow forecasts, choose the right discount rate, and crank out net present value. But finding projects that create value for the shareholders can never be reduced to a mechanical exercise. We therefore devote the next three chapters to ways in which companies can stack the odds in their favor when making investment decisions.

Investment proposals may emerge from many different parts of the organization. So companies need procedures to ensure that every project is assessed consistently. Our first task in this chapter is to review how firms develop plans and budgets for capital investments, how they authorize specific projects, and how they check whether projects perform as promised.

When managers are presented with investment proposals, they do not accept the cash flow forecasts at face value. Instead, they try to understand what makes a project tick and what could go wrong with it. Remember Murphy’s law, “if anything can go wrong, it will,” and O’Reilly’s corollary, “at the worst possible time.”

Once you know what makes a project tick, you may be able to reconfigure it to improve its chance of success. And if you understand why the venture could fail, you can decide whether it is worth trying to rule out the possible causes of failure. Maybe further expenditure on market research would clear up those doubts about acceptance by consumers, maybe another drill hole would give you a better idea of the size of the ore body, and maybe some further work on the test bed would confirm the durability of those welds.

If the project really has a negative NPV, the sooner you can identify it, the better. And even if you decide that it is worth going ahead without further analysis, you do not want to be caught by surprise if things go wrong later. You want to know the danger signals and the actions that you might take.

Our second task in this chapter is to show how managers use sensitivity analysis, break-even analysis, and Monte Carlo simulation to identify the crucial assumptions in investment proposals and to explore what can go wrong. There is no magic in these techniques, just computer-assisted common sense. You do not need a license to use them.

Discounted-cash-flow analysis commonly assumes that companies hold assets passively, and it ignores the opportunities to expand the project if it is successful or to bail out if it is not. However, wise managers recognize these opportunities when considering whether to invest. They look for ways to capitalize on success and to reduce the costs of failure, and they are prepared to pay up for projects that give them this flexibility. Opportunities to modify projects as the future unfolds are known as real options. In the final section of the chapter we describe several important real options, and we show how to use decision trees to set out the possible future choices.

 10-1   The Capital Investment Process

Senior management needs some forewarning of future investment outlays. So for most large firms, the investment process starts with the preparation of an annual capital budget, which is a list of investment projects planned for the coming year.

Most firms let project proposals bubble up from plants for review by divisional management and then from divisions for review by senior management and their planning staff. Of course middle managers cannot identify all worthwhile projects. For example, the managers of plants A and B cannot be expected to see the potential economies of closing their plants and consolidating production at a new plant C. Divisional managers would propose plant C. But the managers of divisions 1 and 2 may not be eager to give up their own computers to a corporationwide information system. That proposal would come from senior management, for example, the company’s chief information officer.

Inconsistent assumptions often creep into expenditure plans. For example, suppose the manager of your furniture division is bullish on housing starts, but the manager of your appliance division is bearish. The furniture division may push for a major investment in new facilities, while the appliance division may propose a plan for retrenchment. It would be better if both managers could agree on a common estimate of housing starts and base their investment proposals on it. That is why many firms begin the capital budgeting process by establishing consensus forecasts of economic indicators, such as inflation and growth in national income, as well as forecasts of particular items that are important to the firm’s business, such as housing starts or the prices of raw materials. These forecasts are then used as the basis for the capital budget.

Preparation of the capital budget is not a rigid, bureaucratic exercise. There is plenty of give-and-take and back-and-forth. Divisional managers negotiate with plant managers and fine-tune the division’s list of projects. The final capital budget must also reflect the corporation’s strategic planning. Strategic planning takes a top-down view of the company. It attempts to identify businesses where the company has a competitive advantage. It also attempts to identify businesses that should be sold or allowed to run down.

A firm’s capital investment choices should reflect both bottom-up and top-down views of the business—capital budgeting and strategic planning, respectively. Plant and division managers, who do most of the work in bottom-up capital budgeting, may not see the forest for the trees. Strategic planners may have a mistaken view of the forest because they do not look at the trees one by one. (We return to the links between capital budgeting and corporate strategy in the next chapter.)

Project Authorizations—and the Problem of Biased Forecasts

Once the capital budget has been approved by top management and the board of directors, it is the official plan for the ensuing year. However, it is not the final sign-off for specific projects. Most companies require appropriation requests for each proposal. These requests include detailed forecasts, discounted-cash-flow analyses, and back-up information.

Many investment projects carry a high price tag; they also determine the shape of the firm’s business 10 or 20 years in the future. Hence final approval of appropriation requests tends to be reserved for top management. Companies set ceilings on the size of projects that divisional managers can authorize. Often these ceilings are surprisingly low. For example, a large company, investing $400 million per year, might require top management to approve all projects over $500,000.

This centralized decision making brings its problems: Senior management can’t process detailed information about hundreds of projects and must rely on forecasts put together by project sponsors. A smart manager quickly learns to worry whether these forecasts are realistic.

Even when the forecasts are not consciously inflated, errors creep in. For example, most people tend to be overconfident when they forecast. Events they think are almost certain to occur may actually happen only 80% of the time, and events they believe are impossible may happen 20% of the time. Therefore project risks are understated. Anyone who is keen to get a project accepted is also likely to look on the bright side when forecasting the project’s cash flows. Such overoptimism seems to be a common feature in financial forecasts. Overoptimism afflicts governments too, probably more than private businesses. How often have you heard of a new dam, highway, or military aircraft that actually cost less than was originally forecasted?

BEYOND THE PAGE

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Overoptimism and cost overruns

brealey.mhhe.com/c10

You can expect plant or divisional managers to look on the bright side when putting forward investment proposals. That is not altogether bad. Psychologists stress that optimism and confidence are likely to increase effort, commitment, and persistence. The problem is that hundreds of appropriation requests may reach senior management each year, all essentially sales documents presented by united fronts and designed to persuade. Alternative schemes have been filtered out at earlier stages.

It is probably impossible to eliminate bias completely, but senior managers should take care not to encourage it. For example, if managers believe that success depends on having the largest division rather than the most profitable one, they will propose large expansion projects that they do not truly believe have positive NPVs. Or if new plant managers are pushed to generate increased earnings right away, they will be tempted to propose quick-payback projects even when NPV is sacrificed.

Sometimes senior managers try to offset bias by increasing the hurdle rate for capital expenditure. Suppose the true cost of capital is 10%, but the CFO is frustrated by the large fraction of projects that don’t subsequently earn 10%. She therefore directs project sponsors to use a 15% discount rate. In other words, she adds a 5% fudge factor in an attempt to offset forecast bias. But it doesn’t work; it never works. Brealey, Myers, and Allen’s Second Law¹ explains why. The law states: The proportion of proposed projects having positive NPVs at the corporate hurdle rate is independent of the hurdle rate.

The law is not a facetious conjecture. It was tested in a large oil company where staff kept careful statistics on capital investment projects. About 85% of projects had positive NPVs. (The remaining 15% were proposed for other reasons, for example, to meet environmental standards.) One year, after several quarters of disappointing earnings, top management decided that more financial discipline was called for and increased the corporate hurdle rate by several percentage points. But in the following year the fraction of projects with positive NPVs stayed rock-steady at 85%.

If you’re worried about bias in forecasted cash flows, the only remedy is careful analysis of the forecasts. Do not add fudge factors to the cost of capital.²

Postaudits

Most firms keep a check on the progress of large projects by conducting postaudits shortly after the projects have begun to operate. Postaudits identify problems that need fixing, check the accuracy of forecasts, and suggest questions that should have been asked before the project was undertaken. Postaudits pay off mainly by helping managers to do a better job when it comes to the next round of investments. After a postaudit the controller may say, “We should have anticipated the extra training required for production workers.” When the next proposal arrives, training will get the attention it deserves.

Postaudits may not be able to measure all of a project’s costs and benefits. It may be impossible to split the project away from the rest of the business. Suppose that you have just taken over a trucking firm that operates a delivery service for local stores. You decide to improve service by installing custom software to keep track of packages and to schedule trucks. You also construct a dispatching center and buy five new diesel trucks. A year later you try a postaudit of the investment in software. You verify that it is working properly and check actual costs of purchase, installation, and operation against projections. But how do you identify the incremental cash inflows? No one has kept records of the extra diesel fuel that would have been used or the extra shipments that would have been lost absent the software. You may be able to verify that service is better, but how much of the improvement comes from the new trucks, how much from the dispatching center, and how much from the software? The only meaningful measures of success are for the delivery business as a whole.

 10-2   Sensitivity Analysis

Uncertainty means that more things can happen than will happen. Whenever you are confronted with a cash-flow forecast, you should try to discover what else can happen.

BEYOND THE PAGE

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Try It! Scooter project spreadsheets

brealey.mhhe.com/c10

Put yourself in the well-heeled shoes of the treasurer of the Otobai Company in Osaka, Japan. You are considering the introduction of an electrically powered motor scooter for city use. Your staff members have prepared the cash-flow forecasts shown in Table 10.1. Since NPV is positive at the 10% opportunity cost of capital, it appears to be worth going ahead.

   TABLE 10.1 Preliminary cash-flow forecasts for Otobai’s electric scooter project (figures in ¥ billions).

Assumptions:

1. Investment is depreciated over 10 years straight-line.

2. Income is taxed at a rate of 50%.

Excel versions of Tables 10.1 to 10.5 are available on the book’s website, www.mcgraw-hill.co.uk/textbooks/brealey.

Before you decide, you want to delve into these forecasts and identify the key variables that determine whether the project succeeds or fails. It turns out that the marketing department has estimated revenue as follows:

The production department has estimated variable costs per unit as ¥300,000. Since projected volume is 100,000 scooters per year, total variable cost is ¥30 billion. Fixed costs are ¥3 billion per year. The initial investment can be depreciated on a straight-line basis over the 10-year period, and profits are taxed at a rate of 50%.

These seem to be the important things you need to know, but look out for unidentified variables. Perhaps there are patent problems, or perhaps you will need to invest in service stations that will recharge the scooter batteries. The greatest dangers often lie in these unknown unknowns, or “unk-unks,” as scientists call them.

   TABLE 10.2 To undertake a sensitivity analysis of the electric scooter project, we set each variable in turn at its most pessimistic or optimistic value and recalculate the NPV of the project.

Having found no unk-unks (no doubt you will find them later), you conduct a sensitivity analysis with respect to market size, market share, and so on. To do this, the marketing and production staffs are asked to give optimistic and pessimistic estimates for the underlying variables. These are set out in the left-hand columns of Table 10.2. The right-hand side shows what happens to the project’s net present value if the variables are set one at a time to their optimistic and pessimistic values. Your project appears to be by no means a sure thing. The most dangerous variables are market share and unit variable cost. If market share is only .04 (and all other variables are as expected), then the project has an NPV of –¥10.4 billion. If unit variable cost is ¥360,000 (and all other variables are as expected), then the project has an NPV of –¥15 billion.

Value of Information

Now you can check whether you could resolve some of the uncertainty before your company parts with the ¥15 billion investment. Suppose that the pessimistic value for unit variable cost partly reflects the production department’s worry that a particular machine will not work as designed and that the operation will have to be performed by other methods at an extra cost of ¥20,000 per unit. The chance that this will occur is only 1 in 10. But, if it does occur, the extra ¥20,000 unit cost will reduce after-tax cash flow by

It would reduce the NPV of youd porject by

putting the NPV of the scooter project underwater at +3.43 – 6.14 = –¥2.71 billion. It is possible that a relatively small change in the scooter’s design would remove the need for the new machine. Or perhaps a ¥10 million pretest of the machine will reveal whether it will work and allow you to clear up the problem. It clearly pays to invest ¥10 million to avoid a 10% probability of a ¥6.14 billion fall in NPV. You are ahead by –10 + .10 × 6,140 = +¥604 million.

On the other hand, the value of additional information about market size is small. Because the project is acceptable even under pessimistic assumptions about market size, you are unlikely to be in trouble if you have misestimated that variable.

Limits to Sensitivity Analysis

Sensitivity analysis boils down to expressing cash flows in terms of key project variables and then calculating the consequences of misestimating the variables. It forces the manager to identify the underlying variables, indicates where additional information would be most useful, and helps to expose inappropriate forecasts.

One drawback to sensitivity analysis is that it always gives somewhat ambiguous results. For example, what exactly does optimistic or pessimistic mean? The marketing department may be interpreting the terms in a different way from the production department. Ten years from now, after hundreds of projects, hindsight may show that the marketing department’s pessimistic limit was exceeded twice as often as the production department’s; but what you may discover 10 years hence is no help now. Of course, you could specify that, when you use the terms “pessimistic” and “optimistic,” you mean that there is only a 10% chance that the actual value will prove to be worse than the pessimistic figure or better than the optimistic one. However, it is far from easy to extract a forecaster’s notion of the true probabilities of possible outcomes.³

Another problem with sensitivity analysis is that the underlying variables are likely to be interrelated. What sense does it make to look at the effect in isolation of an increase in market size? If market size exceeds expectations, it is likely that demand will be stronger than you anticipated and unit prices will be higher. And why look in isolation at the effect of an increase in price? If inflation pushes prices to the upper end of your range, it is quite probable that costs will also be inflated.

Sometimes the analyst can get around these problems by defining underlying variables so that they are roughly independent. But you cannot push one-at-a-time sensitivity analysis too far. It is impossible to obtain expected, optimistic, and pessimistic values for total project cash flows from the information in Table 10.2.

Scenario Analysis

If the variables are interrelated, it may help to consider some alternative plausible scenarios. For example, perhaps the company economist is worried about the possibility of another sharp rise in world oil prices. The direct effect of this would be to encourage the use of electrically powered transportation. The popularity of compact cars after the recent oil price increases leads you to estimate that an immediate 20% rise in the price of oil would enable you to capture an extra 3% of the scooter market. On the other hand, the economist also believes that higher oil prices would prompt a world recession and at the same time stimulate inflation. In that case, market size might be in the region of .8 million scooters and both prices and cost might be 15% higher than your initial estimates. Table 10.3 shows that this scenario of higher oil prices and recession would on balance help your new venture. Its NPV would increase to ¥6.4 billion.

   TABLE 10.3 How the NPV of the electric scooter project would be affected by higher oil prices and a world recession.

Managers often find scenario analysis helpful. It allows them to look at different but consistent combinations of variables. Forecasters generally prefer to give an estimate of revenues or costs under a particular scenario than to give some absolute optimistic or pessimistic value.

Break-Even Analysis

When we undertake a sensitivity analysis of a project or when we look at alternative scenarios, we are asking how serious it would be if sales or costs turned out to be worse than we forecasted. Managers sometimes prefer to rephrase this question and ask how bad sales can get before the project begins to lose money. This exercise is known as break-even analysis.

   TABLE 10.4 NPV of electric scooter project under different assumptions about unit sales (figures in ¥ billions except as noted).

In the left-hand portion of Table 10.4 we set out the revenues and costs of the electric scooter project under different assumptions about annual sales.⁴ In the right-hand portion of the table we discount these revenues and costs to give the present value of the inflows and the present value of the outflows. Net present value is of course the difference between these numbers.

You can see that NPV is strongly negative if the company does not produce a single scooter. It is just positive if (as expected) the company sells 100,000 scooters and is strongly positive if it sells 200,000. Clearly the zero-NPV point occurs at a little under 100,000 scooters.

   FIGURE 10.1 A break-even chart showing the present values of Otobai’s cash inflows and outflows under different assumptions about unit sales. NPV is zero when sales are 85,000.

In Figure 10.1 we have plotted the present value of the inflows and outflows under different assumptions about annual sales. The two lines cross when sales are 85,000 scooters. This is the point at which the project has zero NPV. As long as sales are greater than 85,000, the project has a positive NPV.⁵

   TABLE 10.5 The electric scooter project’s accounting profit under different assumptions about unit sales (figures in ¥ billions except as noted).

   FIGURE 10.2 Sometimes break-even charts are constructed in terms of accounting numbers. After-tax profit is zero when sales are 60,000.

Managers frequently calculate break-even points in terms of accounting profits rather than present values. Table 10.5 shows Otobai’s after-tax profits at three levels of scooter sales. Figure 10.2 once again plots revenues and costs against sales. But the story this time is different. Figure 10.2, which is based on accounting profits, suggests a break-even of 60,000 scooters. Figure 10.1, which is based on present values, shows a break-even at 85,000 scooters. Why the difference?

When we work in terms of accounting profit, we deduct depreciation of ¥1.5 billion each year to cover the cost of the initial investment. If Otobai sells 60,000 scooters a year, revenues will be sufficient both to pay operating costs and to recover the initial outlay of ¥15 billion. But they will not be sufficient to repay the opportunity cost of capital on that ¥15 billion. A project that breaks even in accounting terms will surely have a negative NPV.

Operating Leverage and the Break-Even Point

A project’s break-even point depends on the extent to which its costs vary with the level of sales. Suppose that electric scooters fall out of favor. The bad news is that Otobai’s sales revenue is less than you’d hoped, but you have the consolation that the variable costs also decline. On the other hand, even if Otobai is unable to sell a single scooter, it must make the up-front investment of ¥15 billion and pay the fixed costs of ¥3 billion a year.

Suppose that Otobai’s entire costs were fixed at ¥33 billion. Then it would need only a 3% shortfall in revenues (from ¥37.5 billion to ¥36.4 billion) to turn the project into a negative-NPV investment. Thus, when costs are largely fixed, a shortfall in sales has a greater impact on profitability and the break-even point is higher. Of course, a high proportion of fixed costs is not all bad. The firm whose costs are fixed fares poorly when demand is low, but makes a killing during a boom.

A business with high fixed costs is said to have high operating leverage. Operating leverage is usually defined in terms of accounting profits rather than cash flows⁶ and is measured by the percentage change in profits for each 1% change in sales. Thus degree of operating leverage (DOL) is

The following simple formula⁷ shows how DOL is related to the business’s fixed costs (including depreciation) as a proportion of pretax profits:

In the case of Otobai’s scooter project

A 1% shortfall in the scooter project’s revenues would result in a 2.5% shortfall in profits.

Look now at Table 10.6, which shows how much the profits of some large U.S. companies have typically changed as a proportion of the change in sales. For example, notice that each 1% drop in sales has reduced steel company profits by 2.31%. This suggests that steel companies have an estimated operating leverage of 2.31%. You would expect steel stocks therefore to have correspondingly high betas and this is indeed the case.

   TABLE 10.6 Estimated degree of operating leverage (DOL) for large U.S. companies by industry.

Note: DOL is estimated from a regression of the change in EBITDA on the corresponding change in sales 1990–2010.

 10-3   Monte Carlo Simulation

Sensitivity analysis allows you to consider the effect of changing one variable at a time. By looking at the project under alternative scenarios, you can consider the effect of a limited number of plausible combinations of variables. Monte Carlo simulation is a tool for considering all possible combinations. It therefore enables you to inspect the entire distribution of project outcomes.

Imagine that you are a gambler at Monte Carlo. You know nothing about the laws of probability (few casual gamblers do), but a friend has suggested to you a complicated strategy for playing roulette. Your friend has not actually tested the strategy but is confident that it will on the average give you a 2½% return for every 50 spins of the wheel. Your friend’s optimistic estimate for any series of 50 spins is a profit of 55%; your friend’s pessimistic estimate is a loss of 50%. How can you find out whether these really are the odds? An easy but possibly expensive way is to start playing and record the outcome at the end of each series of 50 spins. After, say, 100 series of 50 spins each, plot a frequency distribution of the outcomes and calculate the average and upper and lower limits. If things look good, you can then get down to some serious gambling.

An alternative is to tell a computer to simulate the roulette wheel and the strategy. In other words, you could instruct the computer to draw numbers out of its hat to determine the outcome of each spin of the wheel and then to calculate how much you would make or lose from the particular gambling strategy.

That would be an example of Monte Carlo simulation. In capital budgeting we replace the gambling strategy with a model of the project, and the roulette wheel with a model of the world in which the project operates. Let us see how this might work with our project for an electrically powered scooter.

Simulating the Electric Scooter Project

Step 1: Modeling the Project The first step in any simulation is to give the computer a precise model of the project. For example, the sensitivity analysis of the scooter project was based on the following implicit model of cash flow:

This model of the project was all that you needed for the simpleminded sensitivity analysis that we described above. But if you wish to simulate the whole project, you need to think about how the variables are interrelated.

For example, consider the first variable—market size. The marketing department has estimated a market size of 1 million scooters in the first year of the project’s life, but of course you do not know how things will work out. Actual market size will exceed or fall short of expectations by the amount of the department’s forecast error:

You expect the forecast error to be zero, but it could turn out to be positive or negative. Suppose, for example, that the actual market size turns out to be 1.1 million. That means a forecast error of 10%, or +.1:

You can write the market size in the second year in exactly the same way:

But at this point you must consider how the expected market size in year 2 is affected by what happens in year 1. If scooter sales are below expectations in year 1, it is likely that they will continue to be below in subsequent years. Suppose that a shortfall in sales in year 1 would lead you to revise down your forecast of sales in year 2 by a like amount. Then

Now you can rewrite the market size in year 2 in terms of the actual market size in the previous year plus a forecast error:

In the same way you can describe the expected market size in year 3 in terms of market size in year 2 and so on.

This set of equations illustrates how you can describe interdependence between different periods. But you also need to allow for interdependence between different variables. For example, the price of electrically powered scooters is likely to increase with market size. Suppose that this is the only uncertainty and that a 10% addition to market size would lead you to predict a 3% increase in price. Then you could model the first year’s price as follows:

Then, if variations in market size exert a permanent effect on price, you can define the second year’s price as

Notice how we have linked each period’s selling price to the actual selling prices (including forecast error) in all previous periods. We used the same type of linkage for market size. These linkages mean that forecast errors accumulate; they do not cancel out over time. Thus, uncertainty increases with time: The farther out you look into the future, the more the actual price or market size may depart from your original forecast.

The complete model of your project would include a set of equations for each of the variables: market size, price, market share, unit variable cost, and fixed cost. Even if you allowed for only a few interdependencies between variables and across time, the result would be quite a complex list of equations.⁸ Perhaps that is not a bad thing if it forces you to understand what the project is all about. Model building is like spinach: You may not like the taste, but it is good for you.

Step 2: Specifying Probabilities Remember the procedure for simulating the gambling strategy? The first step was to specify the strategy, the second was to specify the numbers on the roulette wheel, and the third was to tell the computer to select these numbers at random and calculate the results of the strategy:

The steps are just the same for your scooter project:

Think about how you might go about specifying your possible errors in forecasting market size. You expect market size to be 1 million scooters. You obviously don’t think that you are underestimating or overestimating, so the expected forecast error is zero. On the other hand, the marketing department has given you a range of possible estimates. Market size could be as low as .85 million scooters or as high as 1.15 million scooters. Thus the forecast error has an expected value of 0 and a range of plus or minus 15%. If the marketing department has in fact given you the lowest and highest possible outcomes, actual market size should fall somewhere within this range with near certainty.⁹

That takes care of market size; now you need to draw up similar estimates of the possible forecast errors for each of the other variables that are in your model.

Step 3: Simulate the Cash Flows The computer now samples from the distribution of the forecast errors, calculates the resulting cash flows for each period, and records them. After many iterations you begin to get accurate estimates of the probability distributions of the project cash flows—accurate, that is, only to the extent that your model and the probability distributions of the forecast errors are accurate. Remember the GIGO principle: “Garbage in, garbage out.”

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Try It! Simulating the scooter project

brealey.mhhe.com/c10

Figure 10.3 shows part of the output from an actual simulation of the electric scooter project.¹⁰ Note the positive skewness of the outcomes—very large outcomes are more likely than very small ones. This is common when forecast errors accumulate over time. Because of the skewness the average cash flow is somewhat higher than the most likely outcome; in other words, a bit to the right of the peak of the distribution.¹¹

   FIGURE 10.3 Simulation of cash flows for year 10 of the electric scooter project.

Step 4: Calculate Present Value The distributions of project cash flows should allow you to calculate the expected cash flows more accurately. In the final step you need to discount these expected cash flows to find present value.

Simulation, though complicated, has the obvious merit of compelling the forecaster to face up to uncertainty and to interdependencies. Once you have set up your simulation model, it is a simple matter to analyze the principal sources of uncertainty in the cash flows and to see how much you could reduce this uncertainty by improving the forecasts of sales or costs. You may also be able to explore the effect of possible modifications to the project.

Simulation may sound like a panacea for the world’s ills, but, as usual, you pay for what you get. Sometimes you pay for more than you get. It is not just a matter of the time spent in building the model. It is extremely difficult to estimate interrelationships between variables and the underlying probability distributions, even when you are trying to be honest. But in capital budgeting, forecasters are seldom completely impartial and the probability distributions on which simulations are based can be highly biased.

In practice, a simulation that attempts to be realistic will also be complex. Therefore the decision maker may delegate the task of constructing the model to management scientists or consultants. The danger here is that, even if the builders understand their creation, the decision maker cannot and therefore does not rely on it. This is a common but ironic experience.

 10-4   Real Options and Decision Trees

When you use discounted cash flow (DCF) to value a project, you implicitly assume that the firm will hold the assets passively. But managers are not paid to be dummies. After they have invested in a new project, they do not simply sit back and watch the future unfold. If things go well, the project may be expanded; if they go badly, the project may be cut back or abandoned altogether. Projects that can be modified in these ways are more valuable than those that do not provide such flexibility. The more uncertain the outlook, the more valuable this flexibility becomes.

That sounds obvious, but notice that sensitivity analysis and Monte Carlo simulation do not recognize the opportunity to modify projects.¹² For example, think back to the Otobai electric scooter project. In real life, if things go wrong with the project, Otobai would abandon to cut its losses. If so, the worst outcomes would not be as devastating as our sensitivity analysis and simulation suggested.

Options to modify projects are known as real options. Managers may not always use the term “real option” to describe these opportunities; for example, they may refer to “intangible advantages” of easy-to-modify projects. But when they review major investment proposals, these option intangibles are often the key to their decisions.

The Option to Expand

Long-haul airfreight businesses such as FedEx need to move a massive amount of goods each day. Therefore, when Airbus announced delays to its A380 superjumbo freighter, FedEx turned to Boeing and ordered 15 of its 777 freighters to be delivered between 2009 and 2011. If business continues to expand, FedEx will need more aircraft. But rather than placing additional firm orders, the company secured a place in Boeing’s production line by acquiring options to buy a further 15 aircraft at a predetermined price. These options did not commit FedEx to expand but gave it the flexibility to do so.

Figure 10.4 displays FedEx’s expansion option as a simple decision tree. You can think of it as a game between FedEx and fate. Each square represents an action or decision by the company. Each circle represents an outcome revealed by fate. In this case there is only one outcome—when fate reveals the airfreight demand and FedEx’s capacity needs. FedEx then decides whether to exercise its options and buy additional 777s. Here the future decision is easy: Buy the airplanes only if demand is high and the company can operate them profitably. If demand is low, FedEx walks away and leaves Boeing with the problem of finding another customer for the planes that were reserved for FedEx.

   FIGURE 10.4 FedEx’s expansion option expressed as a simple decision tree.

You can probably think of many other investments that take on added value because of the further options they provide. For example,

•  When launching a new product, companies often start with a pilot program to iron out possible design problems and to test the market. The company can evaluate the pilot project and then decide whether to expand to full-scale production.

•  When designing a factory, it can make sense to provide extra land or floor space to reduce the future cost of a second production line.

•  When building a four-lane highway, it may pay to build six-lane bridges so that the road can be converted later to six lanes if traffic volumes turn out to be higher than expected.

•  When building production platforms for offshore oil and gas fields, companies usually allow ample vacant deck space. The vacant space costs more up front but reduces the cost of installing extra equipment later. For example, vacant deck space could provide an option to install water-flooding equipment if oil or gas prices turn out high enough to justify this investment.

Expansion options do not show up on accounting balance sheets, but managers and investors are well aware of their importance. For example, in Chapter 4 we showed how the present value of growth opportunities (PVGO) contributes to the value of a company’s common stock. PVGO equals the forecasted total NPV of future investments. But it is better to think of PVGO as the value of the firm’s options to invest and expand. The firm is not obliged to grow. It can invest more if the number of positive-NPV projects turns out high or slow down if that number turns out low. The flexibility to adapt investment to future opportunities is one of the factors that makes PVGO so valuable.

The Option to Abandon

If the option to expand has value, what about the decision to bail out? Projects do not just go on until assets expire of old age. The decision to terminate a project is usually taken by management, not by nature. Once the project is no longer profitable, the company will cut its losses and exercise its option to abandon the project.

Some assets are easier to bail out of than others. Tangible assets are usually easier to sell than intangible ones. It helps to have active secondhand markets, which really exist only for standardized items. Real estate, airplanes, trucks, and certain machine tools are likely to be relatively easy to sell. On the other hand, the knowledge accumulated by a software company’s research and development program is a specialized intangible asset and probably would not have significant abandonment value. (Some assets, such as old mattresses, even have negative abandonment value; you have to pay to get rid of them. It is costly to decommission nuclear power plants or to reclaim land that has been strip-mined.)

EXAMPLE 10.1 • Bailing Out of the Outboard-Engine Project

Managers should recognize the option to abandon when they make the initial investment in a new project or venture. For example, suppose you must choose between two technologies for production of a Wankel-engine outboard motor.

1.  Technology A uses computer-controlled machinery custom-designed to produce the complex shapes required for Wankel engines in high volumes and at low cost. But if the Wankel outboard does not sell, this equipment will be worthless.

2.  Technology B uses standard machine tools. Labor costs are much higher, but the machinery can be sold for $17 million if demand turns out to be low.

Just for simplicity, assume that the initial capital outlays are the same for both technologies. If demand in the first year is buoyant, technology A will provide a payoff of $24 million. If demand is sluggish, the payoff from A is $16 million. Think of these payoffs as the project’s cash flow in the first year of production plus the value in year 1 of all future cash flows. The corresponding payoffs to technology B are $22.5 million and $15 million:

Technology A looks better in a DCF analysis of the new product because it was designed to have the lowest possible cost at the planned production volume. Yet you can sense the advantage of the flexibility provided by technology B if you are unsure whether the new outboard will sink or swim in the marketplace. If you adopt technology B and the outboard is not a success, you are better off collecting the first year’s cash flow of $1.5 million and then selling the plant and equipment for $17 million.

Figure 10.5 summarizes Example 10.1 as a decision tree. The abandonment option occurs at the right-hand boxes for technology B. The decisions are obvious: continue if demand is buoyant, abandon otherwise. Thus the payoffs to technology B are

   FIGURE 10.5 Decision tree for the Wankel outboard motor project. Technology B allows the firm to abandon the project and recover $18.5 million if demand is sluggish.

Technology B provides an insurance policy: If the outboard’s sales are disappointing, you can abandon the project and receive $18.5 million. The total value of the project with technology B is its DCF value, assuming that the company does not abandon, plus the value of the option to sell the assets for $17 million. When you value this abandonment option, you are placing a value on flexibility.

Production Options

When companies undertake new investments, they generally think about the possibility that at a later stage they may wish to modify the project. After all, today everybody may be demanding round pegs, but, who knows, tomorrow square ones may be all the rage. In that case you need a plant that provides the flexibility to produce a variety of peg shapes. In just the same way, it may be worth paying up front for the flexibility to vary the inputs. For example in Chapter 22 we will describe how electric utilities often build in the option to switch between burning oil and burning natural gas. We refer to these opportunities as production options.

Timing Options

The fact that a project has a positive NPV does not mean that it is best undertaken now. It might be even more valuable to delay.

Timing decisions are fairly straightforward under conditions of certainty. You need to examine alternative dates for making the investment and calculate its net future value at each of these dates. Then, to find which of the alternatives would add most to the firm’s current value, you must discount these net future values back to the present:

The optimal date to undertake the investment is the one that maximizes its contribution to the value of your firm today. This procedure should already be familiar to you from Chapter 6, where we worked out when it was best to cut a tract of timber.

In the timber-cutting example we assumed that there was no uncertainty about the cash flows, so that you knew the optimal time to exercise your option. When there is uncertainty, the timing option is much more complicated. An opportunity not taken at t = 0 might be more or less attractive at t = 1; there is rarely any way of knowing for sure. Perhaps it is better to strike while the iron is hot even if there is a chance that it will become hotter. On the other hand, if you wait a bit you might obtain more information and avoid a bad mistake. That is why you often find that managers choose not to invest today in projects where the NPV is only marginally positive and there is much to be learned by delay.

More on Decision Trees

We will return to all these real options in Chapter 22, after we have covered the theory of option valuation in Chapters 20 and 21. But we will end this chapter with a closer look at decision trees.

Decision trees are commonly used to describe the real options imbedded in capital investment projects. But decision trees were used in the analysis of projects years before real options were first explicitly identified. Decision trees can help to illustrate project risk and how future decisions will affect project cash flows. Even if you never learn or use option valuation theory, decision trees belong in your financial toolkit.

The best way to appreciate how decision trees can be used in project analysis is to work through a detailed example.

EXAMPLE 10.2 • A Decision Tree for Pharmaceutical R&D

Drug development programs may last decades. Usually hundreds of thousands of compounds may be tested to find a few with promise. Then these compounds must survive several stages of investment and testing to gain approval from the Food and Drug Administration (FDA). Only then can the drug be sold commercially. The stages are as follows:

1.  Phase I clinical trials. After laboratory and clinical tests are concluded, the new drug is tested for safety and dosage in a small sample of humans.

2.  Phase II clinical trials. The new drug is tested for efficacy (Does it work as predicted?) and for potentially harmful side effects.

3.  Phase III clinical trials. The new drug is tested on a larger sample of humans to confirm efficacy and to rule out harmful side effects.

4.  Prelaunch. If FDA approval is gained, there is investment in production facilities and initial marketing. Some clinical trials continue.

5. Commercial launch. After making a heavy initial investment in marketing and sales, the company begins to sell the new drug to the public.

Once a drug is launched successfully, sales usually continue for about 10 years, until the drug’s patent protection expires and competitors enter with generic versions of the same chemical compound. The drug may continue to be sold off-patent, but sales volume and profits are much lower.

The commercial success of FDA-approved drugs varies enormously. The PV of a “blockbuster” drug at launch can be 5 or 10 times the PV of an average drug. A few blockbusters can generate most of a large pharmaceutical company’s profits.¹³

No company hesitates to invest in R&D for a drug that it knows will be a blockbuster. But the company will not find out for sure until after launch. Sometimes a company thinks it has a blockbuster, only to discover that a competitor has launched a better drug first.

Sometimes the FDA approves a drug but limits its scope of use. Some drugs, though effective, can only be prescribed for limited classes of patients; other drugs can be prescribed much more widely. Thus the manager of a pharmaceutical R&D program has to assess the odds of clinical success and the odds of commercial success. A new drug may be abandoned if it fails clinical trials—for example, because of dangerous side effects—or if the outlook for profits is discouraging.

Figure 10.6 is a decision tree that illustrates these decisions. We have assumed that a new drug has passed phase I clinical trials with flying colors. Now it requires an investment of $18 million for phase II trials. These trials take two years. The probability of success is 44%.

If the trials are successful, the manager learns the commercial potential of the drug, which depends on how widely it can be used. Suppose that the forecasted PV at launch depends on the scope of use allowed by the FDA. These PVs are shown at the far right of the decision tree: an upside outcome of NPV = $700 million if the drug can be widely used, a most likely case with NPV = $300 million, and a downside case of NPV = $100 million if the drug’s scope is greatly restricted.¹⁴ The NPVs are the payoffs at launch after investment in marketing. Launch comes three years after the start of phase III if the drug is approved by the FDA. The probabilities of the upside, most likely, and downside outcomes are 25%, 50%, and 25%, respectively.

A further R&D investment of $130 million is required for phase III trials and for the prelaunch period. (We have combined phase III and prelaunch for simplicity.) The probability of FDA approval and launch is 80%.

Now let’s value the investments in Figure 10.6. We assume a risk-free rate of 4% and market risk premium of 7%. If FDA-approved pharmaceutical products have asset betas of .8, the opportunity cost of capital is 4 + .8 × 7 = 9.6%.

   FIGURE 10.6 A simplified decision tree for pharmaceutical R&D. A candidate drug requires an $18 million investment for phase II clinical trials. If the trials are successful (44% probability), the company learns the drug’s scope of use and updates its forecast of the drug’s PV at commercial launch. The investment required for the phase III trials and prelaunch outlays is $130 million. The probability of success in phase III and prelaunch is 80%.

We work back through the tree from right to left. The NPVs at the start of phase III trials are:

Since the downside NPV is negative at –$69 million, the $130 million investment at the start of phase III should not be made in the downside case. There is no point investing $130 million for an 80% chance of a $100 million payoff three years later. Therefore the value of the R&D program at this point in the decision tree is not –$69 million, but zero.

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Try It! Figure 10.6:
Decision tree for the pharmaceutical project

brealey.mhhe.com/c10

Now calculate the NPV at the initial investment decision for phase II trials. The payoff two years later depends on whether the drug delivers on the upside, most likely, or downside: a 25% chance of NPV = +$295 million, a 50% chance of NPV = +$52 million, and a 25% chance of cancellation and NPV = 0. These NPVs are achieved only if the phase II trials are successful: there is a 44% chance of success and a 56% chance of failure. The initial investment is $18 million. Therefore NPV is

Thus the phase II R&D is a worthwhile investment, even though the drug has only a 33% chance of making it to launch (.44 × .75 = .33, or 33%).

Notice that we did not increase the 9.6% discount rate to offset the risks of failure in clinical trials or the risk that the drug will fail to generate profits. Concerns about the drug’s efficacy, possible side effects, and scope of use are diversifiable risks, which do not increase the risk of the R&D project to the company’s diversified stockholders. We were careful to take these concerns into account in the cash-flow forecasts, however. The decision tree in Figure 10.6 keeps track of the probabilities of success or failure and the probabilities of upside and downside outcomes.¹⁵

Figures 10.5 and 10.6 are both examples of abandonment options. We have not explicitly modeled the investments as options, however, so our NPV calculation is incomplete. We show how to value abandonment options in Chapter 22.

Pro and Con Decision Trees

Any cash-flow forecast rests on some assumption about the firm’s future investment and operating strategy. Often that assumption is implicit. Decision trees force the underlying strategy into the open. By displaying the links between today’s decisions and tomorrow’s decisions, they help the financial manager to find the strategy with the highest net present value.

The decision tree in Figure 10.6 is a simplified version of reality. For example, you could expand the tree to include a wider range of NPVs at launch, possibly including some chance of a blockbuster or of intermediate outcomes. You could allow information about the NPVs to arrive gradually, rather than just at the start of phase III. You could introduce the investment decision at phase I trials and separate the phase III and prelaunch stages. You may wish to draw a new decision tree covering these events and decisions. You will see how fast the circles, squares, and branches accumulate.

The trouble with decision trees is that they get so __________ complex so __________ quickly (insert your own expletives). Life is complex, however, and there is very little we can do about it. It is therefore unfair to criticize decision trees because they can become complex. Our criticism is reserved for analysts who let the complexity become overwhelming. The point of decision trees is to allow explicit analysis of possible future events and decisions. They should be judged not on their comprehensiveness but on whether they show the most important links between today’s and tomorrow’s decisions. Decision trees used in real life will be more complex than Figure 10.6, but they will nevertheless display only a small fraction of possible future events and decisions. Decision trees are like grapevines: They are productive only if they are vigorously pruned.

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SUMMARY

Earlier chapters explained how companies calculate a project’s NPV by forecasting the cash flows and discounting them at a rate that reflects project risk. The end result is the project’s contribution to shareholder wealth. Understanding discounted-cash-flow analysis is important, but there is more to good capital budgeting practice than an ability to discount.

First, companies need to establish a set of capital budgeting procedures to ensure that decisions are made in an orderly manner. Most companies prepare an annual capital budget, which is a list of investment projects planned for the coming year. Inclusion of a project in the capital budget does not constitute final approval for the expenditure. Before the plant or division can go ahead with a proposal, it will usually need to submit an appropriation request that includes detailed forecasts, a discounted-cash-flow analysis, and back-up information.

Sponsors of capital investment projects are tempted to overstate future cash flows and understate risks. Therefore firms need to encourage honest and open discussion. They also need procedures to ensure that projects fit in with the company’s strategic plans and are developed on a consistent basis. (These procedures should not include fudge factors added to project hurdle rates in an attempt to offset optimistic forecasts.) Later, after a project has begun to operate, the firm can follow up with a postaudit. Postaudits identify problems that need fixing and help the firm learn from its mistakes.

Good capital budgeting practice also tries to identify the major uncertainties in project proposals. An awareness of these uncertainties may suggest ways that the project can be reconfigured to reduce the dangers, or it may point out some additional research that will confirm whether the project is worthwhile.

There are several ways in which companies try to identify and evaluate the threats to a project’s success. The first is sensitivity analysis. Here the manager considers in turn each forecast or assumption that drives cash flows and recalculates NPV at optimistic and pessimistic values of that variable. The project is “sensitive to” that variable if the resulting range of NPVs is wide, particularly on the pessimistic side.

Sensitivity analysis often moves on to break-even analysis, which identifies break-even values of key variables. Suppose the manager is concerned about a possible shortfall in sales. Then he or she can calculate the sales level at which the project just breaks even (NPV = 0) and consider the odds that sales will fall that far. Break-even analysis is also done in terms of accounting income, although we do not recommend this application.

Sensitivity analysis and break-even analysis are easy, and they identify the forecasts and assumptions that really count for the project’s success or failure. The important variables do not change one at a time, however. For example, when raw material prices are higher than forecasted, it’s a good bet that selling prices will be higher too. The logical response is scenario analysis, which examines the effects on NPV of changing several variables at a time.

Scenario analysis looks at a limited number of combinations of variables. If you want to go whole hog and look at all possible combinations, you will have to turn to Monte Carlo simulation. In that case, you must build a financial model of the project and specify the probability distribution of each variable that determines cash flow. Then you ask the computer to draw random values for each variable and work out the resulting cash flows. In fact you ask the computer to do this thousands of times, in order to generate complete distributions of future cash flows. With these distributions in hand, you can get a better handle on expected cash flows and project risks. You can also experiment to see how the distributions would be affected by altering project scope or the ranges for any of the variables.

Elementary treatises on capital budgeting sometimes create the impression that, once the manager has made an investment decision, there is nothing to do but sit back and watch the cash flows unfold. In practice, companies are constantly modifying their operations. If cash flows are better than anticipated, the project may be expanded; if they are worse, it may be contracted or abandoned altogether. Options to modify projects are known as real options. In this chapter we introduced the main categories of real options: expansion options, abandonment options, timing options, and options providing flexibility in production.

Good managers take account of real options when they value a project. One convenient way to summarize real options and their cash-flow consequences is to create a decision tree. You identify the things that could happen to the project and the main counteractions that you might take. Then, working back from the future to the present, you can consider which action you should take in each case.

Decision trees can help to identify the possible impact of real options on project cash flows, but we largely skirted the issue of how to value real options. We return to this topic in Chapter 22, after we have covered option-valuation methods in the previous two chapters.

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FURTHER READING

Three not-too-technical references on real options are listed below. Additional references follow Chapter 22.

A. Dixit and R. Pindyck, “The Options Approach to Capital Investment,” Harvard Business Review 73 (May–June 1995), pp. 105–115.

W. C. Kester, “Today’s Options for Tomorrow’s Growth,” Harvard Business Review 62 (March–April 1984), pp. 153–160.

A. Triantis and A. Borison, “Real Options: State of the Practice,” Journal of Applied Corporate Finance 14 (Summer 2001), pp. 8–24.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Capital budgeting process True or false?

a.  The approval of a capital budget allows managers to go ahead with any project included in the budget.

b.  Capital budgets and project authorizations are mostly developed “bottom up.” Strategic planning is a “top-down” process.

c.  Project sponsors are likely to be overoptimistic.

2.  Capital budgeting process Explain how each of the following actions or problems can distort or disrupt the capital budgeting process.

a.  Overoptimism by project sponsors.

b.  Inconsistent forecasts of industry and macroeconomic variables.

c.  Capital budgeting organized solely as a bottom-up process.

3.  Terminology Define and briefly explain each of the following terms or procedures:

a.  Sensitivity analysis

b.  Scenario analysis

c.  Break-even analysis

d.  Monte Carlo simulation

e.  Decision tree

f.  Real option

g.  Abandonment value

h.  Expansion value

4.  Project analysis True or false?

a.  Sensitivity analysis is unnecessary for projects with asset betas that are equal to 0.

b.  Sensitivity analysis can be used to identify the variables most crucial to a project’s success.

c.  If only one variable is uncertain, sensitivity analysis gives “optimistic” and “pessimistic” values for project cash flow and NPV.

d.  The break-even sales level of a project is higher when break-even is defined in terms of NPV rather than accounting income.

e.  Risk is reduced when a high proportion of costs are fixed.

f.  Monte Carlo simulation can be used to help forecast cash flows.

5.  Monte Carlo simulation Suppose a manager has already estimated a project’s cash flows, calculated its NPV, and done a sensitivity analysis like the one shown in Table 10.2. List the additional steps required to carry out a Monte Carlo simulation of project cash flows.

6.  Real options True or false?

a.  Decision trees can help identify and describe real options.

b.  The option to expand increases PV.

c.  High abandonment value decreases PV.

d.  If a project has positive NPV, the firm should always invest immediately.

7.  Biased forecasts Explain why setting a higher discount rate is not a cure for upward-biased cash-flow forecasts.

INTERMEDIATE

8.  Capital budgeting process Draw up an outline or flowchart tracing the capital budgeting process from the initial idea for a new investment project to the completion of the project and the start of operations. Assume the idea for a new obfuscator machine comes from a plant manager in the Deconstruction Division of the Modern Language Corporation.

Here are some questions your outline or flowchart should consider: Who will prepare the original proposal? What information will the proposal contain? Who will evaluate it? What approvals will be needed, and who will give them? What happens if the machine costs 40% more to purchase and install than originally forecasted? What will happen when the machine is finally up and running?

9.  Biased forecasts Look back to the cash flows for projects F and G in Section 5-3. The cost of capital was assumed to be 10%. Assume that the forecasted cash flows for projects of this type are overstated by 8% on average. That is, the forecast for each cash flow from each project should be reduced by 8%. But a lazy financial manager, unwilling to take the time to argue with the projects’ sponsors, instructs them to use a discount rate of 18%.

a.  What are the projects’ true NPVs?

b.  What are the NPVs at the 18% discount rate?

c.  Are there any circumstances in which the 18% discount rate would give the correct NPVs? (Hint: Could upward bias be more severe for more-distant cash flows?)

10.  Scenario analysis What is the NPV of the electric scooter project under the following scenario?

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11.  Sensitivity analysis Otobai’s staff (see Section 10-2) has come up with the following revised estimates for the electric scooter project:

Conduct a sensitivity analysis using the spreadsheets (available at www.mcgraw-hill.co.uk/textbooks/brealey). What are the principal uncertainties in the project?

12.  Break-even analysis and operating leverage Otobai is considering still another production method for its electric scooter (see Section 10-2). It would require an additional investment of ¥15 billion but would reduce variable costs by ¥40,000 per unit. Other assumptions follow Table 10.1.

a.  What is the NPV of this alternative scheme?

b.  Draw break-even charts for this alternative scheme along the lines of Figure 10.1.

c.  Explain how you would interpret the break-even figure.

d.  Now suppose Otobai’s management would like to know the figure for variable cost per unit at which the electric scooter project in Section 10-1 would break even. Calculate the level of costs at which the project would earn zero profit and at which it would have zero NPV. Assume that the initial investment is ¥15 billion.

e.  Recalculate DOL.

13.  Sensitivity analysis The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment. The new equipment costs $9 million (the existing equipment has zero salvage value). The attraction of the new machinery is that it is expected to cut manufacturing costs from their current level of $8 a welt to $4. However, as the following table shows, there is some uncertainty both about future sales and about the performance of the new machinery:

Conduct a sensitivity analysis of the replacement decision, assuming a discount rate of 12%. Rustic Welt does not pay taxes.

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14.  Sensitivity analysis Use the spreadsheet for the guano project in Chapter 6 to undertake a sensitivity analysis of the project. Make whatever assumptions seem reasonable to you. What are the critical variables? What should the company’s response be to your analysis?

15.  Operating leverage Suppose that the expected variable costs of Otobai’s project are ¥33 billion a year and that fixed costs are zero. How does this change the degree of operating leverage? Now recompute the operating leverage assuming that the entire ¥33 billion of costs are fixed.

16.  Operating leverage Operating leverage is often measured as the percentage increase in pretax profits after depreciation for a 1% increase in sales.

a.  Calculate the operating leverage for the electric scooter project assuming unit sales are 100,000 (see Section 10-2).

b.  Now show that this figure is equal to 1 + (fixed costs including depreciation divided by pretax profits).

c.  Would operating leverage be higher or lower if sales were 200,000 scooters?

17.  Decision trees Look back at the Vegetron electric mop project in Section 9-4. Assume that if tests fail and Vegetron continues to go ahead with the project, the $1 million investment would generate only $75,000 a year. Display Vegetron’s problem as a decision tree.

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18.  Monte Carlo simulation Our website (www.mcgraw-hill.co.uk/textbooks/brealey) contains an Excel program for simulating the cash flows from the Otobai project. Use this program to examine which are the principal uncertainties surrounding the project. Suppose that some more analysis could effectively remove uncertainty about one of the variables. Suggest where it could be most usefully applied.

19.  Real options Describe the real option in each of the following cases:

a.  Deutsche Metall postpones a major plant expansion. The expansion has positive NPV on a discounted-cash-flow basis but top management wants to get a better fix on product demand before proceeding.

b.  Qin Shi Huang commits to production of digital switching equipment specially designed for the European market. The project has a negative NPV, but it is justified on strategic grounds by the need for a strong market position in the rapidly growing, and potentially very profitable, market.

c.  Qin Shi Huang vetoes a fully integrated, automated production line for the new digital switches. It relies on standard, less-expensive equipment. The automated production line is more efficient overall, according to a discounted-cash-flow calculation.

d.  Mount Fuji Airways buys a jumbo jet with special equipment that allows the plane to be switched quickly from freight to passenger use or vice versa.

20.  Decision trees Look again at the decision tree in Figure 10.6. Expand the possible outcomes as follows:

• Blockbuster: PV = $1.5 billion with 5% probability.

• Above average: PV = $700 million with 20% probability.

• Average: PV = $300 million with 40% probability.

• Below average: PV = $100 million with 25% probability.

• “Dog”: PV = $40 million with 10% probability.

Redraw the decision tree. Is the $18 million investment in phase II trials still positive NPV?

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21 Decision trees Look again at the example in Figure 10.6. The R&D team has put forward a proposal to invest an extra $20 million in expanded phase II trials. The object is to prove that the drug can be administered by a simple inhaler rather than as a liquid. If successful, the scope of use is broadened and the upside PV increases to $1 billion. The probabilities of success are unchanged. Go to the Excel spreadsheet version of Figure 10.6 at www.mcgraw-hill.co.uk/textbooks/brealey. Is the extra $20 million investment worthwhile? Would your answer change if the probability of success in the phase III trials falls to 75%?

CHALLENGE

22.  Decision trees Magna Charter is a new corporation formed by Agnes Magna to provide an executive flying service for the southeastern United States. The founder thinks there will be a ready demand from businesses that cannot justify a full-time company plane but nevertheless need one from time to time. However, the venture is not a sure thing. There is a 40% chance that demand in the first year will be low. If it is low, there is a 60% chance that it will remain low in subsequent years. On the other hand, if the initial demand is high, there is an 80% chance that it will stay high. The immediate problem is to decide what kind of plane to buy. A turboprop costs $550,000. A piston-engine plane costs only $250,000 but has less capacity. Moreover, the piston-engine plane is an old design and likely to depreciate rapidly. Ms. Magna thinks that next year secondhand piston aircraft will be available for only $150,000.

Table 10.7 shows how the payoffs in years 1 and 2 from both planes depend on the pattern of demand. You can see, for example, that if demand is high in both years 1 and 2, the turbo will provide a payoff of $960,000 in year 2. If demand is high in year 1 but low in year 2, the turbo’s payoff in the second year is only $220,000. Think of the payoffs in the second year as the cash flow that year plus the year-2 value of any subsequent cash flows. Also think of these cash flows as certainty equivalents, which can therefore be discounted at the risk-free interest rate of 10%.

   TABLE 10.7 The possible payoffs from Ms. Magna’s flying service. (All figures are in thousands. Probabilities are in parentheses.)

Ms. Magna now has an idea: Why not start out with one piston plane. If demand is low in the first year, Magna Charter can sit tight with this one relatively inexpensive aircraft. On the other hand, if demand is high in the first year she can buy a second piston-engine plane for only $150,000. In this case, if demand continues to be high, the payoff in year 2 from the two piston planes will be $800,000. However, if demand in year 2 were to decline, the payoff would be only $100,000.

a.  Draw a decision tree setting out Magna Charter’s choices.

b.  If Magna Charter buys a piston plane, should it expand if demand turns out to be high in the first year?

c.  Given your answer to b, would you recommend that Ms. Magna buy the turboprop or the piston-engine plane today?

d.  What would be the NPV of an investment in a piston plane if there were no option to expand? How much extra value is contributed by the option to expand?

23.  Monte Carlo simulation Look back at the guano project in Section 6-2. Use the Crystal Ball™ software to simulate how uncertainty about inflation could affect the project’s cash flows.

24.  Decision trees A manufacturing plant in Sicily will cost €90 million to build. The fixed costs of operating the plant will be €25 million per year. Projected net revenues (revenues minus variable costs) are €35 million per year. However, net revenues could turn out to be as high as €45 million (optimistic case) or as low as €20 million (pessimistic case). The probabilities of the optimistic and pessimistic outcomes are each 25%. Assume for simplicity that cash flows are level perpetuities. Ignore taxes. The cost of capital is 12%.

a.  Would you go ahead and build the factory if it has no value in any other use?

b.  Suppose that the factory could be shut down and sold for €50 million in year 2, after actual net revenues are revealed. Now would you build the factory?

MINI-CASE ● ● ● ● ●

Waldo County

Waldo County, the well-known real estate developer, worked long hours, and he expected his staff to do the same. So George Chavez was not surprised to receive a call from the boss just as George was about to leave for a long summer’s weekend.

Mr. County’s success had been built on a remarkable instinct for a good site. He would exclaim “Location! Location! Location!” at some point in every planning meeting. Yet finance was not his strong suit. On this occasion he wanted George to go over the figures for a new $90 million outlet mall designed to intercept tourists heading downeast toward Maine. “First thing Monday will do just fine,” he said as he handed George the file. “I’ll be in my house in Bar Harbor if you need me.”

George’s first task was to draw up a summary of the projected revenues and costs. The results are shown in Table 10.8. Note that the mall’s revenues would come from two sources: The company would charge retailers an annual rent for the space they occupied and in addition it would receive 5% of each store’s gross sales.

   TABLE 10.8 Projected revenues and costs in real terms for the Downeast Tourist Mall (figures in $ millions).

Construction of the mall was likely to take three years. The construction costs could be depreciated straight-line over 15 years starting in year 3. As in the case of the company’s other developments, the mall would be built to the highest specifications and would not need to be rebuilt until year 17. The land was expected to retain its value, but could not be depreciated for tax purposes.

Construction costs, revenues, operating and maintenance costs, and real estate taxes were all likely to rise in line with inflation, which was forecasted at 2% a year. The company’s tax rate was 35% and the cost of capital was 9% in nominal terms.

George decided first to check that the project made financial sense. He then proposed to look at some of the things that might go wrong. His boss certainly had a nose for a good retail project, but he was not infallible. The Salome project had been a disaster because store sales had turned out to be 40% below forecast. What if that happened here? George wondered just how far sales could fall short of forecast before the project would be underwater.

Inflation was another source of uncertainty. Some people were talking about a zero long-term inflation rate, but George also wondered what would happen if inflation jumped to, say, 10%.

A third concern was possible construction cost overruns and delays due to required zoning changes and environmental approvals. George had seen cases of 25% construction cost overruns and delays up to 12 months between purchase of the land and the start of construction. He decided that he should examine the effect that this scenario would have on the project’s profitability.

“Hey, this might be fun,” George exclaimed to Mr. Waldo’s secretary, Fifi, who was heading for Old Orchard Beach for the weekend. “I might even try Monte Carlo.”

“Waldo went to Monte Carlo once,” Fifi replied. “Lost a bundle at the roulette table. I wouldn’t remind him. Just show him the bottom line. Will it make money or lose money? That’s the bottom line.”

“OK, no Monte Carlo,” George agreed. But he realized that building a spreadsheet and running scenarios was not enough. He had to figure out how to summarize and present his results to Mr. County.

QUESTIONS

1.  What is the project’s NPV, given the projections in Table 10.8?

2.  Conduct a sensitivity and a scenario analysis of the project. What do these analyses reveal about the project’s risks and potential value?

___________

¹There is no First Law. We think “Second Law” sounds better. There is a Third Law, but that is for another chapter.

²Adding a fudge factor to the cost of capital also favors quick-payback projects and penalizes longer-lived projects, which tend to have lower rates of return but higher NPVs. Adding a 5% fudge factor to the discount rate is roughly equivalent to reducing the forecast and present value of the first year’s cash flow by 5%. The impact on the present value of a cash flow 10 years in the future is much greater, because the fudge factor is compounded in the discount rate. The fudge factor is not too much of a burden for a 2- or 3-year project, but an enormous burden for a 10- or 20-year project.

³If you doubt this, try some simple experiments. Ask the person who repairs your dishwasher to state a numerical probability that it will work for at least one more year. Or construct your own subjective probability distribution of the number of telephone calls you will receive next week. That ought to be easy. Try it.

⁴Notice that if the project makes a loss, this loss can be used to reduce the tax bill on the rest of the company’s business. In this case the project produces a tax saving—the tax outflow is negative.

⁵We could also calculate break-even sales by plotting equivalent annual costs and revenues. Of course, the break-even point would be identical at 85,000 scooters.

⁶In Chapter 9 we developed a measure of operating leverage that was expressed in terms of cash flows and their present values. We used this measure to show how beta depends on operating leverage.

⁷This formula for DOL can be derived as follows. If sales increase by 1%, then variable costs will also increase by 1%, and profits will increase by .01 × (sales – variable costs) = .01 × (pretax profits + fixed costs). Now recall the definition of DOL:

⁸Specifying the interdependencies is the hardest and most important part of a simulation. If all components of project cash flows were unrelated, simulation would rarely be necessary.

⁹Suppose “near certainty” means “99% of the time.” If forecast errors are normally distributed, this degree of certainty requires a range of plus or minus three standard deviations.

Other distributions could, of course, be used. For example, the marketing department may view any market size between .85 and 1.15 million scooters as equally likely. In that case the simulation would require a uniform (rectangular) distribution of forecast errors.

¹⁰These are actual outputs from Crystal Ball™ software. The simulation assumed annual forecast errors were normally distributed and ran through 10,000 trials. We thank Christopher Howe for running the simulation.

¹¹When you are working with cash-flow forecasts, bear in mind the distinction between the expected value and the most likely (or modal) value. Present values are based on expected cash flows—that is, the probability-weighted average of the possible future cash flows. If the distribution of possible outcomes is skewed to the right as in Figure 10.3, the expected cash flow will be greater than the most likely cash flow.

¹²Some simulation models do recognize the possibility of changing policy. For example, when a pharmaceutical company uses simulation to analyze its R&D decisions, it allows for the possibility that the company can abandon the development at each phase.

¹³The website of the Tufts Center for the Study of Drug Development (http://csdd.tufts.edu) provides a wealth of information about the costs and risks of pharmaceutical R&D.

¹⁴The most likely case is not the average outcome, because PVs in the pharmaceutical business are skewed to the upside. The average PV is .25 × 700 + .5 × 300 + .25 × 100 = $350 million.

¹⁵The market risk attached to the PVs at launch is recognized in the 9.6% discount rate.

Part 3 Best Practices in Capital Budgeting

Investment, Strategy, and Economic Rents

Why is a manager who has learned about discounted cash flows (DCF) like a baby with a hammer? Answer: Because to a baby with a hammer, everything looks like a nail.

Our point is that you should not focus on the arithmetic of DCF and thereby ignore the forecasts that are the basis of every investment decision. Senior managers are continuously bombarded with requests for funds for capital expenditures. All these requests are supported with detailed DCF analyses showing that the projects have positive NPVs.¹ How, then, can managers distinguish the NPVs that are truly positive from those that are merely the result of forecasting errors? We suggest that they should ask some probing questions about the possible sources of economic gain.

To make good investment decisions, you need to understand your firm’s competitive advantages. This is where corporate strategy and finance come together. Good strategy positions the firm to generate the most value from its assets and growth opportunities. The search for good strategy starts with understanding how your firm stacks up versus your competitors, and how they will respond to your initiatives. Are your cash-flow forecasts realistic in your competitive environment? What effects will your competitors’ actions have on the NPVs of your investments?

The first section in this chapter reviews certain common pitfalls in capital budgeting, notably the tendency to apply DCF when market values are already available and no DCF calculations are needed. The second section covers the economic rents that underlie all positive-NPV investments. The third section presents a case study describing how Marvin Enterprises, the gargle blaster company, analyzed the introduction of a radically new product.

 11-1   Look First to Market Values

Let us suppose that you have persuaded all your project sponsors to give honest forecasts. Although those forecasts are unbiased, they are still likely to contain errors, some positive and others negative. The average error will be zero, but that is little consolation because you want to accept only projects with truly superior profitability.

Think, for example, of what would happen if you were to jot down your estimates of the cash flows from operating various lines of business. You would probably find that about half appeared to have positive NPVs. This may not be because you personally possess any superior skill in operating jumbo jets or running a chain of laundromats but because you have inadvertently introduced large errors into your estimates of the cash flows. The more projects you contemplate, the more likely you are to uncover projects that appear to be extremely worthwhile.

What can you do to prevent forecast errors from swamping genuine information? We suggest that you begin by looking at market values.

The Mercedes and the Movie Star

The following parable should help to illustrate what we mean. Your local Mercedes dealer is announcing a special offer. For €104,500 you get not only a brand-new Mercedes S-class but also the chance to meet your favorite movie star. You wonder how much you are paying for that encounter.

There are two possible approaches to the problem. You could evaluate the worth of the Mercedes’s reversing camera, parking guidance, and other features and conclude that the Mercedes is worth €107,000. This would seem to suggest that the dealership is willing to pay you €1,500 to meet with the movie star. Alternatively, you might note that the market price for the Mercedes is €104,000, so that you are really paying €500 for the meeting. As long as there is a competitive market for Mercedes, the latter approach is more appropriate.

Security analysts face a similar problem whenever they value a company’s stock. They must consider the information that is already known to the market about a company, and they must evaluate the information that is known only to them. The information that is known to the market is the Mercedes; the private information is the meeting with the movie star. Investors have already evaluated the information that is generally known. Security analysts do not need to evaluate this information again. They can start with the market price of the stock and concentrate on valuing their private information.

While lesser mortals would instinctively accept the Mercedes’s market value of €104,000, the financial manager is trained to enumerate and value all the costs and benefits from an investment and is therefore tempted to substitute his or her own opinion for the market’s. Unfortunately this approach increases the chance of error. Many capital assets are traded in a competitive market, so it makes sense to start with the market price and then ask why these assets should earn more in your hands than in your rivals’.

EXAMPLE 11.1 • Investing in a New Department Store

We encountered a department store chain that estimated the present value of the expected cash flows from each proposed store, including the price at which it could eventually sell the store. Although the firm took considerable care with these estimates, it was disturbed to find that its conclusions were heavily influenced by the forecasted selling price of each store. Management disclaimed any particular real estate expertise, but it discovered that its investment decisions were unintentionally dominated by its assumptions about future real estate prices.

Once the financial managers realized this, they always checked the decision to open a new store by asking the following question: “Let us assume that the property is fairly priced. What is the evidence that it is best suited to one of our department stores rather than to some other use?” In other words, if an asset is worth more to others than it is to you, then beware of bidding for the asset against them.

Let us take the department store problem a little further. Suppose that the new store costs $100 million.² You forecast that it will generate after-tax cash flow of $8 million a year for 10 years. Real estate prices are estimated to grow by 3% a year, so the expected value of the real estate at the end of 10 years is 100 × (1.03)¹⁰ = $134 million. At a discount rate of 10%, your proposed department store has an NPV of $1 million:

Notice how sensitive this NPV is to the ending value of the real estate. For example, an ending value of $120 million implies an NPV of –$5 million.

It is helpful to imagine such a business as divided into two parts—a real estate subsidiary that buys the building and a retailing subsidiary that rents and operates it. Then figure out how much rent the real estate subsidiary would have to charge, and ask whether the retailing subsidiary could afford to pay the rent.

In some cases a fair market rental can be estimated from real estate transactions. For example, we might observe that similar retail space recently rented for $10 million a year. In that case we would conclude that our department store was an unattractive use for the site. Once the site had been acquired, it would be better to rent it out at $10 million than to use it for a store generating only $8 million.

Suppose, on the other hand, that the property could be rented for only $7 million per year. The department store could pay this amount to the real estate subsidiary and still earn a net operating cash flow of 8 – 7 = $1 million. It is therefore the best current use for the real estate.³

Will it also be the best future use? Maybe not, depending on whether retail profits keep pace with any rent increases. Suppose that real estate prices and rents are expected to increase by 3% per year. The real estate subsidiary must charge 7 × 1.03 = $7.21 million in year 2, 7.21 × 1.03 = $7.43 million in year 3, and so on.⁴ Figure 11.1 shows that the store’s income fails to cover the rental after year 5.

If these forecasts are right, the store has only a five-year economic life; from that point on the real estate is more valuable in some other use. If you stubbornly believe that the department store is the best long-term use for the site, you must be ignoring potential growth in income from the store.⁵

There is a general point here as illustrated in Example 11.1. Whenever you make a capital investment decision, think what bets you are placing. Our department store example involved at least two bets—one on real estate prices and another on the firm’s ability to run a successful department store. But that suggests some alternative strategies. For instance, it would be foolish to make a lousy department store investment just because you are optimistic about real estate prices. You would do better to buy real estate and rent it out to the highest bidders. The converse is also true. You shouldn’t be deterred from going ahead with a profitable department store because you are pessimistic about real estate prices. You would do better to sell the real estate and rent it back for the department store. We suggest that you separate the two bets by first asking, “Should we open a department store on this site, assuming that the real estate is fairly priced?” and then deciding whether you also want to go into the real estate business.

   FIGURE 11.1 Beginning in year 6, the department store’s income fails to cover the rental charge.

Let us look at another example of how market prices can help you make better decisions.

EXAMPLE 11.2 • Opening a Gold Mine

Kingsley Solomon is considering a proposal to open a new gold mine. He estimates that the mine will cost $500 million to develop and that in each of the next 10 years it will produce .1 million ounces of gold at a cost, after mining and refining, of $1,150 an ounce. Although the extraction costs can be predicted with reasonable accuracy, Mr. Solomon is much less confident about future gold prices. His best guess is that the price will rise by 5% per year from its current level of $1,500 an ounce. At a discount rate of 10%, this gives the mine an NPV of –$35 million:

Therefore the gold mine project is rejected.

Unfortunately, Mr. Solomon did not look at what the market was telling him. What is the PV of an ounce of gold? Clearly, if the gold market is functioning properly, it is the current price, $1,500 an ounce. Gold does not produce any income, so $1,500 is the discounted value of the expected future gold price.⁶ Since the mine is expected to produce a total of 1 million ounces (.1 million ounces per year for 10 years), the present value of the revenue stream is 1 × 1,500 = $1,500 million.⁷ We assume that 10% is an appropriate discount rate for the relatively certain extraction costs. Thus

It looks as if Kingsley Solomon’s mine is not such a bad bet after all.⁸

Mr. Solomon’s gold, in Example 11.2, was just like anyone else’s gold. So there was no point in trying to value it separately. By taking the PV of the gold sales as given, Mr. Solomon was able to focus on the crucial issue: Were the extraction costs sufficiently low to make the venture worthwhile? That brings us to another of those fundamental truths: If others are producing a good or service profitably and (like Mr. Solomon) you can make it more cheaply, then you don’t need any NPV calculations to know that you are probably onto a good thing.

We confess that our example of Kingsley Solomon’s mine is somewhat special. Unlike gold, most commodities are not kept solely for investment purposes, and therefore you cannot automatically assume that today’s price is equal to the present value of the future price.⁹

However, here is another way that you may be able to tackle the problem. Suppose that you are considering investment in a new copper mine and that someone offers to buy the mine’s future output at a fixed price. If you accept the offer—and the buyer is completely creditworthy—the revenues from the mine are certain and can be discounted at the risk-free interest rate.¹⁰ That takes us back to Chapter 9, where we explained that there are two ways to calculate PV:

•  Estimate the expected cash flows and discount at a rate that reflects the risk of those flows.

•  Estimate what sure-fire cash flows would have the same values as the risky cash flows. Then discount these certainty-equivalent cash flows at the risk-free interest rate.

When you discount the fixed-price revenues at the risk-free rate, you are using the certainty-equivalent method to value the mine’s output. By doing so, you gain in two ways: You don’t need to estimate future mineral prices, and you don’t need to worry about the appropriate discount rate for risky cash flows.

But here’s the question: What is the minimum fixed price at which you could agree today to sell your future output? In other words, what is the certainty-equivalent price? Fortunately, for many commodities there is an active market in which firms fix today the price at which they will buy or sell copper and other commodities in the future. This market is known as the futures market, which we will cover in Chapter 26. Futures prices are certainty equivalents, and you can look them up in the daily newspaper. So you don’t need to make elaborate forecasts of copper prices to work out the PV of the mine’s output. The market has already done the work for you; you simply calculate future revenues using the price in the newspaper of copper futures and discount these revenues at the risk-free interest rate.

Of course, things are never as easy as textbooks suggest. Trades in organized futures exchanges are largely confined to deliveries over the next year or so, and therefore your newspaper won’t show the price at which you could sell output beyond this period. But financial economists have developed techniques for using the prices in the futures market to estimate the amount that buyers would agree to pay for more-distant deliveries.¹¹

Our two examples of gold and copper producers are illustrations of a universal principle of finance:

When you have the market value of an asset, use it, at least as a starting point in your analysis.

 11-2   Economic Rents and Competitive Advantage

Profits that more than cover the cost of capital are known as economic rents. Economics 101 teaches us that in the long run competition eliminates economic rents. That is, in a long-run competitive equilibrium, no competitor can expand and earn more than the cost of capital on the investment. Economic rents are earned when an industry has not settled down to equilibrium or when your firm has something valuable that your competitors don’t have.

Suppose that demand takes off unexpectedly and that your firm is well-placed to expand production capacity quicker and cheaper than your competitors. This stroke of luck is pretty sure to generate economic rents, at least temporarily as other firms struggle to catch up.

Some competitive advantages are longer lived. They include patents or proprietary technology; reputation, embodied in respected brand names, for example; economies of scale that customers can’t match; protected markets that competitors can’t enter; and strategic assets that competitors can’t easily duplicate.

Here’s an example of strategic assets. Think of the difference between railroads and trucking companies. It’s easy to enter the trucking business but nearly impossible to build a brand-new, long-haul railroad.¹² The interstate lines operated by U.S. railroads are strategic assets. With these assets in place, railroads were able to increase revenues and profits rapidly when shipments surged and energy prices increased. The high cost of diesel fuel was more burdensome for trucks, which are less fuel efficient than railroads. Thus high energy prices actually handed the railroads a competitive advantage.

Corporate strategy aims to find and exploit sources of competitive advantage. The problem, as always, is how to do it. John Kay advises firms to pick out distinctive capabilities—existing strengths, not just ones that would be nice to have—and then to identify the product markets where the capabilities can generate the most value added. The capabilities may come from durable relationships with customers or suppliers, from the skills and experience of employees, from brand names and reputation, and from the ability to innovate.¹³

Michael Porter identifies five aspects of industry structure (or “five forces”) that determine which industries are able to provide sustained economic rents.¹⁴ These are the rivalry among existing competitors, the likelihood of new competition, the threat of substitutes, and the bargaining power both of suppliers and customers.

With increasing global competition, firms cannot rely so easily on industry structure to provide high returns. Therefore, managers also need to ensure that the firm is positioned within its industry so as to secure a competitive advantage. Michael Porter suggests three ways that this can be done—by cost leadership, by product differentiation, and by focus on a particular market niche.¹⁵

In today’s world successful strategies that combine different mixes of cost leadership, product differentiation, and focus appear to be the key to developing a unique position in an industry.¹⁶ Think, for example, of IKEA. It blends elements of all three strategies. It keeps costs low by manufacturing its furniture in low-cost countries and requiring customers to collect and assemble the furniture themselves. It differentiates itself by its distinctive Scandinavian design and by displaying all of its items in its warehouses. And it has a clear focus on a group of customers, who are typically young and price-conscious.

You can see how business strategy and finance reinforce each other. Managers who have a clear understanding of their firm’s competitive strengths are better placed to separate those projects that truly have a positive NPV from those that do not. Therefore when you are presented with a project that appears to have a positive NPV, do not just accept the calculations at face value. They may reflect simple estimation errors in forecasting cash flows. Probe behind the cash-flow estimates, and try to identify the source of economic rents. A positive NPV for a new project is believable only if you believe that your company has some special advantage.

Thinking about competitive advantage can also help ferret out negative-NPV calculations that are negative by mistake. For example, if you are the lowest-cost producer of a profitable product in a growing market, then you should invest to expand along with the market. If your calculations show a negative NPV for such an expansion, then you have probably made a mistake.

We will work through shortly an extended example that shows how a firm’s analysis of its competitive position confirmed that its investment had a positive NPV. But first we look at an example in which the analysis helped a firm to ferret out a negative-NPV transaction and avoid a costly mistake.

EXAMPLE 11.3 • How One Company Avoided a $100 Million Mistake

A U.S. chemical producer was about to modify an existing plant to produce a specialty product, polyzone, which was in short supply on world markets.¹⁷ At prevailing raw material and finished-product prices the expansion would have been strongly profitable. Table 11.1 shows a simplified version of management’s analysis. Note the assumed constant spread between selling price and the cost of raw materials. Given this spread, the resulting NPV was about $64 million at the company’s 8% real cost of capital—not bad for a $100 million outlay.

Then doubt began to creep in. Notice the outlay for transportation costs. Some of the project’s raw materials were commodity chemicals, largely imported from Europe, and much of the polyzone production would be exported back to Europe. Moreover, the U.S. company had no long-run technological edge over potential European competitors. It had a head start perhaps, but was that really enough to generate a positive NPV?

Notice the importance of the price spread between raw materials and finished product. The analysis in Table 11.1 forecasted the spread at a constant $1.20 per pound of polyzone for 10 years. That had to be wrong: European producers, who did not face the U.S. company’s transportation costs, would see an even larger NPV and expand capacity. Increased competition would almost surely squeeze the spread. The U.S. company decided to calculate the competitive spread—the spread at which a European competitor would see polyzone capacity as zero NPV. Table 11.2 shows management’s analysis. The resulting spread of about $.95 per pound was the best long-run forecast for the polyzone market, other things constant of course.

   TABLE 11.1 NPV calculation for proposed investment in polyzone production by a U.S. chemical company (figures in $ millions except as noted).

Note: For simplicity, we assume no inflation and no taxes. Plant and equipment have no salvage value after 10 years.

a Production capacity is 80 million pounds per year.

b Production costs are $.375 per pound after start up ($.75 per pound in year 2, when production is only 40 million pounds).

c Transportation costs are $.10 per pound to European ports.

BEYOND THE PAGE

● ● ● ● ●

Try It! Polyzone project

brealey.mhhe.com/c01

   TABLE 11.2 What is the competitive spread to a European producer? About $.95 per pound of polyzone. Note that European producers face no transportation costs. Compare Table 11.1 (figures in $ millions except as noted).

   TABLE 11.3 Recalculation of NPV for polyzone investment by U.S. company (figures in $ millions except as noted). If expansion by European producers forces competitive spreads by year 5, the U.S. producer’s NPV falls to –$9.8 million. Compare Table 11.1.

How much of a head start did the U.S. producer have? How long before competitors forced the spread down to $.95? Management’s best guess was five years. It prepared Table 11.3, which is identical to Table 11.1 except for the forecasted spread, which would shrink to $.95 by the start of year 5. Now the NPV was negative.

The project might have been saved if production could have been started in year 1 rather than 2 or if local markets could have been expanded, thus reducing transportation costs. But these changes were not feasible, so management canceled the project, albeit with a sigh of relief that its analysis had not stopped at Table 11.1.

This is a perfect example of the importance of thinking through sources of economic rents. Positive NPVs are suspect without some long-run competitive advantage. When a company contemplates investing in a new product or expanding production of an existing product, it should specifically identify its advantages or disadvantages over its most dangerous competitors. It should calculate NPV from those competitors’ points of view. If competitors’ NPVs come out strongly positive, the company had better expect decreasing prices (or spreads) and evaluate the proposed investment accordingly.

 11-3   Marvin Enterprises Decides to Exploit a New Technology—an Example

To illustrate some of the problems involved in predicting economic rents, let us leap forward several years and look at the decision by Marvin Enterprises to exploit a new technology.¹⁸

One of the most unexpected developments of these years was the remarkable growth of a completely new industry. By 2035 annual sales of gargle blasters totaled $1.68 billion, or 240 million units. Although it controlled only 10% of the market, Marvin Enterprises was among the most exciting growth companies of the decade. Marvin had come late into the business, but it had pioneered the use of integrated microcircuits to control the genetic engineering processes used to manufacture gargle blasters. This development had enabled producers to cut the price of gargle blasters from $9 to $7 and had thereby contributed to the dramatic growth in the size of the market. The estimated demand curve in Figure 11.2 shows just how responsive demand is to such price reductions.

   FIGURE 11.2 The demand “curve” for gargle blasters shows that for each $1 cut in price there is an increase in demand of 80 million units.

   TABLE 11.4 Size and cost structure of the gargle blaster industry before Marvin announced its expansion plans.

Note: Selling price is $7 per unit. One unit means one gargle blaster.

Table 11.4 summarizes the cost structure of the old and new technologies. While companies with the new technology were earning 20% on their initial investment, those with first-generation equipment had been hit by the successive price cuts. Since all Marvin’s investment was in the 2031 technology, it had been particularly well placed during this period.

Rumors of new developments at Marvin had been circulating for some time, and the total market value of Marvin’s stock had risen to $460 million by January 2036. At that point Marvin called a press conference to announce another technological breakthrough. Management claimed that its new third-generation process involving mutant neurons enabled the firm to reduce capital costs to $10 and manufacturing costs to $3 per unit. Marvin proposed to capitalize on this invention by embarking on a huge $1 billion expansion program that would add 100 million units to capacity. The company expected to be in full operation within 12 months.

Before deciding to go ahead with this development, Marvin had undertaken extensive calculations on the effect of the new investment. The basic assumptions were as follows:

1.  The cost of capital was 20%.

2.  The production facilities had an indefinite physical life.

3.  The demand curve and the costs of each technology would not change.

4.  There was no chance of a fourth-generation technology in the foreseeable future.

5.  The corporate income tax, which had been abolished in 2026, was not likely to be reintroduced.

Marvin’s competitors greeted the news with varying degrees of concern. There was general agreement that it would be five years before any of them would have access to the new technology. On the other hand, many consoled themselves with the reflection that Marvin’s new plant could not compete with an existing plant that had been fully depreciated.

Suppose that you were Marvin’s financial manager. Would you have agreed with the decision to expand? Do you think it would have been better to go for a larger or smaller expansion? How do you think Marvin’s announcement is likely to affect the price of its stock?

You have a choice. You can go on immediately to read our solution to these questions. But you will learn much more if you stop and work out your own answer first. Try it.

Forecasting Prices of Gargle Blasters

Up to this point in any capital budgeting problem we have always given you the set of cash-flow forecasts. In the present case you have to derive those forecasts.

The first problem is to decide what is going to happen to the price of gargle blasters. Marvin’s new venture will increase industry capacity to 340 million units. From the demand curve in Figure 11.2, you can see that the industry can sell this number of gargle blasters only if the price declines to $5.75:

If the price falls to $5.75, what will happen to companies with the 2023 technology? They also have to make an investment decision: Should they stay in business, or should they sell their equipment for its salvage value of $2.50 per unit? With a 20% opportunity cost of capital, the NPV of staying in business is

Smart companies with 2023 equipment will, therefore, see that it is better to sell off capacity. No matter what their equipment originally cost or how far it is depreciated, it is more profitable to sell the equipment for $2.50 per unit than to operate it and lose $1.25 per unit.

As capacity is sold off, the supply of gargle blasters will decline and the price will rise. An equilibrium is reached when the price gets to $6. At this point 2023 equipment has a zero NPV:

How much capacity will have to be sold off before the price reaches $6? You can check that by going back to the demand curve:

Therefore Marvin’s expansion will cause the price to settle down at $6 a unit and will induce first-generation producers to withdraw 20 million units of capacity.

But after five years Marvin’s competitors will also be in a position to build third generation plants. As long as these plants have positive NPVs, companies will increase their capacity and force prices down once again. A new equilibrium will be reached when the price reaches $5. At this point, the NPV of new third-generation plants is zero, and there is no incentive for companies to expand further:

Looking back once more at our demand curve, you can see that with a price of $5 the industry can sell a total of 400 million gargle blasters:

The effect of the third-generation technology is, therefore, to cause industry sales to expand from 240 million units in 2035 to 400 million five years later. But that rapid growth is no protection against failure. By the end of five years any company that has only first-generation equipment will no longer be able to cover its manufacturing costs and will be forced out of business.

The Value of Marvin’s New Expansion

We have shown that the introduction of third-generation technology is likely to cause gargle blaster prices to decline to $6 for the next five years and to $5 thereafter. We can now set down the expected cash flows from Marvin’s new plant:

Discounting these cash flows at 20% gives us

It looks as if Marvin’s decision to go ahead was correct. But there is something we have forgotten. When we evaluate an investment, we must consider all incremental cash flows. One effect of Marvin’s decision to expand is to reduce the value of its existing 2031 plant. If Marvin decided not to go ahead with the new technology, the $7 price of gargle blasters would hold until Marvin’s competitors started to cut prices in five years’ time. Marvin’s decision, therefore, leads to an immediate $1 cut in price. This reduces the present value of its 2031 equipment by

Considered in isolation, Marvin’s decision has an NPV of $299 million. But it also reduces the value of existing plant by $72 million. The net present value of Marvin’s venture is, therefore, 299 – 72 = $227 million.

Alternative Expansion Plans

Marvin’s expansion has a positive NPV, but perhaps Marvin would do better to build a larger or smaller plant. You can check that by going through the same calculations as above. First you need to estimate how the additional capacity will affect gargle blaster prices. Then you can calculate the net present value of the new plant and the change in the present value of the existing plant. The total NPV of Marvin’s expansion plan is

We have undertaken these calculations and plotted the results in Figure 11.3. You can see how total NPV would be affected by a smaller or larger expansion.

   FIGURE 11.3 Effect on net present value of alternative expansion plans. Marvin’s 100-million-unit expansion has a total NPV of $227 million (total NPV = NPV new plant + change in PV existing plant = 299 – 72 = 227). Total NPV is maximized if Marvin builds 200 million units of new capacity. If Marvin builds 280 million units of new capacity, total NPV is –$144 million.

When the new technology becomes generally available in 2041, firms will construct a total of 280 million units of new capacity.¹⁹ But Figure 11.3 shows that it would be foolish for Marvin to go that far. If Marvin added 280 million units of new capacity in 2036, the discounted value of the cash flows from the new plant would be zero and the company would have reduced the value of its old plant by $144 million. To maximize NPV, Marvin should construct 200 million units of new capacity and set the price just below $6 to drive out the 2023 manufacturers. Output is, therefore, less and price is higher than either would be under free competition.²⁰

The Value of Marvin Stock

Let us think about the effect of Marvin’s announcement on the value of its common stock. Marvin has 24 million units of second-generation capacity. In the absence of any third-generation technology, gargle blaster prices would hold at $7 and Marvin’s existing plant would be worth

Marvin’s new technology reduces the price of gargle blasters initially to $6 and after five years to $5. Therefore the value of existing plant declines to

But the new plant makes a net addition to shareholders’ wealth of $299 million. So after Marvin’s announcement its stock will be worth

Now here is an illustration of something we talked about in Chapter 4: Before the announcement, Marvin’s stock was valued in the market at $460 million. The difference between this figure and the value of the existing plant represented the present value of Marvin’s growth opportunities (PVGO). The market valued Marvin’s ability to stay ahead of the game at $40 million even before the announcement. After the announcement PVGO rose to $299 million.²²

The Lessons of Marvin Enterprises

Marvin Enterprises may be just a piece of science fiction, but the problems that it confronts are very real. Whenever Intel considers developing a new microprocessor or Genentech considers developing a new drug, these firms must face up to exactly the same issues as Marvin. We have tried to illustrate the kind of questions that you should be asking when presented with a set of cash-flow forecasts. Of course, no economic model is going to predict the future with accuracy. Perhaps Marvin can hold the price above $6. Perhaps competitors will not appreciate the rich pickings to be had in the year 2041. In that case, Marvin’s expansion would be even more profitable. But would you want to bet $1 billion on such possibilities? We don’t think so.

Investments often turn out to earn far more than the cost of capital because of a favorable surprise. This surprise may in turn create a temporary opportunity for further investments earning more than the cost of capital. But anticipated and more prolonged rents will naturally lead to the entry of rival producers. That is why you should be suspicious of any investment proposal that predicts a stream of economic rents into the indefinite future. Try to estimate when competition will drive the NPV down to zero, and think what that implies for the price of your product.

Many companies try to identify the major growth areas in the economy and then concentrate their investment in these areas. But the sad fate of first-generation gargle blaster manufacturers illustrates how rapidly existing plants can be made obsolete by changes in technology. It is fun being in a growth industry when you are at the forefront of the new technology, but a growth industry has no mercy on technological laggards.

Therefore, do not simply follow the herd of investors stampeding into high-growth sectors of the economy. Think of the fate of the dot.com companies in the “new economy” of the late 1990s. Optimists argued that the information revolution was opening up opportunities for companies to grow at unprecedented rates. The pessimists pointed out that competition in e-commerce was likely to be intense and that competition would ensure that the benefits of the information revolution would go largely to consumers. The Finance in Practice Box, which contains an extract from an article by Warren Buffett, emphasizes that rapid growth is no guarantee of superior profits.

FINANCE IN PRACTICE

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Warren Buffett on Growth and Profitability

   I thought it would be instructive to go back and look at a couple of industries that transformed this country much earlier in this century: automobiles and aviation. Take automobiles first: I have here one page, out of 70 in total, of car and truck manufacturers that have operated in this country. At one time, there was a Berkshire car and an Omaha car. Naturally I noticed those. But there was also a telephone book of others.

All told, there appear to have been at least 2,000 car makes, in an industry that had an incredible impact on people’s lives. If you had foreseen in the early days of cars how this industry would develop, you would have said, “Here is the road to riches.” So what did we progress to by the 1990s? After corporate carnage that never let up, we came down to three U.S. car companies—themselves no lollapaloozas for investors. So here is an industry that had an enormous impact on America—and also an enormous impact, though not the anticipated one, on investors. Sometimes, incidentally, it’s much easier in these transforming events to figure out the losers. You could have grasped the importance of the auto when it came along but still found it hard to pick companies that would make you money. But there was one obvious decision you could have made back then—it’s better sometimes to turn these things upside down—and that was to short horses. Frankly, I’m disappointed that the Buffett family was not short horses through this entire period. And we really had no excuse: Living in Nebraska, we would have found it super-easy to borrow horses and avoid a “short squeeze.”

U.S. Horse Population

1900: 21 million

1998: 5 million

The other truly transforming business invention of the first quarter of the century, besides the car, was the airplane—another industry whose plainly brilliant future would have caused investors to salivate. So I went back to check out aircraft manufacturers and found that in the 1919–39 period, there were about 300 companies, only a handful still breathing today. Among the planes made then—we must have been the Silicon Valley of that age—were both the Nebraska and the Omaha, two aircraft that even the most loyal Nebraskan no longer relies upon.

Move on to failures of airlines. Here’s a list of 129 airlines that in the past 20 years filed for bankruptcy. Continental was smart enough to make that list twice. As of 1992, in fact—though the picture would have improved since then—the money that had been made since the dawn of aviation by all of this country’s airline companies was zero. Absolutely zero.

Sizing all this up, I like to think that if I’d been at Kitty Hawk in 1903 when Orville Wright took off, I would have been farsighted enough, and public-spirited enough—I owed this to future capitalists—to shoot him down. I mean, Karl Marx couldn’t have done as much damage to capitalists as Orville did.

I won’t dwell on other glamorous businesses that dramatically changed our lives but concurrently failed to deliver rewards to U.S. investors: the manufacture of radios and televisions, for example. But I will draw a lesson from these businesses: The key to investing is not assessing how much an industry is going to affect society, or how much it will grow, but rather determining the competitive advantage of any given company and, above all, the durability of that advantage. The products or services that have wide, sustainable moats around them are the ones that deliver rewards to investors.

Source: C. Loomis, “Mr. Buffett on the Stock Market,” Fortune (November 22, 1999), pp. 110–115. © 1999 Time Inc. All rights reserved.

We do not wish to imply that good investment opportunities don’t exist. For example, good opportunities frequently arise because the firm has invested money in the past, which gives it the option to expand cheaply in the future. Perhaps the firm can increase its output just by adding an extra production line, whereas its rivals would need to construct an entirely new factory.

Marvin also reminds us to include a project’s impact on the rest of the firm when estimating incremental cash flows. By introducing the new technology immediately, Marvin reduced the value of its existing plant by $72 million.

Sometimes the losses on existing plants may completely offset the gains from a new technology. That is why we may see established, technologically advanced companies deliberately slowing down the rate at which they introduce new products. But this can be a dangerous game to play if it opens up opportunities for competitors. For example, for many years Bausch & Lomb was the dominant producer of contact lenses and earned large profits from glass contact lenses that needed to be sterilized every night. Because its existing business generated high returns, the company was slow to introduce disposable lenses. This delay opened up an opportunity for competitors and enabled Johnson & Johnson to introduce disposable lenses.

Marvin’s economic rents were equal to the difference between its costs and those of the marginal producer. The costs of the marginal 2023-generation plant consisted of the manufacturing costs plus the opportunity cost of not selling the equipment. Therefore, if the salvage value of the 2023 equipment were higher, Marvin’s competitors would incur higher costs and Marvin could earn higher rents. We took the salvage value as given, but it in turn depends on the cost savings from substituting outdated gargle blaster equipment for some other asset. In a well-functioning economy, assets will be used so as to minimize the total cost of producing the chosen set of outputs. The economic rents earned by any asset are equal to the total extra costs that would be incurred if that asset were withdrawn.

When Marvin announced its expansion plans, many owners of first-generation equipment took comfort in the belief that Marvin could not compete with their fully depreciated plant. Their comfort was misplaced. Regardless of past depreciation policy, it paid to scrap first-generation equipment rather than keep it in production. Do not expect that numbers in your balance sheet can protect you from harsh economic reality.

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SUMMARY

All good financial managers want to find and undertake positive-NPV projects. They calculate NPVs carefully. But NPVs can be positive for two reasons: (1) The company really can expect to earn economic rents, or (2) there are biases or errors in cash-flow forecasts. Good managers are wary of these “false positives” and try to keep the odds stacked in their favor by investing in areas where the company has clear competitive advantages. They give careful attention to corporate strategy, which attempts to identify distinct capabilities and deploy them in markets where economic rents can be generated. They avoid expansion where competitive advantages are absent and economic rents are unlikely. They do not project favorable current product prices into the future without checking whether entry or expansion by competitors will drive future prices down.

Our story of Marvin Enterprises illustrates the origin of rents and how they determine a project’s cash flows and net present value.

Any present value calculation, including our calculation for Marvin Enterprises, is subject to error. That’s life: There’s no other sensible way to value most capital investment projects. But some assets, such as gold, real estate, crude oil, ships, and airplanes, as well as financial assets, such as stocks and bonds, are traded in reasonably competitive markets. When you have the market value of such an asset, use it, at least as a starting point for your analysis.

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FURTHER READING

The following papers discuss capital investment and strategy:

P. Barwise, P. Marsh, and R. Wensley, “Must Finance and Strategy Clash?” Harvard Business Review, September–October 1989, pp. 2–7.

M. Porter, “What Is Strategy?” Harvard Business Review, November–December 1996, pp. 61–78.

S. C. Myers, “Finance Theory and Financial Strategy,” Midland Corporate Finance Journal 5 (Spring 1987), pp. 6–13. Reprinted from Interfaces (January–February 1984).

The following book describes how to identify economic rents and positive NPVs:

S. Woolley, Sources of Value (Cambridge, UK:/Cambridge University Press, 2009).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

  1.  Economic rents True or false?

 a.  A firm that earns the opportunity cost of capital is earning economic rents.

 b.  A firm that invests in positive-NPV ventures expects to earn economic rents.

 c.  Financial managers should try to identify areas where their firms can earn economic rents, because it is there that positive-NPV projects are likely to be found.

 d.  Economic rent is the equivalent annual cost of operating capital equipment.

  2.  Equilibrium prices Demand for concave utility meters is expanding rapidly, but the industry is highly competitive. A utility meter plant costs $50 million to set up, and it has an annual capacity of 500,000 meters. The production cost is $5 per meter, and this cost is not expected to change. The machines have an indefinite physical life and the cost of capital is 10%. What is the competitive price of a utility meter?

 a.  $5

 b.  $10

 c.  $15

  3.  Market prices Your brother-in-law wants you to join him in purchasing a building on the outskirts of town. You and he would then develop and run a Taco Palace restaurant. Both of you are extremely optimistic about future real estate prices in this area, and your brother-in-law has prepared a cash-flow forecast that implies a large positive NPV. This calculation assumes sale of the property after 10 years.

What further calculations should you do before going ahead?

  4.  Market prices On the London Metals Exchange the price for copper to be delivered in one year is $9,000 a ton. (Note: Payment is made when the copper is delivered.) The risk-free interest rate is .5% and the expected market return is 8%.

 a.  Suppose that you expect to produce and sell 100,000 tons of copper next year. What is the PV of this output? Assume that the sale occurs at the end of the year.

 b.  If copper has a beta of 1.2, what is the expected price of copper at the end of the year? What is the certainty-equivalent price?

  5.  Opportunity costs New-model commercial airplanes are much more fuel-efficient than older models. How is it possible for airlines flying older models to make money when its competitors are flying newer planes? Explain briefly.

INTERMEDIATE

  6.  Market prices Suppose that you are considering investing in an asset for which there is a reasonably good secondary market. Specifically, your company is Delta Airlines, and the asset is a Boeing 757—a widely used airplane. How does the presence of a secondary market simplify your problem in principle? Do you think these simplifications could be realized in practice? Explain.

  7.  Market prices There is an active, competitive leasing (i.e., rental) market for most standard types of commercial jets. Many of the planes flown by the major domestic and international airlines are not owned by them but leased for periods ranging from a few months to several years.

Gamma Airlines, however, owns two long-range DC-11s just withdrawn from Latin American service. Gamma is considering using these planes to develop the potentially lucrative new route from Akron to Yellowknife. A considerable investment in terminal facilities, training, and advertising will be required. Once committed, Gamma will have to operate the route for at least three years. One further complication: The manager of Gamma’s international division is opposing commitment of the planes to the Akron–Yellowknife route because of anticipated future growth in traffic through Gamma’s new hub in Ulaanbaatar.

How would you evaluate the proposed Akron–Yellowknife project? Give a detailed list of the necessary steps in your analysis. Explain how the airplane leasing market would be taken into account. If the project is attractive, how would you respond to the manager of the international division?

  8.  Market prices Suppose the current price of gold is $1,500 an ounce. Hotshot Consultants advises you that gold prices will increase at an average rate of 12% for the next two years. After that the growth rate will fall to a long-run trend of 3% per year. What is the price of 1 million ounces of gold produced in eight years? Assume that gold prices have a beta of 0 and that the risk-free rate is 5.5%.

  9.  Economic rents We characterized the interstate rail lines owned by major U.S. railroads as “strategic assets” that could generate increased profits. In what conditions would you expect these assets to generate economic rents? Keep in mind that railroads compete with trucking companies as well as other railroads. Trucking companies have some advantages, including flexibility.

10.  Economic rents Thanks to acquisition of a key patent, your company now has exclusive production rights for barkelgassers (BGs) in North America. Production facilities for 200,000 BGs per year will require a $25 million immediate capital expenditure. Production costs are estimated at $65 per BG. The BG marketing manager is confident that all 200,000 units can be sold for $100 per unit (in real terms) until the patent runs out five years hence. After that the marketing manager hasn’t a clue about what the selling price will be.

What is the NPV of the BG project? Assume the real cost of capital is 9%. To keep things simple, also make the following assumptions:

•  The technology for making BGs will not change. Capital and production costs will stay the same in real terms.

•  Competitors know the technology and can enter as soon as the patent expires, that is, in year 6.

•  If your company invests immediately, full production begins after 12 months, that is, in year 1.

•  There are no taxes.

•  BG production facilities last 12 years. They have no salvage value at the end of their useful life.

11.  Economic rents How would your answer to Problem 10 change if technological improvements reduce the cost of new BG production facilities by 3% per year? Thus a new plant built in year 1 would cost only 25 (1 – .03) = $24.25 million; a plant built in year 2 would cost $23.52 million; and so on. Assume that production costs per unit remain at $65.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

12.  Economic rents Go to the Excel spreadsheets versions of Tables 11.1-11.3 at www.mcgraw-hill.co.uk/textbooks/brealey. Reevaluate the NPV of the proposed polyzone project under each of the following assumptions. What’s the right management decision in each case?

 a.  Spread in year 4 holds at $1.20 per pound.

 b.  The U.S. chemical company can start up polyzone production at 40 million pounds in year 1 rather than year 2.

 c.  The U.S. company makes a technological advance that reduces its annual production costs to $25 million. Competitors’ production costs do not change.

13.  Market prices Photographic laboratories recover and recycle the silver used in photographic film. Stikine River Photo is considering purchase of improved equipment for their laboratory at Telegraph Creek. Here is the information they have:

•  The equipment costs $100,000 and will cost $80,000 per year to run.

•  It has an economic life of 10 years but can be depreciated over five years by the straight-line method (see Section 6-2).

•  It will recover an additional 5,000 ounces of silver per year.

•  Silver is selling for $40 per ounce. Over the past 10 years, the price of silver has appreciated by 4.5% per year in real terms. Silver is traded in an active, competitive market.

•  Stikine’s marginal tax rate is 35%. Assume U.S. tax law.

•  Stikine’s company cost of capital is 8% in real terms.

•  The nominal interest rate is 6%.

What is the NPV of the new equipment? Make additional assumptions as necessary.

14.  Market prices The Cambridge Opera Association has come up with a unique door prize for its December 2016 fund-raising ball: Twenty door prizes will be distributed, each one a ticket entitling the bearer to receive a cash award from the association on December 31, 2017. The cash award is to be determined by calculating the ratio of the level of the Standard and Poor’s Composite Index of stock prices on December 31, 2017, to its level on June 30, 2017, and multiplying by $100. Thus, if the index turns out to be 1,000 on June 30, 2017, and 1,200 on December 31, 2017, the payoff will be 100 × (1,200/1,000) = $120.

After the ball, a black market springs up in which the tickets are traded. What will the tickets sell for on January 1, 2017? On June 30, 2017? Assume the risk-free interest rate is 10% per year. Also assume the Cambridge Opera Association will be solvent at year-end 2017 and will, in fact, pay off on the tickets. Make other assumptions as necessary.

Would ticket values be different if the tickets’ payoffs depended on the Dow Jones Industrial Index rather than the Standard and Poor’s Composite?

15.  Market prices You are asked to value a large building in northern New Jersey. The valuation is needed for a bankruptcy settlement. Here are the facts:

•  The settlement requires that the building’s value equal the PV of the net cash proceeds the railroad would receive if it cleared the building and sold it for its highest and best nonrailroad use, which is as a warehouse.

•  The building has been appraised at $1 million. This figure is based on actual recent selling prices of a sample of similar New Jersey buildings used as, or available for use as, warehouses.

•  If rented today as a warehouse, the building could generate $80,000 per year. This cash flow is calculated after out-of-pocket operating expenses and after real estate taxes of $50,000 per year:

Gross rents, operating expenses, and real estate taxes are uncertain but are expected to grow with inflation.

•  However, it would take one year and $200,000 to clear out the railroad equipment and prepare the building for use as a warehouse. The $200,000 would have to be invested immediately.

•  The property will be put on the market when ready for use as a warehouse. Your real estate adviser says that properties of this type take, on average, one year to sell after they are put on the market. However, the railroad could rent the building as a warehouse while waiting for it to sell.

•  The opportunity cost of capital for investment in real estate is 8% in real terms.

•  Your real estate adviser notes that selling prices of comparable buildings in northern New Jersey have declined, in real terms, at an average rate of 2% per year over the last 10 years.

•  A 5% sales commission would be paid by the railroad at the time of the sale.

•  The railroad pays no income taxes. It would have to pay property taxes.

CHALLENGE

16.  Economic rents The manufacture of polysyllabic acid is a competitive industry. Most plants have an annual output of 100,000 tons. Operating costs are $.90 a ton, and the sales price is $1 a ton. A 100,000-ton plant costs $100,000 and has an indefinite life. Its current scrap value of $60,000 is expected to decline to $57,900 over the next two years.

Phlogiston, Inc., proposes to invest $100,000 in a plant that employs a new low-cost process to manufacture polysyllabic acid. The plant has the same capacity as existing units, but operating costs are $.85 a ton. Phlogiston estimates that it has two years’ lead over each of its rivals in use of the process but is unable to build any more plants itself before year 2. Also it believes that demand over the next two years is likely to be sluggish and that its new plant will therefore cause temporary overcapacity.

You can assume that there are no taxes and that the cost of capital is 10%.

 a.  By the end of year 2, the prospective increase in acid demand will require the construction of several new plants using the Phlogiston process. What is the likely NPV of such plants?

 b.  What does that imply for the price of polysyllabic acid in year 3 and beyond?

 c.  Would you expect existing plant to be scrapped in year 2? How would your answer differ if scrap value were $40,000 or $80,000?

 d.  The acid plants of United Alchemists, Inc., have been fully depreciated. Can it operate them profitably after year 2?

 e.  Acidosis, Inc., purchased a new plant last year for $100,000 and is writing it down by $10,000 a year. Should it scrap this plant in year 2?

 f.  What would be the NPV of Phlogiston’s venture?

17.  Equilibrium prices The world airline system is composed of the routes X and Y, each of which requires 10 aircraft. These routes can be serviced by three types of aircraft—A, B, and C. There are 5 type A aircraft available, 10 type B, and 10 type C. These aircraft are identical except for their operating costs, which are as follows:

The aircraft have a useful life of five years and a salvage value of $1 million.

The aircraft owners do not operate the aircraft themselves but rent them to the operators. Owners act competitively to maximize their rental income, and operators attempt to minimize their operating costs. Airfares are also competitively determined. Assume the cost of capital is 10%.

 a.  Which aircraft would be used on which route, and how much would each aircraft be worth?

 b.  What would happen to usage and prices of each aircraft if the number of type A aircraft increased to 10?

 c.  What would happen if the number of type A aircraft increased to 15?

 d.  What would happen if the number of type A aircraft increased to 20?

State any additional assumptions you need to make.

18.  Economic rents Taxes are a cost, and, therefore, changes in tax rates can affect consumer prices, project lives, and the value of existing firms. The following problem illustrates this. It also illustrates that tax changes that appear to be “good for business” do not always increase the value of existing firms. Indeed, unless new investment incentives increase consumer demand, they can work only by rendering existing equipment obsolete.

The manufacture of bucolic acid is a competitive business. Demand is steadily expanding, and new plants are constantly being opened. Expected cash flows from an investment in a new plant are as follows:

 a.  What is the value of a one-year-old plant? Of a two-year-old plant?

 b.  Suppose that the government now changes tax depreciation to allow a 100% writeoff in year 1. How does this affect the value of existing one- and two-year-old plants? Existing plants must continue using the original tax depreciation schedule.

 c.  Would it now make sense to scrap existing plants when they are two rather than three years old?

 d.  How would your answers change if the corporate income tax were abolished entirely?

19.  Competitive advantage and NPV Look again at Example 11.3.

 a.  Calculate the NPV to a European producer of expanding polyzone production. Should the European producer invest immediately or wait?

 b.  By 2012 the price of natural gas, the feedstock for polyzone production, dropped below $2.50 per million BTU because of a glut of U.S. shale gas supplies. Cheaper feedstock reduced U.S. production costs from $30 million to $20 million per year. But many forecasters believed that long-run U.S. natural-gas prices would gradually recover, stabilizing at about $4.00 per million BTU by 2017. The higher gas prices would increase U.S. production costs to $25 million per year. Re-calculate the NPV to a European producer. Assume constant European production costs of $30 million per year.

MINI-CASE ● ● ● ● ●

Ecsy-Cola²³

Libby Flannery, the regional manager of Ecsy-Cola, the international soft drinks empire, was reviewing her investment plans for Central Asia. She had contemplated launching Ecsy-Cola in the ex-Soviet republic of Inglistan in 2016. This would involve a capital outlay of $20 million in 2015 to build a bottling plant and set up a distribution system there. Fixed costs (for manufacturing, distribution, and marketing) would then be $3 million per year from 2015 onward. This would be sufficient to make and sell 200 million liters per year—enough for every man, woman, and child in Inglistan to drink four bottles per week! But there would be few savings from building a smaller plant, and import tariffs and transport costs in the region would keep all production within national borders.

The variable costs of production and distribution would be 12 cents per liter. Company policy requires a rate of return of 25% in nominal dollar terms, after local taxes but before deducting any costs of financing. The sales revenue is forecasted to be 35 cents per liter.

Bottling plants last almost forever, and all unit costs and revenues were expected to remain constant in nominal terms. Tax would be payable at a rate of 30%, and under the Inglistan corporate tax code, capital expenditures can be written off on a straight-line basis over four years.

All these inputs were reasonably clear. But Ms. Flannery racked her brain trying to forecast sales. Ecsy-Cola found that the “1–2–4” rule works in most new markets. Sales typically double in the second year, double again in the third year, and after that remain roughly constant. Libby’s best guess was that, if she went ahead immediately, initial sales in Inglistan would be 12.5 million liters in 2017, ramping up to 50 million in 2019 and onward.

Ms. Flannery also worried whether it would be better to wait a year. The soft drink market was developing rapidly in neighboring countries, and in a year’s time she should have a much better idea whether Ecsy-Cola would be likely to catch on in Inglistan. If it didn’t catch on and sales stalled below 20 million liters, a large investment probably would not be justified.

Ms. Flannery had assumed that Ecsy-Cola’s keen rival, Sparky-Cola, would not also enter the market. But last week she received a shock when in the lobby of the Kapitaliste Hotel she bumped into her opposite number at Sparky-Cola. Sparky-Cola would face costs similar to Ecsy-Cola. How would Sparky-Cola respond if Ecsy-Cola entered the market? Would it decide to enter also? If so, how would that affect the profitability of Ecsy-Cola’s project?

Ms. Flannery thought again about postponing investment for a year. Suppose Sparky-Cola were interested in the Inglistan market. Would that favor delay or immediate action?

Maybe Ecsy-Cola should announce its plans before Sparky-Cola had a chance to develop its own proposals. It seemed that the Inglistan project was becoming more complicated by the day.

QUESTIONS

1.  Calculate the NPV of the proposed investment, using the inputs suggested in this case. How sensitive is this NPV to future sales volume?

2.  What are the pros and cons of waiting for a year before deciding whether to invest? (Hint: What happens if demand turns out high and Sparky-Cola also invests? What if Ecsy-Cola invests right away and gains a one-year head start on Sparky-Cola?)

___________

¹Here is another riddle. Are projects proposed because they have positive NPVs, or do they have positive NPVs because they are proposed? No prizes for the correct answer.

²For simplicity we assume the $100 million goes entirely to real estate. In real life there would also be substantial investments in fixtures, information systems, training, and start-up costs.

³The fair market rent equals the profit generated by the real estate’s second-best use.

⁴This rental stream yields a 10% rate of return to the real estate subsidiary. Each year it gets a 7% “dividend” and 3% capital gain. Growth at 3% would bring the value of the property to $134 million by year 10.

  The present value (at r = .10) of the growing stream of rents is

This PV is the initial market value of the property.

⁵Another possibility is that real estate rents and values are expected to grow at less than 3% a year. But in that case the real estate subsidiary would have to charge more than $7 million rent in year 1 to justify its $100 million real estate investment (see footnote 4). That would make the department store even less attractive.

⁶Investing in an ounce of gold is like investing in a stock that pays no dividends: The investor’s return comes entirely as capital gains. Look back at Section 4-2, where we showed that P0, the price of the stock today, depends on DIV1 and P1, the expected dividend and price for next year, and the opportunity cost of capital r:

But for gold DIV1 = 0, so

In words, today’s price is the present value of next year’s price. Therefore, we don’t have to know either P1 or r to find the present value. Also since DIV2 = 0,

and we can express P0 as

In general,

This holds for any asset that pays no dividends, is traded in a competitive market, and costs nothing to store. Storage costs for gold or common stocks are very small compared to asset value.

   We also assume that guaranteed future delivery of gold is just as good as having gold in hand today. This is not quite right. As we will see in Chapter 26, gold in hand can generate a small “convenience yield.”

⁷We assume that the extraction rate does not vary. If it can vary, Mr. Solomon has a valuable operating option to increase output when gold prices are high or to cut back when prices fall. Option pricing techniques are needed to value the mine when operating options are important. See Chapter 22.

⁸As in the case of our department store example, Mr. Solomon is placing two bets: one on his ability to mine gold at a low cost and the other on the price of gold. Suppose that he really does believe that gold is overvalued. That should not deter him from running a low-cost gold mine as long as he can place separate bets on gold prices. For example, he might be able to enter into a long-term contract to sell the mine’s output or he could sell gold futures. (We explain futures in Chapter 26.)

⁹A more general guide to the relationship of current and future commodity prices was proposed by Hotelling, who pointed out that if there are constant returns to scale in mining any mineral, the expected rise in the price of the mineral less extraction costs should equal the cost of capital. If the expected growth were faster, everyone would want to postpone extraction; if it were slower, everyone would want to exploit the resource today. For a review of Hotelling’s principle, see S. Devarajan and A. C. Fisher, “Hotelling’s ‘Economics of Exhaustible Resources’: Fifty Years Later,” Journal of Economic Literature 19 (March 1981), pp. 65–73.

¹⁰We assume that the volume of output is certain (or does not have any market risk).

¹¹After reading Chapter 26, check out E. S. Schwartz, “The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging,” Journal of Finance 52 (July 1997), pp. 923–973; and A. J. Neuberger, “Hedging Long-Term Exposures with Multiple Short-Term Contracts,” Review of Financial Studies 12 (1999), pp. 429–459.

¹²The Dakota, Minnesota & Eastern Railroad has plans (currently on hold) to build a new line to transport coal from Wyoming to the Midwest U.S., but construction would require government subsidies.

¹³John Kay, Why Firms Succeed (New York: Oxford University Press, 1995).

¹⁴See M. E. Porter, Competitive Strategy: Techniques for Analyzing Industries and Competitors (New York: The Free Press, 1980).

¹⁵See M. E. Porter, Competitive Advantage: Creating and Sustaining Superior Advantage (New York: The Free Press, 1985).

¹⁶R. M. Grant, Contemporary Strategy Analysis, 4th ed. (Oxford: Blackwell, 2002), p. 248.

¹⁷This is a true story, but names and details have been changed to protect the innocent.

¹⁸We thank Stewart Hodges for permission to adapt this example from a case prepared by him, and we thank the BBC for permission to use the term gargle blasters.

¹⁹Total industry capacity in 2041 will be 400 million units. Of this, 120 million units are second-generation capacity, and the remaining 280 million units are third-generation capacity.

²⁰Notice that we are assuming that all customers have to pay the same price for their gargle blasters. If Marvin could charge each customer the maximum price that that customer would be willing to pay, output would be the same as under free competition. Such direct price discrimination is illegal and in any case difficult to enforce. But firms do search for indirect ways to differentiate between customers. For example, stores often offer free delivery, which is equivalent to a price discount for customers who live at an inconvenient distance.

²¹To finance the expansion, Marvin is going to have to sell $1,000 million of new stock. Therefore the total value of Marvin’s stock will rise to $1,551 million. But investors who put up the new money will receive shares worth $1,000 million. The value of Marvin’s old shares after the announcement is therefore $551 million.

²²The market value of Marvin stock will be greater than $551 million if investors expect the company to expand again within the five-year period. In other words, PVGO after the expansion may still be positive. Investors may expect Marvin to stay one step ahead of its competitors or to successfully apply its special technology in other areas.

²³We thank Anthony Neuberger for suggesting this topic.

Part 3 Best Practices in Capital Budgeting

Agency Problems, Compensation, and Performance Measurement

So far we’ve concentrated on criteria and procedures for identifying capital investments with positive NPVs. If a firm takes all (and only) positive-NPV projects, it maximizes the firm’s value. But do the firm’s managers want to maximize value?

Managers have no special gene that automatically aligns their personal interests with outside investors’ financial objectives. So how do shareholders ensure that top managers do not feather their own nests or grind their own axes? And how do top managers ensure that middle managers and employees try as hard as they can to find and execute positive-NPV projects?

Here we circle back to the principal–agent problems first raised in Chapter 1. Shareholders are the ultimate principals; top managers are the stockholders’ agents. But middle managers and employees are in turn agents of top management. Thus senior managers, including the chief financial officer, are simultaneously agents vis-à-vis shareholders and principals vis-à-vis the rest of the firm. The problem is to get everyone working together to maximize value.

This chapter summarizes how corporations grapple with that problem. The two main topics we cover are:

•  Incentives: Making sure that managers and employees are rewarded appropriately when they add value to the firm.

•  Performance measurement: You can’t reward value added unless you can measure it. Since you get what you reward, and reward what you measure, you get what you measure.

We describe alternative performance measures, including economic value added. We uncover the biases lurking in standard accounting income and rates of return. Finally, we confront a disturbing fact: some, maybe most, public corporations seem willing to sacrifice NPV to maintain or increase short-run earnings per share.

 12-1   Incentives and Compensation

Top management, including the CFO, must try to ensure that middle managers and employees have the right incentives to find and invest in positive-NPV projects. We will soon see how difficult it is to get incentives right throughout a large corporation. Why not bypass these difficulties, and let the CFO and his or her immediate staff make the important investment decisions?

The bypass won’t work, for at least five reasons. First, top management would have to analyze thousands of projects every year. There’s no way to know enough about each one to make intelligent choices. Top management must rely on analysis done at lower levels.

Second, the design of a capital investment project involves investment decisions that top managers do not see. Think of a proposal to build a new factory. The managers who developed the plan for the factory had to decide its location. Suppose they chose a more expensive site to get closer to a pool of skilled workers. That’s an investment decision: additional investment to generate extra cash flow from access to these workers’ skills. (Outlays for training could be lower, for example.) Does the additional investment generate additional NPV, compared to building the factory at a cheaper but remote site? How is the CFO to know? He or she can’t afford the time to investigate every alternative that was considered but rejected by the project’s sponsors.

Third, many capital investments don’t appear in the capital budget. These include research and development, worker training, and marketing outlays designed to expand a market or lock in satisfied customers.

Fourth, small decisions add up. Operating managers make investment decisions every day. They may carry extra inventories of raw materials so they won’t have to worry about being caught short. Managers at the confabulator plant in Quayle City, Kansas, may decide they need one more forklift. They may hold on to an idle machine tool or an empty warehouse that could have been sold. These are not big decisions ($25,000 here, $50,000 there) but thousands of such decisions add up to real money.

Fifth, the CFO may be subject to the same kinds of temptations that afflict lower layers of management.

We now consider incentives and agency problems in capital investment.

Agency Problems in Capital Budgeting

As you have surely guessed, there is no perfect system of incentives. But it’s easy to see what won’t work. Suppose shareholders decide to pay the financial managers a fixed salary—no bonuses, no stock options, just $X per month. The manager, as the stockholders’ agent, is instructed to find and invest in all positive-NPV projects open to the firm. The manager may sincerely try to do so, but will face various tempting alternatives:

•  Reduced effort. Finding and implementing investment in truly valuable projects is a high-effort, high-pressure activity. The financial manager will be tempted to slack off.

•  Perks. Our hypothetical financial manager gets no bonuses. Only $X per month. But he or she may take a bonus anyway, not in cash, but in tickets to sporting events, lavish office accommodations, planning meetings scheduled at luxury resorts, and so on. Economists refer to these nonpecuniary rewards as private benefits. Ordinary people call them perks (short for perquisites).¹

•  Empire building. Other things equal, managers prefer to run large businesses rather than small ones. Getting from small to large may not be a positive-NPV undertaking. Managers are also reluctant to dismantle their empires. That is, they are reluctant to disinvest.

•  Entrenching investment. Suppose manager Q considers two expansion plans. One plan will require a manager with special skills that manager Q just happens to have. The other plan requires only a general-purpose manager. Guess which plan Q will favor. Projects designed to require or reward the skills of existing managers are called entrenching investments.²

Entrenching investments and empire building are typical symptoms of overinvestment, that is, investing beyond the point where NPV falls to zero. The temptation to overinvest is highest when the firm has plenty of cash but limited investment opportunities. Michael Jensen calls this the free-cash-flow problem.³

A manager on a fixed salary could hardly avoid all these temptations all of the time. The resulting loss in value is an agency cost.

Agency Problems and Risk Taking

Because managers cannot diversify their risks as readily as the shareholders, one might expect them to be too risk-averse. Indeed, evidence suggests that managers seek a “quiet life” when the pressure to perform is relaxed.⁴ But there are plenty of exceptions.

First, the managers who reach the top ranks of a large corporation must have taken some risks along the way. Managers who seek only the quiet life don’t get noticed and don’t get promoted rapidly.

Second, managers who are compensated with stock options have an incentive to take more risk. As we explain in Chapters 20 and 21, the value of an option increases when the risk of the firm increases.

Third, managers sometimes have nothing to lose by taking on risks. Suppose that a regional office suffers large, unexpected losses. The regional manager’s job is on the line, and in response he or she tries a risky strategy that offers a small probability of a big, quick payoff. If the strategy pays off, the losses are covered and the manager’s job may be saved. If it fails, nothing is lost, because the manager would have been fired anyway. This behavior is called gambling for redemption.⁵

Fourth, organizations often hesitate to curtail risky activities that are delivering—at least temporarily—rich profits. The subprime crisis of 2007–2009 provides sobering examples. Charles Prince, the pre-crisis CEO of Citigroup, was asked why that bank’s leveraged lending business was expanding so rapidly. Prince quipped, “When the music stops . . . things will be complicated. But as long as the music is playing, you’ve got to get up and dance. We’re still dancing.”⁶ Citi later took a $1.5 billion loss on this line of business.

Example: Agency Costs and the Subprime Crisis “Subprime” refers to mortgage loans made to home buyers with weak credit. Some of these loans were made to naïve buyers who then struggled to keep up with interest and principal payments. Some were made to opportunistic buyers who were willing to bet that real-estate prices would keep improving, so that they could “flip” their houses at a profit. But prices fell sharply in 2007 and 2008, and many buyers were forced to default.

Why did so many banks and mortgage companies make these loans in the first place? One reason is that they could repackage the loans as mortgage-backed securities and sell them at a profit to other banks and institutional investors. It’s clear with hindsight that many buyers of these mortgage-backed securities were in turn naïve and paid too much. When housing prices fell and defaults increased, the prices of these securities fell drastically. For example, Merrill Lynch wrote off $50 billion of losses and was sold under duress to Bank of America. (In 2012 Bank of America is still dealing with the fallout from this acquisition and its purchase of the mortgage company Countrywide.)

Although there’s plenty of blame to pass around for the subprime crisis, some of it must go to the managers who promoted and sold the subprime mortgages. Were they acting in shareholders’ interests or their own interests? We doubt that their shareholders would have endorsed the managers’ tactics if the shareholders could have seen what was really going on. We think that the managers would have been much more cautious if they had not had the chance for another fat bonus before their game ended. If so, the subprime crisis was partly an agency problem, not value maximization run amok. Agency problems occur when managers do not act in the shareholders’ interests.

Monitoring

Agency costs can be reduced by monitoring a manager’s efforts and actions and by intervening when the manager veers off course.

Monitoring can prevent the more obvious agency costs, such as blatant perks. It can confirm that the manager is putting in sufficient time on the job. But monitoring requires time and money. Some monitoring is almost always worthwhile, but a limit is soon reached at which an extra dollar spent on monitoring would not return an extra dollar of value from reduced agency costs. Like all investments, monitoring encounters diminishing returns.

Some agency costs can’t be prevented even with the most thorough monitoring. Suppose a shareholder undertakes to monitor capital investment decisions. How could he or she ever know for sure whether a capital budget approved by top management includes (1) all the positive-NPV opportunities open to the firm and (2) no projects with negative NPVs due to empire-building or entrenching investments? The managers obviously know more about the firm’s prospects than outsiders ever can. If the shareholder could list all projects and their NPVs, then the managers would hardly be needed!

Who actually does the monitoring?

BEYOND THE PAGE

● ● ● ● ●

SOX

brealey.mhhe.com/c12

Board of Directors In large, public companies, the task of monitoring is delegated to the board of directors, who are elected by shareholders to represent their interests. Boards of directors are sometimes portrayed as passive stooges who always champion the incumbent management. But response to past corporate scandals has tipped the balance toward greater independence. For example, the Sarbanes-Oxley Act (or “SOX”) requires that corporations place more independent directors on the board, that is, more directors who are not managers or are not affiliated with management. Around three-quarters of all directors are now independent.

When managers are not up to the job, boards frequently step in. In 2011 the CEOs of Yahoo!, Hewlett-Packard, Bank of New York Mellon, and First Solar were all replaced. Boards outside the United States, which traditionally have been more management-friendly, have also become more willing to replace underperforming managers. The list of recent departures includes the heads of BP, UBS, Generali, Research in Motion, and Air France-KLM.

Of course, delegation brings its own agency problems. For example, many board members may be long-standing friends of the CEO and may be indebted to the CEO for help or advice. Understandably, they may be reluctant to fire the CEO or enquire too deeply into his or her conduct. If monitors are likely to have their own agenda, then we have Dr. Seuss’s bee-watching problem:

Oh, the jobs people work at!

Out west, near Hawtch-Hawtch,

there’s a Hawtch-Hawtcher Bee Watcher.

His job is to watch . . .

is to keep both his eyes on the lazy town bee.

A bee that is watched will work harder you see!

Well . . . he watched and he watched

But, in spite of his watch,

that bee didn’t work any harder. Not mawtch.

So then somebody said,

“Our bee-watching man

just isn’t bee-watching as hard as he can.

He ought to be watched by another Hawtch-Hawtcher!!

The thing that we need

is a Bee-Watcher-Watcher!”⁷

Fortunately, the company’s directors are not the only people that scrutinize management’s actions. Several other groups act as bee-watcher-watchers.

Auditors The board is required to hire independent accountants to audit the firm’s financial statements. If the audit uncovers no problems, the auditors issue an opinion that the financial statements fairly represent the company’s financial condition and are consistent with Generally Accepted Accounting Principles (GAAP).

If problems are found, the auditors will negotiate changes in assumptions or procedures. Managers almost always agree, because if acceptable changes are not made, the auditors will issue a qualified opinion, which is bad news for the company and its shareholders. A qualified opinion suggests that managers are covering something up and undermines investors’ confidence.

A qualified audit opinion may be bad news, but when investors learn of accounting irregularities that have escaped detection, there can be hell to pay. In January 2004 Adecco, the giant Swiss employment agency, announced that it had discovered material accounting irregularities in its North American operations. The next day Adecco’s share price fell by 40%, wiping $5 billion off the market value of the company.

Lenders Lenders also monitor. When a company takes out a large bank loan, the bank tracks the company’s assets, earnings, and cash flow. By monitoring to protect its loan, the bank generally protects shareholders’ interests also.⁸

Shareholders Shareholders also keep an eagle eye on the company’s management and board of directors. If they believe that the corporation is underperforming and that the board is not holding managers to task, they can attempt to elect representatives to the board to make their voices heard. For example, in 2011 billionaire shareholder activist Carl Icahn believed that the management of Oshkosh was not acting in the shareholders’ interest when it did not pursue a merger with fellow vehicle manufacturer Navistar. He therefore purchased nearly 10% of the stock of each company, and nominated six associates for election to the Oshkosh board.

Smaller stockholders cannot justify the time or money for a proxy battle. However, if they are disgruntled, they can take the “Wall Street Walk” by selling out and moving on to other investments. The Wall Street Walk can send a powerful message. If enough shareholders bail out, the stock price tumbles. This damages top management’s reputation and compensation. A large part of top managers’ paychecks comes from stock options, which pay off if the stock price rises but are worthless if the price falls below a stated threshold. Thus a falling stock price has a direct impact on managers’ personal wealth. A rising stock price is good for managers as well as stockholders.

Rival Companies A company’s management is regularly monitored by other management teams. If the latter believe that the assets are not being used efficiently, then they can try to take over the business, and boot out the existing management. We will have more to say in Chapters 31 and 32 about the role of takeovers in changing corporate control.

Management Compensation

Because monitoring is necessarily imperfect, compensation plans must be designed to attract competent managers and to give them the right incentives.

Figure 12.1 compares the level of compensation in different countries and Figure 12.2 shows the growth of CEO compensation in the U.S. Three features stand out.

1.  The U.S. has unusually high levels of executive pay. CEOs in the States receive nearly double the pay of German CEOs and about four times the pay of Japanese CEOs.

2.  Although CEO compensation in the U.S. fell during the 2008–2009 credit crisis, there has for the most part been a strong upward trend.

3.  A large and increasing fraction of CEO compensation in the U.S. comes from variable bonuses, stock options, and other long-term incentives.

We look first at the size of the pay package. Then we turn to its contents.

High levels of CEO pay undoubtedly encourage CEOs to work hard and (perhaps more important) offer an attractive carrot to lower-level managers who hope to become CEOs. But there has been widespread concern about “excessive” pay, especially pay for mediocre performance. For example, Robert Nardelli received a $210 million severance package on leaving The Home Depot and Henry McKinnell received almost $200 million on leaving Pfizer. Both CEOs left behind troubled and underperforming companies. You can imagine the newspaper headlines.

Those headlines got a lot bigger in 2008 when it was revealed that generous bonuses were to be paid to the senior management of banks that had been bailed out by the government. Merrill Lynch hurried through $3.6 billion in bonuses, including $121 million to just four executives, only days before Bank of America finalized its deal to buy the collapsing firm with the help of taxpayer money. “Bonuses for Boneheads” was the headline in Forbes magazine.

   FIGURE 12.1 Median CEO compensation in 2010 for large companies (those with revenues of more than U.S. $1 billion). Compensation in the U.S. is relatively high and is heavily dependent on performance. We are grateful to Towers Watson for providing these data.

Source: Towers Watson, www.towerswatson.com. Used with permission.

   FIGURE 12.2 Growth in compensation of the CEOs of companies in the Standard & Poor’s Composite Index. The growth has come largely from grants of stock and options.

Source: ExecuComp.

The widespread view that taxpayer money was being used to pay bonuses to bankers whose greed had brought about the credit crisis led to demands that governments curb bankers’ compensation. In France President Sarkozy announced that there would be no bonuses in 2009 at banks that had received state aid. The German government set a €500,000 ($630,000) limit on executive pay at rescued banks. In the U.S., the Obama administration appointed a “pay czar” to oversee the salaries of top executives at companies receiving “exceptional assistance” from the government. The U.S. Congress also set restrictions on the pay of top executives in banks who accepted bail-out funds. Incentive compensation was limited to one-third of total pay, and was to be paid only in the form of stock that could not be cashed in as long as the company remained in receipt of government aid. The banks were also prohibited from giving big handouts to departing executives.

It is easy to point to cases where poorly performing managers have received unjustifiably large payouts. But is there a more general problem? Perhaps high levels of pay simply reflect a shortage of talent. After all, CEOs are not alone in earning large sums. The earnings of top footballers and other professional athletes are equally mouthwatering. In 2012 Christiano Ronaldo’s salary was €12.0 million, while Lionel Messi was paid €10.5 million. Their clubs must have believed that it was worth paying up for stars that would win games and attract supporters.

If star managers are as rare as star footballers, corporations may need to pay up for CEO talent. Suppose that a superior CEO can add 1% to the value and stock price of a large corporation with a market capitalization of $10 billion. One percent on a stock-market value of $10 billion is $100 million. If the CEO can really deliver, then a pay package of, say, $20 million per year sounds like a bargain.⁹

There is also a less charitable explanation of managerial pay. This view stresses the close links between the CEO and the other members of the board of directors. If directors are too chummy with the CEO, they may find it difficult to get tough when it comes to setting compensation packages. Sometimes directors approve extra payments that provide shareholders with little or no prospective benefit. Take the example of the German company, Mannesmann, which was acquired in a $200 billion takeover. After the deal was finalized, Mannesmann’s board of directors voted an ex gratia payment of $74 million to the company’s executives. German Federal prosecutors charged six of the directors with breach of their fiduciary duty and failure to preserve the company’s assets. Although the case was eventually settled out of court, it highlighted the danger that directors may be tempted to act as lords of the manor, rather than as stewards of the estate, when they set compensation levels.

So we have two views of the level of managerial pay. One is that it results from arms-length contracting in a tight market for managerial talent. The other is that poor governance and weak boards allow excessive pay. There is evidence for and against both views. For example, CEOs are not the only group to have seen their compensation increase rapidly in recent years. Corporate lawyers, sports stars, and celebrity entertainers have all increased their share of national income, even though their compensation is determined by arms-length negotiation.¹⁰ However, the shortage-of-talent argument cannot account for wide disparities in pay. For example, compare the CEO of Ford (compensation of $26.5 million in 2011) to the CEO of Toyota (compensation of $1.74 million ) or to General Petraeus when he was the U.S. military commander in Afghanistan (around $250,000). It is difficult to argue that Ford’s CEO delivered the most value or had the most difficult and important job.

Incentive Compensation

The amount of compensation may be less important than how it is structured. The compensation package should encourage managers to maximize shareholder wealth.

Compensation could be based on input (for example, the manager’s effort) or on output (income or value added as a result of the manager’s decisions). But input is difficult to measure. How can outside investors observe effort? They can check that the manager clocks in on time, but hours worked does not measure true effort. (Is the manager facing up to difficult and stressful choices, or is he or she just burning time with routine meetings, travel, and paperwork?)

Because effort is not observable, compensation must be based on output, that is, on verifiable results. Trouble is, results depend not just on the manager’s contribution, but also on events outside the manager’s control. Unless you can separate out the manager’s contribution, you face a difficult trade-off. You want to give the manager high-powered incentives, so that he or she does very well when the firm does very well and poorly when the firm underperforms. But suppose the firm is a cyclical business that always struggles in recessions. Then high-powered incentives will force the manager to bear business cycle risk that is not his or her fault.

There are limits to the risks that managers can be asked to bear. So the result is a compromise. Firms do link managers’ pay to performance, but fluctuations in firm value are shared by managers and shareholders. Managers bear some of the risks that are beyond their control and shareholders bear some of the agency costs if managers fail to maximize firm value. Thus some agency costs are inevitable.

Most major companies around the world now link part of their executive pay to the stock-price performance.¹¹ This compensation is generally in one of three forms: stock options, restricted stock (stock that must be retained for several years), or performance shares (shares awarded only if the company meets an earnings or other target). Sometimes these incentive schemes constitute the major part of the manager’s compensation pay. For example, in 2011 Larry Ellison, CEO of the business software giant Oracle Corporation, received total compensation estimated at $78 million. Only a small fraction (a mere $1) of that amount was salary. The lion’s share was in the form of stock and option grants. Moreover, as founder of Oracle, Ellison holds over 1 billion shares in the firm. No one can say for certain how hard Ellison would have worked with a different compensation package. But one thing is clear: He has a huge personal stake in the success of the firm—and in increasing its market value.

Stock options give managers the right (but not the obligation) to buy their company’s shares in the future at a fixed exercise price. Usually the exercise price is set equal to the company’s stock price on the day when the options are granted. If the company performs well and stock price increases, the manager can buy shares and cash in on the difference between the stock price and the exercise price. If the stock price falls, the manager leaves the options unexercised and hopes for a stock price recovery or compensation through another channel. (If the stock price doesn’t recover, the manager may be granted a new batch of options or given a lower exercise price on the original options.)

The popularity of stock options in the U.S. was encouraged by accounting rules, which allowed companies to grant stock options without recognizing any immediate compensation expense. The rules allowed companies to value options at the excess of the stock price over the exercise price on the grant date. But the exercise price was almost always set equal to the stock price on that date. Thus the excess was zero and the stock options were valued at zero. (We show how to calculate the actual value of options in Chapters 20 and 21.) So companies could grant lots of options at no recorded cost and with no reduction in accounting earnings. Naturally accountants and investors were concerned, because earnings were more and more overstated as the volume of option grants increased. After years of controversy, the accounting rules were changed in 2006. U.S. corporations are now required to value executive stock options more realistically and to deduct these values as a compensation expense.

Options also have a tax advantage in the U.S. Compensation of more than $1 million has since 1994 been considered unreasonable and is not a tax-deductible expense. However, there is no restriction on compensation in the form of stock options.

You can see the advantages of tying compensation to stock price. When a manager works hard to maximize firm value, she helps both the stockholders and herself. But compensation via options or restricted stock also has at least four imperfections. First, the payoffs depend on the absolute change in stock price, not the change relative to the market or to stock prices of other firms in the same industry. Thus they force the manager to bear market or industry risks, which are outside the manager’s control. Therefore some companies measure and reward performance relative to industry peers. For example, the electric utility Entergy bases part of incentive compensation on how well Entergy stock performs relative to the Philadelphia Index of 20 of the largest U.S. utilities.

Here is a second difficult issue. Because a company’s stock price depends on investors’ expectations of future earnings, rates of return depend on how well the company performs relative to expectations. Suppose a company announces the appointment of an outstanding new manager. The stock price leaps up in anticipation of improved performance. If the new manager then delivers exactly the good performance that investors expected, the stock will earn only a normal rate of return. In this case a compensation scheme linked to the stock return after the manager starts would fail to recognize the manager’s special contribution.

Third, incentive plans may tempt managers to withhold bad news or manipulate earnings to pump up stock prices. They may also be tempted to defer valuable investment projects if the projects would depress earnings in the short run. We return to this point at the end of the chapter.

Fourth, stock options can encourage excessive risk taking. For example, when stock prices fall precipitously, as they did for many firms in the crisis of 2007–2009, existing stock options can be far “underwater” and nearly worthless. Managers holding these options may be tempted to gamble for redemption.

Monitoring Pay for Performance

An ideal top-management compensation system makes sure that pay is (1) reasonable, not excessive, and (2) linked to performance. As we have explained, meeting these two goals is not easy.

For U.S. public companies, compensation is the responsibility of the compensation committee of the board of directors. The Securities and Exchange Commission (SEC) and NYSE require that all directors on the compensation committee be independent, that is, not managers or employees and not linked to the company by some other relationship—for example, a lucrative consulting contract—that would undercut their independence. The committee typically hires outside consultants to advise on compensation trends and on compensation levels in peer companies.

You can see how compensation tends to creep up. The problem is that boards don’t want to approve below-average compensation. But if every firm wants to be above-average, then the average will ratchet up.¹²

Once the compensation package is approved by the committee, it is described in an annual Compensation Discussion and Analysis (CD&A), which is sent to shareholders along with director nominations and the company’s 10-K filing. (The 10-K is the annual report to the SEC.) On January 2011, the SEC gave shareholders a nonbinding yes-or-no vote on the CD&A at least once every three years. Other countries that have given shareholders nonbinding votes on compensation include Australia, Sweden, and the UK. Shareholders in the Netherlands have a binding vote. The occasional no vote on management compensation is a disagreeable wake-up call for managers and directors. For example, in 2012 British stockholders overwhelmingly voted against the pay package for WPP’s CEO.

Yet these safeguards don’t satisfy everyone. Just as Dr. Suess predicted, we now have pay-watcher-watchers, such as the consulting company ISS. ISS reviews CD&As for thousands of companies, looking especially at pay-for-performance standards. ISS’s clients are mostly institutional investors, who seek advice on how to vote. (A mutual fund or pension fund may own shares in hundreds of companies. The company may decide to outsource the analysis of CD&As to a specialist company like ISS.)

 12-2   Measuring and Rewarding Performance: Residual Income and EVA

Almost all top executives of firms with publicly traded shares have compensation packages that depend in part on their firms’ stock price performance. But their compensation also includes a bonus that depends on increases in earnings or on other accounting measures of performance. For lower-level managers, compensation packages usually depend more on accounting measures and less on stock returns.

Accounting measures of performance have two advantages:

1.  They are based on absolute performance, rather than on performance relative to investors’ expectations.

2.  They make it possible to measure the performance of junior managers whose responsibility extends to only a single division or plant.

Tying compensation to accounting profits also creates some obvious problems. For example, managers whose pay or promotion depends on short-term profits may cut back on training, advertising, or R&D. This is not a recipe for adding value because these outlays are investments that should pay off in later years. Nevertheless the outlays are treated as current expenses and deducted from current income. Thus an ambitious manager is tempted to cut back, thereby increasing current income, leaving longer-run problems to his or her successor.

In addition, accounting earnings and rates of return can be severely biased measures of true profitability. We ignore this problem for now, but return to it in the next section.

Finally, growth in earnings does not necessarily mean that shareholders are better off. Any investment with a positive rate of return (1% or 2% will do) will eventually increase earnings. Therefore, if managers are told to maximize growth in earnings, they will dutifully invest in projects offering 1% or 2% rates of return—projects that destroy value. But shareholders do not want growth in earnings for its own sake, and they are not content with 1% or 2% returns. They want positive-NPV investments, and only positive-NPV investments. They want the company to invest only if the expected rate of return exceeds the cost of capital.

Look at Table 12.1, which contains a simplified income statement and balance sheet for your company’s Quayle City confabulator plant. There are two methods for judging whether the plant’s returns are higher than the cost of capital.

   TABLE 12.1 Simplified statements of income and assets for the Quayle City confabulator plant (figures in millions).

aIncludes depreciation expense.

bCurrent assets less current liabilities.

Net Return on Investment Book return on investment (ROI) is just the ratio of after-tax operating income to the net (depreciated) book value of assets.¹³ In Chapter 5 we rejected book ROI as a capital investment criterion, and in fact few companies now use it for that purpose. However, managers frequently assess the performance of a division or a plant by comparing its ROI with the cost of capital.

Suppose you need to assess the performance of the Quayle City plant. As you can see from Table 12.1, the corporation has $1,000 million invested in the plant, which is generating earnings of $130 million. Therefore the plant is earning an ROI of 130/1,000 = .13, or 13%.¹⁴ If the cost of capital is (say) 10%, then the plant’s activities are adding to shareholder value. The net return is 13 – 10 = 3%. If the cost of capital is (say) 20%, then shareholders would have been better off investing $1 billion somewhere else. In this case the net return is negative, at 13 – 20 = –7%.

Residual Income or Economic Value Added (EVA®)¹⁵ The second method calculates a net dollar return to shareholders. It asks, What are earnings after deducting a charge for the cost of capital?

When firms calculate income, they start with revenues and then deduct costs, such as wages, raw material costs, overhead, and taxes. But there is one cost that they do not commonly deduct: the cost of capital. True, they allow for depreciation, but investors are not content with a return of their investment; they also demand a return on that investment. As we pointed out in Chapter 10, a business that breaks even in terms of accounting profits is really making a loss; it is failing to cover the cost of capital.

To judge the net contribution to value, we need to deduct the cost of capital contributed to the plant by the parent company and its stockholders. Suppose again that the cost of capital is 10%. Then the dollar cost of capital for the Quayle City plant is .10 × $1,000 = $100 million. The net gain is therefore $130 – 100 = $30 million. This is the addition to shareholder wealth due to management’s hard work (or good luck).

Net income after deducting the dollar return required by investors is called residual income or economic value added (EVA). The formula is

For our example, the calculation is

But if the cost of capital were 20%, EVA would be negative by $70 million.

Net return on investment and EVA are focusing on the same question. When return on investment equals the cost of capital, net return and EVA are both zero. But the net return is a percentage and ignores the scale of the company. EVA recognizes the amount of capital employed and the number of dollars of additional wealth created.

The term EVA has been popularized by the consulting firm Stern–Stewart. But the concept of residual income has been around for some time,¹⁶ and many companies that are not Stern–Stewart clients use this concept to measure and reward managers’ performance.

Other consulting firms have their own versions of residual income. McKinsey & Company uses economic profit (EP), defined as capital invested multiplied by the spread between return on investment and the cost of capital. This is another way to measure residual income. For the Quayle City plant, with a 10% cost of capital, economic profit is the same as EVA:

In Chapter 28 we take a look at EVAs calculated for some well-known companies. But EVA’s most valuable contributions happen inside companies. EVA encourages managers and employees to concentrate on increasing value, not just on increasing earnings.

Pros and Cons of EVA

Let us start with the pros. EVA, economic profit, and other residual income measures are clearly better than earnings or earnings growth for measuring performance. A plant that is generating lots of EVA should generate accolades for its managers as well as value for shareholders. EVA may also highlight parts of the business that are not performing up to scratch. If a division is failing to earn a positive EVA, its management is likely to face some pointed questions about whether the division’s assets could be better employed elsewhere.

EVA sends a message to managers: Invest if and only if the increase in earnings is enough to cover the cost of capital. This is an easy message to grasp. Therefore EVA can be used down deep in the organization as an incentive compensation system. It is a substitute for explicit monitoring by top management. Instead of telling plant and divisional managers not to waste capital and then trying to figure out whether they are complying, EVA rewards them for careful investment decisions. Of course, if you tie junior managers’ compensation to their economic value added, you must also give them power over those decisions that affect EVA. Thus the use of EVA implies delegated decision making.

EVA makes the cost of capital visible to operating managers. A plant manager can improve EVA by (a) increasing earnings or (b) reducing capital employed. Therefore underutilized assets tend to be flushed out and disposed of.

Introduction of residual income measures often leads to surprising reductions in assets employed—not from one or two big capital disinvestment decisions, but from many small ones. Ehrbar quotes a sewing machine operator at Herman Miller Corporation:

[EVA] lets you realize that even assets have a cost. . . . we used to have these stacks of fabric sitting here on the tables until we needed them. . . . We were going to use the fabric anyway, so who cares that we’re buying it and stacking it up there? Now no one has excess fabric. They only have the stuff we’re working on today. And it’s changed the way we connect with suppliers, and we’re having [them] deliver fabric more often.¹⁷

If you propose to tie a manager’s remuneration to her business’s profitability, it is clearly better to use EVA than accounting income which takes no account of the cost of the capital employed. But what are the limitations of EVA? Here we return to the same question that bedevils stock-based measures of performance. How can you judge whether a low EVA is a consequence of bad management or of factors outside the manager’s control? The deeper you go in the organization, the less independence that managers have and therefore the greater the problem in measuring their contribution.

The second limitation with any accounting measure of performance lies in the data on which it is based. We explore this issue in the next section.

 12-3   Biases in Accounting Measures of Performance

Anyone using accounting measures of performance had better hope that the accounting numbers are accurate. Unfortunately, they are often not accurate, but biased. Applying EVA or any other accounting measure of performance therefore requires adjustments to the income statements and balance sheets.

For example, think of the difficulties in measuring the profitability of a pharmaceutical research program, where it typically takes 10 to 12 years to bring a new drug from discovery to final regulatory approval and the drug’s first revenues. That means 10 to 12 years of guaranteed losses, even if the managers in charge do everything right. Similar problems occur in start-up ventures, where there may be heavy capital outlays but low or negative earnings in the first years of operation. This does not imply negative NPV, so long as operating earnings and cash flows are sufficiently high later on. But EVA and ROI would be negative in the start-up years, even if the project were on track to a strong positive NPV.

The problem in these cases is not with EVA or ROI, but with the accounting data. The pharmaceutical R&D program may be showing accounting losses, because generally accepted accounting principles require that outlays for R&D be written off as current expenses. But from an economic point of view, those outlays are an investment, not an expense. If a proposal for a new business predicts accounting losses during a start-up period, but the proposal nevertheless shows a positive NPV, then the start-up losses are really an investment—cash outlays made to generate larger cash inflows when the business hits its stride.

BEYOND THE PAGE

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Try It! Nodhead supermarket

brealey.mhhe.com/c12

Example: Measuring the Profitability of the Nodhead Supermarket

Supermarket chains invest heavily in building and equipping new stores. The regional manager of a chain is about to propose investing $1 million in a new store in Nodhead. Projected cash flows are

Of course, real supermarkets last more than six years. But these numbers are realistic in one important sense: It may take two or three years for a new store to build up a substantial, habitual clientele. Thus cash flow is low for the first few years even in the best locations.

We will assume the opportunity cost of capital is 10%. The Nodhead store’s NPV at 10% is zero. It is an acceptable project, but not an unusually good one:

With NPV = 0, the true (internal) rate of return of this cash-flow stream is also 10%.

Table 12.2 shows the store’s forecasted book profitability, assuming straight-line depreciation over its six-year life. The book ROI is lower than the true return for the first two years and higher afterward.¹⁸ EVA also starts negative for the first two years, then turns positive and grows steadily to year 6. These are typical outcomes, because accounting income is too low when a project or business is young and too high as it matures.

   TABLE 12.2 Forecasted book income, ROI, and EVA for the proposed Nodhead store. Book ROI and EVA are underestimated for the first two years and overestimated thereafter.

Note: There are minor rounding errors in some annual figures.

At this point the regional manager steps up on stage for the following soliloquy:

The Nodhead store’s a decent investment. But if we go ahead, I won’t look very good at next year’s performance review. And what if I also go ahead with the new stores in Russet, Gravenstein, and Sheepnose? Their cash-flow patterns are pretty much the same. I could actually appear to lose money next year. The stores I’ve got won’t earn enough to cover the initial losses on four new ones.

Of course, everyone knows new supermarkets lose money at first. The loss would be in the budget. My boss will understand—I think. But what about her boss? What if the board of directors starts asking pointed questions about profitability in my region? I’m under a lot of pressure to generate better earnings. Pamela Quince, the upstate manager, got a bonus for generating a positive EVA. She didn’t spend much on expansion.

The regional manager is getting conflicting signals. On the one hand, he is told to find and propose good investment projects. Good is defined by discounted cash flow. On the other hand, he is also urged to seek high book income. But the two goals conflict because book income does not measure true income. The greater the pressure for immediate book profits, the more the regional manager is tempted to forgo good investments or to favor quick-payback projects over longer-lived projects, even if the latter have higher NPVs.

Measuring Economic Profitability

Let us think for a moment about how profitability should be measured in principle. It is easy enough to compute the true, or economic, rate of return for a common stock that is continuously traded. We just record cash receipts (dividends) for the year, add the change in price over the year, and divide by the beginning price:

The numerator of the expression for rate of return (cash flow plus change in value) is called economic income:

Any reduction in present value represents economic depreciation; any increase in present value represents negative economic depreciation. Therefore

The concept works for any asset. Rate of return equals cash flow plus change in value divided by starting value:

where PV0 and PV1 indicate the present values of the business at the ends of years 0 and 1.

The only hard part in measuring economic income is calculating present value. You can observe market value if the asset is actively traded, but few plants, divisions, or capital projects have shares traded in the stock market. You can observe the present market value of all the firm’s assets but not of any one of them taken separately.

   TABLE 12.3 Forecasted economic income, rate of return, and EVA for the proposed Nodhead store. Economic income equals cash flow minus economic depreciation. Rate of return equals economic income divided by value at start of year. EVA equals income minus cost of capital times value at start of year.

Note: There are minor rounding errors in some annual figures.

Accountants rarely even attempt to measure present value. Instead they give us net book value (BV), which is original cost less depreciation computed according to some arbitrary schedule. If book depreciation and economic depreciation are different (they are rarely the same), then book earnings will not measure true earnings. (In fact, it is not clear that accountants should even try to measure true profitability. They could not do so without heavy reliance on subjective estimates of value. Perhaps they should stick to supplying objective information and leave the estimation of value to managers and investors.)

It is not hard to forecast economic income and rate of return for the Nodhead store. Table 12.3 shows the calculations. From the cash-flow forecasts we can forecast present value at the start of periods 1 to 6. Cash flow minus economic depreciation equals economic income. Rate of return equals economic income divided by start-of-period value.

Of course, these are forecasts. Actual future cash flows and values will be higher or lower. Table 12.3 shows that investors expect to earn 10% in each year of the store’s six-year life. In other words, investors expect to earn the opportunity cost of capital each year from holding this asset.

Notice that EVA calculated using present value and economic income is zero in each year of the Nodhead project’s life. For year 2, for example,

EVA should be zero, because the project’s true rate of return is only equal to the cost of capital. EVA will always give the right signal if book income equals economic income and asset values are measured accurately.

Do the Biases Wash Out in the Long Run?

Even if the forecasts for the Nodhead store turn out to be correct, ROI and EVA will be biased. That might not be a serious problem if the errors wash out in the long run, when the region settles down to a steady state with an even mix of old and new stores.

It turns out that the errors do not wash out in the steady state. Table 12.4 shows steady-state book ROIs and forecasted EVAs for the supermarket chain if it opens one store a year. For simplicity we assume that the company starts from scratch and that each store’s cash flows are carbon copies of the Nodhead store. The true rate of return on each store is, therefore, 10% and the true EVA is zero. But as Table 12.4 demonstrates, steady-state book ROI and estimated EVA overstate the true profitability.

Thus we still have a problem even in the long run. The extent of the error depends on how fast the business grows. We have just considered one steady state with a zero growth rate. Think of another firm with a 5% steady-state growth rate. Such a firm would invest $1,000 the first year, $1,050 the second, $1,102.50 the third, and so on. Clearly the faster growth means more new projects relative to old ones. The greater weight given to young projects, which have low book ROIs and negative apparent EVAs, the lower the business’s apparent profitability.¹⁹

   TABLE 12.4 Book ROI for a group of stores like the Nodhead store. The steady-state book ROI overstates the 10% economic rate of return. The steady-state EVA is also biased upward.

Note: There are minor rounding errors in some annual figures.

a Book income = cash flow – book depreciation.

b Steady-state book ROI.

c Steady-state EVA.

What Can We Do about Biases in Accounting Profitability Measures?

The dangers in judging profitability by accounting measures are clear from these examples. To be forewarned is to be forearmed. But we can say something beyond just “be careful.”

It is natural for firms to set a standard of profitability for plants or divisions. Ideally that standard should be the opportunity cost of capital for investment in the plant or division. That is the whole point of EVA: to compare actual profits with the cost of capital. But if performance is measured by return on investment or EVA, then these measures need to recognize accounting biases. Ideally, the financial manager should identify and eliminate accounting biases before calculating EVA or net ROI. The managers and consultants that implement these measures work hard to adjust book income closer to economic income. For example, they may record R&D as an investment rather than an expense and construct alternative balance sheets showing R&D as an asset.

Accounting biases are notoriously hard to get rid of, however. Thus, many firms end up asking not “Did the widget division earn more than its cost of capital last year?” but “Was the widget division’s book ROI typical of a successful firm in the widget industry?” The underlying assumptions are that (1) similar accounting procedures are used by other widget manufacturers and (2) successful widget companies earn their cost of capital.

There are some simple accounting changes that could reduce biases in performance measures. Remember that the biases all stem from not using economic depreciation. Therefore why not switch to economic depreciation? The main reason is that each asset’s present value would have to be reestimated every year. Imagine the confusion if this were attempted. You can understand why accountants set up a depreciation schedule when an investment is made and then stick to it. But why restrict the choice of depreciation schedules to the old standbys, such as straight-line? Why not specify a depreciation pattern that at least matches expected economic depreciation? For example, the Nodhead store could be depreciated according to the expected economic depreciation schedule shown in Table 12.3. This would avoid any systematic biases. It would break no law or accounting standard. This step seems so simple and effective that we are at a loss to explain why firms have not adopted it.²⁰

Earnings and Earnings Targets

The biases that we have just described do not come from creative accounting. They are built into GAAP. Of course we should worry about creative accounting also. We have already noted how stock options have tempted managers to fiddle with accounting choices to make reported earnings look good and prop up stock price.

But perhaps there is a deeper problem. CEOs of public companies face constant scrutiny. Much of that scrutiny focuses on earnings. Security analysts forecast earnings per share (EPS) and investors, security analysts, and professional portfolio managers wait to see whether the company can meet or beat the forecasts. Not meeting the forecasts can be a big disappointment.

Monitoring by security analysts and portfolio managers can help constrain agency problems. But CEOs complain about the “tyranny of EPS” and the apparent short-sightedness of the stock market. (The British call it short-termism.) Of course the stock market is not systematically short-sighted. If it were, growth companies would not sell at the high price–earnings ratios observed in practice.²¹ Nevertheless, the pressure on CEOs to generate steady, predictable growth in earnings is real.

CEOs complain about this pressure, but do they do anything about it? Unfortunately the answer appears to be yes, according to Graham, Harvey, and Rajgopal, who surveyed about 400 senior managers.²² Most of the managers said that accounting earnings were the single most important number reported to investors. Most admitted to adjusting their firms’ operations and investments to manage earnings. For example, 80% were willing to decrease discretionary spending in R&D, advertising, or maintenance if necessary to meet earnings targets. Many managers were also prepared to defer or reject investment projects with positive NPVs. There is a good deal of evidence that firms do indeed manage their earnings. For example, Degeorge, Patel, and Zeckhauser studied a large sample of earnings announcements.²³ With remarkable regularity, earnings per share either met or beat security analysts’ forecasts, but only by a few cents. CFOs appeared to report conservatively in good times, building a stockpile of earnings that could be reported later. The rule, it seems, is Make sure that you report sufficiently good results to keep analysts happy, and, if possible, keep something back for a rainy day.²⁴

How much value was lost because of such adjustments? For a healthy, profitable company, spending a little more on advertising or deferring a project start for a few months may cause no significant damage. But we cannot endorse any sacrifice of fundamental shareholder value done just to manage earnings.

We may condemn earnings management, but in practice it’s hard for CEOs and CFOs to break away from the crowd. Graham and his coauthors explain it this way:²⁵

The common belief is that a well-run and stable firm should be able to “produce the numbers”. . . even in a year that is somewhat down. Because the market expects firms to be able to hit or slightly exceed earnings targets, and on average firms do just this, problems can arise when a firm does not deliver. . . . The market might assume that not delivering [reveals] potentially serious problems (because the firm is apparently so near the edge that it cannot produce the dollars to hit earnings . . .). As one CFO put it, “if you see one cockroach, you immediately assume that there are hundreds behind the walls.”

Thus we have a cockroach theory explaining why stock prices sometimes fall sharply when a company’s earnings fall short, even if the shortfall is only a penny or two.

Of course private firms do not have to worry about earnings management—which could help explain the increasing number of firms that have been bought out and returned to private ownership. (We discuss “going private” in Chapters 32 and 33.) Firms in some other countries, where quarterly earnings reports are not required and governance is more relaxed, may find it easier to invest for the long run. But such firms will also accumulate more agency problems. We wish there were simple answers to these trade-offs.

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SUMMARY

Capital investment decisions must be decentralized to a large extent. Consequently, agency problems are inevitable. Plant or divisional managers may be tempted to slack off, to avoid risk, or to propose empire-building or entrenching investments. Of course, top management is also exposed to similar temptations.

Agency problems are mitigated by a combination of monitoring and incentives. For example, shareholders delegate the task of monitoring top management to the board of directors and to the accountants who audit the company’s books.

To encourage managers to maximize shareholder value, a large part of their compensation is usually tied to company performance. Typically, this performance-related pay consists of a mixture of stock or stock options and bonuses that depend on accounting measures of profitability. The U.S is unusual both in the high levels of compensation for top executives and the extent to which pay is performance-related.

If you want to align the interests of the manager and the shareholder, it makes sense to give the manager common stock or stock options. But this is not a complete solution, for at least three reasons. First, stock prices depend on market and industry developments, not just on firm-specific performance. Thus compensation by stock or options exposes managers to risks that are outside their control. Second, today’s stock price already reflects managers’ expected future performance. Therefore, superior performance if it is expected, will not be rewarded with a superior stock-market return. Third, tying too much of management compensation to stock prices tempts managers to pump up stock prices, for example, by manipulating reported earnings per share.

The further you go down in a company, the more tenuous the link between the stock price and a manager’s effort and decisions. Therefore a higher fraction of pay depends on accounting income. Increasing accounting income is not the same thing as increasing value, because accountants do not recognize the cost of capital as an expense. Many companies therefore tie compensation to net return on investment (net ROI) or to Economic Value Added (EVA). Net ROI is the difference between ordinary ROI and the cost of capital. EVA and other residual income measures subtract a charge for capital employed. This charge pushes managers and employees to let go of unneeded assets and to acquire new ones only if the additional earnings exceed the cost of capital.

Of course, any accounting measure of profitability, such as EVA or the book return on investment (ROI), depends on accurate measures of earnings and capital employed. Unless adjustments are made to accounting data, these measures may underestimate the true profitability of new assets and overestimate that of old assets.

In principle, the solution is easy. EVA and ROI should be calculated using true or economic income. Economic income is equal to the cash flow less economic depreciation (that is, the decline in the present value of the asset). Unfortunately, we can’t ask accountants to recalculate each asset’s present value each time income is calculated. But it does seem fair to ask why they don’t at least try to match book depreciation schedules to typical patterns of economic depreciation.

The more pressing problem is that CEOs and CFOs seem to pay too much attention to earnings, at least in the short run, to maintain smooth growth and to meet earnings targets. They manage earnings, not with improper accounting, but by tweaking operating and investment plans. For example, they may defer a positive-NPV project for a few months to move the project’s up-front expenses into the next fiscal year. It’s not clear how much value is lost by this kind of behavior, but any value loss is unfortunate.

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FURTHER READING

Current practices in management remuneration are discussed in:

K. J. Murphy, “Executive Compensation,” in O. Ashenfelter and D. Card (eds.), Handbook of Labor Economics (North-Holland, 1999).

R. K. Aggarwal, “Executive Compensation and Incentives,” in B. E Eckbo (ed.), Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), Chapter 7.

B. J. Hall and K. J. Murphy, “The Trouble with Stock Options,” Journal of Economic Perspectives 17 (Summer 2003), pp. 49–70.

The following surveys argue that executive compensation has been excessive, owing partly to weaknesses in corporate governance:

L. Bebchuk and J. Fried, Pay without Performance: The Unfulfilled Promise of Executive Compensation (Cambridge, MA: Harvard University Press, 2005).

M. C. Jensen, K. J. Murphy, and E. G. Wruck, “Remuneration: Where We’ve Been, How We Got to Here, What Are the Problems, and How to Fix Them,” 2004, at www.ssrn.com, posted July 12, 2004.

The Fall 2005 issue of the Journal of Applied Corporate Finance focuses on executive pay and corporate governance.

The following article is worth reading for survey evidence on earnings and corporate reporting:

J. R. Graham, C. R. Harvey, and S. Rajgopal, “The Economic Implications of Corporate Financial Reporting,” Journal of Accounting and Economics 40 (2005), pp. 3–73.

For easy-to-read descriptions of EVA, see:

A. Ehrbar, EVA: The Real Key to Creating Wealth (New York: John Wiley & Sons, 1998).

J. M. Stern and J. S. Shiely, The EVA Challenge—Implementing Value-added Change in an Organization (New York: John Wiley & Sons, 2001).

● ● ● ● ●

PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

  1.  CEO compensation True or false?

a.  U.S. CEOs are paid much more than CEOs in other countries.

b.  A large fraction of compensation for U.S. CEOs comes from stock-option grants.

c.  Stock-option grants give the manager a certain number of shares delivered at annual intervals, usually over five years.

d.  U.S. accounting rules now require recognition of the value of stock-option grants as a compensation expense.

  2.  Terminology Define the following: (a) Agency costs in capital investment, (b) private benefits, (c) empire building, (d) entrenching investment, (e) delegated monitoring.

  3.  Monitoring Monitoring alone can never completely eliminate agency costs in capital investment. Briefly explain why.

  4.  EVA Here are several questions about economic value added or EVA.

a.  Is EVA expressed as a percentage or a dollar amount?

b.  Write down the formula for calculating EVA.

c.  What is the difference, if any, between EVA and residual income?

d.  What is the point of EVA? Why do firms use it?

e.  Does the effectiveness of EVA depend on accurate measures of accounting income and assets?

  5.  Accounting measures of performance The Modern Language Corporation earned $1.6 million on net assets of $20 million. The cost of capital is 11.5%. Calculate the net ROI and EVA.

  6.  EVA Fill in the blanks:

“A project’s economic income for a given year equals the project’s ______ less its ______ depreciation. New projects may take several years to reach full profitability. In these cases book income is ______ than economic income early in the project’s life and ______ than economic income later in its life.”

  7.  Earnings targets How in practice do managers of public firms meet short-run earnings targets? By creative accounting?

INTERMEDIATE

  8.  Incentives Compare typical compensation and incentive arrangements for (a) top management, for example, the CEO or CFO, and (b) plant or division managers. What are the chief differences? Can you explain them?

  9.  Incentives Suppose all plant and division managers were paid only a fixed salary—no other incentives or bonuses.

 a.  Describe the agency problems that would appear in capital investment decisions.

 b.  How would tying the managers’ compensation to EVA alleviate these problems?

10.  Monitoring Who monitors the top management of public corporations? (We have mentioned several types of monitoring in this chapter.)

11.  Incentives We noted that management compensation must in practice rely on results rather than on effort. Why? What problems are introduced by not rewarding effort?

12.  Incentives Here are a few questions about compensation schemes that tie top management’s compensation to the rate of return earned on the company’s common stock.

 a.  Today’s stock price depends on investors’ expectations of future performance. What problems does this create?

 b.  Stock returns depend on factors outside the managers’ control, for example, changes in interest rates or prices of raw materials. Could this be a serious problem? If so, can you suggest a partial solution?

 c.  Compensation schemes that depend on stock returns do not depend on accounting data. Is that an advantage? Why or why not?

13.  Incentives You chair the compensation committee of the board of directors of Androscoggin Copper. A consultant suggests two stock-option packages for the CEO:

 a.  A conventional stock-option plan, with the exercise price fixed at today’s stock price.

 b.  An alternative plan in which the exercise price depends on the future market value of a portfolio of the stocks of other copper-mining companies. This plan pays off for the CEO only if Androscoggin’s stock price performs better than its competitors’.

The second plan sets a higher hurdle for the CEO, so the number of shares should be higher than in the conventional plan. Assume that the number of shares granted under each plan has been calibrated so that the present values of the two plans are the same. Which plan would you vote for? Explain.

14.  EVA Table 12.5 shows a condensed income statement and balance sheet for Araguaia Copper’s smelting plant.

 a.  Calculate the plant’s EVA. Assume the cost of capital is 9%.

 b.  As Table 12.5 shows, the plant is carried on Araguaia’s books at 96.64 million real. However, it is a modern design, and could be sold to another copper company for 190 million real. How should this fact change your calculation of EVA?

15.  EVA Herbal Resources is a small but profitable producer of dietary supplements for pets. This is not a high-tech business, but Herbal’s earnings have averaged around $1.2 million after tax, largely on the strength of its patented enzyme for making cats nonallergenic. The patent has eight years to run, and Herbal has been offered $4 million for the patent rights.

Herbal’s assets include $2 million of working capital and $8 million of property, plant, and equipment. The patent is not shown on Herbal’s books. Suppose Herbal’s cost of capital is 15%. What is its EVA?

16.  Accounting measures of performance True or false? Explain briefly.

 a.  Book profitability measures are biased measures of true profitability for individual assets. However, these biases “wash out” when firms hold a balanced mix of old and new assets.

 b.  Systematic biases in book profitability would be avoided if companies used depreciation schedules that matched expected economic depreciation. However, few, if any, firms have done this.

   TABLE 12.5 Condensed financial statements for Araguaia’s smelting plant. See Problem 14 (figures in million Brazilian real (BRL)).

17.  Economic income Consider the following project:

The internal rate of return is 20%. The NPV, assuming a 20% opportunity cost of capital, is exactly zero. Calculate the expected economic income and economic depreciation in each year.

18.  Accounting measures of performance Calculate the year-by-year book and economic profitability for investment in polyzone production, as described in Chapter 11. Use the cash flows and competitive spreads shown in Table 11.2, and assume straight-line depreciation over 10 years.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

What is the steady-state book rate of return (ROI) for a mature company producing polyzone? Assume no growth and competitive spreads.

19.  Accounting measures of performance The website www.mcgraw-hill.co.uk/textbooks/brealey contains an Excel program for calculating the profitability of the Nodhead project. Now suppose that the cash flows from Nodhead’s new supermarket are as follows:

 a.  Recalculate economic depreciation. Is it accelerated or decelerated?

 b.  Rework Tables 12.2 and 12.3 to show the relationship between (i) the “true” rate of return and book ROI and (ii) true EVA and forecasted EVA in each year of the project’s life.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

20.  Accounting measures of performance The website www.mcgraw-hill.co.uk/textbooks/brealey contains an Excel program for measuring the profitability of the Nodhead project. Reconstruct Table 12.4 assuming a steady-state growth rate of 10% per year. Your answer will illustrate a fascinating theorem, namely, that book rate of return equals the economic rate of return when the economic rate of return and the steady-state growth rate are the same.

CHALLENGE

21.  Accounting measures of performance Consider an asset with the following cash flows:

The firm uses straight-line depreciation. Thus, for this project, it writes off $4 million per year in years 1, 2, and 3. The discount rate is 10%.

 a.  Show that economic depreciation equals book depreciation.

 b.  Show that the book rate of return is the same in each year.

 c.  Show that the project’s book profitability is its true profitability.

You’ve just illustrated another interesting theorem. If the book rate of return is the same in each year of a project’s life, the book rate of return equals the IRR.

22.  Accounting measures of performance In our Nodhead example, true depreciation was decelerated. That is not always the case. For instance, Table 12.6 shows how on average the market value of a Boeing 737 has varied with its age²⁶ and the cash flow needed in each year to provide a 10% return. (For example, if you bought a 737 for $19.69 million at the start of year 1 and sold it a year later, your total profit would be 17.99 + 3.67 – 19.69 = $1.97 million, 10% of the purchase cost.)

Many airlines write off their aircraft straight-line over 15 years to a salvage value equal to 20% of the original cost.

 a.  Calculate economic and book depreciation for each year of the plane’s life.

 b.  Compare the true and book rates of return in each year.

 c.  Suppose an airline invested in a fixed number of Boeing 737s each year. Would steady-state book return overstate or understate true return?

   TABLE 12.6 Estimated market values of a Boeing 737 in January 1987 as a function of age, plus the cash flows needed to provide a 10% true rate of return (figures in $ millions).

23.  EVA Cosmos India produces dietary supplements. Its earnings are about 60 million rupees (R60 million) per year. Its balance sheet shows working capital of R100 million and net property, plant and equipment of R400 million. It also has valuable patents, which are not shown on the balance sheet. Cosmos has been offered R200 for the patents. Suppose Cosmos’s cost of capital is 15%. What is its EVA?

24.  Compensation and incentives Figure 12.2 shows that growth in compensation for U.S. executives has come mostly from stock and option grants. Such grants are less important in other countries. What are the possible disadvantages of linking compensation tightly to stock-price increases? Give examples.

25.  Compensation and incentives Journalists and policymakers in Europe and the U.K. worry about short-termism, that is, the tendency for top managers to pursue short-term growth in earnings and stock prices at the expense of long-run value maximization. How would you guard against short-termism if it is a significant problem? Would EVA help? Would you replace stock and option grants with bonuses based on growth in sales and earnings? Explain.

26.  Compensation limits European and U.S. governments have limited top-management compensation at banks and other financial institutions implicated in the financial crisis of 2007–2009.

 a.  Do you think that these limits should be continued for the longer run? Would it be better to avoid upper limits on compensation, but instead require claw back rules that force managers to disgorge pay if their companies encounter serious future losses?

 b.  Could limits or claw back rules be implemented country by country, or would an international agreement be necessary? Hint: What happens if compensation is limited in Paris but not in London?

___________

¹But don’t assume that all perks are unwarranted and inefficient. That corporate jet can be a good investment if it saves three or four hours a week that the CEO and CFO would otherwise waste in airports. Also, some large companies require the CEO to fly in the corporate jet for security reasons. Rajan and Wulf argue that it is not correct to treat all perks as managerial excess. See R. Rajan and J. Wulf, “Are Perks Purely Managerial Excess?” Journal of Financial Economics 79 (January 2006), pp. 1–33.

²A. Shleifer and R. W. Vishny, “Management Entrenchment: The Case of Manager-Specific Investments,” Journal of Financial Economics 25 (November 1989), pp. 123–140.

³M. C. Jensen, “Agency Costs of Free Cash Flow, Corporate Finance and Takeovers,” American Economic Review 76 (May 1986), pp. 323–329.

⁴S. Mullainathan and M. Bertrand, “Do Managers Prefer a Quiet Life? Corporate Governance and Managerial Preferences,” Journal of Political Economy 111 (2003), pp. 1043–1075. When corporations are better protected from takeovers, wages increase, fewer new plants are built, and fewer old plants are shut down. Productivity and profitability also decline.

⁵Baring Brothers, a British bank with a 200-year history, was wiped out when its trader Nick Leeson lost $1.4 billion trading in Japanese stock market indexes from a Barings office in Singapore. Leeson was gambling for redemption. As his losses mounted, he kept doubling and redoubling his trading bets in an attempt to recover his losses.

⁶“One firm cannot unilaterally withdraw from the business and maintain its ability to conduct business in the future,” he said later. “And if you are not engaged in the business, people leave . . . it is impossible to say in my view to your bankers we are just not going to participate in the business next year or so until things become a little more rational” in “Prince Finally Explains His Dancing Comment,” Dealbook.NYTimes.com, April 8, 2010. The New York Times © 2010. All rights reserved. Used with permission.

⁷Dr. Seuss, Did I Ever Tell You How Lucky You Are? (New York: Random House, 1973), pp. 26–28.

⁸The interests of lenders and shareholders are not always aligned—see Chapter 18. But a company’s ability to satisfy lenders is normally good news for stockholders, particularly when lenders are well placed to monitor.

⁹Gabaix and Landier argue that high CEO pay is a natural consequence of steadily increasing firm values and the competition for management talent. See X. Gabaix and A. Landier, “Why Has CEO Pay Increased So Much?” Quarterly Journal of Economics 123 (February 2008), pp. 49–100.

¹⁰See S. N. Kaplan and J. D. Rauh, “Wall Street and Main Street: What Contributes to the Rise in the Highest Incomes?” Review of Financial Studies, 23 (2010), pp. 1004–1050.

¹¹The major exceptions are in China, Japan, India, and South Korea, where such incentive schemes are still used by a minority of large firms.

¹²Bizjak, Lemmon, and Naveen found that most firms set pay levels at or above the median of the peer group, and some firms go much higher. For example, Coca-Cola and IBM consistently aim for levels in the top quartile of their peers. See J. M. Bizjak, M. L. Lemmon, and L. Naveen, “Has the Use of Peer Groups Contributed to Higher Pay and Less Efficient Compensation?” Journal of Financial Economics 90 (November 2008), pp. 152–168.

¹³Notice that investment includes the net working capital (current assets minus current liabilities) required to operate the plant. The investment shown is also called net assets or the net capital invested in the plant. We say “ROI,” but you will also hear “return on capital” (ROC). “Return on assets” (ROA) sometimes refers to return on assets defined to include net working capital, as in Table 12.1, but sometimes to return on total assets, where current assets are included but current liabilities are not subtracted. It’s prudent to check definitions when reviewing reported ROIs, ROCs, or ROAs.

¹⁴Notice that earnings are calculated after tax but with no deductions for interest paid. The plant is evaluated as if it were all-equity-financed. This is standard practice (see Chapter 6). It helps to separate investment and financing decisions. The tax advantages of debt financing supported by the plant are picked up not in the plant’s earnings or cash flows but in the discount rate. The cost of capital is the after-tax weighted-average cost of capital, or WACC. WACC was briefly introduced in Chapter 9 and will be further explained in Chapters 17 and 19.

¹⁵EVA is the term used by the consulting firm Stern–Stewart, which has done much to popularize and implement this measure of residual income. With Stern–Stewart’s permission, we omit the copyright symbol in what follows.

¹⁶EVA is conceptually the same as the residual income measure long advocated by some accounting scholars. See, for example, R. Anthony, “Accounting for the Cost of Equity,” Harvard Business Review 51 (1973), pp. 88–102, and “Equity Interest—Its Time Has Come,” Journal of Accountancy 154 (1982), pp. 76–93.

¹⁷A. Ehrbar, EVA: The Real Key to Creating Wealth (New York: John Wiley & Sons, Inc., 1998), pp. 130–131.

¹⁸The errors in book ROI always catch up with you in the end. If the firm chooses a depreciation schedule that overstates a project’s return in some years, it must also understate the return in other years. In fact, you can think of a project’s IRR as a kind of average of the book returns. It is not a simple average, however. The weights are the project’s book values discounted at the IRR. See J. A. Kay, “Accountants, Too, Could Be Happy in a Golden Age: The Accountant’s Rate of Profit and the Internal Rate of Return,” Oxford Economic Papers 28 (1976), pp. 447–460.

¹⁹We could repeat the steady-state analysis in Table 12.4 for different growth rates. It turns out that book income will overstate economic income if the growth rate is less than the internal rate of return and understate economic income if the growth rate exceeds the internal rate of return. Biases disappear if the growth rate and internal rate of return are exactly equal.

²⁰This procedure has been suggested by several authors, for example by Zvi Bodie in “Compound Interest Depreciation in Capital Investment,” Harvard Business Review 60 (May–June 1982), pp. 58–60.

²¹Recall from Chapter 4 that the price–earnings ratio equals 1/rE, where rE is the cost of equity, unless the firm has valuable growth opportunities (PVGO). The higher the PVGO, the lower the earnings–price ratio and the higher the price–earnings ratio. Thus the high price–earnings ratios observed for growth companies (much higher than plausible estimates of 1/rE) imply that investors forecast large PVGOs. But PVGO depends on investments made many years in the future. If investors see significant PVGOs, they can’t be systematically short-sighted.

²²J. R. Graham, C. R. Harvey, and S. Rajgopal, “The Economic Implications of Corporate Financial Reporting,” Journal of Accounting and Economics 40 (2005), pp. 3–73.

²³F. Degeorge, J. Patel, and R. Zeckhauser, “Earnings Management to Exceed Thresholds,” The Journal of Business 72 (January 1999), pp. 1–33.

²⁴Sometimes, instead of adjusting their operations, companies meet their target earnings by bending the accounting rules. For example, in August 2009 GE was fined $50 million for creative accounting in earlier years. The SEC said that GE had met or exceeded analysts’ profit targets in every quarter from 1995 through 2004, but that its top accountants signed off on improper decisions to make its numbers look better and to avoid missing analysts’ earnings expectations.

²⁵Graham, Harvey, and Rajgopal, op. cit., p. 29. © 2005, with permission from Elsevier.

²⁶We are grateful to Mike Staunton for providing us with these estimates.

Part 4 Financing Decisions and Market Efficiency

Efficient Markets and Behavioral Finance

Up to this point we have concentrated almost exclusively on the left-hand side of the balance sheet—the firm’s capital investment decision. Now we move to the right-hand side and to the problems involved in financing the capital investments. To put it crudely, you’ve learned how to spend money, now learn how to raise it.

Of course we haven’t totally ignored financing in earlier chapters. We introduced the weighted-average cost of capital, for example. But in most places we have looked past financing issues and used estimates of the opportunity cost of capital to discount future cash flows. We didn’t ask how the cost of capital might be affected by financing.

Now we are turning the problem around. We take the firm’s present portfolio of real assets and its future investment strategy as given, and then we determine the best financing strategy. For example,

•  Should the firm reinvest most of its earnings in the business, or distribute the cash to shareholders?

•  Is it better to distribute cash to stockholders by paying out dividends or by repurchasing stock?

•  If the firm needs more money, should it issue more stock or should it borrow?

•  Should it borrow short term or long term?

•  Should it borrow by issuing a normal long-term bond or a convertible bond (a bond that can be exchanged for stock by the bondholders)?

There are countless other financing trade-offs, as you will see.

The purpose of holding the firm’s capital investment decision constant is to separate that decision from the financing decision. Strictly speaking, this assumes that investment and financing decisions are independent. In many circumstances this is a reasonable assumption. The firm is generally free to change its capital structure by repurchasing one security and issuing another. In that case there is no need to associate a particular investment project with a particular source of cash. The firm can think, first, about which projects to accept and, second, about how they should be financed.

Sometimes decisions about capital structure depend on project choice or vice versa, and in those cases the investment and financing decisions have to be considered jointly. However, we defer discussion of such interactions of financing and investment decisions until Chapter 19.

We start this chapter by contrasting investment and financing decisions. The objective in each case is the same—to maximize NPV. However, it may be harder to find positive-NPV financing opportunities. The reason it is difficult to add value by clever financing decisions is that capital markets are usually efficient. By this we mean that fierce competition between investors eliminates profit opportunities and causes debt and equity issues to be fairly priced. If you think that sounds like a sweeping statement, you are right. That is why we have devoted this chapter to explaining and evaluating the efficient-market hypothesis.

You may ask why we start our discussion of financing issues with this conceptual point, before you have even the most basic knowledge about securities and issue procedures. We do it this way because financing decisions seem overwhelmingly complex if you don’t learn to ask the right questions. We are afraid you might flee from confusion to the myths that often dominate popular discussion of corporate financing. You need to understand the efficient-market hypothesis not because it is universally true but because it leads you to ask the right questions.

We define the efficient-market hypothesis more carefully in Section 13-2. The hypothesis comes in different strengths, depending on the information available to investors. Sections 13-2 through 13-4 review the evidence for and against efficient markets. The evidence “for” is considerable, but over the years a number of puzzling anomalies have accumulated.

Advocates for rational and efficient markets also have a hard time explaining bubbles. Every decade seems to find its own bubble: the 1980s real estate and stock market bubble in Japan, the 1990s technology stock bubble, and the recent real estate bubble that triggered the subprime crisis. Part of the blame for bubbles goes to the incentive and agency problems that can plague even the most rational people, particularly when they are investing other people’s money. But bubbles may also reflect patterns of irrational behavior that have been well documented by behavioral psychologists. We describe the main features of behavioral finance and the challenge that it poses to the efficient-market hypothesis.

The chapter closes with the six lessons of market efficiency.

 13-1   We Always Come Back to NPV

Although it is helpful to separate investment and financing decisions, there are basic similarities in the criteria for making them. The decisions to purchase a machine tool and to sell a bond each involve valuation of a risky asset. The fact that one asset is real and the other is financial doesn’t matter. In both cases we end up computing net present value.

The phrase net present value of borrowing may seem odd to you. But the following example should help to explain what we mean: As part of its policy of encouraging small business, the government offers to lend your firm $100,000 for 10 years at 3%. This means that the firm is liable for interest payments of $3,000 in each of the years 1 through 10 and that it is responsible for repaying the $100,000 in the final year. Should you accept this offer?

We can compute the NPV of the loan agreement in the usual way. The one difference is that the first cash flow is positive and the subsequent flows are negative:

The only missing variable is r, the opportunity cost of capital. You need that to value the liability created by the loan. We reason this way: The government’s loan to you is a financial asset: a piece of paper representing your promise to pay $3,000 per year plus the final repayment of $100,000. How much would that paper sell for if freely traded in the capital market? It would sell for the present value of those cash flows, discounted at r, the rate of return offered by other securities issued by your firm. All you have to do to determine r is to answer the question: What interest rate would my firm need to pay to borrow money directly from the capital markets rather than from the government?

Suppose that this rate is 10%. Then

Of course, you don’t need any arithmetic to tell you that borrowing at 3% is a good deal when the fair rate is 10%. But the NPV calculations tell you just how much that opportunity is worth ($43,012).¹ It also brings out the essential similarity between investment and financing decisions.

Differences between Investment and Financing Decisions

In some ways investment decisions are simpler than financing decisions. The number of different securities and financing strategies is well into the hundreds (we have stopped counting). You will have to learn the major families, genera, and species. You will also need to become familiar with the vocabulary of financing. You will learn about such matters as red herrings, greenshoes, and bookrunners; behind each of these terms lies an interesting story.

There are also ways in which financing decisions are much easier than investment decisions. First, financing decisions do not have the same degree of finality as investment decisions. They are easier to reverse. That is, their abandonment value is higher. Second, it’s harder to make money by smart financing strategies. The reason is that financial markets are more competitive than product markets. This means it is more difficult to find positive-NPV financing strategies than positive-NPV investment strategies.

When the firm looks at capital investment decisions, it does not assume that it is facing perfect, competitive markets. It may have only a few competitors that specialize in the same line of business in the same geographical area. And it may own some unique assets that give it an edge over its competitors. Often these assets are intangible, such as patents, expertise, or reputation. All this opens up the opportunity to make superior profits and find projects with positive NPVs.

In financial markets your competition is all other corporations seeking funds, to say nothing of the state, local, and federal governments that go to New York, London, Hong Kong, and other financial centers to raise money. The investors who supply financing are comparably numerous, and they are smart: Money attracts brains. The financial amateur often views capital markets as segmented, that is, broken down into distinct sectors. But money moves between those sectors, and it usually moves fast. In general, as we shall see, firms should assume that the securities they issue are fairly priced. That takes us into the main topic of this chapter: efficient capital markets.

 13-2   What Is an Efficient Market?

A Startling Discovery: Price Changes Are Random

As is so often the case with important ideas, the concept of efficient capital markets stemmed from a chance discovery. In 1953 Maurice Kendall, a British statistician, presented a controversial paper to the Royal Statistical Society on the behavior of stock and commodity prices.² Kendall had expected to find regular price cycles, but to his surprise they did not seem to exist. Each series appeared to be “a ‘wandering’ one, almost as if once a week the Demon of Chance drew a random number . . . and added it to the current price to determine the next week’s price.” In other words, the prices of stocks and commodities seemed to follow a random walk.

If you are not sure what we mean by “random walk,” you might like to think of the following example: You are given $100 to play a game. At the end of each week a coin is tossed. If it comes up heads, you win 3% of your investment; if it is tails, you lose 2.5%. Therefore, your capital at the end of the first week is either $103.00 or $97.50. At the end of the second week the coin is tossed again. Now the possible outcomes are:

This process is a random walk with a positive drift of .25% per week.³ It is a random walk because successive changes in value are independent. That is, the odds each week are the same, regardless of the value at the start of the week or of the pattern of heads and tails in the previous weeks.

If you find it difficult to believe that there are no patterns in share price changes, look at the two charts in Figure 13.1. One of these charts shows the outcome from playing our game for five years; the other shows the actual performance of the Standard and Poor’s Index for a five-year period. Can you tell which one is which?⁴

When Maurice Kendall suggested that stock prices follow a random walk, he was implying that the price changes are independent of one another just as the gains and losses in our coin-tossing game were independent. Figure 13.2 illustrates this for four stocks, Microsoft, Deutsche Bank, Philips, and Sony. Each panel shows the change in price of the stock on successive days. The circled dot in the southeast quadrant of the Microsoft panel refers to a pair of days in which a 3% increase was followed by a 3% decrease. If there were a systematic tendency for increases to be followed by decreases, there would be many dots in the southeast quadrant and few in the northeast quadrant. It is obvious from a glance that there is very little pattern in these price movements, but we can test this more precisely by calculating the coefficient of correlation between each day’s price change and the next. If price movements persisted, the correlation would be positive; if there were no relationship, it would be 0. In our example, the correlation between successive price changes in Microsoft stock was –.038; there was a negligible tendency for price rises to be followed by price falls.⁵ For Philips this correlation was also negative at –.015. However, for Deutsche Bank and Sony the correlations were positive at +.060 and +.010, respectively. In these cases there was a negligible tendency for price rises to be followed by further price rises.

   FIGURE 13.1 This chart shows the Standard and Poor’s Index for a five-year period and the results of playing our coin-tossing game for five years. Can you tell which line is which?

   FIGURE 13.2 Each dot shows a pair of returns for a stock on two successive days between December 1991 and November 2011. The circled dot for Microsoft records a daily return of +3% and then –3% on the next day. The scatter diagram shows no significant relationship between returns on successive days.

   FIGURE 13.3 Cycles self-destruct as soon as they are recognized by investors. The stock price instantaneously jumps to the present value of the expected future price.

Figure 13.2 suggests that successive price changes of all four stocks were effectively uncorrelated. Today’s price change gave investors almost no clue as to the likely change tomorrow. Does that surprise you? If so, imagine that it were not the case and that changes in Microsoft’s stock price were expected to persist for several months. Figure 13.3 provides an example of such a predictable cycle. You can see that an upswing in Microsoft’s stock price started last month, when the price was $20, and it is expected to carry the price to $40 next month. What will happen when investors perceive this bonanza? It will self-destruct. Since Microsoft stock is a bargain at $30, investors will rush to buy. They will stop buying only when the stock offers a normal risk-adjusted rate of return. Therefore, as soon as a cycle becomes apparent to investors, they immediately eliminate it by their trading.

Three Forms of Market Efficiency

You should see now why prices in competitive markets must follow a random walk. If past price changes could be used to predict future price changes, investors could make easy profits. But in competitive markets easy profits don’t last. As investors try to take advantage of the information in past prices, prices adjust immediately until the superior profits from studying past price movements disappear. As a result, all the information in past prices will be reflected in today’s stock price, not tomorrow’s. Patterns in prices will no longer exist and price changes in one period will be independent of changes in the next. In other words, the share price will follow a random walk.

In competitive markets today’s stock price must already reflect the information in past prices. But why stop there? If markets are competitive, shouldn’t today’s stock price reflect all the information that is available to investors? If so, securities will be fairly priced and security returns will be unpredictable. No one earns consistently superior returns in such a market. Collecting more information won’t help, because all available information is already impounded in today’s stock prices.

Economists define three levels of market efficiency, which are distinguished by the degree of information reflected in security prices. In the first level, prices reflect the information contained in the record of past prices. This is called weak market efficiency. If markets are efficient in the weak sense, then it is impossible to make consistently superior profits by studying past returns. Prices will follow a random walk.

The second level of efficiency requires that prices reflect not just past prices but all other public information, for example, from the Internet or the financial press. This is known as semistrong market efficiency. If markets are semistrong efficient, then prices will adjust immediately to public information such as the announcement of the last quarter’s earnings, a new issue of stock, or a proposal to merge two companies.

With strong market efficiency, prices reflect all the information that can be acquired by painstaking analysis of the company and the economy. In such a market we would observe lucky and unlucky investors, but we wouldn’t find any superior investment managers who can consistently beat the market.

Efficient Markets: The Evidence

In the years that followed Maurice Kendall’s discovery, financial journals were packed with tests of the efficient-market hypothesis. To test the weak form of the hypothesis, researchers measured the profitability of some of the trading rules used by those investors who claim to find patterns in security prices. They also employed statistical tests, including the test we used to look for patterns in the returns on Microsoft, Deutsche Bank, Philips, and Sony stock. It appears that throughout the world there are few patterns in day-to-day returns.

To analyze the semistrong form of the efficient-market hypothesis, researchers have measured how rapidly security prices respond to different items of news, such as earnings or dividend announcements, news of a takeover, or macroeconomic information.

Before we describe what they found, we should explain how to isolate the effect of an announcement on the price of a stock. Suppose, for example, that you need to understand how stock prices of takeover targets respond when the takeovers are first announced. As a first stab, you could simply calculate the average return on target-company stocks in the days leading up to the announcement and immediately after it. With daily returns on a large sample of targets, the average announcement effect should be clear. There won’t be too much contamination from movements in the overall market around the announcement dates, because daily market returns average out to a very small number.⁶ The potential contamination increases for weekly or monthly returns, however. Thus you will usually want to adjust for market movements. For example, you can simply subtract out the return on the market:

Chapter 8 suggests a refined adjustment based on betas. (Just subtracting the market return assumes that target-firm betas equal 1.0.) This adjustment is called the market model:

Alpha (α) states how much on average the stock price changed when the market index was unchanged. Beta (β) tells us how much extra the stock price moved for each 1% change in the market index.⁷ Suppose that subsequently the stock price return is in a month when the market return is . In that case we would conclude that the abnormal return for that month is

This abnormal return should reflect firm-specific news only.⁸

   FIGURE 13.4 The performance of the stocks of target companies compared with that of the market. The prices of target stocks jump up on the announcement day, but from then on, there are no unusual price movements. The announcement of the takeover attempt seems to be fully reflected in the stock price on the announcement day.

Source: A. Keown and J. Pinkerton, “Merger Announcements and Insider Trading Activity,” Journal of Finance 36 (September 1981), pp. 855–869. © 1981. Used with permission of John Wiley and Sons, via Copyright Clearance Center. Updates courtesy of Jinghua Yan.

Figure 13.4 illustrates how the release of news affects abnormal returns. The graph shows the abnormal return on a sample of nearly 17,000 firms that were targets of takeover attempts. Acquiring firms usually have to pay a substantial takeover premium to get the deal done, so the target firm’s stock price increases as soon as the takeover bid is announced. Figure 13.4 shows the average pattern of the target’s stock returns before and after the announcement of a takeover (day 0 in the figure). Stock prices drift up before date zero, as investors gradually realize that a takeover may be coming. On the announcement day, prices jump up dramatically.⁹ The stock-price adjustment is immediate and complete. After the big price move on the public announcement day, the run-up is over, and there is no significant further drift in the stock price, either upward or downward. Thus within the day, the new stock prices reflect (at least on average) the magnitude of the takeover premium.

Tests of the strong form of the hypothesis have examined the recommendations of professional security analysts and have looked for mutual funds or pension funds that could predictably outperform the market. Some researchers have found a slight persistent outperformance, but just as many have concluded that professionally managed funds fail to recoup the costs of management. Look, for example, at Figure 13.5, which compares the returns on diversified equity funds to the Wilshire 5000 Index. You can see that in some years the mutual funds beat the market, but roughly 60% of the time it was the other way around. Figure 13.5 provides a fairly crude comparison, for mutual funds have tended to specialize in particular sectors of the market, such as low-beta stocks or large-firm stocks, that may have given below-average returns. To control for such differences, each fund needs to be compared with a benchmark portfolio of similar securities. A number of studies have done this. Many have found that the message was unchanged: The funds earned a lower return than the benchmark portfolios after expenses and roughly matched the benchmarks before expenses. It would be surprising if some managers were not smarter than others and could earn superior returns. But it seems difficult to spot the smart ones, and the top-performing managers one year have about an average chance of falling on their faces the next year.¹⁰

   FIGURE 13.5 Diversified equity funds versus the Wilshire 5000 Index, 1971–2011. Notice that mutual funds underperform the market in approximately 60% of the years.

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Mutual fund cumulative returns

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Mutual fund performance

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The evidence on efficient markets has convinced many professional and individual investors to give up pursuit of superior performance. They simply “buy the index,” which maximizes diversification and cuts costs to the bone. Individual investors can buy index funds, which are mutual funds that track stock market indexes. There is no active management, so costs are very low. For example, management fees for the Vanguard 500 Index Fund, which tracks the S&P 500 Index, were .17% per year in 2011 (.06% per year for investments over $10,000). The size of this fund was $102 billion.

How far could indexing go? Not to 100%: If all investors hold index funds then nobody will be collecting information and prices will not respond to new information when it arrives. An efficient market needs some smart investors who gather information and attempt to profit from it. To provide incentives to gather costly information, prices cannot reflect all information.¹¹ There must be some profits available to allow the costs of information to be recouped. But if the costs are small, relative to the total market value of traded securities, then the financial market can still be close to perfectly efficient.

 13-3   The Evidence Against Market Efficiency

Almost without exception, early researchers concluded that the efficient-market hypothesis was a remarkably good description of reality. So powerful was the evidence that any dissenting research was regarded with suspicion. But eventually the readers of finance journals grew weary of hearing the same message. The interesting articles became those that turned up some puzzle. Soon the journals were packed with evidence of anomalies that investors have apparently failed to exploit.

What exactly is an anomaly? So far we have connected market efficiency to the absence of opportunities to make money. Let’s be more precise: in an efficient market it is not possible to find expected returns greater (or less) than the risk-adjusted opportunity cost of capital. This implies that every security trades at its fundamental value, based on future cash flows (Ct) and the opportunity cost of capital (r):

If price equals fundamental value, the expected rate of return is the opportunity cost of capital, no more and no less. If price differs from fundamental value, then investors can earn more than the cost of capital, by selling when the price is too high and buying when it is too low.

You will recall these principles from our discussion of common stock values in Chapter 4. Here the principles tell us that you can’t identify a superior return unless you know what the normal expected return is. Therefore, if you try to determine whether a market is efficient, you usually have to adopt an asset pricing model that specifies the relationship between risk and expected return. Any test of market efficiency is then a combined test of efficiency and the asset pricing model. Any test of an asset pricing model is also a combined test of the model and market efficiency.

The most commonly used asset pricing model is the CAPM. Chapter 8 pointed to some apparent violations of the CAPM, including the abnormally high returns on the stocks of small firms. For example, look back at Figure 8.10, which shows the cumulative difference between the returns on small-firm stocks and large-firm stocks. You can see that since 1926 the stocks of the firms with the lowest market capitalizations have performed substantially better than those with the highest capitalizations.

Now this may mean one (or more) of several things. First, it could be that investors have demanded a higher expected return from small firms to compensate for some extra risk factor that is not captured in the simple capital asset pricing model.

Second, the superior performance of small firms could simply be a coincidence, a finding that stems from the efforts of many researchers to find interesting patterns in the data. There is evidence for and against the coincidence theory. Those who believe that the small-firm effect is a pervasive phenomenon can point to the fact that small-firm stocks have provided a higher return in many other countries. On the other hand, you can see from Figure 8.10 that the small-firm effect seems to have disappeared as soon as it was first documented in 1981. Perhaps investors did underestimate the returns on small firms before 1981, but then bid up the firms’ stock prices as soon as the mispricing was identified.

Third, the small-firm effect could be an important exception to the efficient-market theory, an exception that gave investors the opportunity for consistently superior returns over a period of several decades. If these anomalies offer easy pickings, you would expect to find a number of investors eager to take advantage of them. It turns out that, while many investors do try to exploit such anomalies, it is surprisingly difficult to get rich by doing so. For example, Professor Richard Roll, who probably knows as much as anyone about market anomalies, confesses

Over the past decade, I have attempted to exploit many of the seemingly most promising “inefficiencies” by actually trading significant amounts of money according to a trading rule suggested by the “inefficiencies” . . . I have never yet found one that worked in practice, in the sense that it returned more after cost than a buy-and-hold strategy.¹²

Do Investors Respond Slowly to New Information?

We have dwelt on the small-firm effect, but there is no shortage of other puzzles and anomalies. Some of them relate to the short-term behavior of stock prices. For example, returns appear to be higher in January than in other months, they seem to be lower on a Monday than on other days of the week, and most of the daily return comes at the beginning and end of the day.

To have any chance of making money from such short-term patterns, you need to be a professional trader, with one eye on the computer screen and the other on your annual bonus. If you are a corporate financial manager, these short-term patterns in stock prices may be intriguing conundrums, but they are unlikely to change the major financial decisions about which projects to invest in and how they should be financed.

Corporate financial managers should be more concerned about mispricing that lasts months or years. Here are two examples of possible longer-lasting inefficiency.

The Earnings Announcement Puzzle The earnings announcement puzzle is summarized in Figure 13.6, which shows stock performance following the announcement of unexpectedly good or bad earnings during the years 1972 to 2001. The 10% of the stocks of firms with the best earnings news outperform those with the worst news by about 1% per month over the six-month period following the announcement. It seems that investors underreact to the earnings announcement and become aware of the full significance only as further information arrives.

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Long-run IPO returns

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The New-Issue Puzzle When firms issue stock to the public, investors typically rush to buy. On average those lucky enough to receive stock receive an immediate capital gain. However, researchers have found that these early gains often turn into losses. For example, suppose that you bought stock immediately following each initial public offering (IPO) and then held that stock for five years. Over the period 1970–2009 your average annual return would have been 3.4% less than the return on a portfolio of similar-sized stocks.

The jury is still out on these studies of long-term anomalies. Take, for example, the new-issue puzzle. Most new issues during the past 30 years have involved growth stocks with high market values and limited book assets. When the long-run performance of new issues is compared with a portfolio that is matched in terms of both size and book-to-market ratios, the difference in annual performance falls to 2.2%.¹³ So the new-issue puzzle could turn out to be just the book-to-market ratio puzzle in disguise.¹⁴

   FIGURE 13.6 The average return 1972–2001 on stocks of firms over the six months following an announcement of quarterly earnings. The 10% of stocks with the best earnings news (portfolio 10) outperformed those with the worst news (portfolio 1) by about 1% per month.

Source: T. Chordia and L. Shivakumar, “Inflation Illusion and the Post-earnings Announcement Drift,” Journal of Accounting Research 43 (2005), pp. 521–556. Used with permission of John Wiley and Sons, via Copyright Clearance Center.

Anomalies such as the new-issue puzzle may be a sign of inadequate asset pricing models, and so for many people they are not convincing evidence against market efficiency. However, there are other anomalies that cannot be dismissed so easily. One example is that of “Siamese twins,” two securities with claims on the same cash flows, which nevertheless trade separately. Before the two companies merged in July 2005, the Dutch company Royal Dutch Petroleum and the British company Shell Transport & Trading (T&T) were Siamese twins, each with a fixed share in the profits and dividends of the oil giant. Since both companies participated in the same underlying cash flows, you would expect the stock prices to have moved in exact lockstep. But, as you can see from Figure 13.7, the prices of the two shares sometimes diverged substantially.¹⁵

   FIGURE 13.7 Log deviations from Royal Dutch Shell/Shell T&T parity.

Source: Mathijs van Dijk, www.mathijsavandijk.com/dual-listed-companies. Used with permission.

Bubbles and Market Efficiency

Cases such as the Siamese twins suggest that there are occasions when prices of individual stocks can get out of line. But are there also cases in which prices as a whole can no longer be justified by fundamentals? We will look at the evidence in a moment, but first we should note how difficult it is to value common stocks and to determine whether their prices are irrational.

For example, imagine that in February 2012 you wanted to check whether the stocks forming Standard & Poor’s Composite Index were fairly valued. As a first stab you might use the constant-growth formula that we introduced in Chapter 4. In 2011 the annual dividends paid by the companies in the index were roughly $250 billion. Suppose that these dividends were expected to grow at a steady rate of 4.0% and that investors required a return of 6.0%. Then the constant-growth formula gives a value for the common stocks of

which was roughly their value in February 2012. But how confident could you be about these figures? Perhaps the likely dividend growth was only 3.5% per year. In that case your estimate of the value of the common stocks would decline to

In other words, a reduction of just half a percentage point in the expected rate of dividend growth would reduce the value of common stocks by 20%.

The extreme difficulty of valuing common stocks from scratch has two important consequences. First, investors find it easier to price a common stock relative to yesterday’s price or relative to today’s price of comparable securities. In other words, they generally take yesterday’s price as correct, adjusting upward or downward on the basis of today’s information. If information arrives smoothly, then, as time passes, investors become increasingly confident that today’s price level is correct. But when investors lose confidence in the benchmark of yesterday’s price, there may be a period of confused trading and volatile prices before a new benchmark is established.

Second, most of the tests of market efficiency are concerned with relative prices and focus on whether there are easy profits to be made. It is almost impossible to test whether stocks are correctly valued, because no one can measure true value with any precision. Take, for example, Pepsi stock, which sold for $63 in February 2012. Could we prove that this was its true value? Of course not, but we could be more confident that the price of Pepsi should not be very different from that of Coca-Cola ($69), because both companies had similar earnings and dividends per share and similar growth prospects.

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Two mysterious crashes

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It may be impossible to prove that market levels are, or are not, consistent with fundamentals. However, every now and again investors seem to be caught up in a speculative frenzy, and asset prices then reach levels that (at least with hindsight) cannot easily be justified by the outlook for profits and dividends. Investors refer to such occasions as bubbles. Bubbles can result when prices rise rapidly, and more and more investors join the game on the assumption that prices will continue to rise. These bubbles can be self-sustaining for a while. It can be rational to jump on the bandwagon as long as you are sure that there will be greater fools that you can sell out to. But remember that lots of money will be lost, perhaps by you, when the bubble bursts.¹⁶

The Japanese bubble is a good example. The Nikkei 225 Index rose about 300% between the start of 1985 and December 1989. After a sharp increase in interest rates at the beginning of 1990, stock prices began to fall. By October the Nikkei had sunk to about half its peak. In March 2009, the Nikkei was still down 80% from its peak 19 years before.

The boom in Japanese stock prices was matched by an even greater explosion in land prices. For example, Ziemba and Schwartz document that the few hundred acres of land under the Emperor’s Palace in Tokyo, evaluated at neighborhood land prices, was worth as much as all the land in Canada or California.¹⁷ But then the real estate bubble also burst. By 2005 land prices in the six major Japanese cities had slumped to just 13% of their peak.

Such bubbles are not confined to Japan. Toward the end of the twentieth century investors in technology stocks saw a remarkable run-up in the value of their holdings. The Nasdaq Composite Index, which has a heavy weighting in high-tech stocks, rose 580% from the start of 1995 to its high in March 2000. Then, as rapidly as it began, the boom ended, and by October 2002 the Nasdaq index had fallen 78% from its peak.

Some of the largest gains and losses were experienced by dot.com stocks. For example, Yahoo! shares, which began trading in April 1996, appreciated by 1,400% in four years. In these heady days some companies found that they could boost their stock price simply by adding “dot.com” to the company name.¹⁸

Looking back at the Japanese and dot.com bubbles, it seems difficult to believe that future cash flows could ever have been sufficient to provide investors with a reasonable return.¹⁹ If that is the case, we have two important exceptions to the theory of efficient markets.

 13-4   Behavioral Finance

Why might prices depart from fundamental values? Some believe that the answer lies in behavioral psychology. People are not 100% rational 100% of the time. This shows up in investors’ attitudes to risk and the way they assess probabilities.

1.  Attitudes toward risk. Psychologists have observed that, when making risky decisions, people are particularly loath to incur losses. It seems that investors do not focus solely on the current value of their holdings, but look back at whether their investments are showing a profit or a loss. For example, if I sell my holding of Volkswagen stock for €10,000, I may feel on top of the world if the stock only cost me €5,000, but I will be much less happy if it had cost €11,000. This observation is the basis for prospect theory.²⁰ Prospect theory states that (a) the value investors place on a particular outcome is determined by the gains or losses that they have made since the asset was acquired or the holding last reviewed, and (b) investors are particularly averse to the possibility of even a very small loss and need a high return to compensate for it.

The pain of loss seems also to depend on whether it comes on the heels of earlier losses. Once investors have suffered a loss, they may be even more concerned not to risk a further loss. Conversely, just as gamblers are known to be more willing to make large bets when they are ahead, so investors may be more prepared to run the risk of a stock market dip after they have enjoyed a run of unexpectedly high returns.²¹ If they do then suffer a small loss, they at least have the consolation of still being ahead for the year.

When we discussed portfolio theory in Chapters 7 and 8, we pictured investors as forward-looking only. Past gains or losses were not mentioned. All that mattered was the investor’s current wealth and the expectation and risk of future wealth. We did not allow for the possibility that Nicholas would be elated because his investment is in the black, while Nicola with an equal amount of wealth would be despondent because hers is in the red.

2.  Beliefs about probabilities. Most investors do not have a PhD in probability theory and may make systematic errors in assessing the probability of uncertain events. Psychologists have found that, when judging possible future outcomes, individuals tend to look back at what happened in a few similar situations. As a result, they are led to place too much weight on a small number of recent events. For example, an investor might judge that an investment manager is particularly skilled because he has “beaten the market” for three years in a row, or that three years of rapidly rising prices are a good indication of future profits from investing in the stock market. The investor may not stop to reflect on how little one can learn about expected returns from three years’ experience.

Most individuals are also too conservative, that is, too slow to update their beliefs in the face of new evidence. People tend to update their beliefs in the correct direction but the magnitude of the change is less than rationality would require.

Another systematic bias is overconfidence. For example, an American small business has just a 35% chance of surviving for five years. Yet the great majority of entrepreneurs think that they have a better than 70% chance of success.²² Similarly, most investors think they are better-than-average stock pickers. Two speculators who trade with each other cannot both make money, but nevertheless they may be prepared to continue trading because each is confident that the other is the patsy. Overconfidence also shows up in the certainty that people express about their judgments. They consistently overestimate the odds that the future will turn out as they say and underestimate the chances of unlikely events.

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Overconfident CFOs

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You can see how these behavioral characteristics may help to explain the Japanese and dot.com bubbles. As prices rose, they generated increased optimism about the future and stimulated additional demand. The more that investors racked up profits, the more confident they became in their views and the more willing they became to bear the risk that next month might not be so good.

Limits to Arbitrage

It is not difficult to believe that amateur investors may sometimes be caught up in a scatty whirl of irrational exuberance.²³ But there are plenty of hard-headed professional investors managing huge sums of money. Why don’t these investors bail out of overpriced stocks and force their prices down to fair value? One reason is that there are limits to arbitrage, that is, limits on the ability of the rational investors to exploit market inefficiencies.

Strictly speaking, arbitrage means an investment strategy that guarantees superior returns without any risk. In practice, arbitrage is defined more casually as a strategy that exploits market inefficiency and generates superior returns if and when prices return to fundamental values. Such strategies can be very rewarding, but they are rarely risk-free.

In an efficient market, if prices get out of line, then arbitrage forces them back. The arbitrageur buys the underpriced securities (pushing up their prices) and sells the overpriced securities (pushing down their prices). The arbitrageur earns a profit by buying low and selling high and waiting for prices to converge to fundamentals. Thus arbitrage trading is often called convergence trading.

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Short sales

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In practice arbitrage is harder than it looks. Trading costs can be significant and some trades are difficult to execute. For example, suppose that you identify an overpriced security that is not in your existing portfolio. You want to “sell high,” but how do you sell a stock that you don’t own? It can be done, but you have to sell short.

To sell a stock short, you borrow shares from another investor’s portfolio, sell them, and then wait hopefully until the price falls and you can buy the stock back for less than you sold it for. If you’re wrong and the stock price increases, then sooner or later you will be forced to repurchase the stock at a higher price (therefore at a loss) to return the borrowed shares to the lender. But if you’re right and the price does fall, you repurchase, pocket the difference between the sale and repurchase prices, and return the borrowed shares. Sounds easy, once you see how short selling works, but there are costs and fees to be paid, and in some cases you will not be able to find shares to borrow.²⁴

The perils of selling short were dramatically illustrated in 2008. Given the gloomy outlook for the automobile industry, a number of hedge funds decided to sell Volkswagen (VW) shares short in the expectation of buying them back at a lower price. Then in a surprise announcement Porsche revealed that it had effectively gained control of 74% of VW’s shares. Since a further 20% was held by the state of Lower Saxony, there was not enough stock available for the short sellers to buy back. As they scrambled to cover their positions, the price of VW stock rose in just two days from €209 to a high of €1005, making VW the most highly valued company in the world. Although the stock price drifted rapidly down, those short-sellers who were caught in the short squeeze suffered large losses.

The VW example illustrates that the most important limit to arbitrage is the risk that prices will diverge even further before they converge. Thus an arbitrageur has to have the guts and resources to hold on to a position that may get much worse before it gets better. Take another look at the relative prices of Royal Dutch and Shell T&T in Figure 13.7. Suppose that you were a professional money manager in 1980, when Royal Dutch was about 12% below parity. You decided to buy Royal Dutch, sell Shell T&T short, and wait confidently for prices to converge to parity. It was a long wait. The first time you would have seen any profit on your position was in 1983. In the meantime the mispricing got worse, not better. Royal Dutch fell to more than 30% below parity in mid-1981. Therefore, you had to report a substantial loss on your “arbitrage” strategy in that year. You were fired and took up a new career as a used-car salesman.

The demise in 1998 of Long Term Capital Management (LTCM) provides another example of the problems with convergence trades. LTCM, one of the largest and most profitable hedge funds of the 1990s, believed that interest rates in the different eurozone countries would converge when the euro replaced the countries’ previous currencies. LTCM had taken massive positions to profit from this convergence, as well as massive positions designed to exploit other pricing discrepancies. After the Russian government announced a moratorium on some of its debt payments in August 1998, there was great turbulence in the financial markets, and many of the discrepancies that LTCM was betting on suddenly got much larger.²⁵ LTCM was losing hundreds of millions of dollars daily. The fund’s capital was nearly gone when the Federal Reserve Bank of New York arranged for a group of LTCM’s creditor banks to take over LTCM’s remaining assets and shut down what was left in an orderly fashion.

LTCM’s sudden meltdown has not prevented rapid growth in the hedge fund industry in the 2000s. If hedge funds can push back the limits to arbitrage and avoid the kinds of problems that LTCM ran into, markets will be more efficient going forward. But asking for complete efficiency is probably asking too much. Prices can get out of line and stay out if the risks of an arbitrage strategy outweigh the expected returns.

Incentive Problems and the Subprime Crisis

The limits to arbitrage open the door to individual investors with built-in biases and misconceptions that can push prices away from fundamental values. But there can also be incentive problems that get in the way of a rational focus on fundamentals. We illustrate with a brief look at the subprime crisis in the United States.

Few U.S. homeowners foresaw a collapse in the price of their home. After all, the average house price in the U.S. had not fallen since the Great Depression of the 1930s. But in 2005 The Economist surveyed the widespread increase in property prices and warned:

[T]he total value of the residential property in developed economies rose by more than $30 trillion over the past five years to over $70 trillion, an increase equivalent to 100% of those countries’ combined GDPs. Not only does this dwarf any previous house-price boom, it is larger than the global stock market bubble in the late 1920s (55% of GDP). In other words it looks like the biggest bubble in history.²⁶

Shortly afterward the bubble burst. By March 2009, U.S. house prices had fallen by nearly a third from their peak in 2006.²⁷

How could such a boom and crash arise? In part because banks, credit rating agencies, and other financial institutions all had distorted incentives. Purchases of real estate are generally financed with mortgage loans from banks. In most parts of the U.S., borrowers can default on their mortgages with relatively small penalties. If property prices fall, they can simply walk away. But, if prices rise, they make money. Thus borrowers may be willing to take large risks, especially if the fraction of the purchase price financed with their own money is small.

Why, then, are banks willing to lend money to people who are bound to default if property prices fall significantly? Since the borrowers benefited most of the time, they were willing to pay attractive up-front fees to banks to get mortgage loans. But the banks could pass on the default risk to somebody else by packaging and reselling the mortgages as mortgage-backed securities (MBSs). Many MBS buyers assumed that they were safe investments, because the credit rating agencies said so. As it turned out, the credit ratings were a big mistake. (The rating agencies introduced another agency problem, because issuers paid the agencies to rate the MBS issues, and the agencies consulted with issuers over how MBS issues should be structured.)

The “somebody else” was also the government. Many subprime mortgages were sold to FNMA and FMAC (“Fannie Mae” and “Freddie Mac”). These were private corporations with a special advantage: government credit backup. (The backup was implicit, but quickly became explicit when Fannie and Freddie got into trouble in 2008. The U.S. Treasury had to take them over.) Thus these companies were able to borrow at artificially low rates, channeling money into the mortgage market.

The government was also on the hook because large banks that held subprime MBSs were “too big to fail” in a financial crisis. So the original incentive problem—the temptation of home buyers to take out a large mortgage and hope for higher real estate prices—was never corrected. The government could have cut its exposure by reining in Fannie and Freddie before the crisis but did not do so.

Agency and incentive problems are widespread in the financial services industry. In the U.S. and many other countries, people engage financial institutions such as pension funds and mutual funds to invest their money. These institutions are the investors’ agents, but the agents’ incentives do not always match the investors’ interests. Just as with real estate, these agency relationships can lead to mispricing, and potentially bubbles.²⁸

 13-5   The Six Lessons of Market Efficiency

The efficient-market hypothesis emphasizes that arbitrage will rapidly eliminate any profit opportunities and drive market prices back to fair value. Behavioral-finance specialists may concede that there are no easy profits, but argue that arbitrage is costly and sometimes slow-working, so that deviations from fair value may persist.

Sorting out the puzzles will take time, but we suggest that financial managers should assume, at least as a starting point, that there are no free lunches to be had on Wall Street.

The “no free lunch” principle gives us the following six lessons of market efficiency. After reviewing these lessons, we consider what market inefficiency can mean for the financial manager.

Lesson 1: Markets Have No Memory

The weak form of the efficient-market hypothesis states that the sequence of past price changes contains no information about future changes. Economists express the same idea more concisely when they say that the market has no memory. Sometimes financial managers seem to act as if this were not the case. For example, after an abnormal market rise, managers prefer to issue equity rather than debt.²⁹ The idea is to catch the market while it is high. Similarly, they are often reluctant to issue stock after a fall in price. They are inclined to wait for a rebound. But we know that the market has no memory and the cycles that financial managers seem to rely on do not exist.³⁰

Sometimes a financial manager will have inside information indicating that the firm’s stock is overpriced or underpriced. Suppose, for example, that there is some good news that the market does not know but you do. The stock price will rise sharply when the news is revealed. Therefore, if your company sells shares at the current price, it would offer a bargain to new investors at the expense of present stockholders.

Naturally, managers are reluctant to sell new shares when they have favorable inside information. But such information has nothing to do with the history of the stock price. Your firm’s stock could be selling at half its price of a year ago, and yet you could have special information suggesting that it is still grossly overvalued. Or it may be undervalued at twice last year’s price.

Lesson 2: Trust Market Prices

In an efficient market you can trust prices, for they impound all available information about the value of each security. This means that in an efficient market, there is no way for most investors to achieve consistently superior rates of return. To do so, you not only need to know more than anyone else; you also need to know more than everyone else. This message is important for the financial manager who is responsible for the firm’s exchange-rate policy or for its purchases and sales of debt. If you operate on the basis that you are smarter than others at predicting currency changes or interest-rate moves, you will trade a consistent financial policy for an elusive will-o’-the-wisp.

The company’s assets may also be directly affected by management’s faith in its investment skills. For example, one company may purchase another simply because its management thinks that the stock is undervalued. On approximately half the occasions the stock of the acquired firm will with hindsight turn out to be undervalued. But on the other half it will be overvalued. On average the value will be correct, so the acquiring company is playing a fair game except for the costs of the acquisition.

Lesson 3: Read the Entrails

If the market is efficient, prices impound all available information. Therefore, if we can only learn to read the entrails, security prices can tell us a lot about the future. For example, in Chapter 23 we show how information in a company’s financial statements can help the financial manager to estimate the probability of bankruptcy. But the market’s assessment of the company’s securities can also provide important information about the firm’s prospects. Thus, if the company’s bonds are trading at low prices, you can deduce that the firm is probably in trouble.

Here is another example: Suppose that investors are confident that interest rates are set to rise over the next year. In that case, they will prefer to wait before they make long-term loans, and any firm that wants to borrow long-term money today will have to offer the inducement of a higher rate of interest. In other words, the long-term rate of interest will have to be higher than the one-year rate. Differences between the long-term interest rate and the short-term rate tell you something about what investors expect to happen to short-term rates in the future.

The nearby box shows how market prices reveal opinions about issues as diverse as a presidential election, the weather, or the demand for a new product.

FINANCE IN PRACTICE

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Prediction Markets

   Stock markets allow investors to bet on their favourite stocks. Prediction markets allow them to bet on almost anything else. These markets reveal the collective guess of traders on issues as diverse as New York City snowfall, an avian flu outbreak, and the occurrence of a major earthquake.

Prediction markets are conducted on the majorfutures exchanges and on a number of smaller online exchanges such as Intrade (www.intrade.com) and the Iowa Electronic Markets (www.biz.uiowa.edu/iem). Take the prospects for the euro as an example. On Intrade you could bet that at least one country currently using the euro would no longer do so by the end of 2013. Each contract paid $1 if any country left the euro and nothing otherwise. If you thought that the probability of a currency exiting the euro was 55% (say), you would have been prepared to pay up to $.55 for this contract. Someone who was relatively optimistic about the euro’s future would have been happy to sell you such a contract, for that sale would turn a profit if the euro survived intact. With many participants buying and selling, the market price of a contract revealed the collective wisdom of the crowd.

Take a look at the accompanying figure for the Intrade contract. It shows the prices for the euro contract between August 2010 and October 2012. In the spring of 2011 there was a dip in the price of the contract as the Greek default was finalized, but by the fall of 2011 the price had climbed to $.66. Investors, it seemed, had become increasingly pessimistic about the currency’s prospects.

Participants in prediction markets are putting their money where their mouth is. So the forecasting accuracy of these markets compares favorably with those of major polls. Some businesses have also formed internal prediction markets to survey the views of their staff. For example, Google operates an internal market to forecast product launch dates, the number of Gmail users, and other strategic questions.*

*Google’s experience is analyzed in B. Cowgill, J. Wolfers, and E. Zitzewitz, “Using Prediction Markets to Track Information Flows: Evidence from Google,” Working paper, Dartmouth College, January 2009

Lesson 4: There Are No Financial Illusions

In an efficient market there are no financial illusions. Investors are unromantically concerned with the firm’s cash flows and the portion of those cash flows to which they are entitled. However, there are occasions on which managers seem to assume that investors suffer from financial illusion.

For example, some firms devote considerable ingenuity to the task of manipulating earnings reported to stockholders. This is done by “creative accounting,” that is, by choosing accounting methods that stabilize and increase reported earnings. Presumably firms go to this trouble because management believes that stockholders take the figures at face value.³¹

One way that companies can affect their reported earnings is through the way that they cost the goods taken out of inventory. Companies can choose between two methods. Under the FIFO (first-in, first-out) method, the firm deducts the cost of the first goods to have been placed in inventory. Under the LIFO (last-in, first-out) method companies deduct the cost of the latest goods to arrive in the warehouse. When inflation is high, the cost of the goods that were bought first is likely to be lower than the cost of those that were bought last. So earnings calculated under FIFO appear higher than those calculated under LIFO.

Now, if it were just a matter of presentation, there would be no harm in switching from LIFO to FIFO. But the IRS insists that the same method that is used to report to shareholders also be used to calculate the firm’s taxes. So the lower apparent earnings from using the LIFO method also bring lower immediate tax payments.

If markets are efficient, investors should welcome a change to LIFO accounting, even though it reduces earnings. Biddle and Lindahl, who studied the matter, concluded that this is exactly what happens in the U.S., so that the move to LIFO is associated with an abnormal rise in the stock price.³² It seems that shareholders look behind the figures and focus on the amount of the tax savings.

Lesson 5: The Do-It-Yourself Alternative

In an efficient market investors will not pay others for what they can do equally well themselves. As we shall see, many of the controversies in corporate financing center on how well individuals can replicate corporate financial decisions. For example, companies often justify mergers on the grounds that they produce a more diversified and hence more stable firm. But if investors can hold the stocks of both companies why should they thank the companies for diversifying? It is much easier and cheaper for them to diversify than it is for the firm.

The financial manager needs to ask the same question when considering whether it is better to issue debt or common stock. If the firm issues debt, it will create financial leverage. As a result, the stock will be more risky and it will offer a higher expected return. But stockholders can obtain financial leverage without the firm’s issuing debt; they can borrow on their own accounts. The problem for the financial manager is, therefore, to decide whether the company can issue debt more cheaply than the individual shareholder.

Lesson 6: Seen One Stock, Seen Them All

The elasticity of demand for any article measures the percentage change in the quantity demanded for each percentage addition to the price. If the article has close substitutes, the elasticity will be strongly negative; if not, it will be near zero. For example, coffee, which is a staple commodity, has a demand elasticity of about –.2. This means that a 5% increase in the price of coffee changes sales by –.2 × .05 = –.01; in other words, it reduces demand by only 1%. Consumers are likely to regard different brands of coffee as much closer substitutes for each other. Therefore, the demand elasticity for a particular brand could be in the region of, say, –2.0. A 5% increase in the price of Maxwell House relative to that of Folgers would in this case reduce demand by 10%.

Investors don’t buy a stock for its unique qualities; they buy it because it offers the prospect of a fair return for its risk. This means that stocks should be like very similar brands of coffee, almost perfect substitutes. Therefore, the demand for a company’s stock should be highly elastic. If its prospective return is too low relative to its risk, nobody will want to hold that stock. If the reverse is true, everybody will scramble to buy.

Suppose that you want to sell a large block of stock. Since demand is elastic, you naturally conclude that you need to cut the offering price only very slightly to sell your stock. Unfortunately, that doesn’t necessarily follow. When you come to sell your stock, other investors may suspect that you want to get rid of it because you know something they don’t. Therefore, they will revise their assessment of the stock’s value downward. Demand is still elastic, but the whole demand curve moves down. Elastic demand does not imply that stock prices never change when a large sale or purchase occurs; it does imply that you can sell large blocks of stock at close to the market price as long as you can convince other investors that you have no private information.

Here again we encounter an apparent contradiction with practice. State and federal regulatory commissions, which set the prices charged by local telephone companies, electric companies, and other utilities, have sometimes allowed significantly higher earnings to compensate the firm for price “pressure.” This pressure is the decline in the firm’s stock price that is supposed to occur when new shares are offered to investors. Yet Paul Asquith and David Mullins, who searched for evidence of pressure, found that new stock issues by utilities drove down their stock prices on average by only .9%.³³ We come back to the subject of pressure when we discuss stock issues in Chapter 15.

What If Markets Are Not Efficient? Implications for the Financial Manager

Our six lessons depend on efficient markets. What should financial managers do when markets are not efficient? The answer depends on the nature of the inefficiency.

Trading Opportunities—Are They Really There for Nonfinancial Corporations? Suppose that the treasurer’s staff in your firm notices mispricing in fixed-income or commodities markets, the kind of mispricing that a hedge fund would attempt to exploit in a convergence trade. Should the treasurer authorize the staff to undertake a similar convergence trade? In most cases, the answer should be no. First, the corporation faces the same limits to arbitrage that afflict hedge funds and other investors. Second, the corporation probably has no competitive edge in the convergence-trade business.

Procter & Gamble (P&G) supplied a costly example of this point in early 1994, when it lost $102 million in short order. It seems that in 1993 P&G’s treasury staff believed that interest rates would be stable and decided to act on this belief to reduce P&G’s borrowing costs. They committed P&G to deals with Bankers Trust designed to do just that. Of course there was no free lunch. In exchange for a reduced interest rate, P&G agreed to compensate Bankers Trust if interest rates rose sharply. Rates did increase dramatically in early 1994, and P&G was on the hook.

Then P&G accused Bankers Trust of misrepresenting the transactions—an embarrassing allegation, since P&G was hardly investing as a widow or orphan—and sued Bankers Trust.

We take no stand on the merits of this litigation, which was eventually settled. But think of P&G’s competition when it traded in the fixed-income markets. Its competition included the trading desks of all the major investment banks, hedge funds, and fixed-income portfolio managers. P&G had no special insights or competitive advantages on the fixed-income playing field. There was no evident reason to expect positive NPV on the trades it committed to. Why was it trading at all? P&G would never invest to enter a new consumer market if it had no competitive advantage in that market.

In Chapter 11 we argued that a corporation should not invest unless it can identify a competitive advantage and a source of economic rents. Market inefficiencies may offer economic rents from convergence trades, but few corporations have a competitive edge in pursuing these rents. As a general rule, nonfinancial corporations gain nothing, on average, by speculation in financial markets. They should not try to imitate hedge funds.³⁴

What If Your Company’s Shares Are Mispriced? The financial manager may not have special information about future interest rates, but definitely has special information about the value of his or her own company’s shares. The strong form of market efficiency does not always hold, so the financial manager will often have information that outside investors do not have. Or investors may have the same information as management, but be slow in reacting to that information or may be infected with behavioral biases.

Sometimes you hear managers thinking out loud like this:

Great! Our stock is clearly overpriced. This means we can raise capital cheaply and invest in Project X. Our high stock price gives us a big advantage over our competitors who could not possibly justify investing in Project X.

But that doesn’t make sense. If your stock is truly overpriced, you can help your current shareholders by selling additional stock and using the cash to invest in other capital market securities. But you should never issue stock to invest in a project that offers a lower rate of return than you could earn elsewhere in the capital market. Such a project would have a negative NPV. You can always do better than investing in a negative-NPV project: Your company can go out and buy common stocks. In an efficient market, such purchases are always zero NPV.

What about the reverse? Suppose you know that your stock is underpriced. In that case, it certainly would not help your current shareholders to sell additional “cheap” stock to invest in other fairly priced stocks. If your stock is sufficiently underpriced, it may even pay to forgo an opportunity to invest in a positive-NPV project rather than to allow new investors to buy into your firm at a low price. Financial managers who believe that their firm’s stock is underpriced may be justifiably reluctant to issue more stock, but they may instead be able to finance their investment program by an issue of debt. In this case the market inefficiency would affect the firm’s choice of financing but not its real investment decisions. In Chapter 15 we will have more to say about the financing choice when managers believe their stock is mispriced.

What If Your Firm Is Caught in a Bubble? On occasion, your company’s stock price may be swept up in a bubble like the dot.com boom of the late 1990s. Bubbles can be exhilarating. It’s hard not to join in the enthusiasm of the crowds of investors bidding up your firm’s stock price.³⁵ On the other hand, financial management inside a bubble poses difficult personal and ethical challenges. Managers don’t want to “talk down” a high-flying stock price, especially when bonuses and stock-option payoffs depend on it. The temptation to cover up bad news or manufacture good news can be very strong. But the longer a bubble lasts, the greater the damage when it finally bursts. When it does burst, there will be lawsuits and possibly jail time for managers who have resorted to tricky accounting or misleading public statements in an attempt to sustain the inflated stock price.

When a firm’s stock price is swept upward in a bubble, CEOs and financial managers are tempted to acquire another firm using the stock as currency. One extreme example where this arguably happened is AOL’s acquisition of Time Warner at the height of the dot.com bubble in 2000. AOL was a classic dot.com company. Its stock rose from $2.34 at the end of 1995 to $75.88 at the end of 1999. Time Warner’s stock price also increased during this period, but only from $18.94 to $72.31. AOL’s total market capitalization was a small fraction of Time Warner’s in 1995, but overtook Time Warner’s in 1998. By the end of 1999 AOL’s outstanding shares were worth $173 billion, compared with Time Warner’s $95 billion. AOL managed to complete the acquisition before the Internet bubble burst. AOL-Time Warner’s stock then plummeted, but not by nearly as much as the stocks of dot.com companies that had not managed to find and acquire safer partners.³⁶

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SUMMARY

The patron saint of the Bolsa (stock exchange) in Barcelona, Spain, is Nuestra Señora de la Esperanza—Our Lady of Hope. She is the perfect patroness, for we all hope for superior returns when we invest. But competition between investors will tend to produce an efficient market. In such a market, prices will rapidly impound any new information, and it will be difficult to make consistently superior returns. We may indeed hope, but all we can rationally expect in an efficient market is a return just sufficient to compensate us for the time value of money and for the risks we bear.

The efficient-market hypothesis comes in three different flavors. The weak form of the hypothesis states that prices efficiently reflect all the information in the past series of stock prices. In this case it is impossible to earn superior returns simply by looking for patterns in stock prices; in other words, price changes are random. The semistrong form of the hypothesis states that prices reflect all published information. That means it is impossible to make consistently superior returns just by reading the newspaper, looking at the company’s annual accounts, and so on. The strong form of the hypothesis states that stock prices effectively impound all available information. It tells us that superior information is hard to find because in pursuing it you are in competition with thousands, perhaps millions, of active, intelligent, and greedy investors. The best you can do in this case is to assume that securities are fairly priced and to hope that one day Nuestra Señora will reward your humility.

During the 1960s and 1970s every article on the topic seemed to provide additional evidence that markets are efficient. But then readers became tired of hearing the same message and wanted to read about possible exceptions. During the 1980s and 1990s more and more anomalies and puzzles were uncovered. Bubbles, including the dot.com bubble of the 1990s and the real estate bubble of the 2000s, cast doubt on whether markets were always and everywhere efficient.

Limits to arbitrage can explain why asset prices may get out of line with fundamental values. Behavioral finance, which relies on psychological evidence to interpret investor behavior, is consistent with many of the deviations from market efficiency. Behavioral finance says that investors are averse to even small losses, especially when recent investment returns have been disappointing. Investors may rely too much on a few recent events in predicting the future. They may be overconfident in their predictions and may be sluggish in reacting to new information.

There are plenty of quirks and biases in human behavior, so behavioral finance has plenty of raw material. But if every puzzle or anomaly can be explained by some recipe of quirks, biases, and hindsight, what have we learned? Research in behavioral finance literature is informative and intriguing, but not yet at the stage where a few parsimonious models can account for most of the deviations from market efficiency.

For the corporate treasurer who is concerned with issuing or purchasing securities, the efficient-market theory has obvious implications. In one sense, however, it raises more questions than it answers. The existence of efficient markets does not mean that the financial manager can let financing take care of itself. It provides only a starting point for analysis. It is time to get down to details about securities and issue procedures. We start in Chapter 14.

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FURTHER READING

Malkiel’s book is an-easy-to-read book on market efficiency. Fama has written two classic review articles on the topic:

B. G. Malkiel, A Random Walk Down Wall Street, 10th ed. (New York: W. W. Norton, 2012).

E. F. Fama, “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance 25 (May 1970), pp. 383–417.

E. F. Fama, “Efficient Capital Markets: II,” Journal of Finance 46 (December 1991), pp. 1575–1617.

There are several useful surveys of behavioral finance:

N. Barberis and R. H. Thaler, “A Survey of Behavioral Finance,” in G. M. Constantinides, M. Harris, and R. M. Stulz (eds.), Handbook of the Economics of Finance (Amsterdam: Elsevier Science, 2003).

M. Baker, R. S. Ruback, and J. Wurgler, “Behavioral Corporate Finance,” in B. E. Eckbo (ed.), The Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), Chapter 4.

R. J. Shiller, “Human Behavior and the Efficiency of the Financial System,” in J. B. Taylor and M. Woodford (eds.), Handbook of Macroeconomics (Amsterdam: North-Holland, 1999).

A. Shleifer, Inefficient Markets: An Introduction to Behavioral Finance (Oxford: Oxford University Press, 2000).

R. H. Thaler (ed.), Advances in Behavioral Finance (New York: Russell Sage Foundation, 1993).

Some conflicting views on market efficiency are provided by:

G. W. Schwert, “Anomalies and Market Efficiency,” in G. M. Constantinides, M. Harris, and R. M. Stulz (eds.), Handbook of the Economics of Finance (Amsterdam: Elsevier Science, 2003).

M. Rubinstein, “Rational Markets: Yes or No? The Affirmative Case?” Financial Analysts Journal 57 (May–June 2001), pp. 15–29.

B. G. Malkiel, “The Efficient Market Hypothesis and Its Critics,” Journal of Economic Perspectives 17 (Winter 2003), pp. 59–82.

R. J. Shiller, “From Efficient Markets Theory to Behavioral Finance,” Journal of Economic Perspectives 17 (Winter 2003), pp. 83–104.

E. F. Fama and K. R. French, “Dissecting Anomalies,” Journal of Finance 63 (August 2008), pp. 1653–1678.

Bubbles are discussed in:

M. Brunnermeier, Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis, and Herding (Oxford: Oxford University Press, 2001).

R. J. Shiller, Irrational Exuberance, 2nd ed. (Princeton, NJ: Princeton University Press, 2005).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Market efficiency Which (if any) of these statements are true? Stock prices appear to behave as though successive values (a) are random numbers, (b) follow regular cycles, (c) differ by a random number.

2.  Market efficiency Supply the missing words:

  “There are three forms of the efficient-market hypothesis. Tests of randomness in stock returns provide evidence for the ________ form of the hypothesis. Tests of stock price reaction to well-publicized news provide evidence for the ________ form, and tests of the performance of professionally managed funds provide evidence for the ________ form. Market efficiency results from competition between investors. Many investors search for new information about the company’s business that would help them to value the stock more accurately. Such research helps to ensure that prices reflect all available information; in other words, it helps to keep the market efficient in the ________ form. Other investors study past stock prices for recurrent patterns that would allow them to make superior profits. Such research helps to ensure that prices reflect all the information contained in past stock prices; in other words, it helps to keep the market efficient in the ________ form.”

3.  Market efficiency True or false? The efficient-market hypothesis assumes that

a.  There are no taxes.

b.  There is perfect foresight.

c.  Successive price changes are independent.

d.  Investors are irrational.

e.  There are no transaction costs.

f.  Forecasts are unbiased.

4.  Market efficiency True or false?

a.  Financing decisions are less easily reversed than investment decisions.

b.  Tests have shown that there is almost perfect negative correlation between successive price changes.

c.  The semistrong form of the efficient-market hypothesis states that prices reflect all publicly available information.

d.  In efficient markets the expected return on each stock is the same.

5.  Abnormal returns Analysis of 60 monthly rates of return on United Futon common stock indicates a beta of 1.45 and an alpha of –.2% per month. A month later, the market is up by 5%, and United Futon is up by 6%. What is Futon’s abnormal rate of return?

6.  Behavioral finance True or false?

a.  Most managers tend to be overconfident.

b.  Psychologists have found that, once people have suffered a loss, they are more relaxed about the possibility of incurring further losses.

c.  Psychologists have observed that people tend to put too much weight on recent events when forecasting.

d.  Behavioral biases open up the opportunity for easy arbitrage profits.

7.  Announcement effects Geothermal Corporation has just received good news: Its earnings increased by 20% from last year’s value. Most investors are anticipating an increase of 25%. Will Geothermal’s stock price increase or decrease when the announcement is made?

8.  Six lessons Here again are the six lessons of market efficiency. For each lesson give an example showing the lesson’s relevance to financial managers.

a.  Markets have no memory.

b.  Trust market prices.

c.  Read the entrails.

d.  There are no financial illusions.

e.  The do-it-yourself alternative.

f.  Seen one stock, seen them all.

9.  Anomalies Give two or three examples of research results or events that raise doubts about market efficiency. Briefly explain why.

INTERMEDIATE

10.  Efficient markets How would you respond to the following comments?

a.  “Efficient market, my eye! I know lots of investors who do crazy things.”

b.  “Efficient market? Balderdash! I know at least a dozen people who have made a bundle in the stock market.”

c.  “The trouble with the efficient-market theory is that it ignores investors’ psychology.”

d.  “Despite all the limitations, the best guide to a company’s value is its written-down book value. It is much more stable than market value, which depends on temporary fashions.”

11.  Market efficiency Respond to the following comments:

a.  “The random-walk theory, with its implication that investing in stocks is like playing roulette, is a powerful indictment of our capital markets.”

b.  “If everyone believes you can make money by charting stock prices, then price changes won’t be random.”

c.  “The random-walk theory implies that events are random, but many events are not random. If it rains today, there’s a fair bet that it will rain again tomorrow.”

12.  Market efficiency Which of the following observations appear to indicate market inefficiency? Explain whether the observation appears to contradict the weak, semistrong, or strong form of the efficient-market hypothesis.

a.  U.S. tax-exempt municipal bonds offer lower pretax returns than taxable government bonds.

b.  Managers make superior returns on their purchases of their company’s stock.

c.  There is a positive relationship between the return on the market in one quarter and the change in aggregate profits in the next quarter.

d.  There is disputed evidence that stocks that have appreciated unusually in the recent past continue to do so in the future.

e.  The stock of an acquired firm tends to appreciate in the period before the merger announcement.

f.  Stocks of companies with unexpectedly high earnings appear to offer high returns for several months after the earnings announcement.

g.  Very risky stocks on average give higher returns than safe stocks.

13.  Abnormal returns Here are alphas and betas for two Indian stocks for the 60 months ending November 2012. Alpha is expressed as a percent per month.

Explain how these estimates would be used to calculate an abnormal return.

14.  Market efficiency “If the efficient-market hypothesis is true, the pension fund manager might as well select a portfolio with a pin.” Explain why this is not so.

15.  Six lessons Two financial managers, Alpha and Beta, are contemplating a chart showing the actual performance of the market index over a five-year period. Each manager’s company needs to issue new shares of common stock sometime in the next year.

Alpha: My company’s going to issue right away. The stock market cycle has obviously topped out, and the next move is almost surely down. Better to issue now and get a decent price for the shares.

Beta: You’re too nervous; we’re waiting. It’s true that the market’s been going nowhere for the past year or so, but the figure clearly shows a basic upward trend. The market’s on the way up to a new plateau.

What would you say to Alpha and Beta?

16.  Arbitrage What does the efficient-market hypothesis have to say about these two statements?

a.  “I notice that short-term interest rates are about 1% below long-term rates. We should borrow short-term.”

b.  “I notice that interest rates in Japan are lower than rates in the United States. We would do better to borrow Japanese yen rather than U.S. dollars.”

17.  Market efficiency Fama and French show that average stock returns on firms with small market capitalizations have been significantly higher than average returns for “large-cap” firms. What are the possible explanations for this result? Does the result disprove market efficiency? Explain briefly.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

18.  Abnormal returns Column (A) in Table 13.1 below shows the monthly return on the British FTSE 100 index from May 2007 through February 2009. Columns (B) and (C) show returns on the stocks of two firms—Executive Cheese and Paddington Beer. Both firms announced their earnings in February 2009. Calculate the average abnormal return of the two stocks during the month of the earnings announcement.

19.  Limits to arbitrage On May 15, 1997, the government of Kuwait offered to sell 170 million BP shares, worth about $2 billion. Goldman Sachs was contacted after the stock market closed in London and given one hour to decide whether to bid on the stock. They decided to offer 710.5 pence ($11.59) per share, and Kuwait accepted. Then Goldman Sachs went looking for buyers. They lined up 500 institutional and individual investors worldwide, and resold all the shares at 716 pence ($11.70). The resale was complete before the London Stock Exchange opened the next morning. Goldman Sachs made $15 million overnight.³⁷

What does this deal say about market efficiency? Discuss.

20.  Bubbles Explain how incentive and agency problems can contribute to mispricing of securities or to bubbles. Give examples.

21.  Behavioral finance Many commentators have blamed the subprime crisis on “irrational exuberance.” What is your view? Explain briefly.

   TABLE 13.1 See Problem 18. Rates of return in percent per month.

CHALLENGE

22.  Market efficiency “The strong form of the efficient-market hypothesis is nonsense. Look at mutual fund X; it has had superior performance for each of the last 10 years.” Does the speaker have a point? Suppose that there is a 50% probability that X will obtain superior performance in any year simply by chance.

a.  If X is the only fund, calculate the probability that it will have achieved superior performance for each of the past 10 years.

b.  Now recognize that there are nearly 10,000 mutual funds in the United States. What is the probability that by chance there is at least 1 out of 10,000 funds that obtained 10 successive years of superior performance?

23.  Bubbles Some extreme bubbles are obvious with hindsight, after they burst. But how would you define a bubble? There are many examples of good news and rising stock prices, followed by bad news and falling stock prices. Can you set out rules and procedures to distinguish bubbles from the normal ups and downs of stock prices?

24.  Abnormal returns Here are alphas (in percent per month) and betas for two British stocks, based on monthly returns from March 2005 to February 2010:

a.  How well did these two stocks perform in this period?

b.  Use the market model to calculate abnormal returns for March 2010, when the market returned 6.3%, British Airways 17.2% and Vodafone 6.2%.

c.  Suppose the CAPM holds exactly. Would you change your estimate of abnormal returns for March 2010? Would you need additional information? Explain.

25.  Efficient markets Take another look at Figure 13.4, and notice how the average stock price of the target companies creeps up in the months before the announcement of the takeover offer. This could mean that some investors are trading illegally on inside information about takeovers. But it could also mean that honest investors anticipate when a company could be a target, and bid up the company’s stock price hoping that a takeover will happen sooner or later.

Suppose that the financial-markets regulators in Costaguana construct a version of Figure 13.4 for takeovers in their country. They find a different pattern than in the U.S.: almost all of the news about takeovers appears to be incorporated in prices several days before the official takeover announcements. Does that mean the Costaguanan stock market is exceptionally efficient? Discuss.

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FINANCE ON THE WEB

Use finance.yahoo.com to download daily prices for five U.S. stocks for a recent five-year period.

For each stock, construct a scatter diagram of successive returns as in Figure 13.2. Calculate the correlation among the returns on successive days. Do you find any consistent patterns?

___________

¹We ignore here any tax consequences of borrowing. These are discussed in Chapter 18.

²See M. G. Kendall, “The Analysis of Economic Time Series, Part I. Prices,” Journal of the Royal Statistical Society 96 (1953), pp. 11–25. Kendall’s idea was not wholly new. It had been proposed in an almost forgotten thesis written 53 years earlier by a French doctoral student, Louis Bachelier. Bachelier’s accompanying development of the mathematical theory of random processes anticipated by five years Einstein’s famous work on the random Brownian motion of colliding gas molecules. See L. Bachelier, Théorie de la Speculation (Paris: Gauthiers-Villars, 1900). Reprinted in English (A. J. Boness, trans.) in P. H. Cootner (ed.), The Random Character of Stock Market Prices (Cambridge, MA: MIT Press, 1964), pp. 17–78.

³The drift is equal to the expected outcome: (1/2)(3) + (1/2)(–2.5) = .25%.

⁴The green line in Figure 13.1 shows the actual Standard and Poor’s Index for February 2002 to February 2007; the red is a series of cumulated random numbers. Of course, 50% of you are likely to have guessed right, but we bet it was just a guess.

⁵The correlation coefficient between successive observations is known as the autocorrelation coefficient. An autocorrelation of –.038 implies that, if Microsoft’s stock price rose by 1% more than the average yesterday, your best forecast of today’s change would be .038% less than the average.

⁶Suppose, for example, that the market return is 12% per year. With 250 trading days in the year, the average daily return is (1.12)1/250 – 1 = .00045, or .045%.

⁷It is important when estimating a and b that you choose a period in which you believe that the stock behaved normally. If its performance was abnormal, then estimates of a and b cannot be used to measure the returns that investors expected. As a precaution, ask yourself whether your estimates of expected returns look sensible. Methods for estimating abnormal returns are analyzed in A. C. MacKinlay, “Event Studies in Economics and Finance,” Journal of Economic Literature 35 (1997), pp. 13–39; and also S. P. Kothari and J. B. Warner, “Econometrics of Event Studies,” in B. E. Eckbo (ed.), The Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), Chapter 1.

⁸Abnormal returns are also often calculated using the Fama-French three-factor model, which we discussed in Chapter 8. The stock return is adjusted for the market return, the difference between small- and large-stock returns, and the difference between returns on high and low book-to-market firms.

⁹Big profits await if you can identify target firms before the takeover announcement. Purchases based on confidential inside information are illegal, however, and could land you in jail. For example, Raj Rajaratnam was sentenced to 11 years in jail after being found guilty of insider trading. See “Rajaratnam Sentenced to 11 Years in Jail,” Financial Times, October 13, 2011.

¹⁰See, for example, B. G. Malkiel, “Returns from Investing in Equity Mutual Funds 1971 to 1991,” Journal of Finance 50 (June 1995), pp. 549–572 and M. M. Carhart, “On Persistence in Mutual Fund Performance,” Journal of Finance 52 (March 1997), pp. 57–82. Some evidence of slight persistence in performance is provided in E. F. Fama and K. R. French, “Luck versus Skill in the Cross-Section of Mutual Fund Alpha Estimates,” Journal of Finance 65 (October 2010), pp. 1915–1947; and in R. Kosowski, A. Timmerman, R. Wermers, and H. White, “Can Mutual Fund ‘Stars’ Really Pick Stocks? New Evidence from a Bootstrap Analysis,” Journal of Finance 61 (December 2006), pp. 2551–2595. See also M. J. Gruber, “Another Puzzle: The Growth in Actively Managed Mutual Funds,” Journal of Finance 51 (July 1996), pp. 783–810.

¹¹See S. J. Grossman and J. E. Stiglitz, “On the Impossibility of Informationally Efficient Markets,” American Economic Review 70 (June 1980), pp. 393–408.

¹²R. Roll, “What Every CFO Should Know about Scientific Progress in Financial Economics: What Is Known and What Remains to Be Resolved,” Financial Management 23 (Summer 1994), pp. 69–75.

¹³The long-run underperformance of new issues was documented in R. Loughran and J. R. Ritter, “The New Issues Puzzle,” Journal of Finance 50 (1995), pp. 23–51. The figures are updated on Jay Ritter’s website, where IPO returns are compared with those of a portfolio that is matched in terms of size and book-to-market ratio. (See bear.cba.ufl.edu/ritter.)

¹⁴There may be still other reasons for the poor long-term performance of IPOs, including tax effects. Portfolios of IPOs generate many extreme winners and losers. Investors can sell the losers, deducting the losses against other capital gains, and hold the winners, thus deferring taxes. IPO stocks are a good venue for this tax strategy, so tax-savvy investors may have bid up IPO stock prices.

¹⁵For evidence on the pricing of Siamese twins see K. A. Froot and E. Dabora, “How Are Stock Prices Affected by the Location of Trade?” Journal of Financial Economics 53 (August 1999), pp. 189–216, and, for more recent data, A. De Jong, L. Rosenthal, and M. A. Van Dijk, “The Risk and Return of Arbitrage in Dual-Listed Companies,” Review of Finance 13 (2009), pp. 495–520.

¹⁶Bubbles are not necessarily irrational. See M. Brunnermeier, Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis and Herding (Oxford: Oxford University Press, 2001).

¹⁷See W. T. Ziemba and S. L. Schwartz, Invest Japan (Chicago, IL: Probus Publishing Co., 1992), p. 109.

¹⁸M. Cooper, O. Dimitrov, and P. R. Rau, “A Rose.com by Any Other Name,” Journal of Finance 56 (2001), pp. 2371–2388.

¹⁹For an analysis of Japanese stock prices, see K. French and J. M. Poterba, “Were Japanese Stock Prices Too High?” Journal of Financial Economics 29 (October 1991), pp. 337–364. For more on dot.com stock prices, see E. Ofek and M. Richardson, “The Valuation and Market Rationality of Internet Stock Prices,” Oxford Review of Economic Policy 18 (Autumn 2002), pp. 265–287.

²⁰Prospect theory was first set out in D. Kahneman and A. Tversky, “Prospect Theory: An Analysis of Decision under Risk,” Econometrica 47 (1979), pp. 263–291.

²¹The effect is described in R. H. Thaler and E. J. Johnson, “Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice,” Management Science 36 (1990), pp. 643–660. The implications of prospect theory for stock returns are explored in N. Barberis, M. Huang, and T. Santos, “Prospect Theory and Asset Prices,” Quarterly Journal of Economics 116 (February 2001), pp. 1–53.

²²See D. Kahneman, Thinking Fast and Slow (New York: Farrar, Straus, and Giroux, 2011).

²³The term “irrational exuberance” was coined by Alan Greenspan, former chairman of the Federal Reserve Board, to describe the dot.com boom. It was also the title of a book by Robert Shiller that examined the boom. See R. Shiller, Irrational Exuberance (New York: Broadway Books, 2001).

²⁴Investment and brokerage firms identify shares eligible for lending and arrange to make them available to short-sellers. The supply of shares that can be borrowed is limited. You are charged a fee for borrowing the stock, and you are required to put up collateral to protect the lender in case the share price rises and the short-seller is unable to repurchase and return the shares. Putting up collateral is costless if the short-seller gets a market interest rate, but sometimes only lower interest rates are offered.

²⁵The Russian debt moratorium was unexpected and unusual, because the debt had only recently been issued and was denominated in roubles. The government preferred to default rather than to print roubles to service the debt.

²⁶“In Come the Waves,” The Economist, June 16, 2005. Used with permission via Copyright Clearance Center.

²⁷Investors who did foresee that the fall in house prices would lead to the subprime debacle were able to earn high profits. For example, John Paulson, the hedge fund manager, earned $3.7 billion in 2007 as a result (Financial Times, January 15, 2008, and June 18, 2008).

²⁸See F. Allen, “Do Financial Institutions Matter?” Journal of Finance 56 (2001), pp. 1165–1175.

²⁹See, for example, P. Asquith and D. W. Mullins, Jr., “Equity Issues and Offering Dilution,” Journal of Financial Economics 15 (January–February 1986), pp. 16–89; and (for the UK) P. R. Marsh, “The Choice between Debt and Equity: An Empirical Study,” Journal of Finance 37 (March 1982), pp. 121–144.

³⁰If high stock prices signal expanded investment opportunities and the need to finance these new investments, we would expect to see firms raise more money in total when stock prices are historically high. But this does not explain why firms prefer to raise the extra cash at these times by an issue of equity rather than debt.

³¹For a discussion of the evidence that investors are not fooled by earnings manipulation, see R. Watts, “Does It Pay to Manipulate EPS?” in J. M. Stern and D. H. Chew, Jr. (eds.), The Revolution in Corporate Finance (Oxford: Basil Blackwell, 1992).

³²G. C. Biddle and F. W. Lindahl, “Stock Price Reactions to LIFO Adoptions: The Association between Excess Returns and LIFO Tax Savings,” Journal of Accounting Research 20 (Autumn 1982, Part 2), pp. 551–588.

³³See P. Asquith and D. W. Mullins, “Equity Issues and Offering Dilution,” Journal of Financial Economics 15 (January–February 1986), pp. 61–89.

³⁴There are of course some likely exceptions. Hershey and Nestlé are credible traders in cocoa futures markets. The major oil companies probably have special skills and knowledge relevant to energy markets.

³⁵See J. C. Stein, “Rational Capital Budgeting in an Irrational World,” Journal of Business 69 (October 1996), pp. 429–455.

³⁶Pavel Savor and Qi Lu provide evidence that many other firms were able to benefit from stock acquisitions. See “Do Stock Mergers Create Value for Acquirers?” Journal of Finance 64 (June 2009), pp. 1061–1097.

³⁷“Goldman Sachs Earns a Quick $15 Million Sale of BP Shares,” The Wall Street Journal, May 16, 1997, p. A4.

Part 4 Financing Decisions and Market Efficiency

An Overview of Corporate Financing

We now begin our analysis of long-term financing decisions—an undertaking we will not complete until Chapter 25. This chapter provides an introduction to corporate financing. It reviews, with a broad brush, several topics that we will explore more carefully later on.

We start the chapter by looking at aggregate data on the sources of financing. Much of the money for new investments comes from profits that companies retain and reinvest. The remainder comes from selling new debt or equity securities. These financing patterns raise several interesting questions. Do companies rely too heavily on internal financing rather than on new issues of debt or equity? Are corporate debt ratios dangerously high?

Our second task in the chapter is to review some of the essential features of debt and equity. Lenders and stockholders have different cash-flow rights and also different control rights. The lenders have first claim on cash flow because they are promised definite cash payments for interest and principal. The stockholder receives whatever cash is left over after the lenders are paid. Stockholders, on the other hand, have complete control of the firm, providing that they keep their promises to lenders. As owners of the business, stockholders have the ultimate control over what assets the company buys, how the assets are financed, and how they are used. Of course, in large public corporations, the stockholders delegate these decisions to the board of directors, who in turn appoint senior management. In these cases effective control often ends up with the company’s management.

The simple division of cash flow among debt and equity glosses over the many different types of debt that companies issue. Therefore, we close our discussion of debt and equity with a brief canter through the main categories of debt. We also pause to describe certain less common forms of equity, particularly preferred stock.

The financial manager is the link between the firm and the financial institutions that provide much of the funds that the companies need, together with help in making payments, managing risk, and so on. We, therefore, introduce you to the major financial institutions and look at the roles that financial institutions play in corporate financing and in the economy at large. The financial crisis that started in the summer of 2007 demonstrated the importance of healthy financial markets and institutions. We will review the crisis and its aftermath.

 14-1   Patterns of Corporate Financing

Corporations invest in long-term assets (primarily property, plant, and equipment) and in net working capital (current assets minus current liabilities). Figure 14.1 shows where U.S. corporations get the cash to pay for these investments. Most of the cash is generated internally. That is, it comes from cash flow allocated to depreciation and from retained earnings (earnings not paid out as cash dividends).¹ Shareholders are happy to plow this cash back into the firm, provided that investments are positive NPV. Every positive-NPV outlay increases shareholder value.

   FIGURE 14.1 Sources of funds for U.S. nonfinancial corporations expressed as a fraction of the total.

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts Table F.102 at www.federalreserve.gov/releases/z1/current/data.htm.

U.S. corporations are not alone in relying mostly on internally generated cash. For example, internal cash flow makes up the majority of corporate financing in Germany, Japan, and the UK.

Sometimes internal cash flow more than covers investment, but, if it does not, the company faces a financial deficit. To cover the deficit, the company must cut back on dividends in order to increase retained earnings, or it must raise new debt or equity capital from outside investors. So there are two basic financing decisions. First, what fraction of profits should be plowed back into the business rather than paid out to shareholders? Second, what fraction of the financial deficit should be met with debt rather than equity? Thus the firm needs a payout policy (Chapter 16) and a debt policy (Chapters 17 and 18).

Take a look at U.S. equity issues in Figure 14.1. Net issues were negative in every year. This means that the cash raised by share issues was less than the cash paid out to shareholders by repurchase of previously outstanding shares. (Corporations can buy back their own shares, or they may purchase and retire other firms’ shares in the course of mergers and acquisitions.) The choice between cash dividends and repurchases is another aspect of payout policy.

Stock repurchases in the U.S. were especially large in 2006 and 2007, which accounts for the large negative net equity issues in those years. By contrast, debt issues were positive in every year except 2009.

Do Firms Rely Too Much on Internal Funds?

We have seen that, on average, internal funds (retained earnings plus depreciation) cover most of the cash needed for investment. It seems that internal financing is more convenient than external financing by stock and debt issues. But some observers worry that managers have an irrational or self-serving aversion to external finance. A manager seeking comfortable employment could be tempted to forgo a risky but positive-NPV project if it involved launching a new stock issue and facing awkward questions from potential investors. Perhaps managers take the line of least resistance and dodge the “discipline of capital markets.”

We do not mean to paint managers as loafers. They sometimes have good reasons for relying on internally generated funds. They may seek to avoid the cost of issuing new securities, for example. Moreover, the announcement of a new equity issue is usually bad news for investors, who worry that the decision signals lower future profits or higher risk.² If issues of shares are costly and send a bad-news signal to investors, companies may be justified in looking more carefully at those projects that would require a new stock issue.

How Much Do Firms Borrow?

The mix of debt and equity financing varies widely from industry to industry and from firm to firm. Debt ratios also vary over time for particular firms. These variations are a fact of life: There is no constant, God-given debt ratio, and if there were, it would change. But a few aggregate statistics will do no harm.

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European debt ratios

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Table 14.1 shows the aggregate balance sheet of all U.S. manufacturing corporations. If all these businesses were merged into a single gigantic firm, Table 14.1 would be its balance sheet. Assets and liabilities in the table are entered at book values, that is, accounting values. These do not generally equal market values. The numbers are nevertheless instructive. Notice that firms had long-term debt of $1,618 billion and equity of $3,552 billion. The ratio of long-term debt to long-term debt plus equity was, therefore, $1,618/($1,618 + $3,552) = .31.³

Table 14.1 is of course only a snapshot. Figure 14.2 provides a longer-term perspective. The debt ratios are lower when computed from market values rather than book values. This is because the market value of equity is generally greater than book values. However, in both cases the debt ratio is higher now than it was in 1965.

Should we be concerned that book debt ratios are higher today than 50 years ago? It is true that higher debt ratios mean that more companies will fall into financial distress when a serious recession hits the economy. But all companies live with this risk to some degree, and it does not follow that less risk is better. Finding the optimal debt ratio is like finding the optimal speed limit. We can agree that accidents at 30 miles per hour are generally less dangerous than accidents at 60 miles per hour, but we do not therefore set the speed limit on all roads at 30. Speed has benefits as well as risks. So does debt, as we see in Chapter 18.

   TABLE 14.1 Aggregate balance sheet for manufacturing corporations in the United States, third quarter, 2011 (figures in $ billions).

a See Table 30.1 for a breakdown of current assets and liabilities.

b Includes deferred taxes and several miscellaneous categories.

Source: U.S. Census Bureau, Quarterly Report for Manufacturing, Mining and Trade Corporations, 2011 (www.census.gov/econ/qfr).

   FIGURE 14.2 Ratio of debt to net worth for nonfinancial corporations, 1965–2010.

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts Table B.102 at www.federalreserve.gov/releases/z1/current/data.htm.

 14-2   Common Stock

A corporation is owned by its common stockholders. Some of this common stock is held directly by individual investors, but the greater proportion belongs to financial institutions such as mutual funds, pension funds, and insurance companies. For example, look at Figure 14.3. You can see that in the U.S. about 50% of common stock is held by U.S. financial institutions, with pension funds and mutual funds each holding about 20%.⁴

What do we mean when we say that these stockholders own the corporation? The answer is obvious if the company has issued no other securities. Consider the simplest possible case of a corporation financed solely by common stock, all of which is owned by the firm’s chief executive officer (CEO). This lucky owner-manager receives all the cash flows and makes all investment and operating decisions. She has complete cash-flow rights and also complete control rights.

These rights are split up and reallocated as soon as the company borrows money. If it takes out a bank loan, it enters into a contract with the bank promising to pay interest and eventually repay the principal. The bank gets a privileged, but limited, right to cash flows; the residual cash-flow rights are left with the stockholder. Thus common stock is a residual claim on the firm’s assets and cash flow.

   FIGURE 14.3 Holdings of corporate equities, third quarter, 2011.

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts Table L.213 at www.federalreserve.gov/releases/z1/current/data.htm.

The bank typically protects its claim by imposing restrictions on what the firm can or cannot do. For example, it may require the firm to limit future borrowing, and it may forbid the firm to sell off assets or to pay excessive dividends. The stockholders’ control rights are thereby limited. However, the contract with the bank can never restrict or determine all the operating and investment decisions necessary to run the firm efficiently. (No team of lawyers, no matter how long they scribbled, could ever write a contract covering all possible contingencies.)⁵ The owner of the common stock retains the residual rights of control over these decisions. For example, she may choose to increase the selling price of the firm’s products, to hire temporary rather than permanent employees, or to construct a new plant in Miami Beach rather than Hollywood.⁶

Ownership of the firm can of course change. If the firm fails to make the promised payments to the bank, it may be forced into bankruptcy. Once the firm is under the “protection” of a bankruptcy court, shareholders’ cash-flow and control rights are tightly restricted and may be extinguished altogether. Unless some rescue or reorganization plan can be implemented, the bank becomes the new owner of the firm and acquires the cash-flow and control rights of ownership. (We discuss bankruptcy in Chapter 32.)

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Empty voting

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No law of nature says residual cash-flow rights and residual control rights have to go together. For example, one could imagine a situation where the debtholder gets to make all the decisions. But this would be inefficient. Since the benefits of good decisions are felt mainly by the common stockholders, it makes sense to give them control over how the firm’s assets are used.

We have focused so far on a firm that is owned by a single stockholder. Public corporations are owned by many stockholders. Ownership can be widely dispersed, with tens of thousands of stockholders, none owning a significant block of shares. It has been widely believed that ownership in the U.S. is more widely dispersed than in other countries. However, research by Clifford Holderness shows that this is not the case. He finds that 96% of a sample of U.S. public corporations have block holders with at least 5% of the outstanding shares. Some countries have more concentrated ownership than the U.S., some have less. The U.S. lies in the middle of the pack.⁷

The common stockholders in widely held corporations still have the residual rights over the cash flows and have the ultimate right of control over the company’s affairs. In practice, however, their control is limited to an entitlement to vote, either in person or by proxy, on appointments to the board of directors, and on other crucial matters such as the decision to merge. Many shareholders do not bother to vote. They reason that, since they own so few shares, their vote will have little impact on the outcome. The problem is that, if all shareholders think in the same way, they cede effective control and management gets a free hand to look after its own interests.

Voting Procedures

For many U.S. companies, the entire board of directors comes up for re-election each year. However, approximately half of large companies have classified boards, in which case only a third of the directors come up for re-election each year. Shareholder activists complain that such staggered elections make it more difficult for a dissident group of shareholders to replace the board and therefore help to entrench management. Consequently, in recent years share-holders have pressured many companies into declassifying their boards.

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A Contest over Voting Rights

   The Economist magazine once wrote that, in Switzerland, shareholder-friendly companies were “as rare as Swiss admirals,” and that “safe behind anti-takeover defenses, most managers treated their shareholders with disdain.” However, The Economist perceived one encouraging sign that these attitudes were changing: a proposal by the Union Bank of Switzerland (UBS) to change the rights of its equityholders.

UBS had two classes of shares—bearer shares, which are anonymous, and registered shares, which are not. In Switzerland, where anonymity is prized, bearer shares usually traded at a premium. UBS’s bearer shares had sold at a premium for many years. However, there was another important distinction between the two share classes. The registered shares carried five times as many votes as an equivalent investment in the bearer shares. Presumably attracted by this feature, an investment company, BK Vision, began to accumulate a large position in the registered shares, and their price rose to a 38% premium over the bearer shares.

At this point UBS announced its plan to merge the two classes of shares, so that the registered shares would become bearer shares and would lose their superior voting rights. Since all of UBS’s shares would then sell for the same price, UBS’s announcement led to a rise in the price of the bearer shares and a fall in the price of the registered.

Martin Ebner, the president of BK Vision, objected to the change, complaining that it stripped the registered shareholders of some of their voting rights without providing compensation. The dispute highlighted the question of the value of superior voting stock. If the votes are used to secure benefits for all shareholders, then the stock should not sell at a premium. However, a premium would arise if holders of the superior voting stock expected to secure benefits for themselves alone.

To many observers UBS’s proposal was a welcome attempt to prevent one group of shareholders from profiting at the expense of others and to unite all shareholders in the common aim of maximizing firm value. To others it represented an attempt to take away their rights. In any event, the debate over the proposal was never fully resolved, for UBS shortly afterward agreed to merge with SBC, another Swiss bank.

Those who have studied board elections have found that the move to declassify boards has generally increased company value. It seems that staggered elections do tend to entrench management, deter proxy contests, and reduce the degree to which CEO compensation is linked to firm performance.⁸

Shareholders generally elect directors by a system of majority voting. In this case, each director is voted upon separately and stockholders can cast one vote for each share that they own. If a company’s articles permit cumulative voting, the directors are voted upon jointly and stockholders can, if they wish, allot all their votes to just one candidate.⁹ Cumulative voting makes it easier for a minority group among the stockholders to elect directors who will represent the group’s interests. That is why some shareholder groups campaign for cumulative voting.

On many issues a simple majority of votes cast is sufficient to carry the day, but the company charter may specify some decisions that require a supermajority of, say, 75% of those eligible to vote. For example, a supermajority vote is sometimes needed to approve a merger or a change to the charter. Such provisions have also attracted shareholder complaints that they help to entrench management and prevent worthwhile takeovers.

The issues on which stockholders are asked to vote are rarely contested, particularly in the case of large, publicly traded firms. Occasionally, there are proxy contests in which the firm’s existing management and directors compete with outsiders for effective control of the corporation. But the odds are stacked against the outsiders, for the insiders can get the firm to pay all the costs of presenting their case and obtaining votes.¹⁰

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Google’s stock split

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Dual-Class Shares and Private Benefits

Usually companies have one class of common stock and each share has one vote. Occasionally, however, a firm may have two classes of stock outstanding, which differ in their right to vote. For example, when Google made its first issue of common stock, the founders were reluctant to give up control of the company. Therefore, the company created two classes of shares. The A shares, which were sold to the public, had 1 vote each, while the B shares, which were owned by the founders, had 10 votes each. Both classes of shares had the same cash-flow rights, but they had different control rights.

When two classes of stock coexist, shareholders with the extra voting power may sometimes use it to toss out bad management or to force management to adopt policies that enhance shareholder value. But, as long as both classes of shares have identical cash-flow rights, all shareholders benefit equally from such changes. So here is the question: If everyone gains equally from better management, why do shares with superior voting power typically sell at a premium? The only plausible reason is that there are private benefits captured by the owners of these shares. For example, a holder of a block of voting shares might be able to obtain a seat on the board of directors or access to perquisites provided by the company. (How about a ride to Bermuda on the corporate jet?) The shares might have extra bargaining power in an acquisition. Or they might be held by another company, which could use its voting power and influence to secure a business advantage.

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The value of voting rights

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These private benefits of control seem to be much larger in some countries than others. For example, Tatiana Nenova has looked at a number of countries in which firms may have two classes of stock.¹¹ In the United States the premium that an investor needed to pay to gain voting control amounted to only 2% of firm value, but in Italy it was over 29% and in Mexico it was 36%. It appears that in these two countries majority investors are able to secure large private benefits. The nearby Finance in the News box describes a major dispute in Switzerland over the value of superior voting rights.

Even when only one class of shares exists, minority stockholders may be at a disadvantage; the company’s cash flow and potential value may be diverted to management or to one or a few dominant stockholders holding large blocks of shares. In the U.S., the law protects minority stockholders from exploitation, but minority stockholders in other countries do not always fare so well.¹²

Financial economists sometimes refer to the exploitation of minority shareholders as tunneling; the majority shareholder tunnels into the firm and acquires control of the assets for himself. Let us look at tunneling Russian-style.

EXAMPLE 14.1 • Raiding the Minority Shareholders

To grasp how the scam works, you first need to understand reverse stock splits. These are often used by companies with a large number of low-priced shares. The company making the reverse split simply combines its existing shares into a smaller, more convenient number of new shares. For example, the shareholders might be given two new shares in place of the three shares that they currently own. As long as all shareholdings are reduced by the same proportion, nobody gains or loses by such a move.

However, the majority shareholder of one Russian company realized that the reverse stock split could be used to loot the company’s assets. He therefore proposed that existing shareholders receive 1 new share in place of every 136,000 shares they currently held.¹³

Why did the majority shareholder pick the number “136,000”? Answer: Because the two minority shareholders owned less than 136,000 shares and therefore did not have the right to any shares. Instead they were simply paid off with the par value of their shares and the majority shareholder was left owning the entire company. The majority shareholders of several other companies were so impressed with this device that they also proposed similar reverse stock splits to squeeze out their minority shareholders.

Such blatant exploitation would not be permitted in the U.S. or many other countries.

Equity in Disguise

Common stocks are issued by corporations, but a few equity securities are issued not by corporations but by partnerships or trusts. We will give some brief examples.

Partnerships Plains All American Pipeline LP is a master limited partnership that owns crude oil pipelines in the United States and Canada. You can buy “units” in this partnership on the New York Stock Exchange, thus becoming a limited partner in Plains All American. The most the limited partners can lose is their investment in the company.¹⁴ In this and most other respects, the partnership units are just like the shares in an ordinary corporation. They share in the profits of the business and receive cash distributions (like dividends) from time to time.

Partnerships avoid corporate income tax; any profits or losses are passed straight through to the partners’ tax returns. But various limitations offset this tax advantage. For example, the law regards a partnership merely as a voluntary association of individuals; like its partners, it is expected to have a limited life. A corporation, on the other hand, is an independent legal “person” that can, and often does, outlive all its original shareholders.

Trusts and REITs Would you like to own a part of the oil in the Prudhoe Bay field on the north slope of Alaska? Just call your broker and buy a few units of the Prudhoe Bay Royalty Trust. BP set up this trust and gave it a royalty interest in production from BP’s share of the Prudhoe Bay revenues. As the oil is produced, each trust unit gets its share of the revenues.

This trust is the passive owner of a single asset: the right to a share of the revenues from BP’s Prudhoe Bay production. Operating businesses, which cannot be passive, are rarely organized as trusts, though there are exceptions, notably real estate investment trusts, or REITs (pronounced “reets”).

REITs were created to facilitate public investment in commercial real estate; there are shopping center REITs, office building REITs, apartment REITs, and REITs that specialize in lending to real estate developers. REIT “shares” are traded just like common stocks. The REITs themselves are not taxed, so long as they distribute at least 95% of earnings to the REITs’ owners, who must pay whatever taxes are due on the dividends. However, REITs are tightly restricted to real estate investment. You cannot set up a widget factory and avoid corporate taxes by calling it a REIT.

Preferred Stock

Usually when investors talk about “stock” or “equity,” they are referring to common stock. But some companies also issue preferred stock, and this too forms part of its equity. Despite its name, preferred stock provides only a small part of most companies’ cash needs, and it will occupy less time in later chapters. However, it can be a useful method of financing in mergers and certain other special situations.

Like debt, preferred stock offers a series of fixed payments to the investor. The company can choose not to pay a preferred dividend, but in that case it may not pay a dividend to its common stockholders. Most issues of preferred are known as cumulative preferred stock. This means that the firm must pay all past preferred dividends before common stockholders get a cent. If the company does miss a preferred dividend, the preferred stockholders generally gain some voting rights, so that the common stockholders are obliged to share control of the company with the preferred holders. Directors are also aware that failure to pay the preferred dividend earns the company a black mark with investors, so they do not take such a decision lightly.

 14-3   Debt

When companies borrow money, they promise to make regular interest payments and to repay the principal. However, this liability is limited. Stockholders have the right to default on the debt if they are willing to hand over the corporation’s assets to the lenders. Clearly, they will choose to do this only if the value of the assets is less than the amount of the debt.¹⁵

Debt has first claim on cash flows, but its claim is limited. Therefore, in contrast to equity, it does not have residual cash-flow rights and does not participate in the upsides of the business. Also, unlike equity, debt offers no control rights unless the firm defaults or violates debt covenants. Because lenders are not considered to be owners of the firm, they do not normally have any voting power.

The company’s payments of interest are regarded as a cost and are deducted from taxable income. Thus interest is paid from before-tax income, whereas dividends on common and preferred stock are paid from after-tax income. Therefore the government provides a tax subsidy for debt that it does not provide for equity. We discuss debt and taxes in detail in Chapter 18.

We have seen that financial institutions own the majority of corporate equity. Figure 14.4 shows that this is also true of the company’s bonds. In this case it is the insurance companies that own the largest stake.¹⁶

Debt Comes in Many Forms

The financial manager is faced with an almost bewildering choice of debt securities. In Chapter 24 we look in some detail at the different types of corporate debt. For the moment, simply notice that the mixture of debt securities that each company issues reflects the financial manager’s response to a number of questions:

1.  Should the company borrow short-term or long-term? If your company simply needs to finance a temporary increase in inventories ahead of the holiday season, then it may make sense to take out a short-term bank loan. But suppose that the cash is needed to pay for expansion of an oil refinery. Refinery facilities can operate more or less continuously for 15 or 20 years. In that case it would be more appropriate to issue a long-term bond.¹⁷

Some loans are repaid in a steady, regular way; in other cases, the entire loan is repaid at maturity. Occasionally either the borrower or the lender has the option to terminate the loan early and to demand that it be repaid immediately.

   FIGURE 14.4 Holdings of bonds issued in the U.S. by U.S. and foreign corporations, third quarter, 2011.

Source: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts Table L.212 at www.federalreserve.gov/releases/z1/current/data.htm.

2.  Should the debt be fixed or floating rate? The interest payment, or coupon, on long-term bonds is commonly fixed at the time of issue. If a $1,000 bond is issued when long-term interest rates are 10%, the firm continues to pay $100 per year regardless of how interest rates fluctuate.

Most bank loans and some bonds offer a variable, or floating, rate. For example, the interest rate in each period may be set at 1% above LIBOR (London Interbank Offered Rate), which is the interest rate at which major international banks lend dollars to each other. When LIBOR changes, the interest rate on the loan also changes.

3.  Should you borrow dollars or some other currency? Many firms in the U.S. borrow abroad. Often they may borrow dollars abroad (foreign investors have large holdings of dollars), but firms with overseas operations may decide to issue debt in a foreign currency. After all, if you need to spend foreign currency, it probably makes sense to borrow foreign currency.

Because these international bonds have usually been marketed by the London branches of international banks, they have traditionally been known as eurobonds and the debt is called eurocurrency debt. A eurobond may be denominated in dollars, yen, or any other currency. Unfortunately, when the single European currency was established, it was called the euro. It is, therefore, easy to confuse a eurobond (a bond that is sold internationally) with a bond that is denominated in euros.

4.  What promises should you make to the lender? Lenders want to make sure that their debt is as safe as possible. Therefore, they may demand that their debt is senior to other debt. If default occurs, senior debt is first in line to be repaid. The junior, or subordinated, debtholders are paid only after all senior debtholders are satisfied (though all debtholders rank ahead of the preferred and common stockholders).

The firm may also set aside some of its assets specifically for the protection of particular creditors. Such debt is said to be secured, and the assets that are set aside are known as collateral. Thus a retailer might offer inventory or accounts receivable as collateral for a bank loan. If the retailer defaults on the loan, the bank can seize the collateral and use it to help pay off the debt.

Usually the firm also provides assurances to the lender that it will not take unreasonable risks. For example, a firm that borrows in moderation is less likely to get into difficulties than one that is up to its gunwales in debt. So the borrower may agree to limit the amount of extra debt that it can issue. Lenders are also concerned that, if trouble occurs, others will push ahead of them in the queue. Therefore, the firm may agree not to create new debt that is senior to existing debtholders or to put aside assets for other lenders.

5.  Should you issue straight or convertible bonds? Companies often issue securities that give the owner an option to convert them into other securities. These options may have a substantial effect on value. The most dramatic example is provided by a warrant, which is nothing but an option. The owner of a warrant can purchase a set number of the company’s shares at a set price before a set date. Warrants and bonds are often sold together as a package.

A convertible bond gives its owner the option to exchange the bond for a predetermined number of shares. The convertible bondholder hopes that the issuing company’s share price will zoom up so that the bond can be converted at a big profit. But if the shares zoom down, there is no obligation to convert; the bondholder remains a bondholder.

A Debt by Any Other Name

The word debt sounds straightforward, but companies make a number of promises that look suspiciously like debt but are treated differently in the accounts. Some of these disguised debts are easily spotted. For example, accounts payable are simply obligations to pay for goods that have already been delivered and are therefore like short-term debt.

Other arrangements are less obvious. For example, instead of borrowing to buy new equipment, the company may rent or lease it on a long-term basis. In this case, the firm promises to make a series of lease payments to the owner of the equipment. This is just like the obligation to make payments on an outstanding loan. If the firm gets into deep water, it can’t choose to miss out on its debt interest, and it can’t choose to skip those lease payments.

Here is another example of a disguised debt. When American Airlines filed for bankruptcy in 2011, it had promised its employees pensions valued at $18.5 billion. However, AMR had set aside only $8.3 billion to help meet this obligation. The unfunded obligation amounted to $10.2 billion. This $10.2 billion was a senior debt of the corporation.

There is nothing underhanded about any of these obligations. They are all clearly shown on the balance sheet or explained in the notes to the accounts. Sometimes, however, companies go to considerable lengths to ensure that investors do not know how much the companies have borrowed. For example, Enron was able to borrow $658 million by setting up special-purpose entities (SPEs), which raised cash by a mixture of equity and debt and then used these debts to help fund the parent company. None of this debt showed up on Enron’s balance sheet.

Variety’s the Very Spice of Life

We have indicated several dimensions along which corporate securities can be classified. That gives the financial manager plenty of choice in designing securities. As long as you can convince investors of its attractions, you can issue a convertible, subordinated, floating-rate bond denominated in Swedish kronor. Rather than combining features of existing securities, you may create an entirely new one. We can imagine a coal mining company issuing convertible bonds on which the payment fluctuates with coal prices. We know of no such security, but it is perfectly legal to issue it—and who knows?—it might generate considerable interest among investors.

It does help to remember that equity is a residual claim that participates in the upsides and downsides of the business after debt claims are satisfied. Equity has residual cash-flow rights and residual control rights. Debt has first claim on cash flows, but its claim is limited. It does not participate in the upsides of the business. Debt has no control rights unless the firm defaults or violates debt covenants.

That completes our tour of corporate securities. You may feel like the tourist who has just seen 12 cathedrals in five days. But there will be plenty of time in later chapters for reflection and analysis. It is now time to move on and to look at the markets in which the firm’s securities are traded and at the financial institutions that hold them.

 14-4   Financial Markets and Institutions

The flow of savings to large public corporations is shown in Figure 14.5. Notice that the savings flow from investors worldwide through financial markets, financial intermediaries, or both. Suppose, for example, that Bank of America raises $300 million by a new issue of shares. An Italian investor buys 6,000 of the new shares for $10 per share. Now Bank of America takes that $60,000, along with money raised by the rest of the issue, and makes a $300 million loan to Exxon Mobil. The Italian investor’s savings end up flowing through financial markets (the stock market), to a financial intermediary (Bank of America), and finally to Exxon.

Of course our Italian friend’s $60,000 doesn’t literally arrive at Exxon in an envelope marked “From L. DaVinci.” Investments by the purchasers of the Bank of America’s stock issue are pooled, not segregated. Sr. DaVinci would own a share of all of Bank of America’s assets, not just one loan to Exxon. Nevertheless, investors’ savings are flowing through the financial markets and then the bank to finance Exxon’s capital investments.

Suppose that another investor decides to open a checking account with Bank of America. The bank can take the money in this checking account and also lend it on to Exxon Mobil. In this case, the savings bypass the financial markets and flow directly to a financial intermediary and from there to Exxon.

We now need to flesh out Figure 14.5 by looking at the main financial markets and intermediaries.

Financial Markets

A financial market is a market where financial assets are issued and traded. In our example, Bank of America used the financial markets to raise money from investors by a new issue of shares. Such issues are known as primary issues. But in addition to helping companies to raise cash, financial markets also allow investors to trade stocks or bonds among themselves. For example, Mr. Rosencrantz might decide to raise some cash by selling his Bank of America stock at the same time that Mr. Guildenstern invests his savings in the stock. So they make a trade. The result is simply a transfer of ownership from one person to another, which has no effect on the company’s cash, assets, or operations. Such purchases and sales are known as secondary transactions.

   FIGURE 14.5 Flow of savings to investment for a large, public corporation. Savings come from investors worldwide. The savings may flow through financial markets or financial intermediaries. The corporation also reinvests on shareholders’ behalf.

Some financial assets have less active secondary markets than others. For example, when a bank lends money to a company, it acquires a financial asset (the company’s promise to repay the loan with interest). Banks do sometimes sell packages of these loans to other banks, but generally they retain the loan until it is repaid by the borrower. Other financial assets are regularly traded. Some, such as shares of stock, are traded on organized exchanges like the New York, London, or Hong Kong stock exchanges. In other cases there is no organized exchange, and the assets are traded by a network of dealers. Such markets are known as over-the-counter (OTC) markets. For example, in the United States most government and corporate bonds are traded OTC.

Some financial markets are not used to raise cash but instead help firms to manage their risks. In these markets firms can buy or sell derivatives, whose payoffs depend on the prices of other securities or commodities. For example, if a chocolate producer is worried about rising cocoa prices, it can use the derivatives markets to fix the price at which it buys its future cocoa requirements.

Financial Intermediaries

A financial intermediary is an organization that raises money from investors and provides financing for individuals, companies, and other organizations. Banks, insurance companies, and investment funds are all intermediaries. These intermediaries are important sources of financing for corporations. They are a stop on the road between savings and real investment.

Why is a financial intermediary different from a manufacturing corporation? First, it may raise money in different ways, for example, by taking deposits or selling insurance policies. Second, it invests that money in financial assets, for example, in stocks, bonds, or loans to businesses or individuals. In contrast, a manufacturing company’s main investments are in plant, equipment, or other real assets.

Look at Table 14.2, which shows the financial assets of the different types of intermediaries in the United States. It gives you an idea of the relative importance of different intermediaries. Of course, these assets are not all invested in nonfinancial businesses. For example, banks make loans to individuals as well as to businesses.¹⁸

Investment Funds

We look first at investment funds, such as mutual funds, hedge funds, and pension funds. Mutual funds raise money by selling shares to investors. This money is then pooled and invested in a portfolio of securities.¹⁹ Investors in a mutual fund can increase their stake in the fund’s portfolio by buying additional shares, or they can sell their shares back to the fund if they wish to cash out. The purchase and sale prices depend on the fund’s net asset value (NAV) on the day of purchase or redemption. If there is a net flow of cash into the fund, the manager will use it to buy more stocks or bonds; if there is a net outflow, the fund manager will need to raise the money by selling some of the fund’s investments.

   TABLE 14.2 Financial assets of intermediaries in the United States, third quarter, 2011.

a Total assets of 225 largest U.S. hedge funds, 2011.

Sources: Board of Governors of the Federal Reserve System, Division of Research and Statistics, Flow of Funds Accounts (www.federalreserve.gov); and K. D. Allen, “Billion Dollar Club,” Absolute Return Magazine, March 2, 2011, p. 20. Used with permission of Institutional Investor, Inc., www.iijournals.com. All Rights Reserved.

There are 7,600 mutual funds in the United States. In fact there are more mutual funds than public companies! The funds pursue a wide variety of investment strategies. Some funds specialize in safe stocks with generous dividend payouts. Some specialize in high-tech growth stocks. Some “balanced” funds offer mixtures of stocks and bonds. Some specialize in particular countries or regions. For example, the Fidelity Investments mutual fund group sponsors funds for Canada, Japan, China, Europe, and Latin America.

Mutual funds offer investors low-cost diversification and professional management. For most investors, it’s more efficient to buy a mutual fund than to assemble a diversified portfolio of stocks and bonds. Mutual fund managers also try their best to “beat the market,” that is, to generate superior performance by finding the stocks with better-than-average returns. Whether they can pick winners consistently is another question, which we addressed in Chapter 13. In exchange for their services, the fund’s managers take out a management fee. There are also the expenses of running the fund. For mutual funds that invest in stocks, fees and expenses typically add up to nearly 1% per year.

Most mutual funds invest in shares or in a mixture of shares and bonds. However, one particular type of mutual fund, called a money-market fund, invests only in short-term safe securities, such as Treasury bills or bank certificates of deposit. Money-market funds offer individuals and small- and medium-sized businesses a convenient home in which to park their spare cash. There are about 1,000 money-market funds in the United States. Some of these funds are huge. For example, the JP Morgan Prime Money Market Fund has over $100 billion in assets.

Mutual funds are open-end funds—they stand ready to issue new shares and to buy back existing shares. In contrast, a closed-end fund has a fixed number of shares that are traded on an exchange. If you want to invest in a closed-end fund, you cannot buy new shares from the fund; you must buy existing shares from another stockholder in the fund.

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Exchange traded funds

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If you simply want low-cost diversification, one option is to buy a mutual fund that invests in all the stocks in a stock market index. For example, the Vanguard Index Fund holds all the stocks in the Standard & Poor’s Composite Index. An alternative is to invest in an exchange traded fund, or ETF, which is a portfolio of stocks that can be bought or sold in a single trade. These include Standard & Poor’s Depository Receipts (SPDRs, or “spiders”), which are portfolios matching Standard & Poor’s stock market indexes. You can also buy DIAMONDS, which track the Dow Jones Industrial Average; QUBES or QQQs, which track the Nasdaq 100 index; and Vanguard ETFs that track the Vanguard Total Stock Market index, which is a basket of almost all of the stocks traded in the United States. You can also buy ETFs that track foreign stock markets, bonds, or commodities.

ETFs are in some ways more efficient than mutual funds. To buy or sell an ETF, you simply make a trade, just as if you bought or sold shares of stock. In this respect ETFs are like closed-end investment funds. But, with rare exceptions, ETFs do not have managers with the discretion to try to “pick winners.” ETF portfolios are tied down to indexes or fixed baskets of securities. ETF issuers make sure that the ETF price tracks the price of the underlying index or basket.

Like mutual funds, hedge funds also pool the savings of different investors and invest on their behalf. But they differ from mutual funds in at least two ways. First, because hedge funds usually follow complex investment strategies, access is restricted to knowledgeable investors such as pension funds, endowment funds, and wealthy individuals. Don’t try to send a check for $3,000 or $5,000 to a hedge fund; most hedge funds are not in the “retail” investment business. Second, hedge funds are generally established as limited partnerships. The investment manager is the general partner and the investors are the limited partners. Third, hedge funds try to attract the most talented managers by compensating them with potentially lucrative, performance-related fees.²⁰ In contrast, mutual funds usually charge a fixed percentage of assets under management.

Hedge funds follow many different investment strategies. Some try to make a profit by identifying overvalued stocks or markets that they then sell short. Some hedge funds take bets on firms involved in merger negotiations, others look for mispricing of convertible bonds, and some take positions in currencies and interest rates. “Vulture funds” specialize in the securities of distressed corporations. Hedge funds manage less money than mutual funds, but they sometimes take very big positions and have a large impact on the market.

There are other ways to pool and invest savings. Consider a pension plan set up by a corporation or other organization on behalf of its employees. The most common type of plan is the defined-contribution plan. In this case, a percentage of the employee’s monthly paycheck is contributed to a pension fund. (The employer and employee may each contribute 5%, for example.) Contributions from all participating employees are pooled and invested in securities or mutual funds. (Usually the employees can choose from a menu of funds with different investment strategies.) Each employee’s balance in the plan grows over the years as contributions continue and investment income accumulates. The balance in the plan can be used to finance living expenses after retirement. The amount available for retirement depends on the accumulated contributions and on the rate of return earned on the investments.²¹

Pension funds are designed for long-run investment. They provide professional management and diversification. They also have an important tax advantage: Contributions are tax-deductible, and investment returns inside the plan are not taxed until cash is finally withdrawn.²²

All these investment funds provide a stop on the road from savings to corporate investment. For example, suppose your mutual fund purchases part of that new issue of shares by Bank of America. The orange arrows show the flow of savings to investment:

Financial Institutions

Banks and insurance companies are financial institutions.²³ A financial institution is an intermediary that does more than just pool and invest savings. Institutions raise financing in special ways, for example, by accepting deposits or selling insurance policies, and they provide additional financial services. Unlike most investment funds, they not only invest in securities but also lend money directly to individuals, businesses, or other organizations.

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World bank rankings

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Commercial Banks There are nearly 7,000 commercial banks in the United States. They vary from giants such as JPMorgan Chase with $1.7 trillion of assets to dwarves like Tightwad Bank in Reading, Kansas, with some $20 million.

Commercial banks are major sources of loans for corporations. (In the United States, they are generally not allowed to make equity investments in corporations, although banks in most other countries can do so.) Suppose that a local forest products company negotiates a nine-month bank loan for $2.5 million. The flow of savings is

The bank provides debt financing for the company and, at the same time, provides a place for depositors to park their money safely and withdraw it as needed.

We will have plenty more to say about bank loans in Chapter 24.

Investment Banks We have discussed commercial banks, which raise money from depositors and other investors and then make loans to businesses and individuals. Investment banks are different.²⁴ Investment banks do not take deposits, and they do not usually make loans to companies. Instead, they advise and assist companies in raising financing. For example, investment banks underwrite stock offerings by purchasing the new shares from the issuing company at a negotiated price and reselling the shares to investors. Thus the issuing company gets a fixed price for the new shares, and the investment bank takes responsibility for distributing the shares to thousands of investors. We discuss share issues in more detail in Chapter 15.

Investment banks also advise on takeovers, mergers, and acquisitions. They offer investment advice and manage investment portfolios for individual and institutional investors. They run trading desks for foreign exchange, commodities, bonds, options, and derivatives.

Investment banks can invest their own money in start-ups and other ventures. For example, the Australian Macquarie Bank has invested in airports, toll highways, electric transmission and generation, and other infrastructure projects around the world.

The largest investment banks are financial powerhouses. They include Goldman Sachs, Morgan Stanley, Lazard, Nomura (Japan), and Macquarie Bank.²⁵ In addition, the major commercial banks, including Bank of America and Citigroup, all have investment banking operations.²⁶

Insurance Companies Insurance companies are more important than banks for the long-term financing of business. They are massive investors in corporate stocks and bonds, and they often make long-term loans directly to corporations.

Suppose a company needs a loan of $2.5 million for nine years, not nine months. It could issue a bond directly to investors, or it could negotiate a nine-year loan with an insurance company:

The money to make the loan comes mainly from the sale of insurance policies. Say you buy a fire insurance policy on your home. You pay cash to the insurance company and get a financial asset (the policy) in exchange. You receive no interest payments on this financial asset, but if a fire does strike, the company is obliged to cover the damages up to the policy limit. This is the return on your investment. (Of course, a fire is a sad and dangerous event that you hope to avoid. But if a fire does occur, you are better off getting a return on your investment in insurance than not having insurance at all.)

The company will issue not just one policy but thousands. Normally the incidence of fires “averages out,” leaving the company with a predictable obligation to its policyholders as a group. Of course the insurance company must charge enough for its policies to cover selling and administrative costs, pay policyholders’ claims, and generate a profit for its stockholders.

 14-5   The Role of Financial Markets and Intermediaries

Financial markets and intermediaries provide financing for business. They channel savings to real investment. That much should be loud and clear. But other functions may not be quite so obvious. Financial intermediaries contribute in many ways to our individual well-being and the smooth functioning of the economy. Here are some examples.

The Payment Mechanism

Think how inconvenient life would be if all payments had to be made in cash. Fortunately, checking accounts, credit cards, and electronic transfers allow individuals and firms to send and receive payments quickly and safely over long distances. Banks are the obvious providers of payments services, but they are not alone. For example, if you buy shares in a money-market mutual fund, your money is pooled with that of other investors and is used to buy safe, short-term securities. You can then write checks on this mutual fund investment, just as if you had a bank deposit.

Borrowing and Lending

Financial institutions do not lend only to companies. They also channel savings toward those who can best use them. Thus, if Ms. Jones has more money than she needs now and wishes to save for a rainy day, she can put the money in a bank savings deposit. If Mr. Smith wants to buy a car now and pay for it later, he can borrow money from the bank. In other words, banks provide Jones and Smith with a time machine that allows them to transport their wealth backward and forward over time. Both are happier than if they were forced to spend cash as it arrived.

As we saw in Chapter 1, when individuals have access to borrowing and lending, companies do not have to worry that shareholders may have different time preferences. Companies can simply focus on maximizing firm value and investors can choose separately when they want to spend their wealth.

In principle, you don’t need financial institutions to provide borrowing and lending. Individuals with cash surpluses could take out newspaper advertisements or surf the net looking for those with cash shortages. But it can be cheaper and more convenient to use a financial intermediary, such as a bank, to link up the borrower and lender. For example, banks are equipped to check out the would-be borrower’s creditworthiness and to monitor the use of cash lent out. Would you lend money to a stranger contacted over the Internet? You would be safer lending the money to the bank and letting the bank decide what to do with it.

Notice that banks promise their checking account customers instant access to their money and at the same time make long-term loans to companies and individuals. This mismatch between the liquidity of the bank’s liabilities (the deposits) and most of its assets (the loans) is possible only because the number of depositors is sufficiently large that the bank can be fairly sure that they will not all want to withdraw their money simultaneously.

Pooling Risk

Financial markets and institutions allow firms and individuals to pool their risks. For instance, insurance companies make it possible to share the risk of an automobile accident or a household fire. Here is another example. Suppose that you have only a small sum to invest. You could buy the stock of a single company, but then you would be wiped out if that company went belly-up. It is generally better to buy shares in a mutual fund that invests in a diversified portfolio of common stocks or other securities. In this case you are exposed only to the risk that security prices as a whole will fall.

Information Provided by Financial Markets

In well-functioning financial markets, you can see what securities and commodities are worth, and you can see—or at least estimate—the rates of return that investors can expect on their savings. The information financial markets provide is often essential to a financial manager’s job. Consider these scenarios.

In December, Catalytic Concepts, a manufacturer of catalytic converters, is planning production for the next July. The converters include platinum, which is traded on the New York Mercantile Exchange. How much per ounce should the company budget for purchases of platinum in July? Easy: The company’s CFO looks up the market price of platinum on the New York Mercantile Exchange—$1,567 per ounce for delivery in July (this was the closing price for platinum in December 2011, for delivery the following July). The CFO can lock in that price if she wishes. We explain how in Chapter 26.

Now suppose the CFO of Catalytic Concepts needs to raise $400 million in new financing. She considers an issue of 30-year bonds. If the company’s bonds are rated Baa, what interest rate will it have to pay on the new issue? The CFO sees that existing Baa bonds yield 5.15%. The company should be able to sell its new bonds at a similar rate.

Finally, stock prices and company values summarize investors’ collective assessment of how well a company is doing, both its current performance and its future prospects. Thus an increase in stock price sends a positive signal from investors to managers.²⁷ That is why top management’s compensation is linked to stock prices. A manager who owns shares in his or her company will be motivated to increase the company’s market value. This reduces agency costs by aligning the interests of managers and stockholders. This is one important advantage of going public. A private company can’t use its stock price as a measure of performance. It can still compensate managers with shares, but the shares will not be valued in a financial market.

The basic functions of financial markets are the same the world over. So it is not surprising that similar institutions have emerged to perform these functions. In almost every country you will find banks accepting deposits, making loans, and looking after the payments system. You will also encounter insurance companies offering life insurance and protection against accident. If the country is relatively prosperous, other institutions, such as pension funds and mutual funds, will also have been established to help manage people’s savings. Of course there are differences in institutional structure. Take banks, for example. In many countries where securities markets are relatively undeveloped, banks play a much more dominant role in financing industry. Often the banks undertake a wider range of activities than they do in the United States. For example, they may take large equity stakes in industrial companies; this would not generally be allowed in the United States.

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Time line of the financial crisis

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The Financial Crisis of 2007–2009

The financial crisis of 2007–2009 raised many questions, but it settled one question conclusively: Financial markets and institutions are important. When financial markets and institutions ceased to operate properly, the world was pushed deeper into a global recession.

The financial crisis had its roots in the easy-money policies that were pursued by the U.S. Federal Reserve and other central banks following the collapse of the Internet and telecom stock bubble in 2000. At the same time, large balance-of-payments surpluses in Asian economies were invested back into U.S. debt securities. This also helped to push down interest rates and contribute to the lax credit.

Banks took advantage of this cheap money to expand the supply of subprime mortgages to low-income borrowers. Many banks tempted would-be homeowners with low initial payments, offset by significantly higher payments later.²⁸ (Some home buyers were betting on escalating housing prices so that they could resell or refinance before the higher payments kicked in.) One lender is even said to have advertised what it dubbed its “NINJA” loan—NINJA standing for “No Income, No Job, and No Assets.”

Most subprime mortgages were then packaged together into mortgage-backed securities that could be resold. But, instead of selling these securities to investors who could best bear the risk, many banks kept large quantities of the loans on their own books or sold them to other banks.

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U.S. house prices

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The widespread availability of mortgage finance fueled a dramatic increase in house prices, which doubled in the five years ending June 2006. At that point prices started to slide and homeowners began to default on their mortgages. A year later Bear Stearns, a large investment bank, announced huge losses on the mortgage investments that were held in two of its hedge funds. By the spring of 2008 Bear Stearns was on the verge of bankruptcy, and the U.S. Federal Reserve arranged for it to be acquired by JPMorgan Chase.

The crisis peaked in September 2008, when the U.S. government was obliged to take over the giant federal mortgage agencies Fannie Mae and Freddie Mac, both of which had invested several hundred billion dollars in subprime mortgage-backed securities. Over the next few days the financial system started to melt down. Both Merrill Lynch and Lehman Brothers were in danger of failing. On September 14, the government arranged for Bank of America to take over Merrill in return for financial guarantees. However, it did nothing to rescue Lehman Brothers, which filed for bankruptcy protection the next day. Two days later the government reluctantly lent $85 billion to the giant insurance company AIG, which had insured huge volumes of mortgage-backed securities and other bonds against default. The following day, the Treasury unveiled its first proposal to spend $700 billion to purchase “toxic” mortgage-backed securities.

As the crisis unfolded throughout 2007 and 2008, uncertainty about which domino would be next to fall made banks reluctant to lend to one another, and the interest rate that they charged for such loans rose to 4.6% above the rate on U.S. Treasury debt. (Normally this spread above Treasuries is less than .5%.) The bond market and the market for short-term company borrowing effectively dried up. This had an immediate knock-on effect on the supply of credit to industry, and the economy suffered one of its worst setbacks since the Great Depression.

Few developed economies escaped the crisis. As well as suffering from a collapse in their own housing markets, many foreign banks had made large investments in U.S. subprime mortgages. A roll call of all the banks that had to be bailed out by their governments would fill several pages, but here are just a few members of that unhappy band: the Royal Bank of Scotland in the United Kingdom, UBS in Switzerland, Allied Irish Bank in Ireland, Fortis in Belgium, ING in Holland, Hypo Group in Austria, and West Lb in Germany.

Who was responsible for the financial crisis? In part, the U.S. Federal Reserve for its policy of easy money. The U.S. government also must take some of the blame for encouraging banks to expand credit for low-income housing. The rating agencies were at fault for providing triple-A ratings for many mortgage bonds that shortly afterward went into default. Last but not least, the bankers themselves were guilty of promoting and reselling the subprime mortgages.

The banking crisis and subsequent recession left many governments with huge mountains of debt. By 2010 investors were becoming increasingly concerned about the position of Greece, where for many years government spending had been running well ahead of revenues. Greece’s position was complicated by its membership in the single-currency euro club. Although much of the country’s borrowing was in euros, the government had no control over its currency and could not simply print more euros to service its debt. Investors began to contemplate the likelihood of a Greek government default and the country’s possible exit from the eurozone. The failure of eurozone governments to deal decisively with the Greek problem prompted investors to worry about the prospects for other heavily indebted eurozone countries, such as Ireland, Portugal, Italy, and Spain.

At least with hindsight, we can see that the run-up to the financial crisis saw plenty of examples of foolishness and greed. Three years later, revulsion at these excesses was still evident in the tents of the Occupy Wall Street protesters. But the lesson of the financial crisis is not that we don’t need a financial system; it is that we need it to work honestly and well.

Financial markets in the U.S. and most developed countries work well most of the time, but just like the little girl in the poem, “when they are good, they are very good indeed, but when they are bad, they are horrid.” During the financial crisis markets were very horrid indeed. Think of some of the problems that you would have faced as a financial manager:

•  Many of the world’s largest banks teetered on the edge or had to be rescued, so that there were few, or no, safe havens for cash.

•  Stock and bond prices bounced around like Tigger on stimulants.

•  Periodically, markets for some types of security dried up altogether, making it tough to raise cash.

•  In the eurozone investors could not even be confident that governments would be able to service their bonds or retain the euro as their currency.

•  From the peak in 2006 manufacturing profits fell away sharply and the number of business bankruptcies tripled.

It must have seemed to financial managers as if they were being assailed from all sides.

We hope that these years were just a very unfortunate blip, and that the world has not become permanently more complex and risky.

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SUMMARY

Financial managers are faced with two broad financing decisions:

1.  How much of internally generated cash flow should be plowed back into the business? How much should be paid out to shareholders by cash dividends or share repurchases?

2.  To what extent should the firm use debt rather than equity financing?

The answers to these questions depend on the firm’s payout policy and debt policy.

Figure 14.1 summarizes how U.S. corporations raise and spend money. Have another look at it and try to get a feel for the numbers. Notice that internally generated cash is the major source of financing for investment. Borrowing is also significant. Net equity issues have been negative, however—that is, share repurchases have been larger than share issues.

Common stock is the simplest form of finance. The common stockholders own the corporation. They get all of the cash flow and assets that are left over after the firm’s debts have been paid. Common stock is therefore a residual claim that participates in the upsides and downsides of the business. Debt has first claim on cash flows, but its claim is limited. Debt has no control rights unless the firm defaults or violates debt covenants.

Preferred stock is another form of equity financing. Preferreds promise a fixed dividend, but if the board of directors decides to skip the dividend, holders of the preferred have no recourse. The firm must pay the preferred dividends before it pays any dividends on common stock, however.

Debt is the most important source of external financing. Holders of bonds and other corporate debt are promised interest payments and return of principal. If the company cannot make these payments, the debt investors can sue for payment or force bankruptcy. Bankruptcy usually means that the debtholders take over and either sell the company’s assets or continue to operate them under new management.

Note that the tax authorities treat interest payments as a cost and therefore the company can deduct interest when calculating its taxable income. Interest is paid from pretax income, whereas dividends and retained earnings come from after-tax income. That is one reason why preferred stock is a less important source of financing than debt. Preferred dividends are not tax-deductible.

Book debt ratios in the United States have generally increased over the post–World War II period. However, they are not appreciably higher than the ratios in the other major industrialized countries.

The variety of debt instruments is almost endless. The instruments differ by maturity, interest rate (fixed or floating), currency, seniority, security, and whether the debt can be converted into equity.

The majority of the firm’s debt and equity is owned by financial institutions—notably banks, insurance companies, pension funds, and mutual funds. They finance much of corporate investment, as well as investment in real estate and other assets. They run the payments mechanism, help individuals diversify and manage their portfolios, and help companies manage risk. The crisis of 2007–2009 and its aftermath dramatized the crucial role that these institutions play.

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FURTHER READING

A useful article for comparing financial structure in the United States and other major industrial countries is:

R. G. Rajan and L. Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data,” Journal of Finance 50 (December 1995), pp. 1421–1460.

For a discussion of the allocation of control rights and cash-flow rights between stockholders and debt holders, see:

O. Hart, Firms, Contracts, and Financial Structure (Oxford: Oxford University Press, 1995).

Robert Merton gives an excellent overview of the functions of financial institutions in:

R. Merton, “A Functional Perspective of Financial Intermediation,” Financial Management 24 (Summer 1995), 23–41.

The Winter 2009 issue of the Journal of Financial Perspectives contains several articles on the crisis of 2007–2009. See also:

V. V. Acharya and M. W. Richardson, eds., Restoring Financial Stability (Hoboken, NJ: John Wiley & Sons, 2009).

The following works cover financial crises more generally:

F. Allen and E. Carletti, “An Overview of the Crisis: Causes, Consequences and Solutions,” International Review of Finance 10 (March 2010), pp. 1–27.

F. Allen and D. Gale, Understanding Financial Crises (Oxford: Oxford University Press, 2007).

C. M. Reinhart and K. Rogoff, “The Aftermath of Financial Crises,” American Economic Review 99 (May 2009), pp. 466–472.

C. M. Reinhart and K. Rogoff, This Time Is Different: Eight Centuries of Financial Folly (Princeton: Princeton University Press, 2009).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Sources of funds True or false?

a.  Net stock issues by U.S. nonfinancial corporations are in most years small but positive.

b.  Most capital investment by U.S. companies is funded by retained earnings and reinvested depreciation.

c.  Debt ratios in the U.S. have generally increased over the past 50 years.

2.  Majority voting There are 10 directors to be elected. A shareholder owns 80 shares. What is the maximum number of votes that he or she can cast for a favorite candidate under (a) majority voting? (b) cumulative voting?

3.  Terminology Fill in the blanks, using the following terms: floating rate, common stock, convertible, subordinated, preferred stock, senior, warrant.

a.  If a lender ranks behind the firm’s general creditors in the event of default, his or her loan is said to be _______ .

b.  Interest on many bank loans is based on a _______ of interest.

c.  A(n) _______ bond can be exchanged for shares of the issuing corporation.

d.  A(n) _______ gives its owner the right to buy shares in the issuing company at a predetermined price.

e.  Dividends on _______ cannot be paid unless the firm has also paid any dividends on its _______ .

4.  True/false True or false?

a.  In the United States, most common shares are owned by individual investors.

b.  An insurance company is a financial intermediary.

c.  Investments in partnerships cannot be publicly traded.

INTERMEDIATE

5.  Voting rights Suppose that East Corporation has issued voting and nonvoting stock. Investors hope that holders of the voting stock will use their power to vote out the company’s incompetent management. Would you expect the voting stock to sell for a higher price? Explain.

6.  Tax In 2011 Beta Corporation earned gross profits of $760,000.

a.  Suppose that it is financed by a combination of common stock and $1 million of debt. The interest rate on the debt is 10%, and the corporate tax rate is 35%. How much profit is available for common stockholders after payment of interest and corporate taxes?

b.  Now suppose that instead of issuing debt Beta is financed by a combination of common stock and $1 million of preferred stock. The dividend yield on the preferred is 8% and the corporate tax rate is still 35%. How much profit is now available for common stockholders after payment of preferred dividends and corporate taxes?

7.  Corporate debt Which of the following features would increase the value of a corporate bond? Which would reduce its value?

a.  The borrower has the option to repay the loan before maturity.

b.  The bond is convertible into shares.

c.  The bond is secured by a mortgage on real estate.

d.  The bond is subordinated.

8.  The financial crisis Construct a time line of the important events in the financial crisis that started in the summer of 2007. When do you think the crisis ended? You will probably want to review some of the entries under Further Reading before you answer.

9.  The financial crisis We mention several causes of the financial crisis. What other causes can you identify? You will probably want to review some of the entries under Further Reading before you answer.

CHALLENGE

10.  Majority voting The shareholders of the Pickwick Paper Company need to elect five directors. There are 200,000 shares outstanding. How many shares do you need to own to ensure that you can elect at least one director if (a) the company has majority voting? (b) it has cumulative voting?

11.  Ownership concentration Read the two articles cited in footnote 7 on p. 352. Is ownership in the U.S. really different than in other countries? If so, in what ways? Discuss.

12.  Financial crises Take a look at the book This Time is Different: Eight Centuries of Financial Folly (see Further Reading). Review the “Big Five” crises (starting dates in parentheses): Spain (1977), Norway (1987), Finland (1991), Sweden (1991) and Japan (1992). What were the chief differences between the Big Five and the financial crisis of 2007–2009? Discuss.

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FINANCE ON THE WEB

1.  Use data from finance.yahoo.com to work out the financing proportions given in Figure 14.1 for a particular industrial company for some recent year.

2.  The website www.federalreserve.gov/releases/z1/current/default.htm provides data on sources of funds and an aggregate balance sheet for nonfarm nonfinancial corporations. Look at Table F.102 for the latest year. What proportion of the cash that companies needed was generated internally and how much had to be raised on the financial markets? Is this the usual pattern? Now look at “new equity issues.” Were companies on average issuing new equity or buying their shares back?

3.  An aggregate balance sheet for U.S. manufacturing corporations can be found on www.census.gov/econ/qfr. Find the balance sheet for the latest year. What was the ratio of long-term debt to long-term debt plus equity? What about the ratio of all long-term liabilities to long-term liabilities plus equity?

___________

¹In Figure 14.1, internally generated cash was calculated by adding depreciation to retained earnings. Depreciation is a noncash expense. Thus, retained earnings understate the cash flow available for reinvestment.

²Managers do have insiders’ insights and naturally are tempted to issue stock when the price looks good to them, that is, when they are less optimistic than outside investors. The outside investors realize this and will buy a new issue only at a discount from the preannouncement price. More on stock issues in Chapter 15.

³This debt ratio may be understated, because “Other long-term liabilities” probably include some debt-equivalent claims. We will not pause to sort through these other liabilities, however.

⁴Figure 14.3 does not show U.S. holdings of overseas shares. These amount to 17.4% of the total equity holdings of U.S. investors.

⁵Theoretical economists therefore stress the importance of incomplete contracts. Their point is that contracts pertaining to the management of the firm must be incomplete and that someone must exercise residual rights of control. See, for example, O. Hart, Firms, Contracts, and Financial Structure (Oxford: Oxford University Press, 1995).

⁶Of course, the bank manager may suggest that a particular decision is unwise, or even threaten to cut off future lending, but the bank does not have any right to make these decisions.

⁷See R. La Porta, F. Lopez-de-Silanes, and A. Shleifer, “Corporate Ownership around the World,” Journal of Finance 54 (1999), pp. 471–517; and C. Holderness, “The Myth of Diffuse Ownership in the United States,” Review of Financial Studies 22 (April 2009), pp. 1377–1408.

⁸O. Faleye, “Classified Boards, Firm Value, and Managerial Entrenchment,” Journal of Financial Economics 83 (2007), pp. 501–529.

⁹For example, suppose there are five directors to be elected and you own 100 shares. You therefore have a total of 5 × 100 = 500 votes. Under the majority voting system, you can cast a maximum of 100 votes for any one candidate. Under a cumulative voting system, you can cast all 500 votes for your favorite candidate.

¹⁰In 2010 the SEC proposed Rule 14a-11 that would allow shareholders to add their nominations for the board to the company’s proxy material. This was successfully challenged in the courts. However, an SEC rule that allows shareholders to add proposals to change the bylaws was not overturned.

¹¹T. Nenova, “The Value of Corporate Voting Rights and Control: A Cross-Country Analysis,” Journal of Financial Economics 68 (June 2003) pp. 325–352.

¹²International differences in the opportunities for dominant shareholders to exploit their position are discussed in S. Johnson et al., “Tunnelling,” American Economic Review 90 (May 2000), pp. 22–27.

¹³Since a reverse stock split required only the approval of a simple majority of the shareholders, the proposal was voted through.

¹⁴A partnership can offer limited liability only to its limited partners. The partnership must also have one or more general partners, who have unlimited liability. However, general partners can be corporations. This puts the corporation’s shield of limited liability between the partnership and the human beings who ultimately own the general partner.

¹⁵In practice this handover of assets is far from straightforward. Sometimes thousands of lenders have different claims on the firm. Administration of the handover is usually left to the bankruptcy court (see Chapter 32).

¹⁶Figure 14.4 does not include shorter-term debt such as bank loans. Almost all short-term debt issued by corporations is held by financial institutions.

¹⁷A company might choose to finance a long-term project with short-term debt if it wished to signal its confidence in the future. Investors would deduce that, if the company anticipated declining profits, it would not take the risk of being unable to take out a fresh loan when the first one matured. See D. Diamond, “Debt Maturity Structure and Liquidity Risk,” Quarterly Journal of Economics 106 (1991), pp. 709–737.

¹⁸Intermediaries often invest in each other also. For instance, an investor might buy shares in a mutual fund that then invests in Bank of America’s new share issue. If the money then finds its way from Bank of America to Exxon, it would show up as a financial asset of both Bank of America (its loan to Exxon) and the mutual fund (its shareholding in Bank of America).

¹⁹Mutual funds are not corporations but investment companies. They pay no tax, providing that all income from dividends and price appreciation is passed on to the funds’ shareholders. The shareholders pay personal tax on this income.

²⁰Sometimes these fees can be very large indeed. For example, The Wall Street Journal estimated that hedge fund manager John Paulson earned $1 billion in fees in 2010.

²¹In a defined-benefit plan, the employer promises a certain level of retirement benefits (set by a formula) and the employer invests in the pension plan. The plan’s accumulated investment value has to be large enough to cover the promised benefits. If not, the employer must put in more money. Defined-benefit plans are gradually giving way to defined-contribution plans.

²²Defined-benefit pension plans share these same advantages, except that the employer invests rather than the employees. In a defined-benefit plan, the advantage of tax deferral on investment income accrues to the employer. This deferral reduces the cost of funding the plan.

²³We may be drawing too fine a distinction between financial intermediaries and institutions. A mutual fund could be considered a financial institution. But “financial institution” usually suggests a more complicated intermediary, such as a bank.

²⁴Banks that accept deposits and provide financing to businesses are called commercial banks. Savings banks accept deposits and savings accounts and loan the money out mostly to individuals, for example, as mortgage loans to home buyers. Investment banks do not take deposits and do not loan money to businesses or individuals, except as bridge loans made as temporary financing for takeovers or other transactions.

²⁵Strictly speaking, Goldman Sachs and Morgan Stanley are not investment banks. In 2008 they handed in their investment banking charter in exchange for a banking charter that allows them to accept deposits. However, their principal focus is on investment banking activities.

²⁶Bank of America owns Merrill Lynch, one of the largest investment banks. Merrill was rescued by Bank of America in 2009 after making huge losses from mortgage-related investments.

²⁷We can’t claim that investors’ assessments of value are always correct. Finance can be a risky and dangerous business—dangerous for your wealth, that is. With hindsight we see horrible mistakes by investors—for example, the gross overvaluation of Internet and telecom companies in 2000. On average, however, it appears that financial markets collect and assess information quickly and accurately. We’ll discuss this issue again in the next chapter.

²⁸With a so-called option ARM loan, the minimum mortgage payment was often not even sufficient to cover that month’s interest on the loan. The unpaid interest was then added to the amount of the mortgage, so the homeowner was burdened by an ever-increasing mortgage that one day would need to be paid off.

Part 4 Financing Decisions and Market Efficiency

How Corporations Issue Securities

In Chapter 11 we encountered Marvin Enterprises, one of the most remarkable growth companies of the twenty-first century. It was founded by George and Mildred Marvin, two high-school dropouts, together with their chum Charles P. (Chip) Norton. To get the company off the ground the three entrepreneurs relied on their own savings together with personal loans from a bank. However, the company’s rapid growth meant that they had soon borrowed to the hilt and needed more equity capital. Equity investment in young private companies is generally known as venture capital. Such venture capital may be provided by investment institutions or by wealthy individuals who are prepared to back an untried company in return for a piece of the action. In the first part of this chapter we will explain how companies like Marvin go about raising venture capital.

Venture capital organizations aim to help growing firms over that awkward adolescent period before they are large enough to go public. For a successful firm such as Marvin, there is likely to come a time when it needs to tap a wider source of capital and therefore decides to make its first public issue of common stock. The next section of the chapter describes what is involved in such an issue in the United States. We explain the process for registering the offering with the Securities and Exchange Commission and we introduce you to the underwriters who buy the issue and resell it to the public. We also see that new issues are generally sold below the price at which they subsequently trade. To understand why that is so, we need to make a brief sortie into the field of auction procedures.

A company’s first issue of stock is seldom its last. In Chapter 14 we saw that corporations face a persistent financial deficit, which they meet by selling securities. We therefore look at how established corporations go about raising more capital. In the process we encounter another puzzle: When companies announce a new issue of stock, the stock price generally falls. We suggest that the explanation lies in the information that investors read into the announcement.

If a stock or bond is sold publicly, it can then be traded on the securities markets. But sometimes investors intend to hold on to their securities and are not concerned about whether they can sell them. In these cases there is little advantage to a public issue, and the firm may prefer to place the securities directly with one or two financial institutions. At the end of this chapter we explain how companies arrange a private placement.

 15-1   Venture Capital

On April 1, 2025, George and Mildred Marvin met with Chip Norton in their research lab (which also doubled as a bicycle shed) to celebrate the incorporation of Marvin Enterprises. The three entrepreneurs had raised $100,000 from savings and personal bank loans and had purchased one million shares in the new company. At this zero-stage investment, the company’s assets were $90,000 in the bank ($10,000 had been spent for legal and other expenses of setting up the company), plus the idea for a new product, the household gargle blaster. George Marvin was the first to see that the gargle blaster, up to that point an expensive curiosity, could be commercially produced using microgenetic refenestrators.

Marvin Enterprises’ bank account steadily drained away as design and testing proceeded. Local banks did not see Marvin’s idea as adequate collateral, so a transfusion of equity capital was clearly needed. Preparation of a business plan was a necessary first step. The plan was a confidential document describing the proposed product, its potential market, the underlying technology, and the resources (time, money, employees, and plant and equipment) needed for success.

Most entrepreneurs are able to spin a plausible yarn about their company. But it is as hard to convince a venture capitalist that your business plan is sound as to get a first novel published. Marvin’s managers were able to point to the fact that they were prepared to put their money where their mouths were. Not only had they staked all their savings in the company but they were mortgaged to the hilt. This signaled their faith in the business.

First Meriam Venture Partners was impressed with Marvin’s presentation and agreed to buy one million new shares for $1 each. After this first-stage financing, the company’s market-value balance sheet looked like this:

By agreeing to pay $1 a share for Marvin’s stock, First Meriam placed a value of $1 million on the entrepreneurs’ original shareholdings. This was First Meriam’s estimate of the value of the entrepreneurs’ original idea and their commitment to the enterprise. If the estimate was right, the entrepreneurs could congratulate themselves on a $900,000 paper gain over their original $100,000 investment. In exchange, the entrepreneurs gave up half their company and accepted First Meriam’s representatives to the board of directors.¹

The success of a new business depends critically on the effort put in by the managers. Therefore venture capital firms try to structure a deal so that management has a strong incentive to work hard. That takes us back to Chapters 1 and 12, where we showed how the shareholders of a firm (who are the principals) need to provide incentives for the managers (who are their agents) to work to maximize firm value.

If Marvin’s management had demanded watertight employment contracts and fat salaries, they would not have found it easy to raise venture capital. Instead the Marvin team agreed to put up with modest salaries. They could cash in only from appreciation of their stock. If Marvin failed they would get nothing, because First Meriam actually bought preferred stock designed to convert automatically into common stock when and if Marvin Enterprises succeeded in an initial public offering or consistently generated more than a target level of earnings. But if Marvin Enterprises had failed, First Meriam would have been first in line to claim any salvageable assets. This raised even further the stakes for the company’s management.²

Venture capitalists rarely give a young company up front all the money it will need. At each stage they give enough to reach the next major checkpoint. Thus in spring 2027, having designed and tested a prototype, Marvin Enterprises was back asking for more money for pilot production and test marketing. Its second-stage financing was $4 million, of which $1.5 million came from First Meriam, its original backers, and $2.5 million came from two other venture capital partnerships and wealthy individual investors. The balance sheet just after the second stage was as follows:

Now the after-the-money valuation was $14 million. First Meriam marked up its original investment to $5 million, and the founders noted an additional $4 million paper gain.

Does this begin to sound like a (paper) money machine? It was so only with hindsight. At stage 1 it wasn’t clear whether Marvin would ever get to stage 2; if the prototype hadn’t worked, First Meriam could have refused to put up more funds and effectively closed down the business.³ Or it could have advanced stage 2 money in a smaller amount on less favorable terms. The board of directors could also have fired George, Mildred, and Chip and gotten someone else to try to develop the business.

In Chapter 14 we pointed out that stockholders and lenders differ in their cash-flow rights and control rights. The stockholders are entitled to whatever cash flows remain after paying off the other security holders. They also have control over how the company uses its money, and it is only if the company defaults that the lenders can step in and take control of the company. When a new business raises venture capital, these cash-flow rights and control rights are usually negotiated separately. The venture capital firm will want a say in how that business is run and will demand representation on the board and a significant number of votes. The venture capitalist may agree that it will relinquish some of these rights if the business subsequently performs well. However, if performance turns out to be poor, the venture capitalist may automatically get a greater say in how the business is run and whether the existing management should be replaced.

For Marvin, fortunately, everything went like clockwork. Third-stage mezzanine financing was arranged,⁴ full-scale production began on schedule, and gargle blasters were acclaimed by music critics worldwide. Marvin Enterprises went public on February 3, 2031. Once its shares were traded, the paper gains earned by First Meriam and the company’s founders turned into fungible wealth. Before we go on to this initial public offering, let us look briefly at the venture capital markets today.

The Venture Capital Market

Most new companies rely initially on family funds and bank loans. Some of them continue to grow with the aid of equity investment provided by wealthy individuals known as angel investors. However, like Marvin, many adolescent companies raise capital from specialist venture-capital firms, which pool funds from a variety of investors, seek out fledgling companies to invest in, and then work with these companies as they try to grow. In addition, some large technology firms, such as Intel and Johnson & Johnson, act as corporate venturers by providing equity capital to new innovative companies.

   FIGURE 15.1 Venture capital investment in the United States

Source: Thomson Reuters data in MoneyTree Report, Q2 2011, PricewaterhouseCoopers, National Venture Capital Association.

Figure 15.1 shows the changing level of venture capital investment. During the giddy days of 2000 funds invested more than $100 billion, but since the end of the dot.com boom, venture capital investment has slumped to $20 to $30 billion a year.

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U.S. venture capital investment

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Most venture capital funds are organized as limited private partnerships with a fixed life of about 10 years. Pension funds and other investors are the limited partners. The management company, which is the general partner, is responsible for making and overseeing the investments, and in return receives a fixed fee and a share of the profits, called the carried interest.⁵ You will find that these venture capital partnerships are often lumped together with similar partnerships that provide funds for companies in distress or that buy out whole companies or divisions of public companies and then take them private. The general term for these activities is private equity investing.

Venture capital firms are not passive investors. They tend to specialize in young high-tech firms that are difficult to evaluate and they monitor these firms closely. They also provide ongoing advice to the firms that they invest in and often play a major role in recruiting the senior management team. Their judgment and contacts can be valuable to a business in its early years and can help the firm to bring its products more quickly to market.⁶

Venture capitalists may cash in on their investment in two ways. Once the new business has established a track record, it may be sold out to a larger firm. However, many entrepreneurs do not fit easily into a corporate bureaucracy and would prefer instead to remain the boss. In this case, the company may decide, like Marvin, to go public and so provide the original backers with an opportunity to “cash out,” selling their stock and leaving the original entrepreneurs in control. A thriving venture capital market therefore needs an active stock exchange, such as Nasdaq, that specializes in trading the shares of young, rapidly growing firms.⁷

During the late 1990s the venture capital market in Europe was helped by the formation of new European stock exchanges that modeled themselves on Nasdaq and specialized in trading the stocks of young fast-growing firms. In three years the Neuer Markt exchange in Frankfurt listed over 300 new companies, more than half of which were backed by venture capital firms. But then the exchange was hit by scandal as one high-tech firm, Comroad, revealed that most of its claimed $94 million of revenue was fictitious. As the dot.com boom fizzled out, stock prices on the Neuer Markt fell by 95% and the exchange was finally closed down.

Very few new businesses make it big, but venture capitalists keep sane by forgetting about the many failures and reminding themselves of the success stories—the investors who got in on the ground floor of firms like Federal Express, Genentech, and Intel. For every 10 first-stage venture capital investments, only two or three may survive as successful, self-sufficient businesses. From these statistics come two rules for success in venture capital investment. First, don’t shy away from uncertainty; accept a low probability of success. But don’t buy into a business unless you can see the chance of a big, public company in a profitable market. There’s no sense taking a long shot unless it pays off handsomely if you win. Second, cut your losses; identify losers early, and if you can’t fix the problem—by replacing management, for example—throw no good money after bad.

How successful is venture capital investment? Since you can’t look up the value of new start-up businesses in The Wall Street Journal, it is difficult to say with confidence. However, The National Venture Capital Association, which tracks the performance of a large sample of venture capital funds, calculated that in the 25 years to the end of 2010 investors in these funds would have earned an average annual return of 19% after expenses.⁸ That is 10% more a year than they would have earned from investing in the stocks of large public corporations. We do not know whether this compensates for the extra risks of investing in venture capital.

 15-2   The Initial Public Offering

There comes a stage in the life of many young companies when they decide to make an initial public offering of stock, or IPO. This may be a primary offering, in which new shares are sold to raise additional cash for the company. Or it may be a secondary offering, where the existing shareholders decide to cash in by selling part of their holdings.

Secondary offerings are not confined to small, immature businesses. For example, in 1998 Du Pont sold off a large part of its holding in Conoco for $4.4 billion. The biggest secondary offerings occur when governments sell their shareholdings in companies. For example, the 1985 initial offering by the Japanese government of a 12.5% stake in NTT brought in $15 billion. In 2010, the U.S. Treasury raised $20 billion by selling its holdings of General Motors common and preferred stock. Even these two issues were dwarfed first by the 2006 IPO of the state-owned Industrial and Commercial Bank of China, which raised $22 billion, and then by the $70 billion raised by the Brazilian state-owned oil company Petrobras in 2010.

We have seen that companies may make an IPO to raise new capital or to enable shareholders to cash out, but, as you can see from Figure 15.2, there may be other benefits to going public. For example, the company’s stock price provides a readily available yardstick of performance, and allows the firm to reward the management team with stock options. And, because information about the company becomes more widely available, the company can diversify its sources of finance and reduce its borrowing cost.

While there are advantages to having a market for your shares, we should not give the impression that firms everywhere aim to go public. In many countries it is common for large businesses to remain privately owned. For example, Italy has only about a tenth as many listed companies as the UK although the economies are roughly similar in size.

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The largest U.S. private companies

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Even in the United States many businesses choose to remain as private, unlisted companies. They include some very large operations, such as Bechtel, Cargill, and Levi Strauss. Also you should not think of the issue process in the United States as a one-way street; public firms often go into reverse and return to being privately owned. For a somewhat extreme example, consider the food service company, Aramark. It began life in 1936 as a private company and went public in 1960. In 1984 a management buyout led to the company going private and it remained private until 2001, when it had its second public offering. But the experiment did not last long, for five years later Aramark was once again the object of a buyout that took the company private again.

   FIGURE 15.2 Survey evidence on the motives for going public.

Source: J. C. Brau and S. E. Fawcett, “Evidence on What CFOs Think about the IPO Process: Practice, Theory and Managerial Implications,”Journal of Applied Corporate Finance 18 (October 2006), pp. 107–117. Used with permission of John Wiley and Sons, via Copyright Clearance Center.

Managers often chafe at the red tape involved in running a public company and at the costs of communicating with shareholders. These complaints have become more vocal since the passage of the Sarbanes-Oxley Act. This act sought to prevent a repeat of the corporate scandals that brought about the collapse of Enron and WorldCom, but a consequence has been an increased reporting burden on small public companies and an apparent increase in their readiness to go private.⁹

Arranging an Initial Public Offering

Let us now look at how Marvin arranged to go public. By 2031 the company had grown to the point at which it needed still more capital to implement its second-generation production technology. At the same time the company’s founders were looking to sell some of their shares.¹⁰ In the previous few months there had been a spate of IPOs by high-tech companies and the shares had generally sold like hotcakes. So Marvin’s management hoped that investors would be equally keen to buy the company’s stock.

FINANCE IN PRACTICE

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Where Business Angels Fear to Tread

   European governments have always looked enviously at the U.S. venture capital market and its ability to spawn businesses such as Apple and Microsoft. Europe’s failure to produce such success stories has been attributed to an “equity gap” that reflects a shortage of capital provided for promising new and adolescent ventures. So, while the amount of new venture capital funding declined from €8.2 billion in 2007 to €4.8 billion in 2011, the proportion contributed by government agencies rose from 7% to 34% of the total.¹

One approach is for a government to invest in privately managed funds. For example, the European Investment Fund, which is largely owned by the European Commission and the European Investment Bank, invests in a wide range funds that provide capital to small and medium enterprises (SMEs). Other public bodies finance SMEs directly. For example, Germany’s High-Tech Gründerfonds are public/private partnerships whose shareholders include the Federal Ministry of Economics and Technology and major industrial groups.

There is a bewildering variety of public venture capital funds in Europe. For example, the following table lists just some of the public bodies in the UK that have been set up by the government to invest in emerging businesses.

_______________

¹European Venture Capital Association, 2012 Yearbook.

Management’s first task was to select the underwriters. Underwriters act as financial midwives to a new issue. Usually they play a triple role: First they provide the company with procedural and financial advice, then they buy the issue, and finally they resell it to the public.

After some discussion Marvin settled on Klein Merrick as the managing underwriter and Goldman Stanley as the co-manager. Klein Merrick then formed a syndicate of underwriters who would buy the entire issue and reoffer it to the public.

In choosing Klein Merrick to manage its IPO, Marvin was influenced by Merrick’s proposals for making an active market in the stock in the weeks after the issue.¹¹ Merrick also planned to generate continuing investor interest in the stock by distributing a major research report on Marvin’s prospects.¹² Marvin hoped that this report would encourage investors to hold its stock.

Together with Klein Merrick and firms of lawyers and accountants, Marvin prepared a registration statement for the approval of the Securities and Exchange Commission (SEC).¹³ This statement is a detailed and somewhat cumbersome document that presents information about the proposed financing and the firm’s history, existing business, and plans for the future.

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LinkedIn’s IPO prospectus

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The most important sections of the registration statement are distributed to investors in the form of a prospectus. In the appendix to this chapter we have reproduced the prospectus for Marvin’s first public issue of stock. Real prospectuses would go into much more detail on each topic, but this example should give you some feel for the mixture of valuable information and redundant qualification that characterizes these documents. The Marvin prospectus also illustrates how the SEC insists that investors’ eyes are opened to the dangers of purchase (see “Certain Considerations” in the prospectus). Some investors have joked that if they read each prospectus carefully, they would not dare buy any new issue.

In addition to registering the issue with the SEC, Marvin needed to check that the issue complied with the so-called blue-sky laws of each state that regulate sales of securities within the state.¹⁴ It also arranged for its newly issued shares to be traded on the Nasdaq exchange.

The Sale of Marvin Stock

While the registration statement was awaiting approval, Marvin and its underwriters began to firm up the issue price. First they looked at the price–earnings ratios of the shares of Marvin’s principal competitors. Then they worked through a number of discounted-cash-flow calculations like the ones we described in Chapters 4 and 11. Most of the evidence pointed to a market price in the region of $74 to $76 a share and the company therefore included this provisional figure in the preliminary version of the prospectus.¹⁵

Marvin and Klein Merrick arranged a road show to talk to potential investors. Mostly these were institutional investors, such as managers of mutual funds and pension funds. The investors gave their reactions to the issue and indicated to the underwriters how much stock they wished to buy. Some stated the maximum price that they were prepared to pay, but others said that they just wanted to invest so many dollars in Marvin at whatever issue price was chosen. These discussions with fund managers allowed Klein Merrick to build up a book of potential orders.¹⁶ Although the managers were not bound by their responses, they knew that, if they wanted to keep in the underwriters’ good books, they should be careful not to go back on their expressions of interest. The underwriters also were not obliged to treat all investors equally. Some investors who were keen to buy Marvin stock were disappointed in the allotment that they subsequently received.

Immediately after it received clearance from the SEC, Marvin and the underwriters met to fix the issue price. Investors had been enthusiastic about the story that the company had to tell and it was clear that they were prepared to pay more than $76 for the stock. Marvin’s managers were tempted to go for the highest possible price, but the underwriters were more cautious. Not only would they be left with any unsold stock if they overestimated investor demand, but they also argued that some degree of underpricing was needed to tempt investors to buy the stock. Marvin and the underwriters therefore compromised on an issue price of $80. Potential investors were encouraged by the fact that the offer price was higher than the $74 to $76 proposed in the preliminary prospectus and decided that the underwriters must have encountered considerable enthusiasm for the issue.

Although Marvin’s underwriters were committed to buy only 900,000 shares from the company, they chose to sell 1,035,000 shares to investors. This left the underwriters short of 135,000 shares or 15% of the issue. If Marvin’s stock had proved unpopular with investors and traded below the issue price, the underwriters could have bought back these shares in the marketplace. This would have helped to stabilize the price and would have given the underwriters a profit on these extra shares that they sold. As it turned out, investors fell over themselves to buy Marvin stock and by the end of the first day the stock was trading at $105. The underwriters would have incurred a heavy loss if they had been obliged to buy back the shares at $105. However, Marvin had provided underwriters with a greenshoe option that allowed them to buy an additional 135,000 shares from the company. This ensured that the underwriters were able to sell the extra shares to investors without fear of loss.

The Underwriters

Marvin’s underwriters were prepared to enter into a firm commitment to buy the stock and then offer it to the public. Thus they took the risk that the issue might flop and they would be left with unwanted stock. Occasionally, where the sale of common stock is regarded as particularly risky, the underwriters may be prepared to handle the sale only on a best-efforts basis. In this case the underwriters promise to sell as much of the issue as possible but do not guarantee to sell the entire amount.¹⁷

Successful underwriting requires financial muscle and considerable experience. The names of Marvin’s underwriters are of course fictitious, but Table 15.1 shows that underwriting is dominated by the major investment banks and large commercial banks. Foreign players are also heavily involved in underwriting securities that are sold internationally.

Underwriting is not always fun. In April 2008 the British bank, HBOS, offered its shareholders two new shares at a price of £2.75 for each five shares that they currently held.¹⁸ The underwriters to the issue, Morgan Stanley and Dresdner Kleinwort, guaranteed that at the end of eight weeks they would buy any new shares that the stockholders did not want. At the time of the offer HBOS shares were priced at about £5, so the underwriters felt confident that they would not have to honor their pledge. Unfortunately, they reckoned without the turbulent market in bank shares that year. The bank’s shareholders worried that the money they were asked to provide would largely go to bailing out the bondholders and depositors. By the end of the eight weeks the price of HBOS stock had slumped below the issue price, and the underwriters were left with 932 million unwanted shares worth £3.6 billion.

Companies get to make only one IPO, but underwriters are in the business all the time. Wise underwriters, therefore, realize that their reputation is on the line and will not handle an issue unless they believe the facts have been presented fairly to investors. So, when a new issue goes wrong, the underwriters may be blamed for overhyping the issue and failing in their “due diligence.” For example, in December 1999 the software company Va Linux went public at $30 a share. The next day trading opened at $299 a share, but then the price began to sag. Within two years it had fallen below $2. Disgruntled Va Linux investors sued the underwriters, complaining that the prospectus was “materially false.” These underwriters had plenty of company, for following the collapse of the dot.com stocks in 2000, investors in many other high-tech IPOs sued the underwriters. There was further embarrassment when it emerged that several well-known underwriters had engaged in “spinning”—that is, allocating stock in popular new issues to managers of their important corporate clients. The underwriter’s seal of approval for a new issue no longer seemed as valuable as it once had.

   TABLE 15.1 The top managing underwriters, 2011. Values include global debt and equity issues.

Source: Thomson Reuters (www.thomsonreuters.com). © 2011 Thomson Reuters.

Costs of a New Issue

We have described Marvin’s underwriters as filling a triple role—providing advice, buying the new issue, and reselling it to the public. In return they received payment in the form of a spread; that is, they were allowed to buy the shares for less than the offering price at which the shares were sold to investors.¹⁹ Klein Merrick as syndicate manager kept 20% of this spread. A further 25% of the spread was used to pay those underwriters who bought the issue. The remaining 55% went to the firms that provided the sales force.

The underwriting spread on the Marvin issue amounted to 7% of the total sum raised from investors. Since many of the costs incurred by underwriters are fixed, you would expect that the percentage spread would decline with issue size. This in part is what we find. For example, a $5 million IPO might carry a spread of 10%, while the spread on a $300 million issue might be only 5%. However, Chen and Ritter found that for almost every IPO between $20 and $80 million the spread was exactly 7%.²⁰ Since it is difficult to believe that there are no scale economies, this clustering at 7% is a puzzle.²¹

In addition to the underwriting fee, Marvin’s new issue entailed substantial administrative costs. Preparation of the registration statement and prospectus involved management, legal counsel, and accountants, as well as the underwriters and their advisers. In addition, the firm had to pay fees for registering the new securities, printing and mailing costs, and so on. You can see from the first page of the Marvin prospectus (see this chapter’s appendix) that these administrative costs totaled $820,000 or just over 1% of the proceeds.

Underpricing of IPOs

Marvin’s issue was costly in yet another way. Since the offering price was less than the true value of the issued securities, investors who bought the issue got a bargain at the expense of the firm’s original shareholders.

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Hot IPOs

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These costs of underpricing are hidden but nevertheless real. For IPOs they generally exceed all other issue costs. Whenever any company goes public, it is very difficult to judge how much investors will be prepared to pay for the stock. Sometimes the underwriters misjudge dramatically. For example, when the prospectus for the IPO of eBay was first published, the underwriters indicated that the company would sell 3.5 million shares at a price between $14 and $16 each. However, the enthusiasm for eBay’s web-based auction system was such that the underwriters increased the issue price to $18. The next morning dealers were flooded with orders to buy eBay; over 4.5 million shares traded and the stock closed the day at a price of $47.375.

FINANCE IN THE NEWS

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The IPO of the Industrial and Commercial Bank of China

   At the height of the 2007-2009 financial crisis, the three largest banks by market capitalization in the world were all Chinese. The banks did not suffer from financial stability problems and this helped China to come through the crisis well. In this box we focus on the IPO of the largest bank in China, Industrial and Commercial Bank of China (ICBC), to show how China liberalized their financial sector by taking a state-owned bank public and combining government and private ownership.

On 27 October 2006, ICBC was simultaneously listed on both the Hong Kong Stock Exchange (HKSE) as an H-share (global) offering in HKD and an A-share offering in RMB on the Shanghai Stock Exchange (SHSE). (Class H shares are shares of Chinese companies listed and traded on the HKSE, while Class A shares are shares issued to and traded by Chinese investors on the SHSE and the Shenzhen Stock Exchange.) The Hong Kong H-share underwriting syndicate included Merrill Lynch Far East Limited, China International Capital Corporation (CICC-Hong Kong) Limited, Credit Suisse (Hong Kong) Limited, Deutsche Bank AG (Hong Kong Branch), and ICEA Capital Limited. The Shanghai A-share underwriting syndicate included CICC, CITI Securities Co., Ltd., Guotai Junan Securities Co., Ltd., and Shenyin & Wanguo Securities Co., Ltd. As is standard in Chinese IPOs, the underwriters used a bookbuilding procedure to assess demand and set the issue price. It was the world’s largest IPO at that time, valued at US$21.9 billion. It was also the first company to be listed simultaneously on both the Hong Kong and Shanghai stock exchanges. The offering prices for H-shares and A-shares were the same taking currency conversion (RMB and HKD) into account.

The IPO raised at least US$14 billion in Hong Kong (H-shares) and another US$5.1 billion in Shanghai (A-shares). Due to heavy subscriptions, the greenshoe (i.e. over-allotment) placements were exercised, which added US$2.9 billion to the amount raised. At the end of its first day of trading, the bank’s shares closed up almost 15% at HK$3.52 in Hong Kong, compared with the listing price of HK$3.07, which was set at the top of the indicative range due to the strong demand. Meanwhile, ICBC’s Shanghai-listed A-shares recorded more modest gains and ended up 5.1% from the offering price of RMB 3.12.

We admit that the eBay issue was unusual.²² But researchers have found that investors who buy at the issue price on average realize very high returns over the following days. For example, one study of nearly 12,000 U.S. IPOs from 1960 to 2008 found average underpricing of 16.9%.²³

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Chinese IPOs

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Figure 15.3 shows that the United States is not the only country in which IPOs are underpriced. In China the gains from buying IPOs have averaged 137%.²⁴

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Facebook’s IPO

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You might think that shareholders would prefer not to sell stock in their company for less than its market price, but many investment bankers and institutional investors argue that underpricing is in the interests of the issuing firm. They say that a low offering price on an IPO raises the price when it is subsequently traded in the market and enhances the firm’s ability to raise further capital.

There is another possible reason that it may make sense to underprice new issues. Suppose that you successfully bid for a painting at an art auction. Should you be pleased? It is true that you now own the painting, which was presumably what you wanted, but everybody else at the auction apparently thought that the painting was worth less than you did. In other words, your success suggests that you may have overpaid. This problem is known as the winner’s curse. The highest bidder in an auction is most likely to have overestimated the object’s value and, unless bidders recognize this in their bids, the buyer will on average overpay. If bidders are aware of the danger, they are likely to adjust their bids down correspondingly.

   FIGURE 15.3 Average initial returns from investing in IPOs in different countries.

Source: T. Loughran, J. R. Ritter, and K. Rydqvist, “Initial Public Offerings: International Insights,” Pacific Basin Finance Journal 3, pp.139–140, extended and updated on bear.cba.ufl.edu/ritter. © 1995, with permission from Elsevier.

The same problem arises when you apply for a new issue of securities. For example, suppose that you decide to apply for every new issue of common stock. You will find that you have no difficulty in getting stock in the issues that no one else wants. But, when the issue is attractive, the underwriters will not have enough stock to go around, and you will receive less stock than you wanted. The result is that your money-making strategy may turn out to be a loser. If you are smart, you will play the game only if there is substantial underpricing on average. Here then we have a possible rationale for the underpricing of new issues. Uninformed investors who cannot distinguish which issues are attractive are exposed to the winner’s curse. Companies and their underwriters are aware of this and need to underprice on average to attract the uninformed investors.²⁵

These arguments could well justify some degree of underpricing, but it is not clear that they can account for underpricing of 100% or more. Skeptics point out that such underpricing is largely in the interests of the underwriters, who want to reduce the risk that they will be left with unwanted stock and also to court popularity by allotting stock to favored clients.

If the skeptics are right, you might expect issuing companies to rebel at being asked to sell stock for much less than it is worth. Think back to our example of eBay. If the company had sold 3.5 million shares at the market price of $47.375 rather than $18, it would have netted an additional $103 million. So why weren’t eBay’s existing shareholders hopping mad? Loughran and Ritter suggest that the explanation lies in behavioral psychology and argue that the cost of underpricing may be outweighed in shareholders’ minds by the happy surprise of finding that they are wealthier than they thought. EBay’s largest shareholder was Pierre Omidyar, the founder and chairman, who retained his entire holding of 15.2 million shares. The initial jump in the stock price from $18 to $47.375 added $447 million to Mr. Omidyar’s wealth. This may well have pushed the cost of underpricing to the back of his mind.²⁶

Hot New-Issue Periods

Figure 15.4 shows that the degree of underpricing fluctuates sharply from year to year. In 1999, around the peak of the dot.com boom, new issues raised $65 billion and the average first-day return on IPOs was 70%. Nearly $37 billion was left on the table that year. But, as the number of new issues slumped, so did the amount of underpricing. The year 2008 saw just 21 IPOs and the average first-day return was a measly 6.4%.

Some observers believe that these hot new-issue periods arise because investors are prone to periods of excessive optimism and would-be issuers time their IPOs to coincide with these periods. Other observers stress the fact that a fall in the cost of capital or an improvement in the economic outlook may mean that a number of new or dormant projects suddenly become profitable. At such times, many entrepreneurs rush to raise new cash to invest in these projects.²⁷

   FIGURE 15.4 IPO proceeds in the United States and average first-day returns, 1990–2011.

Source: J. R. Ritter, “Initial Public Offerings: Underpricing Statistics Through 2011,” May 2012, bear.cba.ufl.edu/ritter. Used with permission.

 15-3   Alternative Issue Procedures for IPOs

Table 15.2 summarizes the main steps involved in making an initial public offering of stock in the United States. You can see that Marvin’s new issue was a typical IPO in almost every respect. In particular most IPOs in the United States use the bookbuilding method in which the underwriter builds a book of likely orders and uses this information to set the issue price.

The bookbuilding method is in some ways like an auction, since potential buyers indicate how many shares they are prepared to buy at given prices. However, these indications are not binding, and are used only as a guide to fix the price of the issue. The advantage of the bookbuilding method is that it allows underwriters to give preference to those investors whose bids are most helpful in setting the issue price and to offer them a reward in the shape of underpricing.²⁸ Critics of bookbuilding point to the abuses of the 1990s, and emphasize the dangers of allowing the underwriter to decide who is allotted stock.

Bookbuilding has rapidly gained popularity throughout the world, but it is not the only way to sell new stock. One alternative is to conduct an open auction. In this case investors are invited to submit their bids, stating how many shares they wish to buy and the price. The securities are then sold to the highest bidders. Most governments, including the U.S. Treasury, sell their bonds by auction. In the United States auctions of common stock have accounted for only 1% of IPOs in the 10 years to 2009. However, in 2004, Google simultaneously raised eyebrows and $1.7 billion in the world’s largest initial public offering to be sold by auction.²⁹

Fans of auctions often point to countries such as France, Israel, and Japan, where auctions were once commonly used to sell new issues of stock. Japan is a particularly interesting case, for the bookbuilding method was widely used until it was revealed that investment banks had been allocating shares in hot IPOs to government officials. In 1989 the finance ministry responded to this scandal by ruling that in the future all IPOs were to be auctioned. This resulted in a sharp fall in underpricing. However, in 1997 the restrictions were lifted, bookbuilding returned to favor, and the level of underpricing increased.³⁰

Types of Auction: A Digression

Suppose that a government wishes to auction four million bonds and three would-be buyers submit bids. Investor A bids $1,020 each for one million bonds, B bids $1,000 for three million bonds, and C bids $980 for two million bonds. The bids of the two highest bidders (A and B) absorb all the bonds on offer and C is left empty-handed. What price do the winning bidders, A and B, pay?

   TABLE 15.2 The main steps involved in making an initial public offering of stock in the United States.

The answer depends on whether the sale is a discriminatory auction or a uniform-price auction. In a discriminatory auction every winner is required to pay the price that he or she bid. In this case A would pay $1,020 and B would pay $1,000. In a uniform-price auction both would pay $1,000, which is the price of the lowest winning bidder (investor B).

It might seem from our example that the proceeds from a uniform-price auction would be lower than from a discriminatory auction. But this ignores the fact that the uniform-price auction provides better protection against the winner’s curse. Wise bidders know that there is little cost to overbidding in a uniform-price auction, but there is potentially a very high cost to doing so in a discriminatory auction.³¹ Economists therefore often argue that the uniform-price auction should result in higher proceeds.³²

Sales of bonds by the U.S. Treasury used to take the form of discriminatory auctions so that successful buyers paid their bid. However, in 1998 the government switched to a uniform-price auction.³³

 15-4   Security Sales by Public Companies

A company’s first public issue of stock is seldom its last. As the firm grows, it is likely to make further issues of debt and equity. Public companies can issue securities either by offering them to investors at large or by making a rights issue that is limited to existing stockholders. We begin by describing general cash offers, which are now used for almost all debt and equity issues in the United States. We then describe rights issues, which are widely used in other countries for issues of common stock.

General Cash Offers

When a corporation makes a general cash offer of debt or equity in the United States, it goes through much the same procedure as when it first went public. In other words, it registers the issue with the SEC³⁴ and then sells the securities to an underwriter (or a syndicate of underwriters), who in turn offers the securities to the public. Before the price of the issue is fixed the underwriter will build up a book of likely demand for the securities, just as in the case of Marvin’s IPO.

The SEC’s Rule 415 allows large companies to file a single registration statement covering financing plans for up to three years into the future. The actual issues can then be done with scant additional paperwork, whenever the firm needs the cash or thinks it can issue securities at an attractive price. This is called shelf registration—the registration statement is “put on the shelf,” to be taken down and used as needed.

Think of how you as a financial manager might use shelf registration. Suppose your company is likely to need up to $200 million of new long-term debt over the next year or so. It can file a registration statement for that amount. It then has prior approval to issue up to $200 million of debt, but it isn’t obligated to issue a penny. Nor is it required to work through any particular underwriters; the registration statement may name one or more underwriters the firm thinks it may work with, but others can be substituted later.

Now you can sit back and issue debt as needed, in bits and pieces if you like. Suppose Morgan Stanley comes across an insurance company with $10 million ready to invest in corporate bonds. Your phone rings. It’s Morgan Stanley offering to buy $10 million of your bonds, priced to yield, say, 8.5%. If you think that’s a good price, you say OK and the deal is done, subject only to a little additional paperwork. Morgan Stanley then resells the bonds to the insurance company, it hopes at a higher price than it paid for them, thus earning an intermediary’s profit.

Here is another possible deal: Suppose that you perceive a window of opportunity in which interest rates are temporarily low. You invite bids for $100 million of bonds. Some bids may come from large investment banks acting alone; others may come from ad hoc syndicates. But that’s not your problem; if the price is right, you just take the best deal offered.³⁵

Not all companies eligible for shelf registration actually use it for all their public issues. Sometimes they believe they can get a better deal by making one large issue through traditional channels, especially when the security to be issued has some unusual feature or when the firm believes that it needs the investment banker’s counsel or stamp of approval on the issue. Consequently, shelf registration is less often used for issues of common stock or convertible securities than for garden-variety corporate bonds.

International Security Issues

Instead of borrowing in their local market, companies often issue bonds in another country’s domestic market, in which case the issue will be governed by the rules of that country.

A second alternative is to make an issue of eurobonds, which is underwritten by a group of international banks and offered simultaneously to investors in a number of countries. The borrower must provide a prospectus or offering circular that sets out the detailed terms of the issue. The underwriters will then build up a book of potential orders, and finally the issue will be priced and sold. Very large debt issues may be sold as global bonds, with one part sold internationally in the eurobond market and the remainder sold in the company’s domestic market.

Equity issues too may be sold overseas. In fact some companies’ stocks do not trade at all in their home country. For example, in 2009 Changyou.com, the Chinese online game company, raised $120 million by an IPO in the United States. Its stock was not traded in China. Presumably, the company thought it could get a better price and more active follow-on trading by listing overseas.

Traditionally New York has been the natural home for such issues, but in recent years many companies have preferred to list in London or Hong Kong. This has led many U.S. observers to worry that New York may be losing its competitive edge to other financial centers that have more flexible regulatory systems and fewer corporate lawsuits.

The Costs of a General Cash Offer

Whenever a firm makes a cash offer of securities, it incurs substantial administrative costs. Also the firm needs to compensate the underwriters by selling them securities below the price that they expect to receive from investors. Table 15.3 lists underwriting spreads for a few recent issues.

Notice that the underwriting spreads for debt securities are lower than for common stocks, less than 1% for many issues. Larger issues tend to have lower spreads than smaller issues. This may partly stem from the fact that there are fixed costs to selling securities, but large issues are generally made by large companies, which are better known and easier for the underwriter to monitor. So do not assume that a small company could make a jumbo issue at a negligible percentage spread.³⁶

   TABLE 15.3 Gross underwriting spreads of selected issues. Spreads are percentages of gross proceeds.

Figure 15.5 summarizes a study of total issue costs (spreads plus administrative costs) for several thousand issues between 2004 and 2008.

Market Reaction to Stock Issues

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Seasoned issue returns

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Economists who have studied seasoned issues of common stock have generally found that announcement of the issue results in a decline in the stock price. For industrial issues in the United States this decline amounts to 3–4%.³⁷ While this may not sound overwhelming, the fall in market value is equivalent, on average, to nearly a third of the new money raised by the issue.

What’s going on here? One view is that the price of the stock is simply depressed by the prospect of the additional supply. On the other hand, there is little sign that the extent of the price fall increases with the size of the stock issue. There is an alternative explanation that seems to fit the facts better.

Suppose that the CFO of a restaurant chain is strongly optimistic about its prospects. From her point of view, the company’s stock price is too low. Yet the company wants to issue shares to finance expansion into the new state of Northern California.³⁸ What is she to do? All the choices have drawbacks. If the chain sells common stock, it will favor new investors at the expense of old shareholders. When investors come to share the CFO’s optimism, the share price will rise, and the bargain price to the new investors will be evident.

   FIGURE 15.5 Total direct costs as a percentage of gross proceeds. The total direct costs for initial public offerings (IPOs), seasoned equity offerings (SEOs), convertible bonds, and straight bonds are composed of underwriter spreads and other direct expenses.

Source: SDC Platinum.

Notes: There were 5706 domestic issues between 2004 and 2008. Closed-end funds (SIC 6726), REITS (SIC 6798), ADRs, mortgage-backed and federal agency (SIC 6011, 6019, 6111 and 999B) issues are excluded.

If the CFO could convince investors to accept her rosy view of the future, then new shares could be sold at a fair price. But this is not so easy. CEOs and CFOs always take care to sound upbeat, so just announcing “I’m optimistic” has little effect. But supplying detailed information about business plans and profit forecasts is costly and is also of great assistance to competitors.

The CFO could scale back or delay the expansion until the company’s stock price recovers. That too is costly, but it may be rational if the stock price is severely undervalued and a stock issue is the only source of financing.

If a CFO knows that the company’s stock is overvalued, the position is reversed. If the firm sells new shares at the high price, it will help existing shareholders at the expense of the new ones. Managers might be prepared to issue stock even if the new cash is just put in the bank.

Of course, investors are not stupid. They can predict that managers are more likely to issue stock when they think it is overvalued and that optimistic managers may cancel or defer issues. Therefore, when an equity issue is announced, they mark down the price of the stock accordingly. Thus the decline in the price of the stock at the time of the new issue may have nothing to do with the increased supply but simply with the information that the issue provides.³⁹

Cornett and Tehranian devised a natural experiment that pretty much proves this point.⁴⁰ They examined a sample of stock issues by commercial banks. Some of these issues were necessary to meet capital standards set by banking regulators. The rest were ordinary, voluntary stock issues designed to raise money for various corporate purposes. The necessary issues caused a much smaller drop in stock prices than the voluntary ones, which makes perfect sense. If the issue is outside the manager’s discretion, announcement of the issue conveys no information about the manager’s view of the company’s prospects.⁴¹

Most financial economists now interpret the stock price drop on equity issue announcements as an information effect and not a result of the additional supply.⁴² But what about an issue of preferred stock or debt? Are they equally likely to provide information to investors about company prospects? A pessimistic manager might be tempted to get a debt issue out before investors become aware of the bad news, but how much profit can you make for your shareholders by selling overpriced debt? Perhaps 1% or 2%. Investors know that a pessimistic manager has a much greater incentive to issue equity rather than preferred stock or debt. Therefore, when companies announce an issue of preferred or debt, there is a barely perceptible fall in the stock price.⁴³

There is, however, at least one puzzle left. As we saw in Chapter 13, it appears that the long-run performance of companies that issue shares is substandard. Investors who bought these companies’ shares after the stock issue earned lower returns than they would have if they had bought into similar companies. This result holds for both IPOs and seasoned issues.⁴⁴ It seems that investors fail to appreciate fully the issuing companies’ information advantage. If so, we have an exception to the efficient-market theory.

Rights Issues

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Rights issues terminology

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Instead of making an issue of stock to investors at large, companies sometimes give their existing shareholders the right of first refusal. Such issues are known as privileged subscription, or rights, issues. In the United States rights issues are largely confined to closed-end investment companies. However, in Europe and Asia rights issues are common and in many countries obligatory.

We have already come across one example of a rights issue—the offer by the British bank HBOS, which ended up in the hands of its underwriters. Let us look more closely at another issue. In 2011 the Canadian company Ivanhoe Mines needed to raise C$1.2 billion to finance the development of its huge Oyu Tolgoi copper mine in Mongolia. It did so by offering its existing shareholders the right to buy 3 new shares for every 20 that they currently held. The new shares were priced at C$13.93 each, some 44% below the preannouncement price of C$24.73.

Imagine that just before the rights issue you held 20 shares of Ivanhoe valued at 20 × C$24.73 = C$494.60. Ivanhoe’s offer would give you the right to buy three new shares for an additional outlay of 3 × C$13.93 = C$41.79. If you take up the offer, your holding increases to 23 shares and the value of your investment increases by the extra cash to C$494.60 + C$41.79 = C$536.39. Therefore, after the issue, the value of each share is no longer C$24.73 but a little lower at C$536.39/23 = C$23.32. This is termed the ex-rights price.

How much is the right to buy each new share for C$13.93 worth? The answer is C$23.32 – C$13.93 = C$9.39.⁴⁵ An investor who could buy a share worth C$23.32 for C$13.93 would be willing to pay C$9.39 for the privilege.⁴⁶

It should be clear on reflection that Ivanhoe could have raised the same amount of money on a variety of terms. For example, it could have offered shareholders the right to buy 7 new shares at C$5.97 for every 20 shares that they held. In this case, a shareholder with 20 shares would end up with 27 shares worth in total 20 × C$24.73 + 7 × C$5.97 = C$536.39. The value of each share would be C$536.39/27 = C$19.87. Under this new arrangement the ex-rights share price is lower, but you end up with 27 shares rather than 23. The total value of your holding remains the same. Suppose that you wanted to sell your right to buy one new share for C$5.97. Investors would be prepared to pay you C$13.90 for this right. They would then pay C$5.97 to Ivanhoe and receive a share worth C$19.87.

Ivanhoe’s shareholders were given six weeks to decide whether they wished to take up the offer of new shares. If the stock price in the meantime fell below the issue price, shareholders would have no incentive to buy the new shares. For this reason companies making a rights issue generally arrange for the underwriters to buy any unwanted stock. Underwriters are not often left holding the baby, but we saw earlier that in the case of the HBOS issue they were left with a very large (and bouncing) baby.

Our example illustrates that, as long as the company successfully sells the new shares, the issue price in a rights offering is irrelevant. That is not the case in a general cash offer. If the company sells stock to new shareholders for less than the market will bear, the buyer makes a profit at the expense of existing shareholders. General cash offers are typically sold at a small discount of about 3% on the previous day’s closing price,⁴⁷ so underpricing is not a major worry. But, since this cost can be avoided completely by using a rights issue, we are puzzled by the apparent preference of companies for general cash offers.

 15-5   Private Placements and Public Issues

Whenever a company makes a public offering, it is obliged to register the issue with the SEC. It could avoid this costly process by selling the securities privately. The rules on what constitutes a private placement are complicated, but the SEC generally insists that the security be sold to no more than 35 knowledgeable investors.

One of the drawbacks of a private placement is that the investor cannot easily resell the security. However, institutions such as life insurance companies invest huge amounts in corporate debt for the long haul and are less concerned about its marketability. Consequently, an active private placement market has evolved for corporate debt. Often this debt is negotiated directly between the company and the lender, but, if the issue is too large to be absorbed by one institution, the company will generally employ an investment bank to draw up a prospectus and identify possible buyers.

As you would expect, it costs less to arrange a private placement than to make a public issue. This is a particular advantage for companies making smaller issues.

In 1990 the SEC adopted Rule 144A, which relaxed its restrictions on who can buy and trade unregistered securities. The rule allows large financial institutions (known as qualified institutional buyers) to trade unregistered securities among themselves. Rule 144A was intended to increase liquidity and reduce interest rates and issue costs for private placements. It was aimed largely at foreign corporations deterred by registration requirements in the United States. The SEC argued that such firms would welcome the opportunity to issue unregistered stocks and bonds that could then be freely traded by large U.S. financial institutions.

Rule 144A issues have proved very popular, particularly with foreign issuers. There has also been an increasing volume of secondary trading in Rule 144A issues.

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SUMMARY

In this chapter we have summarized the various procedures for issuing corporate securities. We first looked at how infant companies raise venture capital to carry them through to the point at which they can make their first public issue of stock. We then looked at how companies can make further public issues of securities by a general cash offer. Finally, we reviewed the procedures for a private placement.

It is always difficult to summarize a summary. Instead we will remind you of some of the most important implications for the financial manager who must decide how to raise financing.

•  Larger is cheaper. There are economies of scale in issuing securities. It is cheaper to go to the market once for $100 million than to make two trips for $50 million each. Consequently firms bunch security issues. That may often mean relying on short-term financing until a large issue is justified. Or it may mean issuing more than is needed at the moment in order to avoid another issue later.

•  Watch out for underpricing. Underpricing is often a serious hidden cost to the existing shareholders.

•  The winner’s curse may be a serious problem with IPOs. Would-be investors in an initial public offering (IPO) do not know how other investors will value the stock and they worry that they are likely to receive a larger allocation of the overpriced issues. Careful design of issue procedure may reduce the winner’s curse.

•  New stock issues may depress the price. The extent of this price pressure varies, but for industrial issues in the United States the fall in the value of the existing stock may amount to a significant proportion of the money raised. This pressure is due to the information that the market reads into the company’s decision to issue stock.

•  Shelf registration often makes sense for debt issues by blue-chip firms. Shelf registration reduces the time taken to arrange a new issue, it increases flexibility, and it may cut underwriting costs. It seems best suited for debt issues by large firms that are happy to switch between investment banks. It seems less suited for issues of unusually risky or complex securities or for issues by small companies that are likely to benefit from a close relationship with an investment bank.

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FURTHER READING

Metrick and Yasuda, Megginson, Gompers, and Gompers and Lerner provide an overview of the venture capital industry, while Sahlman looks at the form of the venture capital contract:

A. Metrick and A. Yasuda, Venture Capital and the Finance of Innovation, 2nd ed. (New York: John Wiley & Sons, 2010).

W. L. Megginson, “Toward a Global Model of Venture Capital?” Journal of Applied Corporate Finance 16 (Winter 2004), pp. 89–107.

P. Gompers, “Venture Capital,” in B. E. Eckbo (ed.), Handbook of Corporate Finance: Empirical Corporate Finance (Amsterdam: Elsevier/North Holland, 2007).

P. Gompers and J. Lerner, “The Venture Capital Revolution,” Journal of Economic Perspectives 15 (Spring 2001), pp. 145–168.

W. A. Sahlman, “Aspects of Financial Contracting in Venture Capital,” Journal of Applied Corporate Finance (Summer 1988), pp. 23–26.

Here are four comprehensive surveys of the literature on new issues:

B. E. Eckbo, R. W. Masulis, and Ø. Norli, “Security Offerings: A Survey,” in B. E. Eckbo (ed.), Handbook of Corporate Finance: Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007).

A. P. Ljungqvist, “IPO Underpricing,” in B. E. Eckbo (ed.), Handbook of Corporate Finance: Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007).

J. R. Ritter, “Investment Banking and Securities Issuance,” in G. M. Constantinides, M. Harris, and R. Stulz (eds.), Handbook of the Economics of Finance (Amsterdam: Elsevier Science, 2003).

T. Jenkinson and A. P. Ljungqvist, Going Public: The Theory and Evidence on How Companies Raise Equity Finance, 2nd ed. (Oxford: Oxford University Press, 2001).

Two useful articles on IPOs are:

R. G. Ibbotson, J. L. Sindelar, and J. R. Ritter, “The Market’s Problems with the Pricing of Initial Public Offerings,” Journal of Applied Corporate Finance 7 (Spring 1994), pp. 66–74.

L. M. Benveniste and W. J. Wilhelm, Jr., “Initial Public Offerings: Going by the Book,” Journal of Applied Corporate Finance 10 (Spring 1997) pp. 98–108.

A useful introduction to the design of auctions is:

P. Milgrom, “Auctions and Bidding: A Primer,” Journal of Economic Perspectives 2 (1989), pp. 3–22.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Types of issue After each of the following issue methods, we have listed two types of issue. Choose the one more likely to employ that method.

a.  Rights issue (initial public offer/further sale of an already publicly traded stock)

b.  Rule 144A issue (international bond issue/U.S. bond issue by a foreign corporation)

c.  Private placement (issue of existing stock/bond issue by an industrial company)

d.  Shelf registration (initial public offer/bond issue by a large industrial company)

2.  Definitions Each of the following terms is associated with one of the events beneath. Can you match them up?

a.  Best efforts

b.  Bookbuilding

c.  Shelf registration

d.  Rule 144A

Events:

A.  Investors indicate to the underwriter how many shares they would like to buy in a new issue and these indications are used to help set the price.

B.  The underwriter accepts responsibility only to try to sell the issue.

C.  Some issues are not registered but can be traded freely among qualified institutional buyers.

D.  Several tranches of the same security may be sold under the same registration. (A “tranche” is a batch, a fraction of a larger issue.)

3.  Definitions Explain what each of the following terms or phrases means:

a.  Venture capital

b.  Bookbuilding

c.  Underwriting spread

d.  Registration statement

e.  Winner’s curse

4.  Underwriting costs For each of the following pairs of issues, which is likely to involve the lower proportionate underwriting and administrative costs?

a.  A large issue/a small issue

b.  A bond issue/a common stock issue

c.  Initial public offering/subsequent issue of stock

d.  A small private placement of bonds/a small general cash offer of bonds

5.  Stock issues True or false?

a.  Venture capitalists typically provide first-stage financing sufficient to cover all development expenses. Second-stage financing is provided by stock issued in an IPO.

b.  Underpricing in an IPO is only a problem when the original investors are selling part of their holdings.

c.  Stock price generally falls when the company announces a new issue of shares. This is attributable to the information released by the decision to issue.

6.  Private placements You need to choose between making a public offering and arranging a private placement. In each case the issue involves $10 million face value of 10-year debt. You have the following data for each:

• A public issue: The interest rate on the debt would be 8.5%, and the debt would be issued at face value. The underwriting spread would be 1.5%, and other expenses would be $80,000.

• A private placement: The interest rate on the private placement would be 9%, but the total issuing expenses would be only $30,000.

a.  What is the difference in the proceeds to the company net of expenses?

b.  Other things being equal, which is the better deal?

c.  What other factors beyond the interest rate and issue costs would you wish to consider before deciding between the two offers?

7.  Rights issues Associated Breweries plc is planning to market alcohol-free beer. To finance the venture it proposes to make a rights issue at £10 of one new share for each two shares held. (The company currently has outstanding 100,000 shares priced at £40 a share.) Assuming that the new money is invested to earn a fair return, give values for the following:

a.  Number of new shares.

b.  Amount of new investment.

c.  Total value of company after issue.

d.  Total number of shares after issue.

e.  Stock price after the issue.

f.  Price of the right to buy one new share.

INTERMEDIATE

8.  Definitions Here is a further vocabulary quiz. Briefly explain each of the following:

a.  Zero-stage vs. first- or second-stage financing.

b.  Carried interest.

c.  Rights issue.

d.  Road show.

e.  Best-efforts offer.

f.  Qualified institutional buyer.

g.  Blue-sky laws.

h.  Greenshoe option.

9.  Venture capital

a.  “A signal is credible only if it is costly.” Explain why management’s willingness to invest in Marvin’s equity was a credible signal. Was its willingness to accept only part of the venture capital that would eventually be needed also a credible signal?

b.  “When managers take their reward in the form of increased leisure or executive jets, the cost is borne by the shareholders.” Explain how First Meriam’s financing package tackled this problem.

10.  Underpricing In some UK IPOs any investor may be able to apply to buy shares. Mr. Bean has observed that on average these stocks are underpriced by about 9% and for some years has followed a policy of applying for a constant proportion of each issue. He is therefore disappointed and puzzled to find that this policy has not resulted in a profit. Explain to him why this is so.

11.  Issue costs Why are the costs of debt issues less than those of equity issues? List the possible reasons.

12.  Price impact There are three reasons that a common stock issue might cause a fall in price: (a) the price fall is needed to absorb the extra supply, (b) the issue causes temporary price pressure until it has been digested, and (c) management has information that stockholders do not have. Explain these reasons more fully. Which do you find most plausible? Is there any way that you could seek to test whether you are right?

13.  Underpricing Construct a simple example to show the following:

a.  Existing shareholders are made worse off when a company makes a cash offer of new stock below the market price.

b.  Existing shareholders are not made worse off when a company makes a rights issue of new stock below the market price even if the new stockholders do not wish to take up their rights.

14.  Rights issues In 2010 the Irish Company, Pandora Box, made a rights issue at €5 a share of one new share for every four shares held. Before the issue there were 10 million shares outstanding and the share price was €6.

a.  What was the total amount of new money raised?

b.  What was the value of the right to buy one new share?

c.  What was the prospective stock price after the issue?

d.  How far could the total value of the company fall before shareholders would be unwilling to take up their rights?

15.  Rights issues Problem 14 contains details of a rights offering by Pandora Box. Suppose that the company had decided to issue new stock at €4. How many new shares would it have needed to sell to raise the same sum of money? Recalculate the answers to questions (b) to (d) in Problem 14. Show that the shareholders are just as well off if the company issues the shares at €4 rather than €5.

16.  Cash offers Suppose that instead of having a rights issue of new stock at €4 (see Problem 15), Pandora decided to make a general cash offer at €4. Would existing shareholders still be just as well off? Explain.

17.  IPOs Refer to the Marvin Prospectus Appendix at the end of this chapter to answer the following questions.

a.  If there is unexpectedly heavy demand for the issue, how many extra shares can the underwriter buy?

b.  How many shares are to be sold in the primary offering? How many will be sold in the secondary offering?

c.  One day post-IPO, Marvin shares traded at $105. What was the degree of underpricing? How does that compare with the average degree of underpricing for IPOs in the United States?

d.  There are three kinds of cost to Marvin’s new issue—underwriting expense, administrative costs, and underpricing. What was the total dollar cost of the Marvin issue?

18.  IPOs Find the prospectus for a recent IPO. How do the issue costs compare with (a) those of the Marvin issue and (b) those shown in Table 15.3? Can you suggest reasons for the differences?

CHALLENGE

19.  Venture capital

a.  Why do venture capital companies prefer to advance money in stages? If you were the management of Marvin Enterprises, would you have been happy with such an arrangement? With the benefit of hindsight did First Meriam gain or lose by advancing money in stages?

b.  The price at which First Meriam would invest more money in Marvin was not fixed in advance. But Marvin could have given First Meriam an option to buy more shares at a preset price. Would this have been better?

c.  At the second stage Marvin could have tried to raise money from another venture capital company in preference to First Meriam. To protect themselves against this, venture capital firms sometimes demand first refusal on new capital issues. Would you recommend this arrangement?

20.  Auctions Explain the difference between a uniform-price auction and a discriminatory auction. Why might you prefer to sell securities by one method rather than another?

21.  Dilution Here is recent financial data on Pisa Construction, Inc.

Pisa has not performed spectacularly to date. However, it wishes to issue new shares to obtain $80,000 to finance expansion into a promising market. Pisa’s financial advisers think a stock issue is a poor choice because, among other reasons, “sale of stock at a price below book value per share can only depress the stock price and decrease shareholders’ wealth.” To prove the point they construct the following example: “Suppose 2,000 new shares are issued at $40 and the proceeds are invested. (Neglect issue costs.) Suppose return on investment does not change. Then

Thus, EPS declines, book value per share declines, and share price will decline proportionately to $38.70.”

Evaluate this argument with particular attention to the assumptions implicit in the numerical example.

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FINANCE ON THE WEB

Look up a recent IPO on www.hoovers.com or biz.yahoo.com/ipo and then use the Edgar database to find the prospectus. (You may find it easiest to look up the company on finance.yahoo.com and use the link to SEC filings. In any case finding the final prospectus can be a matter of trial and error.) Compare the IPO with that of Marvin. For example, who were the existing shareholders? Was the company raising more capital or were existing shareholders selling? Were existing shareholders prevented by a lock-up agreement from selling more shares? How did the underwriting and other costs compare with those of Marvin? Did the underwriters have a greenshoe option? Did the issue turn out to be underpriced? (The Yahoo! website should help here.) If so, how much money was left on the table?

APPENDIX ● ● ● ● ●

Marvin’s New-Issue Prospectus⁴⁸

PROSPECTUS

900,000 Shares

Marvin Enterprises Inc.

Common Stock ($.10 par value)

Of the 900,000 shares of Common Stock offered hereby, 500,000 shares are being sold by the Company and 400,000 shares are being sold by the Selling Stockholders. See “Principal and Selling Stockholders.” The Company will not receive any of the proceeds from the sale of shares by the Selling Stockholders.

Before this offering there has been no public market for the Common Stock. These securities involve a high degree of risk. See “Certain Considerations.”

THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND EXCHANGE COMMISSION NOR HAS THE COMMISSION PASSED ON THE ACCURACY OR ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

The Common Stock is offered subject to receipt and acceptance by the Underwriters, to prior sale, and to the Underwriters’ right to reject any order in whole or in part and to withdraw, cancel, or modify the offer without notice.

Klein Merrick Inc.

February 3, 2031

No person has been authorized to give any information or to make any representations, other than as contained therein, in connection with the offer contained in this Prospectus, and, if given or made, such information or representations must not be relied upon. This Prospectus does not constitute an offer of any securities other than the registered securities to which it relates or an offer to any person in any jurisdiction where such an offer would be unlawful. The delivery of this Prospectus at any time does not imply that information herein is correct as of any time subsequent to its date.

IN CONNECTION WITH THIS OFFERING, THE UNDERWRITERS MAY OVERALLOT OR EFFECT TRANSACTIONS WHICH STABILIZE OR MAINTAIN THE MARKET PRICE OF THE COMMON STOCK OF THE COMPANY AT A LEVEL ABOVE THAT WHICH MIGHT OTHERWISE PREVAIL IN THE OPEN MARKET. SUCH STABILIZING, IF COMMENCED, MAY BE DISCONTINUED AT ANY TIME.

Prospectus Summary

The following summary information is qualified in its entirety by the detailed information and financial statements appearing elsewhere in this Prospectus.

The Offering

Use of Proceeds

For the construction of new manufacturing facilities and to provide working capital.

The Company

Marvin Enterprises Inc. designs, manufactures, and markets gargle blasters for domestic use. Its manufacturing facilities employ integrated nanocircuits to control the genetic engineering processes used to manufacture gargle blasters.

The Company was organized in Delaware in 2025.

Proceeds

The net proceeds of this offering are expected to be $36,744,445. Of the net proceeds, approximately $27.0 million will be used to finance expansion of the Company’s principal manufacturing facilities. The balance will be used for working capital.

Certain Considerations

Investment in the Common Stock involves a high degree of risk. The following factors should be carefully considered in evaluating the Company:

Substantial Capital Needs The Company will require additional financing to continue its expansion policy. The Company believes that its relations with its lenders are good, but there can be no assurance that additional financing will be available in the future.

Licensing The expanded manufacturing facilities are to be used for the production of a new imploding gargle blaster. An advisory panel to the U.S. Food and Drug Administration (FDA) has recommended approval of this product for the U.S. market but no decision has yet been reached by the full FDA committee.

Dividend Policy

The company has not paid cash dividends on its Common Stock and does not anticipate that dividends will be paid on the Common Stock in the foreseeable future.

Management

The following table sets forth information regarding the Company’s directors, executive officers, and key employees.

George Marvin—George Marvin established the Company in 2025 and has been its Chief Executive Officer since that date. He is a past president of the Institute of Gargle Blasters and has recently been inducted into the Confrérie des Gargarisateurs.

Mildred Marvin—Mildred Marvin has been employed by the Company since 2025.

Chip Norton—Mr. Norton has been General Manager of the Company since 2025. He is a former vice-president of Amalgamated Blasters, Inc.

Executive Compensation

The following table sets forth the cash compensation paid for services rendered for the year 2030 by the executive officers:

Certain Transactions

At various times between 2026 and 2029 First Meriam Venture Partners invested a total of $8.5 million in the Company. In connection with this investment, First Meriam Venture Partners was granted certain rights to registration under the Securities Act of 1933, including the right to have their shares of Common Stock registered at the Company’s expense with the Securities and Exchange Commission.

Principal and Selling Stockholders

The following table sets forth certain information regarding the beneficial ownership of the Company’s voting Common Stock as of the date of this prospectus by (i) each person known by the Company to be the beneficial owner of more than 5 percent of its voting Common Stock, and (ii) each director of the Company who beneficially owns voting Common Stock. Unless otherwise indicated, each owner has sole voting and dispositive power over his or her shares.

Lock-up Agreements

The holders of the Common Stock have agreed with the underwriters not to sell, pledge, or otherwise dispose of their shares, other than as specified in this prospectus, for a period of 180 days after the date of the prospectus without the prior consent of Klein Merrick.

Description of Capital Stock

The Company’s authorized capital stock consists of 10,000,000 shares of voting Common Stock.

As of the date of this Prospectus, there are 10 holders of record of the Common Stock.

Under the terms of one of the Company’s loan agreements, the Company may not pay cash dividends on Common Stock except from net profits without the written consent of the lender.

Underwriting

Subject to the terms and conditions set forth in the Underwriting Agreement, the Company has agreed to sell to each of the Underwriters named below, and each of the Underwriters, for whom Klein Merrick Inc. are acting as Representatives, has severally agreed to purchase from the Company, the number of shares set forth opposite its name below.

In the Underwriting Agreement, the several Underwriters have agreed, subject to the terms and conditions set forth therein, to purchase all shares offered hereby if any such shares are purchased. In the event of a default by any Underwriter, the Underwriting Agreement provides that, in certain circumstances, purchase commitments of the nondefaulting Underwriters may be increased or the Underwriting Agreement may be terminated.

There is no public market for the Common Stock. The price to the public for the Common Stock was determined by negotiation between the Company and the Underwriters and was based on, among other things, the Company’s financial and operating history and condition, its prospects and the prospects for its industry in general, the management of the Company, and the market prices of securities for companies in businesses similar to that of the Company.

Legal Matters

The validity of the shares of Common Stock offered by the Prospectus is being passed on for the Company by Dodson and Fogg and for the Underwriters by Kenge and Carboy.

Experts

The consolidated financial statements of the Company have been so included in reliance on the reports of Hooper Firebrand, independent accountants, given on the authority of that firm as experts in auditing and accounting.

Financial Statements

[Text and tables omitted.]

___________

¹Venture capital investors do not necessarily demand a majority on the board of directors. Whether they do depends, for example, on how mature the business is and on what fraction they own. A common compromise gives an equal number of seats to the founders and to outside investors; the two parties then agree to one or more additional directors to serve as tie-breakers in case a conflict arises. Regardless of whether they have a majority of directors, venture capital companies are seldom silent partners; their judgment and contacts can often prove useful to a relatively inexperienced management team.

²Notice the trade-off here. Marvin’s management is being asked to put all its eggs into one basket. That creates pressure for managers to work hard, but it also means that they take on risk that could have been diversified away.

³If First Meriam had refused to invest at stage 2, it would have been an exceptionally hard sell convincing another investor to step in in its place. The other outside investors knew they had less information about Marvin than First Meriam and would have read its refusal as a bad omen for Marvin’s prospects.

⁴Mezzanine financing does not necessarily come in the third stage; there may be four or five stages. The point is that mezzanine investors come in late, in contrast to venture capitalists who get in on the ground floor.

⁵A typical arrangement might be for the management company to receive a fee of 2% plus 20% of the profits.

⁶For evidence on the role of venture capitalists in assisting new businesses, see T. Hellman and M. Puri, “The Interaction between Product Market and Financial Strategy: The Role of Venture Capital,” Review of Financial Studies 13 (2000), pp. 959–984; and S. N. Kaplan and P. Stromberg, “Contracts, Characteristics and Actions: Evidence from Venture Capitalist Analyses,” Journal of Finance 59 (October 2004), pp. 2177–2210.

⁷This argument is developed in B. Black and R. Gilson, “Venture Capital and the Structure of Capital Markets: Banks versus Stock Markets,” Journal of Financial Economics 47 (March 1998), pp. 243–277.

⁸Gompers and Lerner, who studied the period 1979–1997, found somewhat higher returns. P. A. Gompers and J. Lerner, “Risk and Reward in Private Equity Investments: The Challenge of Performance Assessment,” Journal of Private Equity, Winter 1997, pp. 5–12.

⁹Companies can alleviate the reporting burden by reducing the number of shareholders to less than 300 and delisting their stock from the exchange. This procedure is known as “going dark.” In recent years there has been an increase in the number of companies going dark.

¹⁰First Meriam also wanted to cash in on its investment, but venture capital companies usually believe that selling out at the time of the IPO would send a bad signal to investors. Therefore First Meriam planned to wait until well after the IPO and then either sell its holding or distribute its shares in Marvin to the investors in the First Meriam fund.

¹¹On average the managing underwriter accounts for 40% to 60% of trading volume in the stock during the first 60 days after an IPO. See K. Ellis, R. Michaely, and M. O’Hara, “When the Underwriter Is the Market Maker: An Examination of Trading in the IPO Aftermarket,” Journal of Finance 55 (June 2000), pp. 1039–1074.

¹²The 40 days after the IPO are designated as a quiet period. Merrick is obliged to wait until after this period before commenting on the valuation of the company. Survey evidence suggests that, in choosing an underwriter, firms place considerable importance on its ability to provide follow-up research reports. See L. Krigman, W. H. Shaw, and K. L. Womack, “Why Do Firms Switch Underwriters?” Journal of Financial Economics 60 (May–June 2001), pp. 245–284.

¹³The rules governing the sale of securities derive principally from the Securities Act of 1933. The SEC is concerned solely with disclosure and it has no power to prevent an issue as long as there has been proper disclosure. Some public issues are exempt from registration. These include issues by small businesses and loans maturing within nine months.

¹⁴In 1980, when Apple Computer Inc. went public, the Massachusetts state government decided the offering was too risky and barred the sale of the shares to individual investors in the state. The state relented later after the issue was out and the price had risen. Needless to say, this action was not acclaimed by Massachusetts investors.

States do not usually reject security issues by honest firms through established underwriters. We cite the example to illustrate the potential power of state securities laws and to show why underwriters keep careful track of them.

¹⁵The company is allowed to circulate a preliminary version of the prospectus (known as a red herring) before the SEC has approved the registration statement.

¹⁶The managing underwriter is therefore often known as the bookrunner.

¹⁷The alternative is to enter into an all-or-none arrangement. In this case, either the entire issue is sold at the offering price or the deal is called off and the issuing company receives nothing.

¹⁸This arrangement is known as a rights issue. We describe rights issues later in the chapter.

¹⁹In the more risky cases the underwriter usually receives some extra noncash compensation, such as warrants to buy additional common stock in the future.

²⁰H. C. Chen and J. R. Ritter, “The Seven Percent Solution,” Journal of Finance 55 (June 2000), pp. 1105–1132.

²¹Chen and Ritter argue that the fixed spread suggests the underwriting market is not competitive. The U.S. Department of Justice was led to investigate whether the spread constituted evidence of price-fixing. Robert Hansen disagrees that the market is not competitive. Among other things, he provides evidence that the 7% spread is not abnormally profitable and argues that it is part of a competitive and efficient market. See R. Hansen, “Do Investment Banks Compete in IPOs?: The Advent of the 7% Plus Contract,” Journal of Financial Economics 59 (2001) pp. 313–346.

²²It does not, however, hold the record. That honor goes to VA Linux.

²³Our figure is an equally weighted average of first-day returns and is calculated from data on bear.cba.ufl.edu/ritter. As we saw in Chapter 13, there is some evidence that these early gains are not maintained and in the five years following an IPO the shares underperform the market.

²⁴The Chinese returns are for A shares, which are traded only domestically. (see nearby box).

²⁵Notice that the winner’s curse would disappear if only investors knew what the market price was going to be. One response is to allow trading in a security before it has been issued. This is known as the gray market, which in the U.S. is most common for debt issues. Investors can observe the price in the gray market and can be more confident that they are not overbidding when the actual issue takes place.

²⁶T. Loughran and J. Ritter, “Why Don’t Issuers Get Upset about Leaving Money on the Table in IPOs?” Review of Financial Studies 15 (2002), pp. 413–443.

²⁷For examples of these explanations, see A. P. Ljungqvist, V. Nanda, and R. Singh, “Hot Markets, Investor Sentiment, and IPO Pricing,” Journal of Business 79 (July 2006), pp. 1667–1702; and L. Pastor and P. Veronesi, “Rational IPO Waves,” Journal of Finance 60 (2005), pp. 1713–1757.

²⁸See L. M. Benveniste and P. A. Spindt, “How Investment Bankers Determine the Offer Price and Allocation of New Issues,” Journal of Financial Economics 24 (1989), pp. 343–362; and F. Cornelli and D. Goldreich, “Bookbuilding and Strategic Allocation,” Journal of Finance 56 (December 2001), pp. 2337–2369.

²⁹Google’s issue was followed in 2005 by a $140 million auction of stock by Morningstar.

³⁰T. Kaneko and R. Pettway, “Auctions versus Bookbuilding of Japanese IPOs,” Pacific Basin Journal 11 (2003), pp. 439–462.

³¹In addition, the price in the uniform-price auction depends not only on the views of B but also on those of A (for example, if A had bid $990 rather than $1,020, then both A and B would have paid $990 for each bond). Since the uniform-price auction takes advantage of the views of both A and B, it reduces the winner’s curse.

³²Sometimes auctions reduce the winner’s curse by allowing uninformed bidders to enter noncompetitive bids, whereby they submit a quantity but not a price. For example, in U.S. Treasury auctions investors may submit noncompetitive bids and receive their full allocation.

³³Experience in the United States with uniform-price auctions suggests that they do indeed reduce the winner’s curse problem and realize higher prices for the seller. See D. Goldreich, “Underpricing in Discriminatory and Uniform-Price Auctions,” Journal of Financial and Quantitative Analysis 42 (June 2007), pp. 443–466.

³⁴In 2005 the SEC created a new category of firm termed “a well-known seasoned issuer” (or WKSI). These firms are exempt from certain filing requirements.

³⁵These two deals are examples of accelerated underwritings. For a good description of such issues, see B. Bortolotti, W. Megginson, and S. B. Smart, “The Rise of Accelerated Seasoned Equity Underwritings,” Journal of Applied Corporate Finance 20 (Summer 2008), pp. 35–57.

³⁶This point is emphasized in O. Altinkilic and R. S. Hansen, “Are There Economies of Scale in Underwriting Fees? Evidence of Rising External Financing Costs,” Review of Financial Studies 13 (Spring 2000), pp. 191–218.

³⁷Jung, Kooyul, Y. Kim, and R. Stulz, “Timing, Investment Opportunities, Managerial Discretion, and the Security Issue Decision,” Journal of Financial Economics 42 (October 1996), pp. 159–185.

³⁸Northern California seceded from California and became the fifty-second state in 2016.

³⁹This explanation was developed in S. C. Myers and N. S. Majluf, “Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have,” Journal of Financial Economics 35 (1998), pp. 99–122.

⁴⁰M. M. Cornett and H. Tehranian, “An Examination of Voluntary versus Involuntary Issuances by Commercial Banks,” Journal of Financial Economics 35 (1994), pp. 99–122.

⁴¹The “involuntary issuers” did make a choice: they could have forgone the stock issue and run the risk of failing to meet the regulatory capital standards. The banks that were more concerned with this risk were more likely to issue. Thus it is no surprise that Cornett and Tehranian found some drop in stock price even for the involuntary issues.

⁴²There is another possible information effect. Just as an unexpected increase in the dividend suggests to investors that the company is generating more cash than they thought, the announcement of a new issue may have the reverse implication. However, this effect cannot explain why the announcement of an issue of debt does not result in a similar fall in the stock price.

⁴³See L. Shyam-Sunder, “The Stock Price Effect of Risky vs. Safe Debt,” Journal of Financial and Quantitative Analysis 26 (December 1991), pp. 549–558.

⁴⁴See, for example, T. Loughran and J. R. Ritter, “The New Issues Puzzle,” Journal of Finance 50 (March 1995), pp. 23–51; and Jay Ritter’s website: bear.cba.ufl.edu/ritter.

⁴⁵In fact, he should be prepared to pay slightly more because he is not compelled to buy the stock and can choose not to do so. In practice, since the option is usually well in the money and its time to expiration is short, its value is usually negligible.

⁴⁶There is a minor, but potentially confusing, difference between North American and European rights issues. In the Ivanhoe issue shareholders were offered one right for each share held, but they needed more than one right to buy a new share. A similar issue in Europe would generally give shareholders fewer rights for each share held. However, they would need only one right to buy one new share, and each right would be worth correspondingly more. For example, if Ivanhoe had been a European company, shareholders would have received one right for every 20/3 shares owned, but this right would have been 20/3 times as valuable.

You may encounter formulas for the value of a right. Remember to check whether the formula is referring to a U.S. or a European issue.

⁴⁷See S. A. Corwin, “The Determinants of Underpricing for Seasoned Equity Offers,” Journal of Finance 58 (October 1993), pp. 2249–2279; and S. Mola and T. Loughran, “Discounting and Clustering in Seasoned Equity Offering Price,” Journal of Financial and Quantitative Analysis 39 (March 2004), pp. 1–23.

⁴⁸Most prospectuses have content similar to that of the Marvin prospectus but go into considerably more detail. Also we have omitted Marvin’s financial statements.

Part 5 Payout Policy and Capital Structure

Payout Policy

Payout policy resolves two questions. First, how much cash should the corporation pay out to its shareholders? Second, how should the cash be distributed, by paying cash dividends or by repurchasing shares? We will cover these questions in reverse order, “how” before “how much.”

Suppose a corporation has surplus cash. Should it distribute that cash by paying a dividend, or should it do so by repurchasing shares? In an ideal, frictionless world, the choice between dividend and repurchase does not matter. In practice the choice can be important.

First, investors expect a firm that has made regular dividend payments to continue doing so and to increase those payments steadily as earnings increase. Dividends are rarely cut back, unless the firm suffers significant, continuing losses, and managers don’t increase dividends unless they are confident that the dividend can be maintained. Announcement of a dividend increase is therefore good news for shareholders, who infer that managers are confident about the future. Repurchases, on the other hand, are more flexible and do not convey as much information to investors.

Second, repurchases are tax-advantaged. When shareholders sell, they pay tax at capital gains rates, which have generally been lower, often much lower, than tax rates on dividends.

Repurchases have grown dramatically over the last 30 years, and in the U.S. they now rival dividends in importance. Of course, cash dividends are still paid. Large, mature firms distribute huge amounts as dividends. But most of these firms also repurchase shares. Many other firms use repurchases exclusively.

Next we consider “how much.” How does a financial manager conclude that cash is really surplus? Before deciding to pay dividends or repurchase shares, the manager asks a series of questions. First, is the business generating positive free cash flow after making all investments with positive NPVs? Is that positive free cash flow likely to continue? Second, is the firm’s debt ratio prudent? If the ratio is too high, paying down debt usually takes priority. Third, are the company’s holdings of cash a sufficient cushion for unexpected setbacks and a sufficient war chest for unexpected opportunities? If the answer to all three questions is yes, then the cash is truly surplus. If a corporation has surplus cash, it’s best to pay the cash back to shareholders. Paying out surplus cash reassures shareholders that the cash will not be wasted on questionable investments or consumed by perks or excessive compensation.

We begin this chapter with a review of how dividends are paid and repurchases carried out. We also consider the information content of dividends and repurchases. That is, we consider what investors can learn from managers’ payout decisions and how stock prices react to payout announcements. Then we examine the pros and cons of cash dividends versus repurchases. Finally we discuss how corporations should manage total payout, that is, the sum of dividends and repurchases.

 16-1   Facts About Payout

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The growth in repurchases

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Corporations pay out cash by distributing dividends or by buying back some of their outstanding shares. As Figure 16.1 shows, repurchases were rare in the early 1980s, but the total value of repurchases in the U.S. is now similar to total dividends. In 2007, a record year for repurchases, 28 U.S. companies each bought back more than $5 billion of stock. Exxon Mobil bought back $31 billion, Microsoft $28 billion, IBM $19 billion, and GE $14 billion.

The fraction of companies that pay dividends has decreased from 48% in 1980 to 31% in 2010.¹ Some companies used to pay dividends, but then fell on hard times and ceased to do so. However, most non–dividend payers are young growth companies that have never paid a dividend and will not pay one in the foreseeable future. These zero-dividend companies include such household names as Berkshire Hathaway, Amazon, and Google, as well as a multitude of smaller growth firms.

The decline in the fraction of firms paying dividends does not mean that fewer firms are paying out cash to investors. Here is a table of payout practices for U.S. firms from 2001 to 2010:

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How companies pay out

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On average in each year 13.9% of the firms paid a dividend and also repurchased shares. The fraction that paid dividends but did not repurchase was 19.4%. The corresponding fraction for repurchases but no dividends was 11.5%. But 55.1% of firms did not pay dividends or repurchase shares.

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Payouts in the EU

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Figure 16.1 also shows that dividends are more stable than repurchases. Notice how repurchases were cut back in the early 2000s and in the crisis of 2007–2009. Dividends also fell in the crisis, but by less than repurchases.

   FIGURE 16.1 Dividends and stock repurchases in the United States, 1980–2010 (figures in $ billions).

Source: Standard & Poor’s Compustat.

How Firms Pay Dividends

A company’s dividend is set by the board of directors. The announcement of the dividend states that the payment will be made to all stockholders who are registered on a particular record date. Then a few weeks later dividend checks are mailed to stockholders. Stocks are normally bought or sold with dividend (or cum dividend) until two business days before the record date, and then they trade ex dividend. If you buy stock on the ex-dividend date, your purchase will not be entered on the company’s books before the record date and you will not be entitled to the dividend.

Figure 16.2 illustrates this sequence of events. On January 5, 2012, Exxon Mobil declared a quarterly dividend of $.47 per share. The dividend was paid on March 9 to all shareholders who were registered on the company’s books on February 10. Two days earlier on February 8 the shares began to trade ex dividend. Any investor who bought shares on that date would not have had his purchase registered by the record date and would not have been entitled to the dividend.

The company is not free to declare whatever dividend it chooses. In some countries, such as Brazil and Chile, companies are obliged by law to pay out a minimum proportion of their earnings. Conversely, some restrictions may be imposed by lenders, who are concerned that excessive dividend payments would not leave enough in the kitty to repay their loans. In the U.S., state law also helps to protect the firm’s creditors against excessive dividend payments. For example, companies are not allowed to pay a dividend out of legal capital, which is generally defined as the par value of outstanding shares.²

Most U.S. companies pay a regular cash dividend each quarter, but occasionally this is supplemented by a one-off extra or special dividend. Many companies offer shareholders automatic dividend reinvestment plans (DRIPs). Often the new shares are issued at a 5% discount from the market price. Sometimes 10% or more of total dividends will be reinvested under such plans.³

Dividends are not always in the form of cash. Companies also declare stock dividends. For example, if the firm pays a stock dividend of 5%, it sends each shareholder 5 extra shares for every 100 shares currently owned. A stock dividend is essentially the same as a stock split. Both increase the number of shares but do not affect the company’s assets, profits, or total value. So both reduce value per share.⁴ In this chapter we focus on cash dividends.

   FIGURE 16.2 Exxon Mobil’s first dividend in 2012.

How Firms Repurchase Stock

Instead of paying a dividend to its stockholders, the firm can use the cash to repurchase stock. The reacquired shares are kept in the company’s treasury and may be resold if the company needs money. There are four main ways to repurchase stock. By far the most common method is for the firm to announce that it plans to buy its stock in the open market, just like any other investor.⁵ However, companies sometimes use a tender offer where they offer to buy back a stated number of shares at a fixed price, which is typically set at about 20% above the current market level. Shareholders can then choose whether to accept this offer. A third procedure is to employ a Dutch auction. In this case the firm states a series of prices at which it is prepared to repurchase stock. Shareholders submit offers declaring how many shares they wish to sell at each price and the company calculates the lowest price at which it can buy the desired number of shares. Finally, repurchase sometimes takes place by direct negotiation with a major shareholder.

In the past many countries banned or severely restricted the use of stock repurchases. As a result, firms that had amassed large amounts of cash were tempted to invest it at very low rates of return rather than hand it back to shareholders, who could have reinvested it in firms that were short of cash. But many of these limitations have now been removed. For example, Japan permitted repurchases in 1995 and Sweden in 2000, while Germany relaxed its restrictions in 1998. Many multinational giants now repurchase huge amounts of stock. For example, in 2007 the Spanish bank BBVA, BP, Royal Dutch Shell, and Glaxo Smith Kline all spent huge sums on buying back their stock.

 16-2   The Information Content of Dividends and Repurchases

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The Lintner model of payouts

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A survey in 2004 asked senior executives about their companies’ dividend policies. Figure 16.3 paraphrases their responses. Three themes stand out:

1.  Managers are reluctant to make dividend changes that may have to be reversed. They are particularly worried about having to rescind a dividend increase and, if necessary, would issue shares or borrow to maintain the dividend.

2.  Managers “smooth” dividends. Dividend changes follow shifts in long-run, sustainable earnings. Transitory earnings changes are unlikely to affect dividends.

3.  Managers focus more on dividend changes than on absolute dividend levels. Thus paying a dividend of $2.00 per share is an important financial decision if last year’s dividend was $1.50, but no big deal if last year’s dividend was also $2.00.

From these responses, you can see why announcement of a dividend increase is good news to investors. Investors know that managers are reluctant to reduce dividends and will not increase dividends unless they are confident that the payment can be maintained. Therefore announcement of a dividend increase signals managers’ confidence in future profits. That is why investors and financial managers refer to the information content of dividends.

The information content of dividends implies that dividend increases predict future profitability. Evidence on this point is somewhat elusive. But Healy and Palepu, who focus on companies that paid a dividend for the first time, find that on average earnings jumped 43% in the year a dividend was paid. If managers thought that this was a temporary windfall, they might have been cautious about committing themselves to paying out cash. But it looks as if these managers had good reason to be confident about prospects, for earnings continued to rise in the following years.⁶

   FIGURE 16.3 A 2004 survey of financial executives on dividend policy.

Source: A. Brav, J. R. Graham, C. R. Harvey, and R. Michaely, “Payout Policy in the 21st Century,” Journal of Financial Economics 77 (September 2005), pp. 483–527. © 2005 Elsevier Science, used with permission.

Investors certainly appear to take comfort from an increase in dividends. When the increase is announced, analysts generally up their forecast of the current year’s earnings.⁷ It is no surprise, therefore, to find that a higher dividend prompts a rise in the stock price, whereas a dividend cut results in a fall in price. For example, in the case of the dividend initiations studied by Healy and Palepu, the dividend announcement resulted in a 4% stock-price increase on average.⁸

Notice that investors do not get excited about the level of a company’s dividend; they worry about the change, which they view as an important indicator of the sustainability of earnings.

It seems that in some other countries investors are less preoccupied with dividend changes. For example, in Japan there is a much closer relationship between corporations and major stockholders, and therefore information may be more easily shared with investors. Consequently, Japanese corporations are more prone to cut their dividends when there is a drop in earnings, but investors do not mark the stocks down as sharply as in the U.S.⁹

Do not assume that all dividend cuts are bad news, however. The box on the next page explains how investors endorsed a drastic dividend cut announced by the Spanish company Telefónica.

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Good News: Telefónica Cuts its Dividend

  In July 2012, Telefónica, the Spanish telecoms giant, scrapped its dividend of €1.5 per share and abandoned its share buy-back program. The share price opened lower on the announcement, but then climbed steadily as investors digested the news.

Usually dividend cuts are bad news because investors infer trouble. Investors take the cut as a signal of an earnings shortfall and they are usually right. However, shareholders in Telefónica were already fully aware of the difficulties that lay ahead. The company had €58 billion of debt and a debt-equity ratio of 3.3. With the Spanish economy in deep trouble, and the government and the banks in need of a bail out, the outlook for Telefónica was particularly uncertain. Investors evidently concluded that in these circumstances Telefónica and its investors were better off if the company used the cash to reduce leverage instead of paying it out to its shareholders. That way Telefónica should come out a leaner and stronger company.

The Information Content of Share Repurchases

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Repurchase motives

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Announcement of a share repurchase is not a commitment to continue repurchases in later years. So the information content of a repurchase announcement is less strongly positive than the announcement of a dividend increase. Nevertheless, a study by Comment and Jarrell, who looked at the announcements of open-market repurchase programs, found that on average they resulted in an abnormal price rise of 2%.¹⁰

Investors may applaud repurchases if they worry that managers would otherwise fritter away the money on perks or unprofitable empire building. Repurchases can also reflect management optimism, perhaps their view that their company’s shares are underpriced by investors.

Stock repurchases may also be used to signal a manager’s confidence in the future. Suppose that you, the manager, believe that your stock is substantially undervalued. You announce that the company is prepared to buy back a fifth of its stock at a price that is 20% above the current market price. But (you say) you are certainly not going to sell any of your own stock at that price. Investors jump to the obvious conclusion—you must believe that the stock is a good value even at 20% above the current price.

When companies offer to repurchase their stock at a premium, senior management and directors usually commit to hold on to their stock.¹¹ So it is not surprising that researchers have found that announcements of offers to buy back shares above the market price have prompted a larger rise in the stock price, averaging about 11%.¹²

 16-3   Dividends or Repurchases? The Payout Controversy

Announcements of dividends and repurchases can convey information about management’s confidence and so affect the stock price. But eventually the stock price change would happen anyway as information seeps out through other channels. Does payout policy affect value in the long run?

Suppose you are CFO of a successful, profitable public company. The company is maturing. Growth is slowing down, and you plan to distribute free cash flow to stockholders. Does it matter whether you initiate dividends or a repurchase program? Does the choice affect the market value of your firm in any fundamental way?

One of the endearing features of economics is its ability to accommodate not just two, but three opposing points of view. And so it is with the choice between dividends and repurchases. On the right are conservatives who argue that investors pay more for firms with generous, stable dividends. On the left, another group argues that repurchases are better because repurchases mean higher stock prices, and capital gains have been taxed at lower effective rates than dividends. And in the center, a middle-of-the-road party claims that the choice between dividends and repurchases has no effect on value.

Payout Policy Is Irrelevant in Perfect Capital Markets

The middle-of-the-road party was founded in 1961 by Miller and Modigliani (always referred to as “MM”), when they published a proof that dividend policy is value-irrelevant in a world without taxes, transaction costs, and other market imperfections.¹³

MM insisted that one must consider dividend policy only after holding the firm’s assets, investments, and borrowing policy fixed. Suppose they were not fixed. For example, suppose that the firm decides to reduce capital investment and to pay out the cash saved as a dividend. In this case the effect of the dividend on shareholder value is tangled up with the profitability of the foregone investment. Or suppose that the firm decides to borrow more aggressively and to pay out the debt proceeds as dividends. In this case the effect of the dividend can’t be separated from the effect of the additional borrowing.

Think what happens if you want to up the dividend without changing the investment policy or capital structure. The extra cash for the dividend must come from somewhere. If the firm fixes its borrowing, the only way it can finance the extra dividend is to sell more shares. Alternatively, rather than increasing dividends and selling new shares, the firm can pay lower dividends. With investment policy and borrowing fixed, the cash that is saved can only be used to buy back some of the firm’s existing shares. Thus any change in dividend payout must be offset by the sale or repurchase of shares.

Repurchases were rare when MM wrote in 1961, but we can easily apply their reasoning to the choice between dividends and repurchases. A simple example is enough to show MM’s irrelevance result. Then we will show that value is also unaffected if the company increases the dividend and finances the increase with an issue of shares.

Dividends or Repurchases? An Example

Rational Demiconductor has at this moment one million shares outstanding and the following market-value balance sheet:

For simplicity we assume it has no debt. All of its fixed assets are paid for. We assume that its working capital includes enough cash to support its operations, so the $1 million cash entered at the top left of its balance sheet is surplus.

Rational’s market capitalization is $11 million, so each of its one million shares is worth $11. If it now pays out the surplus cash, market capitalization must fall to $10 million:

But the price per share depends on whether the surplus cash is paid out as a dividend or by repurchases. If a dividend of $1 per share is paid, one million shares are still outstanding, and stock price is $10. Shareholders’ wealth, including the cash dividends, is $10 + 1 = $11 per share.

Suppose Rational pays no cash dividend, but repurchases shares instead. It spends $1 million to repurchase 90,909 shares at $11 each, leaving 909,091 shares outstanding. Stock price remains at $11 ($10 million divided by 909,091 shares).¹⁴ Shareholders’ wealth is $11 per share. It doesn’t matter whether a particular shareholder decides to sell shares back to the firm. If she sells, she gets $11 per share in cash. If she doesn’t want to sell, she retains shares worth $11 each.

Thus shareholder wealth is the same with dividends as with repurchases. If Rational pays a cash dividend, wealth is $10 + 1 = $11, including the dividend. If Rational repurchases, there is no dividend but each share is worth $11.

You may hear a claim that share repurchases should increase the stock price. That’s not quite right, as our example illustrates. A repurchase does not increase the stock price, but it avoids the fall in stock price that would occur on the ex-dividend day if the amount spent on repurchases were paid out as cash dividends. Repurchases do not guarantee a higher stock price, but only a stock price higher than if a dividend were paid instead. Repurchases also reduce the number of shares outstanding, so future earnings per share are higher than if the same amount were paid out as dividends.

If MM and the middle-of-the-roaders are correct and payout policy does not affect value, then the choice between dividends and repurchases is merely tactical. A company will decide to repurchase if it wants to retain the flexibility to cut back payout if valuable investment opportunities arise. Another company may decide to pay dividends to assure stockholders that it will run a tight ship, paying out free cash flow to limit the temptation for careless spending.

Stock Repurchases and DCF Models of Share Price

Our example looked at a one-time choice between a cash dividend and repurchase program. In practice a company that pays a dividend today also makes an implicit promise to continue paying dividends in later years, smoothing the dividends and increasing them gradually as earnings grow. Repurchases are not smoothed in the same way as dividends, although a repurchase today is often followed by more repurchases later.

A repurchase program reduces the number of outstanding shares and increases earnings and dividends per share. Thus we should pause and consider what repurchases imply for the DCF dividend-discount models that we derived and applied in Chapter 4. These models say that stock price equals the PV of future dividends per share. How do we apply these models when the number of shares is changing?

When repurchases are important, you should consider two valuation approaches for common stocks.

1.  Calculate market capitalization (the aggregate value of all shares) by forecasting and discounting the free cash flow paid out to shareholders. Then calculate price per share by dividing market capitalization by the number of shares currently outstanding. With this approach, you don’t have to worry about how payout of free cash flow is split between dividends and repurchases.

2.  Calculate the present value of dividends per share, taking account of the increased growth rate of dividends per share caused by the declining number of shares as shares are repurchased.

The first valuation approach, which focuses on the total free cash flow available for payout to shareholders, is easier and more reliable when future repurchases are erratic or unpredictable.

We illustrate by continuing the Rational Demiconductor example. Suppose that Rational has just paid a cash dividend of $1 per share, reducing ex-dividend market capitalization to $10 million. We now reveal the source of Rational’s equity value. Its operations are expected to generate a level, perpetual stream of earnings and free cash flow of $1 million per year (no forecasted growth or decline). The cost of capital is r = .10, or 10%. Thus the market capitalization of all of Rational’s currently outstanding shares is PV = FCF/r = 1/.10 = $10 million.

The price per share equals market capitalization divided by the shares currently outstanding: $10 million divided by $1 million = $10 per share. This is the first valuation approach.

The second approach requires an assumption about future payout policy. Life is easy if Rational commits to dividends only, no repurchases. In that case, the forecasted dividend stream is level and perpetual at $1 per share. We can use the constant-growth DCF model with a growth rate g = 0. Share price is

But suppose that Rational announces instead that henceforth it will pay out exactly 50% of free cash flow as dividends and 50% as repurchases. This means that next year’s dividend will be only $.50. On the other hand, Rational will use $500,000 (50% of free cash flow) to buy back shares. It will repurchase 47,619 shares at the ex-dividend price of $10.50 per share, and shares outstanding will fall to 1,000,000 – 47,619 = 952,381 shares.¹⁵ Thus expected free cash flow per share for year 2 increases to $1 million divided by 952,381 = $1.05 per share. So the $.50 reduction in the dividend for year 1 has been offset by 5% growth in future free cash flow per share, from $1 to $1.05 in year 2. And if you carry this example forward to year 3 and beyond, you will see that using 50% of free cash flow for repurchases continues to generate a growth rate of 5% per year.

So the DCF model comes back to exactly the same value for Rational’s shares today, just as MM would predict. The repurchase program decreases next year’s dividend from $1.00 to $.50 per share, but generates 5% growth in earnings and dividends per share.

Thus we can get to Rational’s price per share in two ways. The easy first method is to calculate equity market capitalization based on total free cash flow, and then divide by the current number of shares outstanding. The second, more difficult method is to forecast and discount dividends per share, taking account of the growth in dividends per share caused by repurchases. We recommend the easy way when repurchases are important. Note also that the second way, which works out nicely in our example, becomes much more difficult to do precisely when repurchases are irregular or unpredictable.

Our example illustrates several general points. First, absent tax effects or other market frictions, today’s market capitalization and share price are not affected by how payout is split between dividends and repurchases. Second, shifting payout to repurchases reduces current dividends but produces an offsetting increase in future earnings and dividends per share. Third, when valuing cash flow per share, it is double-counting to include both the forecasted dividends per share and cash received from repurchases. If you sell back your share, you don’t get any subsequent dividends.

Dividends and Share Issues

We have considered dividend policy as the choice between cash dividends or repurchases. If we hold total payout constant, smaller dividends mean larger repurchases. But, as we noted earlier, MM derived their dividend-irrelevance theorem when repurchases were rare. So MM asked whether a corporation could increase value by paying larger cash dividends. But they insisted on holding investment and debt-financing policy fixed.

Suppose a company like Rational Demiconductor has paid out any surplus cash. Now it wants to try to impress investors by paying out an even larger dividend. The extra money must come from somewhere. If the firm fixes its borrowing, the only way it can finance the extra dividend is to print some more shares and sell them. The new stockholders are going to part with their money only if you can offer them shares that are worth as much as they cost. But how can the firm sell more shares when its assets, earnings, investment opportunities, and, therefore, market value are all unchanged? The answer is that there must be a transfer of value from the old to the new stockholders. The new ones get the newly printed shares, each one worth less than before the extra dividend was announced, and the old ones suffer a capital loss on their shares. The capital loss borne by the old shareholders just offsets the extra cash dividend they receive.

   FIGURE 16.4 Company Z pays out a third of its worth as a dividend and raises the money by selling new shares. The transfer of value to the new stockholders is equal to the dividend payment. The total value of the firm is unaffected.

Turn back to the first Rational Demiconductor balance sheet, which shows the company starting with $1 million of surplus cash, $1 per share. Suppose it decides to pay a dividend of $2 per share. To do so it will have to issue new shares (sooner or later) to replace the extra $1 million of cash that just went out the door. The ex-dividend stock price is $9, so it will have to issue 111,111 shares to raise $1 million. The issue brings Rational’s equity market capitalization back to 1,111,111 × 9 = $10 million. Thus Rational’s shareholders receive a dividend of $2 versus $1 per share, but the extra cash in their pockets is exactly offset by a lower stock price. They own a smaller fraction of the firm, because Rational had to finance the extra dividend by issuing 111,111 new shares.

Figure 16.4 shows how this transfer of value occurs. Assume that Company Z pays out a third of its total value as a dividend and it raises the money to do so by selling new shares. The capital loss suffered by the old stockholders is represented by the reduction in the size of the red boxes. But that capital loss is exactly offset by the fact that the new money raised (the black boxes) is paid over to them as dividends. The firm that sells shares to pay higher dividends is simply recycling cash. To suggest that this makes shareholders better off is like advising the cook to cool the kitchen by leaving the refrigerator door open.

Does it make any difference to the old stockholders that they receive an extra dividend payment plus an offsetting capital loss? It might if that were the only way they could get their hands on cash. But as long as there are efficient capital markets, they can raise the cash by selling shares. Thus the old shareholders can cash in either by persuading the management to pay a higher dividend or by selling some of their shares. In either case there will be a transfer of value from old to new shareholders. The only difference is that in the former case this transfer is caused by a dilution in the value of each of the firm’s shares, and in the latter case it is caused by a reduction in the number of shares held by the old shareholders. The two alternatives are compared in Figure 16.5.

Because investors do not need dividends to get their hands on cash, they will not pay higher prices for the shares of firms with high payouts. Therefore firms should not worry about paying low dividends or no dividends at all.

   FIGURE 16.5 Two ways of raising cash for the firm’s original shareholders. In each case the cash received is offset by a decline in the value of the old stockholders’ claim on the firm. If the firm pays a dividend, each share is worth less because more shares have to be issued against the firm’s assets. If the old stockholders sell some of their shares, each share is worth the same but the old stockholders have fewer shares.

Of course, this conclusion ignores taxes, issue costs, and a variety of other complications. We turn to these in a moment. The really crucial assumption in our proof is that the new shares are sold at a fair price. The shares that are sold for $1,000 must be worth $1,000. In other words, we have assumed efficient markets.

 16-4   The Rightists

MM said that dividend policy is irrelevant because it does not affect shareholder value. MM did not say that payout should be random or erratic; for example, it may change over the life cycle of the firm. A young growth firm pays out little or nothing, to maximize the cash flow available for investment. As the firm matures, positive-NPV investment opportunities are harder to come by and growth slows down. There is cash available for payout to shareholders. In old age, profitable growth opportunities disappear, and payout may become much more generous.

Of course MM assumed absolutely perfect and efficient capital markets. In MM’s world, everyone is a rational optimizer. The right-wing payout party points to real-world imperfections that could make high dividend payout ratios better than low ones. There is a natural clientele for high-payout stocks, for example. Some financial institutions are legally restricted from holding stocks lacking established dividend records. Trusts and endowment funds may prefer high-dividend stocks because dividends are regarded as spendable “income,” whereas capital gains are “additions to principal.”

There is also a natural clientele of investors, such as the elderly, who look to their stock portfolios for a steady source of cash to live on.¹⁶ In principle, this cash could be easily generated from stocks paying no dividends at all; the investor could just sell off a small fraction of his or her holdings from time to time. But it is simpler and cheaper for the company to send a quarterly check than for its shareholders to sell, say, one share every three months. Regular dividends relieve many of its shareholders of transaction costs and considerable inconvenience.

FINANCE IN PRACTICE

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Microsoft’s Payout Bonanza

  There is a point at which hoarding money becomes embarrassing. . . . Microsoft, which grew into the world’s largest software company . . . and which has been generating cash at the rate of $1 billion a month, passed that point years ago. On July 20th, it finally addressed the issue.

Its solution was to give back to its shareholders, in various forms, an unprecedented $75 billion. One dollop, to the tune of $32 billion, will be a one-time dividend to be paid in December. Another will be share buybacks worth $30 billion over four years. The third will be a doubling of Microsoft’s ongoing dividend to 32 cents a share annually, payable in quarterly instalments. Not bad for a company that has not even turned 30 yet, and that only declared its first dividend in January 2003.

The decision is impressive for the mature analysis by Microsoft of its role in the industry and the prospects for the future that it implies.

Source: “An End to Growth?” The Economist © The Economist Newspaper Limited, London (July 24, 2004). Used with permission via Copyright Clearance Center.

Some observers have appealed to behavioral psychology to explain why we may prefer to receive those regular dividends rather than sell small amounts of stock.¹⁷ We are all, they point out, liable to succumb to temptation. Some of us may hanker after fattening foods, while others may be dying for a drink. We could seek to control these cravings by willpower, but that can be a painful struggle. Instead, it may be easier to set simple rules for ourselves (“cut out chocolate,” or “wine with meals only”). In just the same way, we may welcome the self-discipline that comes from spending only dividend income, and thereby sidestep the difficult decision of how much we should dip into capital.

Clearly some clienteles of investors prefer stocks with regular and stable cash dividends. These investors might be willing to pay more for stocks of companies that paid out cash by dividends rather than repurchases. But do they have to pay more? Corporations are free to adjust the supply of dividends to demand. If they could increase their stock prices simply by shifting payout from repurchases to cash dividends, they would presumably have done so already. The investors who prefer cash dividends already have a wide choice of dividend-paying stocks. If the supply of such stocks is sufficient to satisfy those investors, then additional firms have no incentive to switch from repurchases to cash dividends. If this is indeed the outcome, the middle-of-the-road party wins, even if the rightists have correctly identified clienteles that prefer cash dividends.

Payout Policy, Investment Policy, and Management Incentives

Perhaps the most persuasive argument in favor of the rightist position is that paying out funds to shareholders prevents managers from misusing or wasting funds.¹⁸ Suppose a company has plenty of free cash flow but few profitable investment opportunities. Shareholders may not trust the managers to spend retained earnings wisely and may fear that the money will be plowed back into building a larger empire rather than a more profitable one. In such cases investors may demand higher dividends or a stock repurchase not because these are valuable in themselves, but because they encourage a more careful, value-oriented investment policy.

The box on the previous page describes how Microsoft announced the largest cash distribution in corporate history. By 2004 the company’s investment opportunities had diminished, and investors were, therefore, happy to see Microsoft distribute its cash mountain.

Microsoft paid out its gigantic special dividend willingly. Other cash-cow corporations may let go of cash grudgingly under pressure from investors. Stock price falls when investors sense excessive perks or empire building. The threat of a falling stock price is an excellent motivator, particularly for top managers holding valuable stock options.

The willingness of mature corporations to make generous payouts shows that corporate governance works in the U.S. and other developed economies. But governance is less effective in many emerging economies, and managers’ and stockholders’ interests are not always closely aligned. Dividend payout ratios are smaller where governance is weak.

 16-5   Taxes and the Radical Left

The left-wing dividend creed is simple: Whenever dividends are taxed more heavily than capital gains, firms should pay the lowest cash dividend they can get away with. Available cash should be used to repurchase shares.

By shifting their distribution policies in this way, corporations can transmute dividends into capital gains. If this financial alchemy results in lower taxes, it should be welcomed by any taxpaying investor. That is the basic point made by the leftist party when it argues for repurchases instead of dividends.

There is no doubt that taxes on dividends can make a difference. For example, Microsoft’s $32 billion special dividend came after the maximum U.S. tax rate on dividends was lowered to 15%.

BEYOND THE PAGE

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U.S. tax rates

brealey.mhhe.com/c16

The leftists quickly run into two problems, however. First, if they are right, why should any firm ever pay a cash dividend? If cash is paid out, repurchases should always be the best channel as long as the firm has taxable shareholders.¹⁹ Second, the difference in taxation of dividends and capital gains is much less now than historically. As we write this in 2012, the top U.S. tax rate on both dividends and capital gains is 15%.²⁰

Capital gains still offer some tax advantage, even at these low rates. Taxes on dividends have to be paid immediately, but taxes on capital gains can be deferred until shares are sold and gains realized. The longer investors wait to sell, the lower the PV of their tax liability.²¹

The distinction between dividends and capital gains is not important for many financial institutions, which operate free of all taxes. For example, pension funds are not taxed. These funds hold $3.7 billion of common stocks, so their clout in the U.S. stock market is enormous. Only corporations have a tax reason to prefer cash dividends. They pay corporate income tax on only 30% of dividends received. Thus the effective tax rate is 30% of 35% (the marginal corporate rate), or 10.5%. But corporations have to pay 35% tax on the full amount of realized capital gains.

The low-payout party has nevertheless maintained that the market rewards firms that have low-payout policies. They have claimed that firms that paid dividends and as a result had to issue shares from time to time were making a serious mistake. Any such firm was essentially financing its dividends by issuing stock; it should have cut its dividends at least to the point at which stock issues were unnecessary. This would not only have saved taxes for shareholders but it would also have avoided the transaction costs of the stock issues.²²

Empirical Evidence on Dividends and Taxes

It is hard to deny that taxes are important to investors. You can see that in the bond market. Interest on municipal bonds is not taxed, and so municipals have often sold at low pretax yields. Interest on federal government bonds is taxed, and so these bonds have sold at higher pretax yields. It does not seem likely that investors in bonds just forget about taxes when they enter the stock market.

There is some evidence that in the past taxes have affected U.S. investors’ choice of stocks.²³ Lightly taxed institutional investors have tended to hold high-yield stocks and retail investors have preferred low-yield stocks. Moreover, this preference for low-yield stocks has been somewhat more marked for high-income individuals. Nevertheless, it seems that taxes have been only a secondary consideration with these investors, and have not deterred individuals in high-tax brackets from holding substantial amounts of dividend-paying stocks.

If investors are concerned about taxes, we might also expect that, when the tax penalty on dividends is high, companies would think twice about increasing the payout. Only about a fifth of U.S. financial managers cite investor taxes as an important influence when the firm makes its dividend decision. On the other hand, firms have sometimes responded to major shifts in the way that investors are taxed. For example, when Australia introduced a tax change in 1987 that effectively eliminated the tax penalty on dividends for Australian investors, firms became more willing to increase their payout.²⁴

If tax considerations are important, we would expect to find a historical tendency for high-dividend stocks to sell at lower prices and therefore to offer higher returns. Unfortunately, there are difficulties in measuring this effect. For example, suppose that stock A is priced at $100 and is expected to pay a $5 dividend. The expected yield is, therefore, 5/100 = .05, or 5%. The company now announces bumper earnings and a $10 dividend. Thus with the benefit of hindsight, A’s actual dividend yield is 10/100 = .10, or 10%. If the unexpected increase in earnings causes a rise in A’s stock price, we will observe that a high actual yield is accompanied by a high actual return. But that would not tell us anything about whether a high expected yield was accompanied by a high expected return. To measure the effect of dividend policy, we need to estimate the dividends that investors expected.

A second problem is that nobody is quite sure what is meant by high dividend yield. For example, utility stocks have generally offered high yields. But did they have a high yield all year, or only in months or on days that dividends were paid? Perhaps for most of the year, they had zero yields and were perfect holdings for the highly taxed individuals.²⁵ Of course, high-tax investors did not want to hold a stock on the days dividends were paid, but they could sell their stock temporarily to a security dealer. Dealers are taxed equally on dividends and capital gains and therefore should not have demanded any extra return for holding stocks over the dividend period. If shareholders could pass stocks freely between each other at the time of the dividend payment, we should not observe any tax effects at all.

A number of researchers have attempted to tackle these problems and to measure whether investors demand a higher return from high-yielding stocks. Their findings offer some limited comfort to the dividends-are-bad school, for most of the researchers have suggested that high-yielding stocks have provided higher returns. However, most of these studies date back to a time when there was a dramatic difference in the taxation of dividends and capital gains. Moreover, the estimated tax rates differ substantially from one study to another. For example, while Litzenberger and Ramaswamy concluded that investors have priced stocks as if dividend income attracted an extra 14% to 23% rate of tax, Miller and Scholes used a different methodology and came up with a negligible 4% difference in the rate of tax.²⁶

Alternative Tax Systems

In the U.S. shareholders’ returns are taxed twice. They are taxed at the corporate level (corporate tax) and in the hands of the shareholder (income tax or capital gains tax). These two tiers of tax are illustrated in Table 16.1, which shows the after-tax return to the shareholder if the company distributes all its income as dividends. We assume the company earns $100 a share before tax and therefore pays corporate tax of .35 × 100 = $35. This leaves $65 a share to be paid out as a dividend, which is then subject to a second layer of tax. For example, a shareholder who is taxed at 15% pays tax on this dividend of .15 × 65 = $9.75. Only a tax-exempt pension fund or charity would retain the full $65.

Of course, dividends are regularly paid by companies that operate under very different tax systems. For example, Germany partly compensates for the corporate layer of tax by levying income tax on only half an individual’s dividend income.

In some other countries, such as Australia and New Zealand, shareholders’ returns are not taxed twice. For example, in Australia shareholders are taxed on dividends, but they may deduct from this tax bill their share of the corporate tax that the company has paid. This is known as an imputation tax system. Table 16.2 shows how the imputation system works. Suppose that an Australian company earns pretax profits of A$100 a share. After it pays corporate tax at 30%, the profit is A$70 a share. The company now declares a net dividend of A$70 and sends each shareholder a check for this amount. This dividend is accompanied by a tax credit saying that the company has already paid A$30 of tax on the shareholder’s behalf. Thus shareholders are treated as if each received a total, or gross, dividend of 70 + 30 = A$100 and paid tax of A$30. If the shareholder’s tax rate is 30%, there is no more tax to pay and the shareholder retains the net dividend of A$70. If the shareholder pays tax at the top personal rate of 45%, then he or she is required to pay an additional $15 of tax; if the tax rate is 15% (the rate at which Australian pension funds are taxed), then the shareholder receives a refund of 30 – 15 = A$15.²⁷

   TABLE 16.1 In the U.S. returns to shareholders are taxed twice. This example assumes that all income after corporate taxes is paid out as cash dividends to an investor in the top income tax bracket (figures in dollars per share).

   TABLE 16.2 Under imputation tax systems, such as that in Australia, shareholders receive a tax credit for the corporate tax that the firm has paid (figures in Australian dollars per share).

Under an imputation tax system, millionaires have to cough up the extra personal tax on dividends. If this is more than the tax that they would pay on capital gains, then millionaires would prefer that the company does not distribute earnings. If it is the other way around, they would prefer dividends.²⁸ Investors with low tax rates have no doubts about the matter. If the company pays a dividend, these investors receive a check from the revenue service for the excess tax that the company has paid, and therefore they prefer high payout rates.

Look once again at Table 16.2 and think what would happen if the corporate tax rate were zero. The shareholder with a 15% tax rate would still end up with A$85, and the shareholder with the 45% rate would still receive A$55. Thus, under an imputation tax system, when a company pays out all its earnings, there is effectively only one layer of tax—the tax on the shareholder. The revenue service collects this tax through the company and then sends a demand to the shareholder for any excess tax or makes a refund for any overpayment.²⁹

Taxes and Payout—A Summary

Taxes are important, but cannot be the whole story of payout. Many companies paid generous dividends in the 1960s and 1970s, when U.S. tax rates on dividends were much higher than today. The shift from dividends to repurchases accelerated in the 2000s, when tax rates on both dividends and capital gains were much lower than historical levels. Payout has also shifted to repurchases in countries such as Australia which have imputation tax systems that remove the double taxation of dividends.

Nevertheless it seems safe to say that the tax advantages of repurchases are one reason that they have grown so much in the U.S. and other developed economies.

But financial markets clearly have room for a diversity of payout policies. Smaller growth companies reinvest all earnings and pay out nothing at all. Some pay out entirely through repurchases, some occasionally, some regularly. Some both pay dividends and repurchase. Very few companies pay out exclusively through cash dividends. Some historical evidence suggests that investors demand higher expected rates of return from high-dividend companies, but the evidence is not strong or sufficiently up-to-date to deter a corporation that wants to initiate cash dividends.

 16-6   Payout Policy and the Life Cycle of the Firm

MM said that dividend policy does not affect shareholder value. Shareholder value is driven by the firm’s investment policy, including its future growth opportunities. Financing policy, including the choice between debt and equity, can also affect value, as we will see in Chapter 18.

In MM’s analysis, payout is a residual, a by-product of other financial policies. The firm should make investment and financing decisions, and then pay out whatever cash is left over. Therefore decisions about how much to pay out should change over the life cycle of the firm.

MM assumed a perfect and rational world, but many of the complications discussed in this chapter actually reinforce the life cycle of payout. Let’s review the life-cycle story.³⁰

Young growth firms have plenty of profitable investment opportunities. During this time it is efficient to retain and reinvest all operating cash flow. Why pay out cash to investors if the firm then has to replace the cash by borrowing or issuing more shares? Retaining cash avoids costs of issuing securities and minimizes shareholders’ taxes. Investors are not worried about wasteful overinvestment, because investment opportunities are good, and managers’ compensation is tied to stock price.

As the firm matures, positive-NPV projects become scarcer relative to cash flow. The firm begins to accumulate cash. Now investors begin to worry about overinvestment or excessive perks. The investors pressure management to start paying out cash. Sooner or later, managers comply—otherwise stock price stagnates. The payout may come as share repurchases, but initiating a regular cash dividend sends a stronger and more reassuring signal of financial discipline. The commitment to financial discipline can outweigh the tax costs of dividends. (The middle-of-the-road party argues that the tax costs of paying cash dividends may not be that large, particularly in recent years, when U.S. personal tax rates on dividends and capital gains have been low.) Regular dividends may also be attractive to some types of investors, for example, retirees who depend on dividends for living expenses.

As the firm ages, more and more payout is called for. The payout may come as higher dividends or larger repurchases. Sometimes the payout comes as the result of a takeover. Shareholders are bought out, and the firm’s new owners generate cash by selling assets and restructuring operations. We discuss takeovers in Chapter 32.

The life cycle of the firm is not always predictable. It’s not always obvious when the firm is “mature” and ready to start paying cash back to shareholders. The following three questions can help the financial manager decide:

1.  Is the company generating positive free cash flow after making all investments with positive NPVs and is the positive free cash flow likely to continue?

2.  Is the firm’s debt ratio prudent?

3.  Are the company’s holdings of cash a sufficient cushion for unexpected setbacks and a sufficient war chest for unexpected opportunities?

If the answer to all three questions is yes, then the free cash flow is surplus, and payout is called for.

In March 2012 Apple’s answer to all three questions was “yes.” Yes, it was continuing to accumulate cash at a rate of $30 billion per year. Yes, because it had no debt to speak of. Yes, because no conceivable investment or acquisition could soak up its excess cash flow.

Some critics had argued that Apple should pay out the cash because it was earning interest at less than 1% per year. That was a spurious argument because shareholders had no better opportunities. Safe interest rates were extremely low, and neither Apple nor investors could do anything about it.

Note also two further points. First, Apple did not just initiate a cash dividend. It announced a combination of dividends and repurchases. This two-part payout strategy is now standard for large, mature corporations. Second, Apple did not initiate repurchases because its stock was undervalued but because it had surplus cash. You will hear critics who claim that companies should repurchase shares in bad times, when profits disappoint, and forbear in good times when profits are high. It is true that repurchases are sometimes triggered by management’s view that their company’s stock is underappreciated by investors. But repurchases are primarily a device for distributing surplus cash to investors. It’s no surprise that repurchases increase when profits are high and more surplus cash is available.

Payout and Corporate Governance

Most of this chapter has considered payout policy by public corporations in developed economies with good corporate governance. Payout can play a still more important role in countries where corporations are more opaque and governance less effective.

In some countries you cannot trust the financial information that companies provide. A passion for secrecy and a tendency to construct multilayered corporate organizations produce earnings figures that are doubtful and sometimes meaningless. Thanks to creative accounting, the situation is little better for some companies in the U.S., although accounting standards have tightened since passage of the Sarbanes-Oxley legislation in 2002.

How does an investor separate the winners and losers when governance is weak and corporations are opaque? One clue is payout. Investors can’t read managers’ minds, but they can learn from their actions. They know that a firm that reports good earnings and pays out a significant fraction of the earnings is putting its money where its mouth is. We can understand, therefore, why investors would be skeptical about reported earnings unless they were backed up by consistent payout policy.

Of course firms can cheat in the short run by overstating earnings and scraping up cash for payout. But it is hard to cheat in the long run because a firm that is not making money will not have cash to pay out. If a firm pays a high dividend or commits to substantial repurchases without generating sufficient cash flow, it will ultimately have to seek additional debt or equity financing. The requirement for new financing would reveal management’s game to investors.

The implications for payout in developing countries could go either way. On the one hand, managers who are committed to shareholder value have a stronger motive to pay out cash when corporate governance is weak and corporate financial statements are opaque. Payout makes the firm’s reported earnings more credible. On the other hand, weak corporate governance may also weaken managers’ commitment to shareholders. In this case they will pay out less, and instead deploy cash more in their own interests. It turns out that dividend payout ratios are on average smaller where governance is weak.³¹

FINANCE IN THE NEWS

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Apple Commits to Dividend and Buyback

  Figure 16.6 shows how Apple’s holdings of cash and marketable securities have grown over the past decade. By the start of 2012, Apple Inc. had accumulated cash and long-term securities of about $100 billion. Steve Jobs, the architect of Apple’s explosive growth, had preferred to keep the war chest of cash for investment or possible acquisitions. Job’s fiscal conservatism may seem quaint when Apple’s forecasted income for 2012 was over $40 billion. But Jobs could remember tough times for Apple; the company was near bankruptcy when Jobs took over in 1997. Apple had paid cash dividends in the early 1990s, but was forced to stop in 1995 as its cash reserves dwindled.

After Jobs died in October 2011, the pressure from investors for payout steadily increased. “They have a ridiculous amount of cash,” said Douglas Skinner, a professor of accounting at the Chicago Booth School of Business. “There is no feasible acquisition that Apple could do that would need that much cash.”

On March 19, 2012, Apple announced that it would pay a quarterly dividend of $2.65 per share and spend $10 billion for share buybacks. It forecasted $45 billion in payout over the following three years. Apple’s stock price jumped by $15.53 to $601 by the close of trading on the announcement day. Apple’s dividend yield went from zero to (2.65 × 4)/601 = 1.8%.

Was Apple’s payout sufficiently generous? Analysts’ opinions varied. “A pretty vanilla return-of-cash program” (A. M. Sacconaghi, Bernstein Research). “It’s not too piddling, and on the other hand not so large to signal that growth prospects are not what they thought” (David A. Rolfe, Wedgewood Partners). Bill Choi (Janney Montgomery Scott) pointed out that income-oriented mutual funds would now be more comfortable holding Apple stock.

   FIGURE 16.6 The growth in Apple’s holdings of cash and marketable securities, 2002–2011.

Source: N. Wingfield, “Flush with Cash, Apple Declares a Dividend and Buyback,” The New York Times, March 20, 2012, pp. B1, B9.

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SUMMARY

A corporation’s payout policy is the answer to two questions. First, how much cash should the company pay out to its stockholders? Second, how should the cash be distributed, by paying cash dividends or by repurchasing shares?

The answer to “How much?” is often zero. Younger companies with profitable growth opportunities do not pay out cash and rarely repurchase stock. They finance investment as much as possible with internally generated cash flow. But as they mature, growth opportunities gradually fade away and surplus cash accumulates. Then investors press for payout because they worry that managers will overinvest if too much idle cash is lying around.

Cash is surplus when these three criteria are met:

1.  Free cash flow is reliably positive. Recall that free cash flow is the operating cash flow left over after the firm has made all positive-NPV investments.

2.  The firm’s debt level is prudent and manageable. Otherwise free cash flow is better used to pay down debt.

3.  The firm has a sufficient war chest of cash or unused debt capacity to cover unexpected opportunities or setbacks.

A firm with surplus cash will probably start by repurchasing shares. Repurchases are more flexible than dividends. Once a company announces a regular cash dividend, investors expect the dividend to continue unless the company encounters serious financial trouble. Thus financial managers do not start or increase a cash dividend unless they are confident that the dividend can be maintained. Announcements of dividend initiations or increases usually cause a stock price increase, because the announcements signal managers’ confidence. This is the information content of dividends.

Regular cash dividends are paid by mature, profitable firms. But most firms that pay regular cash dividends also repurchase shares. If we lived in an ideally simple and perfect world, the choice between cash dividends and stock repurchase would have no effect on market value. For example, when a company shifts payout from repurchases to cash dividends, then shareholders’ extra cash is exactly offset by a lower stock price.

The most obvious and serious market imperfection has been the different tax treatment of dividends and capital gains. U.S. tax rates on dividends have in the past been much higher than on capital gains. By 2012, the tax rate on both dividends and capital gains was 15%, although the effective tax rate on capital gains was lower because payment can be deferred until shares are sold. Thus taxes have favored repurchases.

Taxes alone cannot explain payout policy, however. For example, corporations paid out massive sums in cash dividends even in the 1960s, 1970s, and early 1980s, when the top income-tax rate on dividends was 70%.

Of course some investors—widows and orphans, for example—may depend on regular cash dividends. But the supply of dividends should expand to satisfy this clientele, and if the supply of dividends already meets demand, then no single firm can increase its market value simply by paying dividends. (A dividend announcement may be good news for investors, but that news would come out sooner or later through other channels.)

It is difficult to be dogmatic about payout. But remember, if investment and capital-structure decisions are held constant, then arguments about payout policy are largely about shuffling money from one pocket to another. Unless large tax consequences accompany these shuffles, it’s unlikely that firm value is much affected by the choice between dividends and repurchases. The short-run choice is tactical. Longer-run payout strategy depends on the life cycle of the firm from youth and growth to profitable maturity.

Investors seem interested in payout mostly because of the information they read into payout decisions. Investors also push mature firms to pay out cash. Committing to a regular cash dividend is a particularly effective signal of financial discipline.

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FURTHER READING

For comprehensive reviews of the literature on payout policy, see:

F. Allen and R. Michaely, “Payout Policy,” in G. Constantinides, M. Harris, and R. Stulz, (eds.), Handbook of the Economics of Finance: Corporate Finance (Amsterdam: North-Holland, 2003).

H. DeAngelo, L. DeAngelo, and D. Skinner, “Corporate Payout Policy,” Foundations and Trends in Finance 3 (2008), pp. 95–287.

For a recent survey of managers’ attitudes to the payout decision, see:

A. Kalay and M. Lemmon, “Payout Policy,” in B. E. Eckbo (ed.), Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), Chapter 10.

A. Brav, J. R. Graham, C. R. Harvey, and R. Michaely, “Payout Policy in the 21st Century,” Journal of Financial Economics 77 (September 2005), pp. 483–527.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Dividend payments In 2012 Entergy paid a regular quarterly dividend of $.83 per share.

a.  Match each of the following dates.

b.  On one of these dates, the stock price fell by about $.83. Which date? Why?

c.  Entergy’s stock price in February 2012 was $68. What was the dividend yield?

d.  Entergy forecasted earnings per share of about $6 for 2012. What was the payout ratio?

e.  Suppose that Entergy paid a 10% stock dividend. What would happen to the stock price?

2.  Dividend policy Here are several “facts” about typical corporate dividend policies. Which are true and which false?

a.  Companies decide each year’s dividend by looking at their capital expenditure requirements and then distributing whatever cash is left over.

b.  Managers and investors seem more concerned with dividend changes than with dividend levels.

c.  Managers often increase dividends temporarily when earnings are unexpectedly high for a year or two.

d.  Companies undertaking substantial share repurchases usually finance them with an offsetting reduction in cash dividends.

3.  Dividend payments Seashore Salt Co. has surplus cash. Its CFO decides to pay back $4 per share to investors by initiating a regular dividend of $1 per quarter or $4 per year. The stock price jumps to $90 when the payout is announced.

a.  Why does the stock price increase?

b.  What happens to the stock price when the stock goes ex dividend?

4.  Repurchases Look again at Problem 3. Assume instead that the CFO announces a stock repurchase of $4 per share instead of a cash dividend.

a.  What happens to the stock price when the repurchase is announced? Would you expect the price to increase to $90? Explain briefly.

b.  Suppose the stock is repurchased immediately after the announcement. Would the repurchase result in an additional stock-price increase?

5.  Dividends and stock price Go back to the first Rational Demiconductor balance sheet. Now assume that Rational wins a lawsuit and is paid $1 million in cash. Its market capitalization rises by that amount. It decides to pay out $2 per share instead of $1 per share. Explain what happens to Rational’s stock price if (a) the payout comes as a cash dividend or (b) as a share repurchase.

6.  Dividends and stock price Go back to the first Rational Demiconductor balance sheet one more time. Assume that Rational does not win the lawsuit and is left with only $1 million in surplus cash. Nevertheless Rational decides to pay a cash dividend of $2 per share. What must Rational do to finance the $2 dividend if it holds its debt and investment policies constant? What happens to price per share?

7.  Dividends and shareholders Mr. Milquetoast admires Warren Buffet and believes that Berkshire Hathaway is a good investment. He wants to invest $100,000, but hesitates because Berkshire Hathaway has never paid a dividend. He needs to generate $5,000 per year in cash for living expenses. What should Mr. Milquetoast do? (Note that Berkshire Hathaway’s Class A shares have in recent years sold for more than $100,000 but class B shares are available for substantially less.)

8.  Payout and valuation Surf & Turf Hotels is a mature business, although it pays no cash dividends. Next year’s earnings are forecasted at $56 million. There are 10 million outstanding shares. The company has traditionally paid out 50% of earnings by repurchases and reinvested the remaining earnings. With reinvestment, the company has generated steady growth averaging 5% per year. Assume the cost of equity is 12%.

a.  Calculate Surf & Turf’s current stock price, using the constant-growth DCF model from Chapter 4. (Hint: Take the easy route and value overall market capitalization.)

b.  Now Surf & Turf”s CFO announces a switch from repurchases to a regular cash dividend. Next year’s dividend will be $2.80 per share. The CFO reassures investors that the company will continue to pay out 50% of earnings and reinvest 50%. All future payouts will come as dividends, however. What would you expect to happen to Surf & Turf’s stock price? Why?

9.  Dividends and stock prices Some types of investors prefer dividend-paying stocks because dividends provide a regular, convenient source of income. Does demand from these investors necessarily lift the prices of dividend-paying stocks relative to stocks of companies that pay no dividends but repurchase shares instead? Explain briefly.

10.  Dividends and taxes Which of the following U.S. investors have tax reasons to prefer companies that pay out cash by repurchases instead of cash dividends? Which should not care?

a.  A pension fund

b.  An individual investor in the top income-tax bracket

c.  A corporation

d.  An endowment for a charity or university

11.  Payout policy Halfshell Seafood is still generating good profits, but growth is slowing down. How should its CFO decide when to start up a program of paying out cash to stockholders? What questions should the CFO ask?

INTERMEDIATE

12.  Dividends and repurchases Go to the Apple website or to a financial source like Yahoo! Finance.

a.  Has Apple’s dividend increased from the initial quarterly rate of $2.65?

b.  What was the announcement date of the most recent dividend?

c.  When did Apple stock last go ex dividend?

d.  What happened to the stock price on the ex-dividend date? When was the dividend actually paid?

e.  What is Apple’s dividend yield?

f.  Look up estimates of Apple’s EPS for the next year. What is the dividend payout ratio?

g.  How much does Apple plan to spend on repurchases in the next year? What is the overall payout ratio (dividends plus repurchases)?

13.  Dividend policy Investors and financial managers focus more on changes in cash dividends than on the level of cash dividends. Why?

14.  Information content of dividends What is meant by “the information content of dividends”? Explain.

15.  Information content of dividends Does the good news conveyed by the announcement of a dividend increase mean that a firm can increase its stock price in the long run simply by paying cash dividends? Explain.

16.  Payout policy MM insisted that payout policy should be analyzed holding debt and investment policy constant. Why? Explain.

17.  Dividends and value Little Oil has outstanding one million shares with a total market value of $20 million. The firm is expected to pay $1 million of dividends next year, and thereafter the amount paid out is expected to grow by 5% a year in perpetuity. Thus the expected dividend is $1.05 million in year 2, $1.105 million in year 3, and so on. However, the company has heard that the value of a share depends on the flow of dividends, and therefore it announces that next year’s dividend will be increased to $2 million and that the extra cash will be raised immediately by an issue of shares. After that, the total amount paid out each year will be as previously forecasted, that is, $1.05 million in year 2 and increasing by 5% in each subsequent year.

a.  At what price will the new shares be issued in year 1?

b.  How many shares will the firm need to issue?

c.  What will be the expected dividend payments on these new shares, and what therefore will be paid out to the old shareholders after year 1?

d.  Show that the present value of the cash flows to current shareholders remains $20 million.

18.  Dividends and value We stated in Section 16-3 that MM’s proof of dividend irrelevance assumes that new shares are sold at a fair price. Look back at Problem 17. Assume that new shares are issued in year 1 at $10 a share. Show who gains and who loses. Is dividend policy still irrelevant? Why or why not?

19.  Payout and valuation Look back one last time at Problem 17. How would you value Little Oil if it paid out $500,000 in cash dividends year in and year out, with no expected growth or decline? Remaining free cash flow will be used to repurchase shares. Assume that Little Oil’s free cash flow continues to grow at 5% as in Problem 17.

20.  Dividends vs. repurchases House of Haddock has 5,000 shares outstanding and the stock price is $140. The company is expected to pay a dividend of $20 per share next year and thereafter the dividend is expected to grow indefinitely by 5% a year. The President, George Mullet, now makes a surprise announcement: He says that the company will henceforth distribute half the cash in the form of dividends and the remainder will be used to repurchase stock.

a.  What is the total value of the company before and after the announcement? What is the value of one share?

b.  What is the expected stream of dividends per share for an investor who plans to retain his shares rather than sell them back to the company? Check your estimate of share value by discounting this stream of dividends per share.

21.  Dividends vs. repurchases Here are key financial data for House of Herring, Inc.:

House of Herring plans to pay the entire dividend early in January 2019. All corporate and personal taxes were repealed in 2017.

a.  Other things equal, what will be House of Herring’s stock price after the planned dividend payout?

b.  Suppose the company cancels the dividend and announces that it will use the money saved to repurchase shares. What happens to the stock price on the announcement date? Assume that investors learn nothing about the company’s prospects from the announcement. How many shares will the company need to repurchase?

c.  Suppose the company increases dividends to $5.50 per share and then issues new shares to recoup the extra cash paid out as dividends. What happens to the with- and ex-dividend share prices? How many shares will need to be issued? Again, assume investors learn nothing from the announcement about House of Herring’s prospects.

22.  Dividends and shareholders Respond to the following comment: “It’s all very well saying that I can sell shares to cover cash needs, but that may mean selling at the bottom of the market. If the company pays a regular cash dividend, investors avoid that risk.”

23.  Dividends and stock prices Fromagerie Hors d’Age has been paying a regular cash dividend of €4 per share each year for over a decade. The company is paying out all its earnings as dividends and is not expected to grow. There are 100,000 shares outstanding selling for €80 per share. The company has sufficient cash on hand to pay the next annual dividend.

Suppose that Hors d’Age decides to cut its cash dividend to zero and announces that it will repurchase shares instead.

a.  What is the immediate stock price reaction? Ignore taxes, and assume that the repurchase program conveys no information about operating profitability or business risk.

b.  How many shares will Hors d’Age purchase?

c.  Project and compare future stock prices for the old and new policies. Do this for at least years 1, 2, and 3.

24.  Repurchases An article on stock repurchase in the Los Angeles Times noted: “An increasing number of companies are finding that the best investment they can make these days is in themselves.” Discuss this view. How is the desirability of repurchase affected by company prospects and the price of its stock?

25.  Payout and the cost of capital Comment briefly on each of the following statements:

a.  “Unlike American firms, which are always being pressured by their shareholders to increase dividends, Japanese companies pay out a much smaller proportion of earnings and so enjoy a lower cost of capital.”

b.  “Unlike new capital, which needs a stream of new dividends to service it, retained earnings have zero cost.”

c.  “If a company repurchases stock instead of paying a dividend, the number of shares falls and earnings per share rise. Thus stock repurchase must always be preferred to paying dividends.”

26.  Dividends and valuation Generous dividend payouts and high price–earnings multiples are correlated positively. Does this imply that paying out cash as dividends instead of repurchases increases share price? (Hint: Could the level of dividends be telling investors something about long-run earnings?)

27.  Repurchases and EPS “Many companies use stock repurchases to increase earnings per share. For example, suppose that a company is in the following position:

The company now repurchases 200,000 shares at $200 a share. The number of shares declines to 800,000 shares and earnings per share increase to $12.50. Assuming the price–earnings ratio stays at 20, the share price must rise to $250.” Discuss.

28.  Dividends and taxes The middle-of-the-road party holds that dividend policy doesn’t matter because the supply of high-, medium-, and low-payout stocks has already adjusted to satisfy investors’ demands. Investors who like generous dividends hold stocks that give them all the dividends that they want. Investors who want capital gains see ample low-payout stocks to choose from. Thus, high-payout firms cannot gain by transforming to low-payout firms, or vice versa.

Suppose the government reduces the tax rate on dividends but not on capital gains. Suppose that before this change the supply of dividends matched investor needs. How would you expect the tax change to affect the total cash dividends paid by U.S. corporations and the proportion of high- versus low-payout companies? Would dividend policy still be irrelevant after any dividend supply adjustments are completed? Explain.

CHALLENGE

29.  Dividend policy and the dividend discount model Consider the following two statements: “Dividend policy is irrelevant,” and “Stock price is the present value of expected future dividends.” (See Chapter 4.) They sound contradictory. This question is designed to show that they are fully consistent.

The current price of the shares of Charles River Mining Corporation is $50. Next year’s earnings and dividends per share are $4 and $2, respectively. Investors expect perpetual growth at 8% per year. The expected rate of return demanded by investors is r = 12%.

We can use the perpetual-growth model to calculate stock price:

Suppose that Charles River Mining announces that it will switch to a 100% payout policy, issuing shares as necessary to finance growth. Use the perpetual-growth model to show that current stock price is unchanged.

30.  Dividends and taxes Suppose that there are just three types of investors with the following tax rates:

Individuals invest a total of $80 billion in stock and corporations invest $10 billion. The remaining stock is held by the institutions. All three groups simply seek to maximize their after-tax income.

These investors can choose from three types of stock offering the following pretax payouts:

These payoffs are expected to persist in perpetuity. The low-payout stocks have a total market value of $100 billion, the medium-payout stocks have a value of $50 billion, and the high-payout stocks have a value of $120 billion.

a.  Who are the marginal investors that determine the prices of the stocks?

b.  Suppose that this marginal group of investors requires a 12% after-tax return. What are the prices of the low-, medium-, and high-payout stocks?

c.  Calculate the after-tax returns of the three types of stock for each investor group.

d.  What are the dollar amounts of the three types of stock held by each investor group?

31.  Taxes and dividends What are the implications of an imputation tax system for dividend policy? How would you expect dividend policy to change if a country with a two-tier tax system, like the U.S., changes over to an imputation system like Australia’s?

32.  Dividend policy In Chile firms are obliged to pay out at least 30% of net earnings as dividends to shareholders. Brazil, Colombia, Ecuador, and Uruguay have similar dividend requirements. Why might such restrictions help to reduce conflicts of interest between managers and shareholders?

33.  Taxes and dividends Hong Kong has an unusual tax system. Dividends and capital gains are not taxable. The Peng Corporation currently pays a quarterly dividend of HK$5 per share. It has 5 million shares outstanding at a price of HK$267.

a.  What will happen to the share price on the first day when registered owners are no longer eligible to receive the quarterly dividend of HK$5 per share?

b.  What will happen to the share price if Peng announces a new payout policy? Peng will cut quarterly dividends by HK$2 per share and use the cash to repurchase shares instead.

c.  What if Peng eliminates its next dividend and uses the cash to repurchase shares. Can it repurchase at the current market price of HK$267?

34.  Imputation tax systems Barossa is an Australian corporation. Its corporate tax rate is 30%. Its current stock price is $A126, and with 153 million shares outstanding. Remember that Australia has an imputation tax system. How much income tax will the following shareholders have to pay if Barossa pays a cash dividend of $A1.65 per share?

a.  An individual in a 30% tax bracket who owns 1,000 shares.

b.  An individual with 12,000 shares paying 47% tax.

c.  A pension fund with 100,000 shares and a tax rate of 15%.

___________

¹The declining use of dividends is documented in D. J. Skinner, “The Evolving Relation between Earnings, Dividends, and Stock Repurchases,” Journal of Financial Economics 87 (March 2008), pp. 582–609. In Europe the decline in dividend payers has been particularly steep in Germany. See D. J. Denis and I. Osobov, “Why Do Firms Pay Dividends? International Evidence on the Determinants of Dividend Policy,” Journal of Financial Economics 89 (July 2008), pp. 62–82.

²Where there is no par value, legal capital is defined as part or all of the receipts from the issue of shares. Companies with wasting assets, such as mining companies, are sometimes permitted to pay out legal capital.

³Sometimes companies not only allow shareholders to reinvest dividends but also allow them to buy additional shares at a discount. For an amusing and true rags-to-riches story, see M. S. Scholes and M. A. Wolfson, “Decentralized Investment Banking: The Case of Dividend-Reinvestment and Stock-Purchase Plans,” Journal of Financial Economics 24 (September 1989), pp. 7–36.

⁴The distinction between a stock dividend and a stock split is technical. A stock dividend is shown in the accounts as a transfer from retained earnings to equity capital. A split is shown as a reduction in the par value of each share.

⁵The U.S. Securities and Exchange Commission’s rule 10b-18 protects repurchasing firms from accusations of share-price manipulation. Open-market repurchases are subject to several restrictions, however. For example, repurchases cannot exceed a small fraction of daily trading volume.

⁶P. Healy and K. Palepu, “Earnings Information Conveyed by Dividend Initiations and Omissions,” Journal of Financial Economics 21 (1988), pp. 149–175. For an example of a study that finds no information in dividend changes, see G. Grullon, R. Michaely, and B. Swaminathan, “Are Dividend Changes a Sign of Firm Maturity?” Journal of Business 75 (July 2002), pp. 387–424.

⁷A. R. Ofer and D. R. Siegel, “Corporate Financial Policy, Information, and Market Expectations: An Empirical Investigation of Dividends,” Journal of Finance 42 (September 1987), pp. 889–911.

⁸The 4% average return was adjusted for market returns. Healy and Palepu also looked at companies that stopped paying a dividend. In this case the stock price on average declined by 9.5% on the announcement and earnings fell over the next four quarters.

⁹The dividend policies of Japanese keiretsus are analyzed in K. L. Dewenter and V. A. Warther, “Dividends, Asymmetric Information, and Agency Conflicts: Evidence from a Comparison of the Dividend Policies of Japanese and U.S. Firms,” Journal of Finance 53 (June 1998), pp. 879–904.

¹⁰R. Comment and G. Jarrell, “The Relative Signalling Power of Dutch-Auction and Fixed Price Self-Tender Offers and Open-Market Share Repurchases,” Journal of Finance 46 (September 1991), pp. 1243–1271. There is also evidence of continuing superior performance during the years following a repurchase announcement. See D. Ikenberry, J. Lakonishok, and T. Vermaelen, “Market Underreaction to Open Market Share Repurchases,” Journal of Financial Economics 39 (October 1995), pp. 181–208.

¹¹Not only do managers hold on to their stock; on average they also add to their holdings before the announcement of a repurchase. See D. S. Lee, W. Mikkelson, and M. M. Partch, “Managers’ Trading around Stock Repurchases,” Journal of Finance 47 (December 1992), pp. 1947–1961.

¹²See R. Comment and G. Jarrell, op. cit.

¹³M. H. Miller and F. Modigliani, “Dividend Policy, Growth and the Valuation of Shares,” Journal of Business 34 (October 1961), pp. 411–433. MM’s results were anticipated by J. B. Williams, The Theory of Investment Value (Cambridge, MA: Harvard University Press, 1938). Also a proof similar to MM’s was developed in J. Lintner, “Dividends, Earnings, Leverage and Stock Prices and the Supply of Capital to Corporations,” Review of Economics and Statistics (August 1962), pp. 243–269. MM recognized that dividends could convey information, but their proofs focused on value, not information about value. The examples in this section put aside the information content of dividends.

¹⁴The original market price of $11 per share is the only price at which repurchase works. Shareholders will not sell their shares for less than $11, because then $1 million would purchase more than 90,909 shares, leaving less than 909,091 shares outstanding and a price above $11 when the repurchase is completed. The firm should not offer more than $11, because that would repurchase fewer than 90,909 shares and hand a “free gift” to selling stockholders.

¹⁵You can check that next year’s ex-dividend price of $10.50 per share is the only price at which repurchase works. Shareholders will not sell their shares for less than $10.50, because then $500,000 would purchase more than 47,619 shares, leaving less than 952,381 shares outstanding and a price above $10.50 when the repurchase is completed. The firm should not offer more than $10.50 because that would repurchase fewer than 47,619 shares and hand a free gift to selling stockholders.

¹⁶See, for example, J. R. Graham and A. Kumar, “Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors,” Journal of Finance 61 (June 2006), pp. 1305–1336; and M. Baker, S. Nagel, and J. Wurgler, “The Effect of Dividends on Consumption,” Brookings Papers on Economic Activity (2007), pp. 277–291.

¹⁷See H. Shefrin and M. Statman, “Explaining Investor Preference for Cash Dividends,” Journal of Financial Economics 13 (June 1984), pp. 253–282.

¹⁸See F. Easterbrook, “Two Agency Cost Explanations of Dividends,” American Economic Review 74 (1984), pp. 650–659; and especially M. Jensen, “Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers,” American Economic Review 76 (May 1986), pp. 323–329.

¹⁹A firm that eliminates dividends and makes regular repurchases may find that the Internal Revenue Service interprets the repurchases as de facto dividends and taxes the payout accordingly. In practice this tax risk is a threat only for privately held firms, however. Nevertheless public corporations do not usually announce that they are repurchasing shares to save investor taxes on dividends. They may say, “Our stock is a good investment” or “We want to have shares available to finance possible future acquisitions.” What do you think of these rationales?

²⁰These rates were set in 2003 and extended until the end of 2012. If they expire, the top rates on capital gains and dividends will go to 23.8% and 43.4%, and the leftist case for repurchases instead of dividends will gain new vigor.

²¹When securities are sold, capital gains tax is paid on the difference between the selling price and the purchase price or basis. Shares purchased in 2007 for $20 (the basis) and sold in 2012 for $30 would generate a capital gain of $10 per share and a tax of $1.50 at a 15% rate.

Suppose sale is deferred one year to 2013. If the interest rate is 5%, the PV of the tax, viewed from 2012, falls to 1.50/1.05 = $1.43. The effective capital gains tax rate is 14.3%. The longer sale is deferred, the lower the effective tax rate.

The effective tax rate falls to zero if the investor dies before selling because under current U.S. estate-tax law, his or her heirs get to “step up” the basis without realizing a taxable gain. Suppose the price is still $30 when the investor dies. The heirs could sell for $30 and pay no tax because they could step up to a $30 basis. The investor’s stock holdings may be subject to estate taxes, however.

²²These costs can be substantial. Refer back to Chapter 15, especially Figure 15.5.

²³See, for example, Y. Grinstein and R. Michaely, “Institutional Holdings and Payout Policy,” Journal of Finance 60 (June 2005), pp. 1389–1426; and J. R. Graham and A. Kumar, “Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors,” Journal of Finance 61 (June 2006), pp. 1305–1336.

²⁴K. Pattenden and G. Twite, “Taxes and Dividend Policy under Alternative Tax Regimes,” Journal of Corporate Finance 14 (2008), pp. 1–16.

²⁵Suppose there are 250 trading days in a year. Think of a stock paying quarterly dividends. We could say that the stock offers a high dividend yield on 4 days but a zero dividend yield on the remaining 246 days.

²⁶See R. H. Litzenberger and K. Ramaswamy, “The Effects of Dividends on Common Stock Prices: Tax Effects or Information Effects,” Journal of Finance 37 (May 1982), pp. 429–443; and M. H. Miller and M. Scholes, “Dividends and Taxes: Some Empirical Evidence,” Journal of Political Economy 90 (1982), pp. 1118–1141. Merton Miller provides a broad review of the empirical literature in “Behavioral Rationality in Finance: The Case of Dividends,” Journal of Business 59 (October 1986), pp. S451–S468.

²⁷In Australia, shareholders receive a credit for the full amount of corporate tax that has been paid on their behalf. In other countries the tax credit is less than the corporate tax rate. You can think of the tax system in these countries as lying between the Australian and U.S. systems.

²⁸In the case of Australia the tax rate on capital gains is the same as the tax rate on dividends. However, for securities that are held for more than 12 months only half of the gain is taxed.

²⁹This is only true for earnings that are paid out as dividends. Retained earnings are subject to corporate tax. Shareholders get the benefit of retained earnings in the form of capital gains.

³⁰Here we are following a life-cycle theory set out in H. DeAngelo, L. DeAngelo, and D. Skinner, “Corporate Payout Policy,” Foundations and Trends in Finance 3 (2008), pp. 95–287.

³¹See R. LaPorta, F. Lopez de Silanes, A. Shleifer, and R. W. Vishny, “Agency Problems and Dividend Policy around the World,” Journal of Finance 55 (February 2000), pp. 1–24.

Part 5 Payout Policy and Capital Structure

Does Debt Policy Matter?

A firm’s basic resource is the stream of cash flows produced by its assets. When the firm is financed entirely by common stock, all those cash flows belong to the stockholders. When it issues both debt and equity securities, it splits the cash flows into two streams, a relatively safe stream that goes to the debtholders and a riskier stream that goes to the stockholders.

The firm’s mix of debt and equity financing is called its capital structure. Of course capital structure is not just “debt versus equity.” There are many different flavors of debt, at least two flavors of equity (common versus preferred), plus hybrids such as convertible bonds. The firm can issue dozens of distinct securities in countless combinations. It attempts to find the particular combination that maximizes the overall market value of the firm.

Are such attempts worthwhile? We must consider the possibility that no combination has any greater appeal than any other. Perhaps the really important decisions concern the company’s assets, and decisions about capital structure are mere details—matters to be attended to but not worried about.

Modigliani and Miller (MM), who showed that payout policy doesn’t matter in perfect capital markets, also showed that financing decisions don’t matter in perfect markets. Their famous “proposition 1” states that a firm cannot change the total value of its securities just by splitting its cash flows into different streams: The firm’s value is determined by its real assets, not by the securities it issues. Thus capital structure is irrelevant as long as the firm’s investment decisions are taken as given.

MM’s proposition 1 allows complete separation of investment and financing decisions. It implies that any firm could use the capital budgeting procedures presented in Chapters 5 through 12 without worrying about where the money for capital expenditures comes from. In those chapters, we assumed all-equity financing without really thinking about it. If MM are right, that is exactly the right approach. If the firm uses a mix of debt and equity financing, its overall cost of capital will be exactly the same as its cost of equity with all-equity financing.

We believe that in practice capital structure does matter, but we nevertheless devote all of this chapter to MM’s argument. If you don’t fully understand the conditions under which MM’s theory holds, you won’t fully understand why one capital structure is better than another. The financial manager needs to know what kinds of market imperfection to look for.

For example, the firm may invent some new security that a particular clientele of investors is willing to buy at a premium price, thereby increasing the overall market value of the firm. (We argue, however, that such financial innovations are easily copied and that any gains in value will be confined to the first few issuers.)

In Chapter 18 we undertake a detailed analysis of the imperfections that are most likely to make a difference, including taxes, the costs of bankruptcy and financial distress, the costs of writing and enforcing complicated debt contracts, differences created by imperfect information, and the effects of debt on incentives for management. In Chapter 19 we show how such imperfections (especially taxes) affect the weighted-average cost of capital and the value of the firm.

 17-1   The Effect of Financial Leverage in a Competitive Tax-free Economy

Financial managers try to find the combination of securities that has the greatest overall appeal to investors—the combination that maximizes the market value of the firm. Before tackling this problem, we should check whether a policy that maximizes the total value of the firm’s securities also maximizes the wealth of the shareholders.

Let D and E denote the market values of the outstanding debt and equity of the Wapshot Mining Company. Wapshot’s 1,000 shares sell for $50 apiece. Thus

Wapshot has also borrowed $25,000, and so V, the aggregate market value of all Wapshot’s outstanding securities, is

Wapshot’s stock is known as levered equity. Its stockholders face the benefits and costs of financial leverage, or gearing. Suppose that Wapshot “levers up” still further by borrowing an additional $10,000 and paying the proceeds out to shareholders as a special dividend of $10 per share. This substitutes debt for equity capital with no impact on Wapshot’s assets.

What will Wapshot’s equity be worth after the special dividend is paid? We have two unknowns, E and V:

If V is $75,000 as before, then E must be V – D = 75,000 – 35,000 = $40,000. Stockholders have suffered a capital loss that exactly offsets the $10,000 special dividend. But if V increases to, say, $80,000 as a result of the change in capital structure, then E = $45,000 and the stockholders are $5,000 ahead. In general, any increase or decrease in V caused by a shift in capital structure accrues to the firm’s stockholders. We conclude that a policy that maximizes the market value of the firm is also best for the firm’s stockholders.

This conclusion rests on two important assumptions: first, that Wapshot can ignore payout policy and, second, that after the change in capital structure the old plus new debt are worth $35,000.

Payout policy may or may not be relevant, but there is no need to repeat the discussion of Chapter 16. We need only note that shifts in capital structure sometimes force important decisions about payout policy. Perhaps Wapshot’s cash dividend has costs or benefits that should be considered in addition to any benefits achieved by its increased financial leverage.

Our second assumption that old plus new debt ends up worth $35,000 seems innocuous. But it could be wrong. Perhaps the new borrowing has increased the risk of the old bonds. If the holders of old bonds cannot demand a higher rate of interest to compensate for the increased risk, the value of their investment is reduced. In this case Wapshot’s stockholders gain at the expense of the holders of old bonds even though the overall value of the firm is unchanged.

But this anticipates issues better left to Chapter 18. In this chapter we assume that any new issue of debt has no effect on the market value of existing debt.

Enter Modigliani and Miller

Let us accept that the financial manager would like to find the combination of securities that maximizes the value of the firm. How is this done? MM’s answer is that the financial manager should stop worrying: In a perfect market any combination of securities is as good as another. The value of the firm is unaffected by its choice of capital structure.¹

You can see this by imagining two firms that generate the same stream of operating income and differ only in their capital structure. Firm U is unlevered. Therefore the total value of its equity EU is the same as the total value of the firm VU. Firm, L, on the other hand, is levered. The value of its stock is, therefore, equal to the value of the firm less the value of the debt: EL = VL – DL.

Now think which of these firms you would prefer to invest in. If you don’t want to take much risk, you can buy common stock in the unlevered firm U. For example, if you buy 1% of firm U’s shares, your investment is .01VU and you are entitled to 1% of the gross profits:

Now compare this with an alternative strategy. This is to purchase the same fraction of both the debt and the equity of firm L. Your investment and return would then be as follows:

Both strategies offer the same payoff: 1% of the firm’s profits. The law of one price tells us that in well-functioning markets two investments that offer the same payoff must have the same price. Therefore, .01VU must equal .01VL: the value of the unlevered firm must equal the value of the levered firm.

Suppose that you are willing to run a little more risk. You decide to buy 1% of the outstanding shares in the levered firm. Your investment and return are now as follows:

But there is an alternative strategy. This is to borrow .01DL on your own account and purchase 1% of the stock of the unlevered firm. In this case, your strategy gives you 1% of the profits from VU, but you have to pay interest on your loan equal to 1% of the interest that is paid by firm L. Your total investment and net return are as follows:

Again both strategies offer the same payoff: 1% of profits after interest. Therefore, both investments must have the same cost. The investment .01(VU – DL) must equal .01(VL – DL) and VU must equal VL.

It does not matter whether the world is full of risk-averse chickens or venturesome lions. All would agree that the value of the unlevered firm U must be equal to the value of the levered firm L. As long as investors can borrow or lend on their own account on the same terms as the firm, they can “undo” the effect of any changes in the firm’s capital structure. This is the basis for MM’s famous proposition 1: “The market value of any firm is independent of its capital structure.”

The Law of Conservation of Value

MM’s argument that debt policy is irrelevant is an application of an astonishingly simple idea. If we have two streams of cash flow, A and B, then the present value of A + B is equal to the present value of A plus the present value of B. That’s common sense: If you have a dollar in your left pocket and a dollar in your right, your total wealth is $2. We met this principle of value additivity in our discussion of capital budgeting, where we saw that the present value of two assets combined is equal to the sum of their present values considered separately.

In the present context we are not combining assets but splitting them up. But value additivity works just as well in reverse. We can slice a cash flow into as many parts as we like; the values of the parts will always sum back to the value of the unsliced stream. (Of course, we have to make sure that none of the stream is lost in the slicing. We cannot say, “The value of a pie is independent of how it is sliced,” if the slicer is also a nibbler.)

This is really a law of conservation of value. The value of an asset is preserved regardless of the nature of the claims against it. Thus proposition 1: Firm value is determined on the left-hand side of the balance sheet by real assets—not by the proportions of debt and equity securities issued to buy the assets.

The simplest ideas often have the widest application. For example, we could apply the law of conservation of value to the choice between issuing preferred stock, common stock, or some combination. The law implies that the choice is irrelevant, assuming perfect capital markets and providing that the choice does not affect the firm’s investment and operating policies. If the total value of the equity “pie” (preferred and common combined) is fixed, the firm’s owners (its common stockholders) do not care how this pie is sliced.

The law also applies to the mix of debt securities issued by the firm. The choices of long-term versus short-term, secured versus unsecured, senior versus subordinated, and convertible versus nonconvertible debt all should have no effect on the overall value of the firm.

Combining assets and splitting them up will not affect values as long as they do not affect investors’ choices. When we showed that capital structure does not affect choice, we implicitly assumed that both companies and individuals can borrow and lend at the same risk-free rate of interest. As long as this is so, individuals can undo the effect of any changes in the firm’s capital structure.

In practice corporate debt is not risk-free and firms cannot escape with rates of interest appropriate to a government security. Some people’s initial reaction is that this alone invalidates MM’s proposition. It is a natural mistake, but capital structure can be irrelevant even when debt is risky.

If a company borrows money, it does not guarantee repayment: It repays the debt in full only if its assets are worth more than the debt obligation. The shareholders in the company therefore have limited liability.

Many individuals would like to borrow with limited liability. They might, therefore, be prepared to pay a small premium for levered shares if the supply of levered shares were insufficient to meet their needs.² But there are literally thousands of common stocks of companies that borrow. Therefore it is unlikely that an issue of debt would induce them to pay a premium for your shares.³

   TABLE 17.1 Macbeth Spot Removers is entirely equity-financed. Although it expects to have an income of $1,500 a year in perpetuity, this income is not certain. This table shows the return to the stockholder under different assumptions about operating income. We assume no taxes.

An Example of Proposition 1

Macbeth Spot Removers is reviewing its capital structure. Table 17.1 shows its current position. The company has no leverage and all the operating income is paid as dividends to the common stockholders (we assume still that there are no taxes). The expected earnings and dividends per share are $1.50, but this figure is by no means certain—it could turn out to be more or less than $1.50. The price of each share is $10. Since the firm expects to produce a level stream of earnings in perpetuity, the expected return on the share is equal to the earnings–price ratio, 1.50/10.00 = .15, or 15%.

Ms. Macbeth, the firm’s president, has come to the conclusion that shareholders would be better off if the company had equal proportions of debt and equity. She therefore proposes to issue $5,000 of debt at an interest rate of 10% and use the proceeds to repurchase 500 shares. To support her proposal, Ms. Macbeth has analyzed the situation under different assumptions about operating income. The results of her calculations are shown in Table 17.2.

To see more clearly how leverage would affect earnings per share, Ms. Macbeth has also produced Figure 17.1. The brown line shows how earnings per share would vary with operating income under the firm’s current all-equity financing. It is, therefore, simply a plot of the data in Table 17.1. The green line shows how earnings per share would vary given equal proportions of debt and equity. It is, therefore, a plot of the data in Table 17.2.

Ms. Macbeth reasons as follows: “It is clear that the effect of leverage depends on the company’s income. If income is greater than $1,000, the return to the equityholder is increased by leverage. If it is less than $1,000, the return is reduced by leverage. The return is unaffected when operating income is exactly $1,000. At this point the return on the market value of the assets is 10%, which is exactly equal to the interest rate on the debt. Our capital structure decision, therefore, boils down to what we think about income prospects. Since we expect operating income to be above the $1,000 break-even point, I believe we can best help our shareholders by going ahead with the $5,000 debt issue.”

   TABLE 17.2 Macbeth Spot Removers is wondering whether to issue $5,000 of debt at an interest rate of 10% and repurchase 500 shares. This table shows the return to the shareholder under different assumptions about operating income.

   FIGURE 17.1 Borrowing increases Macbeth’s EPS (earnings per share) when operating income is greater than $1,000 and reduces EPS when operating income is less than $1,000. Expected EPS rises from $1.50 to $2.

As financial manager of Macbeth Spot Removers, you reply as follows: “I agree that leverage will help the shareholder as long as our income is greater than $1,000. But your argument ignores the fact that Macbeth’s shareholders have the alternative of borrowing on their own account. For example, suppose that an investor borrows $10 and then invests $20 in two unlevered Macbeth shares. This person has to put up only $10 of his or her own money. The payoff on the investment varies with Macbeth’s operating income [as shown in Table 17.3]. This is exactly the same set of payoffs as the investor would get by buying one share in the levered company. [Compare the last two lines of Tables 17.2 and 17.3.] Therefore, a share in the levered company must also sell for $10. If Macbeth goes ahead and borrows, it will not allow investors to do anything that they could not do already, and so it will not increase value.”

   TABLE 17.3 Individual investors can replicate Macbeth’s leverage.

The argument that you are using is exactly the same as the one MM used to prove proposition 1.

 17-2   Financial Risk and Expected Returns

Consider now the implications of MM’s proposition 1 for the expected returns on Macbeth stock:

Leverage increases the expected stream of earnings per share but not the share price. The reason is that the change in the expected earnings stream is exactly offset by a change in the rate at which the earnings are discounted. The expected return on the share (which for a perpetuity is equal to the earnings–price ratio) increases from 15% to 20%. We now show how this comes about.

The expected return on Macbeth’s assets rA is equal to the expected operating income divided by the total market value of the firm’s securities:

We have seen that in perfect capital markets the company’s borrowing decision does not affect either the firm’s operating income or the total market value of its securities. Therefore the borrowing decision also does not affect the expected return on the firm’s assets rA.

Suppose that an investor holds all of a company’s debt and all of its equity. This investor is entitled to all the firm’s operating income; therefore, the expected return on the portfolio is just rA.

The expected return on a portfolio is equal to a weighted average of the expected returns on the individual holdings. Therefore the expected return on a portfolio consisting of all the firm’s securities is

This formula is of course an old friend from Chapter 9. The overall expected return rA is called the company cost of capital or the weighted-average cost of capital (WACC).

We can turn the formula around to solve for rE, the expected return to equity for a levered firm:

Proposition 2

This is MM’s proposition 2: The expected rate of return on the common stock of a levered firm increases in proportion to the debt–equity ratio (D/E), expressed in market values; the rate of increase depends on the spread between rA, the expected rate of return on a portfolio of all the firm’s securities, and rD, the expected return on the debt. Note that rE = rA if the firm has no debt.

We can check out this formula for Macbeth Spot Removers. Before the decision to borrow

If the firm goes ahead with its plan to borrow, the expected return on assets rA is still 15%. The expected return on equity is

When the firm was unlevered, equity investors demanded a return of rA. When the firm is levered, they require a premium of (rA – rD)D/E to compensate for the extra risk.

MM’s proposition 1 says that financial leverage has no effect on shareholders’ wealth. Proposition 2 says that the rate of return they can expect to receive on their shares increases as the firm’s debt–equity ratio increases. How can shareholders be indifferent to increased leverage when it increases expected return? The answer is that any increase in expected return is exactly offset by an increase in risk and therefore in shareholders’ required rate of return.

Look at what happens to the risk of Macbeth shares if it moves to equal debt–equity proportions. Table 17.4 shows how a shortfall in operating income affects the payoff to the shareholders.

   TABLE 17.4 Financial leverage increases the risk of Macbeth shares. A $1,000 drop in operating income reduces earnings per share by $1 with all-equity financing, but by $2 with 50% debt.

The debt–equity proportion does not affect the dollar risk borne by equityholders. Suppose operating income drops from $1,500 to $500. Under all-equity financing, equity earnings drop by $1 per share. There are 1,000 outstanding shares, and so total equity earnings fall by $1 × 1,000 = $1,000. With 50% debt, the same drop in operating income reduces earnings per share by $2. But there are only 500 shares outstanding, and so total equity income drops by $2 × 500 = $1,000, just as in the all-equity case.

However, the debt–equity choice does amplify the spread of percentage returns. If the firm is all-equity-financed, a decline of $1,000 in the operating income reduces the return on the shares by 10%. If the firm issues risk-free debt with a fixed interest payment of $500 a year, then a decline of $1,000 in the operating income reduces the return on the shares by 20%. In other words, the effect of the proposed leverage is to double the amplitude of the swings in Macbeth’s shares. Whatever the beta of the firm’s shares before the refinancing, it would be twice as high afterward.

Now you can see why investors require higher returns on levered equity. The required return simply rises to match the increased risk.

EXAMPLE 17.1 • Leverage and the Cost of Equity

Let us revisit a numerical example from Chapter 9. We looked at a company with the following market-value balance sheet:

and an overall cost of capital of

If the firm is contemplating investment in a project that has the same risk as the firm’s existing business, the opportunity cost of capital for this project is the same as the firm’s cost of capital; in other words, it is 12.75%.

What would happen if the firm issued an additional 10% of debt and used the cash to repurchase 10% of its equity? The revised market-value balance sheet is

The change in financial structure does not affect the amount or risk of the cash flows on the total package of debt and equity. Therefore, if investors required a return of 12.75% on the total package before the refinancing, they must require a 12.75% return on the firm’s assets afterward.

Although the required return on the package of debt and equity is unaffected, the change in financial structure does affect the required return on the individual securities. Since the company has more debt than before, the debtholders are likely to demand a higher interest rate. Suppose that the expected return on the debt rises to 7.875%. Now you can write down the basic equation for the return on assets

and solve for the return on equity rE = 16.0%.

Increasing the amount of debt increased debtholder risk and led to a rise in the return that debtholders required (rD rose from 7.5 to 7.875%). The higher leverage also made the equity riskier and increased the return that shareholders required (rE rose from 15% to 16%). The weighted-average return on debt and equity remained at 12.75%:

Suppose that the company decided instead to repay all its debt and to replace it with equity. In that case all the cash flows would go to the equityholders. The company cost of capital, rA, would stay at 12.75%, and rE would also be 12.75%.

How Changing Capital Structure Affects Beta

We have looked at how changes in financial structure affect expected return. Let us now look at the effect on beta.

The stockholders and debtholders both receive a share of the firm’s cash flows, and both bear part of the risk. For example, if the firm’s assets turn out to be worthless, there will be no cash to pay stockholders or debtholders. But debtholders usually bear much less risk than stockholders. Debt betas of large firms are typically in the range of 0 to .2.

If you owned a portfolio of all the firm’s securities, you wouldn’t share the cash flows with anyone. You wouldn’t share the risks with anyone either; you would bear them all. Thus the firm’s asset beta is equal to the beta of a portfolio of all the firm’s debt and its equity.

The beta of this hypothetical portfolio is just a weighted average of the debt and equity betas:

Think back to our example. If the debt before the refinancing has a beta of .1 and the equity has a beta of 1.1, then

What happens after the refinancing? The risk of the total package is unaffected, but both the debt and the equity are now more risky. Suppose that the debt beta increases to .2. We can work out the new equity beta:

Our example shows how borrowing creates financial leverage or gearing. Financial leverage does not affect the risk or the expected return on the firm’s assets, but it does push up the risk of the common stock. Shareholders demand a correspondingly higher return because of this financial risk.

Now you can see how to unlever betas, that is, how to go from an observed βE to βA. You have the equity beta, say 1.2. You also need the debt beta, say .2, and the relative market values of debt (D/V) and equity (E/V). If debt accounts for 40% of overall value V, then the unlevered beta is

This runs the previous example in reverse. Just remember the basic relationship:

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Does MM apply to banks?

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MM’s propositions warn us that higher leverage increases both expected equity returns and equity risk. It does not increase shareholder value. Having worked through the example of Macbeth, this much should now seem obvious. But watch out for hidden changes in leverage, such as a decision to lease new equipment or to underfund the pension scheme. Do not interpret any resultant increase in the expected equity return as creating additional shareholder value.

 17-3   The Weighted-Average Cost of Capital

What did financial experts think about debt policy before MM? It is not easy to say because with hindsight we see that they did not think too clearly.⁴ However, a “traditional” position emerged in response to MM. To understand it, we have to return to the weighted-average cost of capital.

Figure 17.2 sums up the implications of MM’s propositions for the costs of debt and equity and the weighted-average cost of capital. The figure assumes that the firm’s bonds are essentially risk-free at low debt levels. Thus rD is independent of D/E, and rE increases linearly as D/E increases. As the firm borrows more, the risk of default increases and the firm is required to pay higher rates of interest. Proposition 2 predicts that when this occurs the rate of increase in rE slows down. This is also shown in Figure 17.2. The more debt the firm has, the less sensitive rE is to further borrowing.

   FIGURE 17.2 MM’s proposition 2. The expected return on equity rE increases linearly with the debt–equity ratio so long as debt is risk-free. But if leverage increases the risk of the debt, debtholders demand a higher return on the debt. This causes the rate of increase in rE to slow down.

Why does the slope of the rE line in Figure 17.2 taper off as D/E increases? Essentially because holders of risky debt bear some of the firm’s business risk. As the firm borrows more, more of that risk is transferred from stockholders to bondholders.

Two Warnings

Sometimes the objective in financing decisions is stated not as “maximize overall market value” but as “minimize the weighted-average cost of capital.” If MM’s proposition 1 holds, then these are equivalent objectives. If MM’s proposition 1 does not hold, then the capital structure that maximizes the value of the firm also minimizes the weighted-average cost of capital, provided that operating income is independent of capital structure. Remember that the weighted-average cost of capital is the expected rate of return on the market value of all of the firm’s securities. Anything that increases the value of the firm reduces the weighted-average cost of capital if operating income is constant. But if operating income is varying too, all bets are off.

In Chapter 18 we show that financial leverage can affect operating income in several ways. Therefore maximizing the value of the firm is not always equivalent to minimizing the weighted-average cost of capital.

Warning 1 Shareholders want management to increase the firm’s value. They are more interested in being rich than in owning a firm with a low weighted-average cost of capital.

Warning 2 Trying to minimize the weighted-average cost of capital seems to encourage logical short circuits like the following. Suppose that someone says, “Shareholders demand—and deserve—higher expected rates of return than bondholders do. Therefore debt is the cheaper capital source. We can reduce the weighted-average cost of capital by borrowing more.” But this doesn’t follow if the extra borrowing leads stockholders to demand a still higher expected rate of return. According to MM’s proposition 2 the cost of equity capital rE increases by just enough to keep the weighted-average cost of capital constant.

This is not the only logical short circuit you are likely to encounter. We have cited two more in Problem 15 at the end of this chapter.

Rates of Return on Levered Equity—The Traditional Position

You may ask why we have even mentioned the aim of minimizing the weighted-average cost of capital if it is often wrong or confusing. We had to because the traditionalists accept this objective and argue their case in terms of it.

The logical short circuit we just described rested on the assumption that rE, the expected rate of return demanded by stockholders, does not rise, or rises very slowly, as the firm borrows more. Suppose, just for the sake of argument, that this is true. Then rA, the weighted-average cost of capital, must decline as the debt–equity ratio rises.

The traditionalists’ position is shown in Figure 17.3. They say that a moderate degree of financial leverage may increase the expected equity return rE, but not as much as predicted by MM’s proposition 2. But irresponsible firms that borrow excessively find rE shooting up faster than MM predict. Therefore the weighted-average cost of capital declines at first, then rises. It reaches a minimum at some intermediate debt ratio. Remember that minimizing the weighted-average cost of capital is equivalent to maximizing firm value if operating income is not affected by borrowing.

Two arguments could be advanced in support of this position. First, perhaps investors do not notice or appreciate the financial risk created by moderate borrowing, although they wake up when debt is “excessive.” If so, stockholders in moderately leveraged firms may accept a lower rate of return than they really should.

That seems naive.⁵ The second argument is better. It accepts MM’s reasoning as applied to perfect capital markets but holds that actual markets are imperfect. Because of these imperfections, firms that borrow may provide a valuable service for investors. If so, levered shares might trade at premium prices compared to their theoretical values in perfect markets.

   FIGURE 17.3 The dashed lines show MM’s view of the effect of leverage on the expected return on equity rE and the weighted-average cost of capital rA. (See Figure 17.2.) The solid lines show the traditional view. Traditionalists say that borrowing at first increases rE more slowly than MM predict but that rE shoots up with excessive borrowing. If so, the weighted-average cost of capital can be minimized if you use just the right amount of debt.

Suppose that corporations can borrow more cheaply than individuals. Then it would pay investors who want to borrow to do so indirectly by holding the stock of levered firms. They would be willing to live with expected rates of return that do not fully compensate them for the business and financial risk they bear.

Is corporate borrowing really cheaper? It’s hard to say. Interest rates on home mortgages are not too different from rates on high-grade corporate bonds.⁶ Rates on margin debt (borrowing from a stockbroker with the investor’s shares tendered as security) are not too different from the rates firms pay banks for short-term loans.

There are some individuals who face relatively high interest rates, largely because of the costs lenders incur in making and servicing small loans. There are economies of scale in borrowing. A group of small investors could do better by borrowing via a corporation, in effect pooling their loans and saving transaction costs.⁷

Suppose that this class of investors is large, both in number and in the aggregate wealth it brings to capital markets. That creates a clientele for whom corporate borrowing is better than personal borrowing. That clientele would, in principle, be willing to pay a premium for the shares of a levered firm.

But maybe it doesn’t have to pay a premium. Perhaps smart financial managers long ago recognized this clientele and shifted the capital structures of their firms to meet its needs. The shifts would not have been difficult or costly. But if the clientele is now satisfied, it no longer needs to pay a premium for levered shares. Only the financial managers who first recognized the clientele extracted any advantage from it.

Maybe the market for corporate leverage is like the market for automobiles. Americans need millions of automobiles and are willing to pay thousands of dollars apiece for them. But that doesn’t mean that you could strike it rich by going into the automobile business. You’re at least 90 years too late.

Today’s Unsatisfied Clienteles Are Probably Interested in Exotic Securities

So far we have made little progress in identifying cases where firm value might plausibly depend on financing. But our examples illustrate what smart financial managers look for. They look for an unsatisfied clientele, investors who want a particular kind of financial instrument but because of market imperfections can’t get it or can’t get it cheaply.

MM’s proposition 1 is violated when the firm, by imaginative design of its capital structure, can offer some financial service that meets the needs of such a clientele. Either the service must be new and unique or the firm must find a way to provide some old service more cheaply than other firms or financial intermediaries can.

Now, is there an unsatisfied clientele for garden-variety debt or levered equity? We doubt it. But perhaps you can invent an exotic security and uncover a latent demand for it.

In the next several chapters we will encounter a number of new securities that have been invented by companies and advisers. These securities take the company’s basic cash flows and repackage them in ways that are thought to be more attractive to investors. However, while inventing these new securities is easy, it is more difficult to find investors who will rush to buy them.

Imperfections and Opportunities

The most serious capital market imperfections are often those created by government.

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Bank regulation and CDOs

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An imperfection that supports a violation of MM’s proposition 1 also creates a money-making opportunity. Firms and intermediaries will find some way to reach the clientele of investors frustrated by the imperfection.

For many years the U.S. government imposed a limit on the rate of interest that could be paid on savings accounts. It did so to protect savings institutions by limiting competition for their depositors’ money. The fear was that depositors would run off in search of higher yields, causing a cash drain that savings institutions would not be able to meet. Interest-rate regulation provided financial institutions with an opportunity to create value by offering money-market funds. These are mutual funds invested in Treasury bills, commercial paper, and other high-grade, short-term debt instruments. Any saver with a few thousand dollars to invest can gain access to these instruments through a money-market fund and can withdraw money at any time by writing a check against his or her fund balance. Thus the fund resembles a checking or savings account that pays close to market interest rates. These money-market funds have become enormously popular. By 2011 their assets were $2.6 trillion.⁸

Long before interest-rate ceilings were finally removed, most of the gains had gone out of issuing the new securities to individual investors. Once the clientele was finally satisfied, MM’s proposition 1 was restored (until the government creates a new imperfection). The moral of the story is this: If you ever find an unsatisfied clientele, do something right away, or capital markets will evolve and steal it from you.

This is actually an encouraging message for the economy as a whole. If MM are right, investors’ demands for different types of securities are satisfied at minimal cost. The cost of capital will reflect only business risk. Capital will flow to companies with positive-NPV investments, regardless of the companies’ capital structures. This is the efficient outcome.

 17-4   A Final Word on the After-Tax Weighted-Average Cost of Capital

MM left us a simple message. When the firm changes its mix of debt and equity securities, the risk and expected returns of these securities change, but the company’s overall cost of capital does not change.

Now if you think that message is too neat and simple, you’re right. The complications are spelled out in the next two chapters. But we must note one complication here: In the U.S. and many other countries, interest paid on a firm’s borrowing can be deducted from taxable income. Thus the after-tax cost of debt is rD(1 – Tc), where Tc is the marginal corporate tax rate. So, when companies discount an average-risk project, they do not use the company cost of capital as we have just computed it. Instead they use the after-tax cost of debt to compute the after-tax weighted-average cost of capital or WACC:

We briefly introduced this formula in Chapter 9, where we used it to estimate the weighted-average cost of capital for Union Pacific. In 2011 Union Pacific’s long-term borrowing rate was rD = 4.8%, and its estimated cost of equity was rE = 9.7%. With a 35% corporate tax rate, the after-tax cost of debt was rD(1 – Tc) = 4.8(1 – .35) = 3.1%. The ratio of debt to overall company value was D/V = 14.3%. Therefore

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Try It! Figure 17.4:
Changing leverage and the cost of capital

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MM’s proposition 2 states that in the absence of taxes the company cost of capital stays the same regardless of the amount of leverage. But, if companies receive a tax shield on their interest payments, then the after-tax WACC declines as debt increases. This is illustrated in Figure 17.4, which shows how Union Pacific’s WACC changes as the debt–equity ratio changes.

   FIGURE 17.4 Estimated after-tax WACC for Union Pacific at different debt–equity ratios. The figure assumes rE = 9.7% at a 14.3% debt ratio (equivalent to a 16.7% debt–equity ratio) and a borrowing rate of rD = 4.8%. Notice that the debt interest rate is assumed to increase with the debt–equity ratio.

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SUMMARY

Think of the financial manager as taking all of the firm’s real assets and selling them to investors as a package of securities. Some financial managers choose the simplest package possible: all-equity financing. Some end up issuing dozens of debt and equity securities. The problem is to find the particular combination that maximizes the market value of the firm.

Modigliani and Miller’s (MM’s) famous proposition 1 states that no combination is better than any other—that the firm’s overall market value (the value of all its securities) is independent of capital structure. Firms that borrow do offer investors a more complex menu of securities, but investors yawn in response. The menu is redundant. Any shift in capital structure can be duplicated or “undone” by investors. Why should they pay extra for borrowing indirectly (by holding shares in a levered firm) when they can borrow just as easily and cheaply on their own accounts?

MM agree that borrowing raises the expected rate of return on shareholders’ investments. But it also increases the risk of the firm’s shares. MM show that the higher risk exactly offsets the increase in expected return, leaving stockholders no better or worse off.

Proposition 1 is an extremely general result. It applies not just to the debt–equity trade-off but to any choice of financing instruments. For example, MM would say that the choice between long-term and short-term debt has no effect on firm value.

The formal proofs of proposition 1 all depend on the assumption of perfect capital markets. MM’s opponents, the “traditionalists,” argue that market imperfections make personal borrowing excessively costly, risky, and inconvenient for some investors. This creates a natural clientele willing to pay a premium for shares of levered firms. The traditionalists say that firms should borrow to realize the premium.

But this argument is incomplete. There may be a clientele for levered equity, but that is not enough; the clientele has to be unsatisfied. There are already thousands of levered firms available for investment. Is there still an unsatiated clientele for garden-variety debt and equity? We doubt it.

Proposition 1 is violated when financial managers find an untapped demand and satisfy it by issuing something new and different. The argument between MM and the traditionalists finally boils down to whether this is difficult or easy. We lean toward MM’s view: Finding unsatisfied clienteles and designing exotic securities to meet their needs is a game that’s fun to play but hard to win.

If MM are right, the overall cost of capital—the expected rate of return on a portfolio of all the firm’s outstanding securities—is the same regardless of the mix of securities issued to finance the firm. The overall cost of capital is usually called the company cost of capital or the weighted-average cost of capital (WACC). MM say that WACC doesn’t depend on capital structure. But MM assume away lots of complications. The first complication is taxes. When we recognize that debt interest is tax-deductible, and compute WACC with the after-tax interest rate, WACC declines as the debt ratio increases. There is more—lots more—on taxes and other complications in the next two chapters.

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FURTHER READING

The fall 1988 issue of the Journal of Economic Perspectives contains a collection of articles, including one by Modigliani and Miller, that review and assess the MM propositions. The summer 1989 issue of Financial Management contains three more articles under the heading “Reflections on the MM Propositions 30 Years Later.”

Two surveys of financial innovation include:

F. Allen and G. Yago, Financing the Future: Market-Based Innovations for Growth, Wharton School Publishing-Milken Institute Series on Financial Innovations (Upper Saddle River, NJ: Pearson Education, 2010).

P. Tufano, “Financial Innovation,” in G. M. Constantinides, M. Harris, and R. Stulz (eds.), Handbook of the Economics of Finance, vol. 1A (Amsterdam: Elsevier/North-Holland, 2003).

Miller reviews the MM propositions in:

M. H. Miller, “The Modigliani-Miller Propositions after Thirty Years,” Journal of Applied Corporate Finance 2 (Spring 1989), pp. 6–18.

For a skeptic’s view of MM’s arguments see:

S. Titman, “The Modigliani-Miller Theorem and the Integration of Financial Markets,” Financial Management 31 (Spring 2002), pp. 101–115.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Homemade leverage Ms. Kraft owns 50,000 shares of the common stock of Copperhead Corporation with a market value of $2 per share, or $100,000 overall. The company is currently financed as follows:

Copperhead now announces that it is replacing $1 million of short-term debt with an issue of common stock. What action can Ms. Kraft take to ensure that she is entitled to exactly the same proportion of profits as before?

2.  Leverage and the cost of capital Spam Corp. is financed entirely by common stock and has a beta of 1.0. The firm is expected to generate a level, perpetual stream of earnings and dividends. The stock has a price–earnings ratio of 8 and a cost of equity of 12.5%. The company’s stock is selling for $50. Now the firm decides to repurchase half of its shares and substitute an equal value of debt. The debt is risk-free, with a 5% interest rate. The company is exempt from corporate income taxes. Assuming MM are correct, calculate the following items after the refinancing:

a.  The cost of equity.

b.  The overall cost of capital (WACC).

c.  The price–earnings ratio.

d.  The stock price.

e.  The stock’s beta.

3.  Leverage and the cost of capital The common stock and debt of Northern Sludge are valued at $50 million and $30 million, respectively. Investors currently require a 16% return on the common stock and an 8% return on the debt. If Northern Sludge issues an additional $10 million of common stock and uses this money to retire debt, what happens to the expected return on the stock? Assume that the change in capital structure does not affect the risk of the debt and that there are no taxes.

4.  Leverage and the cost of capital Suppose that Macbeth Spot Removers issues only $2,500 of debt and uses the proceeds to repurchase 250 shares.

a.  Rework Table 17.2 to show how earnings per share and share return now vary with operating income.

b.  If the beta of Macbeth’s assets is .8 and its debt is risk-free, what would be the beta of the equity after the debt issue?

5.  MM’s propositions True or false?

a.  MM’s propositions assume perfect financial markets, with no distorting taxes or other imperfections.

b.  MM’s proposition 1 says that corporate borrowing increases earnings per share but reduces the price–earnings ratio.

c.  MM’s proposition 2 says that the cost of equity increases with borrowing and that the increase is proportional to D/V, the ratio of debt to firm value.

d.  MM’s proposition 2 assumes that increased borrowing does not affect the interest rate on the firm’s debt.

e.  Borrowing does not increase financial risk and the cost of equity if there is no risk of bankruptcy.

f.  Borrowing increases firm value if there is a clientele of investors with a reason to prefer debt.

6.  Leverage and the cost of capital Look back to Section 17-1. Suppose that Ms. Macbeth’s investment bankers have informed her that since the new issue of debt is risky, debtholders will demand a return of 12.5%, which is 2.5% above the risk-free interest rate.

a.  What are rA and rE?

b.  Suppose that the beta of the unlevered stock was .6. What will βA, βE, and βD be after the change to the capital structure?

7.  Leverage and the cost of capital Note the two blank graphs in Figure 17.5, below. On graph (a), assume MM are right, and plot the relationship between financial leverage (debt–equity ratio) and (i) the rates of return on debt and equity and (ii) the weighted-average cost of capital. Then fill in graph (b), assuming the traditionalists are right.

   FIGURE 17.5 See Problem 7.

8.  Leverage and the cost of capital Gaucho services starts life with all-equity financing and a cost of equity of 14%. Now it refinances with 45% debt (at rD = 9.5%) and 55% equity (market value). The marginal tax rate is TC = 40%. Calculate Gaucho’s after-tax weighted average cost of capital.

INTERMEDIATE

9.  Homemade leverage Companies A and B differ only in their capital structure. A is financed 30% debt and 70% equity; B is financed 10% debt and 90% equity. The debt of both companies is risk-free.

a.  Rosencrantz owns 1% of the common stock of A. What other investment package would produce identical cash flows for Rosencrantz?

b.  Guildenstern owns 2% of the common stock of B. What other investment package would produce identical cash flows for Guildenstern?

c.  Show that neither Rosencrantz nor Guildenstern would invest in the common stock of B if the total value of company A were less than that of B.

10.  MM proposition 1 Here is a limerick:

There once was a man named Carruthers,

Who kept cows with miraculous udders.

He said, “Isn’t this neat?

They give cream from one teat,

And skim milk from each of the others!”

What is the analogy between Mr. Carruthers’s cows and firms’ financing decisions? What would MM’s proposition 1, suitably adapted, say about the value of Mr. Carruthers’s cows? Explain.

11.  MM proposition 1 Executive Chalk is financed solely by common stock and has outstanding 25 million shares with a market price of $10 a share. It now announces that it intends to issue $160 million of debt and to use the proceeds to buy back common stock.

a.  How is the market price of the stock affected by the announcement?

b.  How many shares can the company buy back with the $160 million of new debt that it issues?

c.  What is the market value of the firm (equity plus debt) after the change in capital structure?

d.  What is the debt ratio after the change in structure?

e.  Who (if anyone) gains or loses?

Now try the next question.

12.  MM proposition 1 Executive Cheese has issued debt with a market value of $100 million and has outstanding 15 million shares with a market price of $10 a share. It now announces that it intends to issue a further $60 million of debt and to use the proceeds to buy back common stock. Debtholders, seeing the extra risk, mark the value of the existing debt down to $70 million.

a.  How is the market price of the stock affected by the announcement?

b.  How many shares can the company buy back with the $60 million of new debt that it issues?

c.  What is the market value of the firm (equity plus debt) after the change in capital structure?

d.  What is the debt ratio after the change in structure?

e.  Who (if anyone) gains or loses?

13.  Leverage and the cost of capital Amanohashidate Cameras is financed 80% by common stock and 20% by bonds. The expected return on the common stock is 12% and the rate of interest on the bonds is 6%. Assuming that the bonds are default-risk-free, draw a graph that shows the expected return of Amanohashidate’s common stock (rE) and the expected return on the package of common stock and bonds (rA) for different debt–equity ratios.

14.  MM proposition 1 “MM totally ignore the fact that as you borrow more, you have to pay higher rates of interest.” Explain carefully whether this is a valid objection.

15.  Leverage and the cost of capital Indicate what’s wrong with the following arguments:

a.  “As the firm borrows more and debt becomes risky, both stockholders and bondholders demand higher rates of return. Thus by reducing the debt ratio we can reduce both the cost of debt and the cost of equity, making everybody better off.”

b.  “Moderate borrowing doesn’t significantly affect the probability of financial distress or bankruptcy. Consequently moderate borrowing won’t increase the expected rate of return demanded by stockholders.”

16.  Leverage and the cost of capital Each of the following statements is false or at least misleading. Explain why in each case.

a.  “A capital investment opportunity offering a 10% DCF rate of return is an attractive project if it can be 100% debt-financed at an 8% interest rate.”

b.  “The more debt the firm issues, the higher the interest rate it must pay. That is one important reason why firms should operate at conservative debt levels.”

17.  Debt clienteles Can you invent any new kinds of debt that might be attractive to investors? Why do you think they have not been issued?

18.  Leverage and market values Imagine a firm that is expected to produce a level stream of operating profits. As leverage is increased, what happens to

a.  The ratio of the market value of the equity to income after interest?

b.  The ratio of the market value of the firm to income before interest if (i) MM are right and (ii) the traditionalists are right?

19.  Leverage and the cost of capital Archimedes Levers is financed by a mixture of debt and equity. You have the following information about its cost of capital:

Can you fill in the blanks?

20.  Leverage and the cost of capital Look back to Problem 19. Suppose now that Archimedes repurchases debt and issues equity so that D/V = .3. The reduced borrowing causes rD to fall to 11%. How do the other variables change?

21.  Leverage and the cost of capital Omega Corporation has 10 million shares outstanding, now trading at $55 per share. The firm has estimated the expected rate of return to shareholders at about 12%. It has also issued long-term bonds at an interest rate of 7%. It pays tax at a marginal rate of 35%.

a.  What is Omega’s after-tax WACC?

b.  How much higher would WACC be if Omega used no debt at all? (Hint: For this problem you can assume that the firm’s overall beta [βA] is not affected by its capital structure or by the taxes saved because debt interest is tax-deductible.)

22.  Leverage and the cost of capital Gamma Airlines has an asset beta of 1.5. The risk-free interest rate is 6%, and the market risk premium is 8%. Assume the capital asset pricing model is correct. Gamma pays taxes at a marginal rate of 35%. Draw a graph plotting Gamma’s cost of equity and after-tax WACC as a function of its debt-to-equity ratio D/E, from no debt to D/E = 1.0. Assume that Gamma’s debt is risk-free up to D/E = .25. Then the interest rate increases to 6.5% at D/E = .5, 7% at D/E = .8, and 8% at D/E = 1.0. As in Problem 21, you can assume that the firm’s overall beta (βA) is not affected by its capital structure or the taxes saved because debt interest is tax-deductible.

CHALLENGE

23.  Investor choice Consider the following three tickets: ticket A pays $10 if ________ is elected as president, ticket B pays $10 if ________ is elected, and ticket C pays $10 if neither is elected. (Fill in the blanks yourself.) Could the three tickets sell for less than the present value of $10? Could they sell for more? Try auctioning off the tickets. What are the implications for MM’s proposition 1?

24.  Investor choice People often convey the idea behind MM’s proposition 1 by various supermarket analogies, for example, “The value of a pie should not depend on how it is sliced,” or, “The cost of a whole chicken should equal the cost of assembling one by buying two drumsticks, two wings, two breasts, and so on.”

Actually proposition 1 doesn’t work in the supermarket. You’ll pay less for an uncut whole pie than for a pie assembled from pieces purchased separately. Supermarkets charge more for chickens after they are cut up. Why? What costs or imperfections cause proposition 1 to fail in the supermarket? Are these costs or imperfections likely to be important for corporations issuing securities on the U.S. or world capital markets? Explain.

25.  Investor choice Suppose that new security designs could be patented.⁹ The patent holder could restrict use of the new design or charge other firms royalties for using it. What effect would such patents have on MM’s capital-structure irrelevance theory?

26.  MM proposition In Bermuda there are no corporate income taxes. Consider two Bermuda firms with exactly the same assets and operating earnings. The first is Debt Galore and the second is Debt Zero. Both companies are expected to earn $35 million (before interest) on average in perpetuity. Debt Galore has $150 million of perpetual debt. The interest rate on this debt is 7%. It has 1.5 million shares priced at $135 per share. Debt Zero has no debt. It has 3.6 million shares at $90 per share. Capital markets are perfect and there are no transaction costs. Is there an arbitrage opportunity? If so, demonstrate how shareholders of Debt Zero or Debt Galore could take advantage of the opportunity.

___________

¹F. Modigliani and M. H. Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review 48 (June 1958), pp. 261–297. MM’s basic argument was anticipated in 1938 by J. B. Williams and to some extent by David Durand. See J. B. Williams, The Theory of Investment Value (Cambridge, MA: Harvard University Press, 1938) and D. Durand, “Cost of Debt and Equity Funds for Business: Trends and Problems of Measurement,” Conference on Research in Business Finance (New York: National Bureau of Economic Research, 1952).

²Of course, individuals could create limited liability if they chose. In other words, the lender could agree that borrowers need repay their debt in full only if the assets of company X are worth more than a certain amount. Presumably individuals don’t enter into such arrangements because they can obtain limited liability more simply by investing in the stocks of levered companies.

³Capital structure is also irrelevant if each investor holds a fully diversified portfolio. In that case he or she owns all the risky securities offered by a company (both debt and equity). But anybody who owns all the risky securities doesn’t care about how the cash flows are divided among different securities.

⁴Financial economists in 20 years may remark on Brealey, Myers, and Allen’s blind spots and clumsy reasoning. On the other hand, they may not remember us at all.

⁵This first argument may reflect a confusion between financial risk and the risk of default. Default is not a serious threat when borrowing is moderate; stockholders worry about it only when the firm goes “too far.” But stockholders bear financial risk—in the form of increased volatility of rates of return and a higher beta—even when the chance of default is nil.

⁶One of the authors once obtained a home mortgage at a rate 1/2 percentage point less than the contemporaneous yield on long-term AAA bonds.

⁷Even here there are alternatives to borrowing on personal account. Investors can draw down their savings accounts or sell a portion of their investment in bonds. The impact of reductions in lending on the investor’s balance sheet and risk position is exactly the same as increases in borrowing.

⁸Money-market funds are not totally safe. In 2008 the Reserve Primary Fund incurred heavy losses on its holdings of Lehman Brothers debt and became only the second money-market fund in history to “break the buck” by paying investors only 97 cents on the dollar.

⁹So far security designs cannot be patented, but other financial applications have received patent protection. See J. Lerner, “Where Does State Street Lead? A First Look at Finance Patents,” Journal of Finance 57 (April 2002), pp. 901–930.

Part 5 Payout Policy and Capital Structure

How Much Should a Corporation Borrow?

In Chapter 17 we found that debt policy rarely matters in well-functioning capital markets with no frictions or imperfections. Few financial managers would accept that conclusion as a practical guideline. If debt policy doesn’t matter, then they shouldn’t worry about it—financing decisions could be routine or erratic—it wouldn’t matter. Yet financial managers do worry about debt policy. This chapter explains why.

If debt policy were completely irrelevant, then actual debt ratios should vary randomly from firm to firm and industry to industry. Yet in some industries, companies borrow much more heavily than in others. Look, for example, at Table 18.1. You can see that hotels and airlines are huge issuers of debt. On the other hand, high-tech businesses—such as biotech, software, and Internet companies—finance almost entirely with equity. Glamorous growth companies rarely use much debt despite rapid expansion and often heavy requirements for capital.

The explanation of these patterns lies partly in the things we left out of the last chapter. We mostly ignored taxes. We assumed bankruptcy was cheap, quick, and painless. It isn’t, and there are costs associated with financial distress even if legal bankruptcy is ultimately avoided. We ignored potential conflicts of interest between the firm’s security holders. For example, we did not consider what happens to the firm’s “old” creditors when new debt is issued or when a shift in investment strategy takes the firm into a riskier business. We ignored the information problems that favor debt over equity when cash must be raised from new security issues. We ignored the incentive effects of financial leverage on management’s investment and payout decisions.

Now we will put all these things back in: taxes first, then the costs of bankruptcy and financial distress. This will lead us to conflicts of interest and to information and incentive problems. In the end we will have to admit that debt policy does matter.

However, we will not throw away the MM theory we developed so carefully in Chapter 17. We’re shooting for a theory combining MM’s insights plus the effects of taxes, costs of bankruptcy and financial distress, and various other complications. We’re not dropping back to a theory based on inefficiencies in the capital market. Instead, we want to see how well-functioning capital markets respond to taxes and the other things covered in this chapter.

   TABLE 18.1 Ratios of debt to debt-plus-equity for a sample of nonfinancial businesses, 2010.

Source: Compustat.

Note: Debt to total capital ratio = D/(D + E), where D and E are the book values of long-term debt and equity.

 18-1   Corporate Taxes

BEYOND THE PAGE

● ● ● ● ●

Industry debt ratios

brealey.mhhe.com/c18

Debt financing has one important advantage under the corporate income tax system in the U.S. and many other countries. The interest that the company pays is a tax-deductible expense. Thus the return to bondholders escapes taxation at the corporate level.

Table 18.2 shows simple income statements for firm U, which has no debt, and firm L, which has borrowed $1,000 at 8%. L’s tax bill is $28 less than U’s. This is the tax shield provided by the debt of L. In effect the government pays 35% of the interest expense of L. The total income that L can pay out to its bondholders and stockholders increases by that amount.

Tax shields can be valuable assets. Suppose that the debt of L is fixed and permanent. (That is, the company commits to refinance its present debt obligations when they mature and to keep rolling over its debt obligations indefinitely.) Then L can look forward to a permanent stream of cash flows of $28 per year. The risk of these flows is likely to be less than the risk of the operating assets of L. The tax shields depend only on the corporate tax rate¹ and on the ability of L to earn enough to cover interest payments. The corporate tax rate has been pretty stable. And the ability of L to earn its interest payments must be reasonably sure; otherwise it could not have borrowed at 8%. Therefore we should discount the interest tax shields at a relatively low rate.

But what rate? One common assumption is that the risk of the tax shields is the same as that of the interest payments generating them. Thus we discount at 8%, the expected rate of return demanded by investors who are holding the firm’s debt:

In effect the government assumes 35% of the $1,000 debt obligation of L.

Under these assumptions, the present value of the tax shield is independent of the return on the debt rD. It equals the corporate tax rate Tc times the amount borrowed D:

   TABLE 18.2 The tax deductibility of interest increases the total income that can be paid out to bondholders and stockholders.

Of course, PV(tax shield) is less if the firm does not plan to borrow a permanent fixed amount,² or if it may not have enough taxable income to use the interest tax shields.³

How Do Interest Tax Shields Contribute to the Value of Stockholders’ Equity?

MM’s proposition 1 amounts to saying that the value of a pie does not depend on how it is sliced. The pie is the firm’s assets, and the slices are the debt and equity claims. If we hold the pie constant, then a dollar more of debt means a dollar less of equity value.

But there is really a third slice, the government’s. Look at Table 18.3. It shows an expanded balance sheet with pretax asset value on the left and the value of the government’s tax claim recognized as a liability on the right. MM would still say that the value of the pie—in this case pretax asset value—is not changed by slicing. But anything the firm can do to reduce the size of the government’s slice obviously makes stockholders better off. One thing it can do is borrow money, which reduces its tax bill and, as we saw in Table 18.2, increases the cash flows to debt and equity investors. The after-tax value of the firm (the sum of its debt and equity values as shown in a normal market value balance sheet) goes up by PV(tax shield).

Recasting Johnson & Johnson’s Capital Structure

Johnson & Johnson is a large, successful firm that uses relatively little long-term debt. Table 18.4a shows simplified book and market value balance sheets for Johnson & Johnson in October 2011.

Suppose that you were Johnson & Johnson’s financial manager with complete responsibility for its capital structure. You decide to borrow an additional $10 billion on a permanent basis and use the proceeds to repurchase shares.

   TABLE 18.3 Normal and expanded market value balance sheets. In a normal balance sheet, assets are valued after tax. In the expanded balance sheet, assets are valued pretax, and the value of the government’s tax claim is recognized on the right-hand side. Interest tax shields are valuable because they reduce the government’s claim.

   TABLE 18.4a Simplified balance sheets for Johnson & Johnson, October 2011 (figures in millions).

Notes:

1. Market value is equal to book value for net working capital, long-term debt, and other long-term liabilities. Market value of equity = number of shares times closing price for October 2011. The difference between the market and book values of long-term assets is equal to the difference between the market and book values of equity.

2. PV interest tax shield assumes fixed, perpetual debt, with a 35% tax rate.

   TABLE 18.4b Balance sheets for Johnson & Johnson with additional $10 billion of long-term debt substituted for stockholders’ equity (figures in millions).

Table 18.4b shows the new balance sheets. The book version simply has $10,000 million more long-term debt and $10,000 million less equity. But we know that Johnson & Johnson’s assets must be worth more because its tax bill has been reduced by 35% of the interest on the new debt. In other words, Johnson & Johnson has an increase in PV(interest tax shield), which is worth TcD = .35 × $10,000 million = $3,500 million. If the MM theory holds except for taxes, firm value must increase by $3,500 million to $200,153 million. Johnson & Johnson’s equity ends up worth $161,545 million.

Now you have repurchased $10 billion worth of shares, but Johnson & Johnson’s equity value has dropped by only $6.5 billion. Therefore Johnson & Johnson’s stockholders must be $3.5 billion ahead. Not a bad day’s work.⁴

MM and Taxes

We have just developed a version of MM’s proposition 1 as corrected by them to reflect corporate income taxes.⁵ The new proposition is

In the special case of fixed, permanent debt,

Our imaginary financial surgery on Johnson & Johnson provides the perfect illustration of the problems inherent in this “corrected” theory. That $3.5 billion came too easily; it seems to violate the law that there is no such thing as a money machine. And if Johnson & Johnson’s stockholders would be richer with $23,031 million of corporate debt, why not $33,031 or $43,031 million? At what debt level should Johnson & Johnson stop borrowing? Our formula implies that firm value and stockholders’ wealth continue to go up as D increases. The optimal debt policy appears to be embarrassingly extreme. All firms should be 100% debt-financed.

MM were not that fanatical about it. No one would expect the formula to apply at extreme debt ratios. There are several reasons why our calculations overstate the value of interest tax shields. First, it’s wrong to think of debt as fixed and perpetual; a firm’s ability to carry debt changes over time as profits and firm value fluctuate. Second, many firms face marginal tax rates less than 35%. Third, you can’t use interest tax shields unless there will be future profits to shield—and no firm can be absolutely sure of that.

But none of these qualifications explains why companies like Johnson & Johnson survive and thrive at low debt ratios. It’s hard to believe that its financial managers are simply missing the boat.

We seem to have argued ourselves into a blind alley. But there may be two ways out:

1.  Perhaps a fuller examination of the U.S. system of corporate and personal taxation will uncover a tax disadvantage of corporate borrowing, offsetting the present value of the interest tax shield.

2.  Perhaps firms that borrow incur other costs—bankruptcy costs, for example.

We now explore these two escape routes.

 18-2   Corporate and Personal Taxes

When personal taxes are introduced, the firm’s objective is no longer to minimize the corporate tax bill; the firm should try to minimize the present value of all taxes paid on corporate income. “All taxes” include personal taxes paid by bondholders and stockholders.

Figure 18.1 illustrates how corporate and personal taxes are affected by leverage. Depending on the firm’s capital structure, a dollar of operating income will accrue to investors either as debt interest or equity income (dividends or capital gains). That is, the dollar can go down either branch of Figure 18.1.

Notice that Figure 18.1 distinguishes between Tp, the personal tax rate on interest, and TpE, the effective personal tax rate on equity income. This rate can be well below Tp, depending on the mix of dividends and capital gains realized by shareholders. The top marginal rate on dividends and capital gains is now (2012) only 15% while the top rate on other income, including interest income, is 35%. Also capital gains taxes can be deferred until shares are sold, so the top effective capital gains rate is usually less than 15%.

The firm’s objective should be to arrange its capital structure to maximize after-tax income. You can see from Figure 18.1 that corporate borrowing is better if (1 – Tp) is more than (1 – TpE) × (1 – Tc); otherwise it is worse. The relative tax advantage of debt over equity is

   FIGURE 18.1 The firm’s capital structure determines whether operating income is paid out as interest or equity income. Interest is taxed only at the personal level. Equity income is taxed at both the corporate and the personal levels. However, TpE, the personal tax rate on equity income, can be less than Tp, the personal tax rate on interest income.

This suggests two special cases. First, suppose that debt and equity income were taxed at the same effective personal rate. But with TpE = Tp, the relative advantage depends only on the corporate rate:

In this case, we can forget about personal taxes. The tax advantage of corporate borrowing is exactly as MM calculated it.⁶ They do not have to assume away personal taxes. Their theory of debt and taxes requires only that debt and equity be taxed at the same rate.

The second special case occurs when corporate and personal taxes cancel to make debt policy irrelevant. This requires

This case can happen only if Tc, the corporate rate, is less than the personal rate Tp and if TpE, the effective rate on equity income, is small. Merton Miller explored this situation at a time when U.S. tax rates on interest and dividends were much higher than now, but we won’t go into the details of his analysis here.⁷

In any event we seem to have a simple, practical decision rule. Arrange the firm’s capital structure to shunt operating income down that branch of Figure 18.1 where the tax is least. Unfortunately that is not as simple as it sounds. What’s TpE, for example? The shareholder roster of any large corporation is likely to include tax-exempt investors (such as pension funds or university endowments) as well as millionaires. All possible tax brackets will be mixed together. And it’s the same with Tp, the personal tax rate on interest. The large corporation’s “typical” bondholder might be a tax-exempt pension fund, but many taxpaying investors also hold corporate debt.

Some investors may be much happier to buy your debt than others. For example, you should have no problems inducing pension funds to lend; they don’t have to worry about personal tax. But taxpaying investors may be more reluctant to hold debt and will be prepared to do so only if they are compensated by a high rate of interest. Investors paying tax on interest at the top rate of 35% may be particularly reluctant to hold debt. They will prefer to hold common stock or tax-exempt bonds issued by states and municipalities.

To determine the net tax advantage of debt, companies would need to know the tax rates faced by the marginal investor—that is, an investor who is equally happy to hold debt or equity. This makes it hard to put a precise figure on the tax benefit, but we can nevertheless provide a back-of-the-envelope calculation. On average, over the past 10 years, large U.S. companies have paid out about half of their earnings. Suppose the marginal investor is in the top tax bracket, paying 35% on interest and 15% on dividends and capital gains. Let’s assume that deferred realization of capital gains cuts the effective capital gains rate in half, to 15/2 = 7.5%. Therefore, if the investor invests in the stock of a company with a 50% payout, the tax on each $1.00 of equity income is TpE = (.5 × 15) + (.5 × 7.5) = 11.25%.

Now we can calculate the effect of shunting a dollar of income down each of the two branches in Figure 18.1:

The advantage to debt financing appears to be about seven cents on the dollar.

We should emphasize that our back-of-the-envelope calculation is just that. But it’s interesting to see how debt’s tax advantage shrinks when we account for the relatively low personal tax rate on equity income.

Most financial managers believe that there is a moderate tax advantage to corporate borrowing, at least for companies that are reasonably sure they can use the corporate tax shields. For companies that cannot benefit from corporate tax shields there is probably a moderate tax disadvantage.

Do companies make full use of interest tax shields? John Graham argues that they don’t. His estimates suggest that a typical tax-paying corporation could add 7.5% to firm value by levering up to a still-conservative debt ratio.⁸ This is hardly spare change. Therefore it still appears that financial managers have passed by some easy tax savings. Perhaps they saw some offsetting disadvantage to increased borrowing. We now explore this second escape route.

 18-3   Costs of Financial Distress

Financial distress occurs when promises to creditors are broken or honored with difficulty. Sometimes financial distress leads to bankruptcy. Sometimes it only means skating on thin ice.

As we will see, financial distress is costly. Investors know that levered firms may fall into financial distress, and they worry about it. That worry is reflected in the current market value of the levered firm’s securities. Thus, the value of the firm can be broken down into three parts:

The costs of financial distress depend on the probability of distress and the magnitude of costs encountered if distress occurs.

Figure 18.2 shows how the trade-off between the tax benefits and the costs of distress could determine optimal capital structure. PV(tax shield) initially increases as the firm borrows more. At moderate debt levels the probability of financial distress is trivial, and so PV(cost of financial distress) is small and tax advantages dominate. But at some point the probability of financial distress increases rapidly with additional borrowing; the costs of distress begin to take a substantial bite out of firm value. Also, if the firm can’t be sure of profiting from the corporate tax shield, the tax advantage of additional debt is likely to dwindle and eventually disappear. The theoretical optimum is reached when the present value of tax savings due to further borrowing is just offset by increases in the present value of costs of distress. This is called the trade-off theory of capital structure.

Costs of financial distress cover several specific items. Now we identify these costs and try to understand what causes them.

Bankruptcy Costs

You rarely hear anything nice said about corporate bankruptcy. But there is some good in almost everything. Corporate bankruptcies occur when stockholders exercise their right to default. That right is valuable; when a firm gets into trouble, limited liability allows stockholders simply to walk away from it, leaving all its troubles to its creditors. The former creditors become the new stockholders, and the old stockholders are left with nothing.

   FIGURE 18.2 The value of the firm is equal to its value if all-equity-financed plus PV tax shield minus PV costs of financial distress. According to the trade-off theory of capital structure, the manager should choose the debt ratio that maximizes firm value.

Stockholders in corporations automatically get limited liability. But suppose that this were not so. Suppose that there are two firms with identical assets and operations. Each firm has debt outstanding, and each has promised to repay $1,000 (principal and interest) next year. But only one of the firms, Ace Limited, enjoys limited liability. The other firm, Ace Unlimited, does not; its stockholders are personally liable for its debt.⁹

Figure 18.3 compares next year’s possible payoffs to the creditors and stockholders of these two firms. The only differences occur when next year’s asset value turns out to be less than $1,000. Suppose that next year the assets of each company are worth only $500. In this case Ace Limited defaults. Its stockholders walk away; their payoff is zero. Bondholders get the assets worth $500. But Ace Unlimited’s stockholders can’t walk away. They have to cough up $500, the difference between asset value and the bondholders’ claim. The debt is paid whatever happens.

   FIGURE 18.3 Comparison of limited and unlimited liability for two otherwise identical firms. If the two firms’ asset values are less than $1,000, Ace Limited stockholders default and its bondholders take over the assets. Ace Unlimited stockholders keep the assets, but they must reach into their own pockets to pay off its bondholders. The total payoff to both stockholders and bondholders is the same for the two firms.

Suppose that Ace Limited does go bankrupt. Of course, its stockholders are disappointed that their firm is worth so little, but that is an operating problem having nothing to do with financing. Given poor operating performance, the right to go bankrupt—the right to default—is a valuable privilege. As Figure 18.3 shows, Ace Limited’s stockholders are in better shape than Unlimited’s are.

The example illuminates a mistake people often make in thinking about the costs of bankruptcy. Bankruptcies are thought of as corporate funerals. The mourners (creditors and especially shareholders) look at their firm’s present sad state. They think of how valuable their securities used to be and how little is left. But they may also think of the lost value as a cost of bankruptcy. That is the mistake. The decline in the value of assets is what the mourning is really about. That has no necessary connection with financing. The bankruptcy is merely a legal mechanism for allowing creditors to take over when the decline in the value of assets triggers a default. Bankruptcy is not the cause of the decline in value. It is the result.

Be careful not to get cause and effect reversed. When a person dies, we do not cite the implementation of his or her will as the cause of death.

We said that bankruptcy is a legal mechanism allowing creditors to take over when a firm defaults. Bankruptcy costs are the costs of using this mechanism. There are no bankruptcy costs at all shown in Figure 18.3. Note that only Ace Limited can default and go bankrupt. But, regardless of what happens to asset value, the combined payoff to the bondholders and stockholders of Ace Limited is always the same as the combined payoff to the bondholders and stockholders of Ace Unlimited. Thus the overall market values of the two firms now (this year) must be identical. Of course, Ace Limited’s stock is worth more than Ace Unlimited’s stock because of Ace Limited’s right to default. Ace Limited’s debt is worth correspondingly less.

Our example was not intended to be strictly realistic. Anything involving courts and lawyers cannot be free. Suppose that court and legal fees are $200 if Ace Limited defaults. The fees are paid out of the remaining value of Ace’s assets. Thus if asset value turns out to be $500, creditors end up with only $300. Figure 18.4 shows next year’s total payoff to bondholders and stockholders net of this bankruptcy cost. Ace Limited, by issuing risky debt, has given lawyers and the court system a claim on the firm if it defaults. The market value of the firm is reduced by the present value of this claim.

It is easy to see how increased leverage affects the present value of the costs of financial distress. If Ace Limited borrows more, it increases the probability of default and the value of the lawyers’ claim. It increases PV (costs of financial distress) and reduces Ace’s present market value.

   FIGURE 18.4 Total payoff to Ace Limited security holders. There is a $200 bankruptcy cost in the event of default (shaded area).

The costs of bankruptcy come out of stockholders’ pockets. Creditors foresee the costs and foresee that they will pay them if default occurs. For this they demand compensation in advance in the form of higher payoffs when the firm does not default; that is, they demand a higher promised interest rate. This reduces the possible payoffs to stockholders and reduces the present market value of their shares.

Evidence on Bankruptcy Costs

Bankruptcy costs can add up fast. The failed energy giant Enron paid $757 million in legal, accounting, and other professional fees during the time that it spent in bankruptcy. The costs of sorting out the 65,000 claims on the assets of Lehman Brothers are likely to reach a record $1.5 billion.

Daunting as such numbers may seem, they are not a large fraction of the companies’ asset values. Lawrence Weiss, who studied 31 firms that went bankrupt between 1980 and 1986, found average costs of about 3% of total book assets and 20% of the market value of equity in the year prior to bankruptcy. A study by Andrade and Kaplan of a sample of troubled and highly leveraged firms estimated costs of financial distress amounting to 10% to 20% of predistress market value, although they found it hard to decide whether these costs were caused by financial distress or by the business setbacks that led to distress.¹⁰

Bankruptcy eats up a larger fraction of asset value for small companies than for large ones. There are significant economies of scale in going bankrupt. For example, a study of smaller UK bankruptcies by Franks and Sussman found that fees (legal and accounting) and other costs soaked up roughly 20% to 40% of the proceeds from liquidation of the companies.¹¹

Direct versus Indirect Costs of Bankruptcy

So far we have discussed the direct (that is, legal and administrative) costs of bankruptcy. There are indirect costs too, which are nearly impossible to measure. But we have circumstantial evidence indicating their importance.

Managing a bankrupt firm is not easy. Consent of the bankruptcy court is required for many routine business decisions, such as the sale of assets or investment in new equipment. At best this involves time and effort; at worst proposals to reform and revive the firm are thwarted by impatient creditors, who stand first in line for cash from asset sales or liquidation of the entire firm.

Sometimes the problem is reversed: The bankruptcy court is so anxious to maintain the firm as a going concern that it allows the firm to engage in negative-NPV activities. When Eastern Airlines entered the “protection” of the bankruptcy court in 1989, it still had some valuable, profit-making routes and salable assets such as planes and terminal facilities. The creditors would have been best served by a prompt liquidation, which probably would have generated enough cash to pay off all debt and preferred stockholders. But the bankruptcy judge was keen to keep Eastern’s planes flying at all costs, so he allowed the company to sell many of its assets to fund hefty operating losses. When Eastern finally closed down after two years, it was not just bankrupt, but administratively insolvent: There was almost nothing for creditors, and the company was running out of cash to pay legal expenses.¹²

We do not know what the sum of direct and indirect costs of bankruptcy amounts to. We suspect it is a significant number, particularly for large firms for which proceedings would be lengthy and complex. Perhaps the best evidence is the reluctance of creditors to force bankruptcy. In principle, they would be better off to end the agony and seize the assets as soon as possible. Instead, creditors often overlook defaults in the hope of nursing the firm over a difficult period. They do this in part to avoid costs of bankruptcy. There is an old financial saying, “Borrow $1,000 and you’ve got a banker. Borrow $10,000,000 and you’ve got a partner.”

Creditors may also shy away from bankruptcy because they worry about violations of absolute priority. Absolute priority means that creditors are paid in full before stockholders receive a penny. But sometimes reorganizations provide something for everyone, including consolation prizes for stockholders. Sometimes other claimants move up in the queue. For example, after the Chrysler bankruptcy in 2009, the State of Indiana sued (unsuccessfully) on behalf of local pension funds that had invested in Chrysler bonds. The funds complained bitterly about the terms of sale of the bankrupt company’s assets to Fiat, arguing that they would get only $.29 on the dollar, while other, more junior claimants fared better. The Chrysler bankruptcy was a special case, however. One of the key players in the proceedings was the U.S. government, which was anxious to protect tens of thousands of jobs in the middle of a severe recession.

We cover bankruptcy procedures in more detail in Chapter 32.

Financial Distress without Bankruptcy

Not every firm that gets into trouble goes bankrupt. As long as the firm can scrape up enough cash to pay the interest on its debt, it may be able to postpone bankruptcy for many years. Eventually the firm may recover, pay off its debt, and escape bankruptcy altogether.

But the mere threat of financial distress can be costly to the threatened firm. Customers and suppliers are extra cautious about doing business with a firm that may not be around for long. Customers worry about resale value and the availability of service and replacement parts. (This was a serious drag on Chrysler’s sales pre-bankruptcy, for example.) Suppliers are disinclined to put effort into servicing the distressed firm’s account and may demand cash on the nail for their products. Potential employees are unwilling to sign on and existing staff keep slipping away from their desks for job interviews.

High debt, and thus high financial risk, also appears to reduce firms’ appetites for business risk. For example, Luigi Zingales looked at the fortunes of U.S. trucking companies after the trucking industry was deregulated in the late 1970s.¹³ The deregulation sparked a wave of competition and restructuring. Survival required new investment and improvements in operating efficiency. Zingales found that conservatively financed trucking companies were more likely to survive in the new competitive environment. High-debt firms were more likely to drop out of the game.

Debt and Incentives

When a firm is in trouble, both bondholders and stockholders want it to recover, but in other respects their interests may be in conflict. In times of financial distress the security holders are like many political parties—united on generalities but threatened by squabbling on any specific issue.

Financial distress is costly when these conflicts of interest get in the way of proper operating, investment, and financing decisions. Stockholders are tempted to forsake the usual objective of maximizing the overall market value of the firm and to pursue narrower self-interest instead. They are tempted to play games at the expense of their creditors. We now illustrate how such games can lead to costs of financial distress.

Here is the Circular File Company’s book balance sheet:

We will assume there is only one share and one bond outstanding. The stockholder is also the manager. The bondholder is somebody else.

Here is its balance sheet in market values—a clear case of financial distress, since the face value of Circular’s debt ($50) exceeds the firm’s total market value ($30):

If the debt matured today, Circular’s owner would default, leaving the firm bankrupt. But suppose that the bond actually matures one year hence, that there is enough cash for Circular to limp along for one year, and that the bondholder cannot “call the question” and force bankruptcy before then.

The one-year grace period explains why the Circular share still has value. Its owner is betting on a stroke of luck that will rescue the firm, allowing it to pay off the debt with something left over. The bet is a long shot—the owner wins only if firm value increases from $30 to more than $50.¹⁴ But the owner has a secret weapon: He controls investment and operating strategy.

Risk Shifting: The First Game

Suppose that Circular has $10 cash. The following investment opportunity comes up:

This is a wild gamble and probably a lousy project. But you can see why the owner would be tempted to take it anyway. Why not go for broke? Circular will probably go under anyway, so the owner is essentially betting with the bondholder’s money. But the owner gets most of the loot if the project pays off.

Suppose that the project’s NPV is – $2 but that it is undertaken anyway, thus depressing firm value by $2. Circular’s new balance sheet might look like this:

Firm value falls by $2, but the owner is $3 ahead because the bond’s value has fallen by $5.¹⁵ The $10 cash that used to stand behind the bond has been replaced by a very risky asset worth only $8.

Thus a game has been played at the expense of Circular’s bondholder. The game illustrates the following general point: Stockholders of levered firms gain when business risk increases. Financial managers who act strictly in their shareholders’ interests (and against the interests of creditors) will favor risky projects over safe ones. They may even take risky projects with negative NPVs.

This warped strategy for capital budgeting clearly is costly to the firm and to the economy as a whole. Why do we associate the costs with financial distress? Because the temptation to play is strongest when the odds of default are high. A blue-chip company like Exxon Mobil would never invest in our negative-NPV gamble. Its creditors are not vulnerable to one risky project.

Refusing to Contribute Equity Capital: The Second Game

We have seen how stockholders, acting in their immediate, narrow self-interest, may take projects that reduce the overall market value of their firm. These are errors of commission. Conflicts of interest may also lead to errors of omission.

Assume that Circular cannot scrape up any cash, and therefore cannot take that wild gamble. Instead a good opportunity comes up: a relatively safe asset costing $10 with a present value of $15 and NPV = +$5.

This project will not in itself rescue Circular, but it is a step in the right direction. We might therefore expect Circular to issue $10 of new stock and to go ahead with the investment. Suppose that two new shares are issued to the original owner for $10 cash. The project is taken. The new balance sheet might look like this:

The total value of the firm goes up by $15 ($10 of new capital and $5 NPV). Notice that the Circular bond is no longer worth $25, but $33. The bondholder receives a capital gain of $8 because the firm’s assets include a new, safe asset worth $15. The probability of default is less, and the payoff to the bondholder if default occurs is larger.

The stockholder loses what the bondholder gains. Equity value goes up not by $15 but by $15 – $8 = $7. The owner puts in $10 of fresh equity capital but gains only $7 in market value. Going ahead is in the firm’s interest but not the owner’s.

Again, our example illustrates a general point. If we hold business risk constant, any increase in firm value is shared among bondholders and stockholders. The value of any investment opportunity to the firm’s stockholders is reduced because project benefits must be shared with bondholders. Thus it may not be in the stockholders’ self-interest to contribute fresh equity capital even if that means forgoing positive-NPV investment opportunities.

This problem theoretically affects all levered firms, but it is most serious when firms land in financial distress. The greater the probability of default, the more bondholders have to gain from investments that increase firm value.

And Three More Games, Briefly

As with other games, the temptation to play the next three games is particularly strong in financial distress.

Cash In and Run Stockholders may be reluctant to put money into a firm in financial distress, but they are happy to take the money out—in the form of a cash dividend, for example. The market value of the firm’s stock goes down by less than the amount of the dividend paid, because the decline in firm value is shared with creditors. This game is just “refusing to contribute equity capital” run in reverse.¹⁶

Playing for Time When the firm is in financial distress, creditors would like to salvage what they can by forcing the firm to settle up. Naturally, stockholders want to delay this as long as they can. There are various devious ways of doing this, for example, through accounting changes designed to conceal the true extent of trouble, by encouraging false hopes of spontaneous recovery, or by cutting corners on maintenance, research and development, and so on, in order to make this year’s operating performance look better.

Bait and Switch This game is not always played in financial distress, but it is a quick way to get into distress. You start with a conservative policy, issuing a limited amount of relatively safe debt. Then you suddenly switch and issue a lot more. That makes all your debt risky, imposing a capital loss on the “old” bondholders. Their capital loss is the stockholders’ gain.

A dramatic example of bait and switch occurred in October 1988, when the management of RJR Nabisco announced its intention to acquire the company in a leveraged buy-out (LBO). This put the company “in play” for a transaction in which existing shareholders would be bought out and the company would be “taken private.” The cost of the buy-out would be almost entirely debt-financed. The new private company would start life with an extremely high debt ratio.

RJR Nabisco had debt outstanding with a market value of about $2.4 billion. The announcement of the coming LBO drove down this market value by $298 million.¹⁷

What the Games Cost

Why should anyone object to these games so long as they are played by consenting adults? Because playing them means poor decisions about investments and operations. These poor decisions are agency costs of borrowing.

The more the firm borrows, the greater is the temptation to play the games (assuming the financial manager acts in the stockholders’ interest). The increased odds of poor decisions in the future prompt investors to mark down the present market value of the firm. The fall in value comes out of the shareholders’ pockets. Therefore it is ultimately in their interest to avoid temptation. The easiest way to do this is to limit borrowing to levels at which the firm’s debt is safe or close to it.

Banks and other corporate lenders are also not financial innocents. They realize that games may be played at their expense and so protect themselves by rationing the amount that they will lend or by imposing restrictions on the company’s actions.

EXAMPLE 18.1 • Ms. Ketchup Faces Credit Rationing

Consider the case of Henrietta Ketchup, a budding entrepreneur with two possible investment projects that offer the following payoffs:

Project 1 is surefire and very profitable; project 2 is risky and a rotten project. Ms. Ketchup now approaches her bank and asks to borrow the present value of $10 (she will find the remaining money out of her own purse). The bank calculates that the payoff will be split as follows:

If Ms. Ketchup accepts project 1, the bank’s debt is certain to be paid in full; if she accepts project 2, there is only a 50% chance of payment and the expected payoff to the bank is only $5. Unfortunately, Ms. Ketchup will prefer to take project 2, for if things go well, she gets most of the profit, and if they go badly, the bank bears most of the loss. Unless Ms. Ketchup can convince the bank that she will not gamble with its money, the bank will limit the amount that it is prepared to lend.¹⁸

How can Ms. Ketchup in Example 18.1 reassure the bank of her intentions? The obvious answer is to give it veto power over potentially dangerous decisions. There we have the ultimate economic rationale for all that fine print backing up corporate debt. Debt contracts frequently limit dividends or equivalent transfers of wealth to stockholders; the firm may not be allowed to pay out more than it earns, for example. Additional borrowing is almost always limited. For example, many companies are prevented by existing bond indentures from issuing any additional long-term debt unless their ratio of earnings to interest charges exceeds 2.0.

Sometimes firms are restricted from selling assets or making major investment outlays except with the lenders’ consent. The risks of playing for time are reduced by specifying accounting procedures and by giving lenders access to the firm’s books and its financial forecasts.

Of course, fine print cannot be a complete solution for firms that insist on issuing risky debt. The fine print has its own costs; you have to spend money to save money. Obviously a complex debt contract costs more to negotiate than a simple one. Afterward it costs the lender more to monitor the firm’s performance. Lenders anticipate monitoring costs and demand compensation in the form of higher interest rates; thus the monitoring costs—another agency cost of debt—are ultimately paid by stockholders.

Perhaps the most severe costs of the fine print stem from the constraints it places on operating and investment decisions. For example, an attempt to prevent the risk-shifting game may also prevent the firm from pursuing good investment opportunities. At the minimum there are delays in clearing major investments with lenders. In some cases lenders may veto high-risk investments even if net present value is positive. The lenders are tempted to play a game of their own, forcing the firm to stay in cash or low-risk assets even if good projects are forgone.

Debt contracts cannot cover every possible manifestation of the games we have just discussed. Any attempt to do so would be hopelessly expensive and doomed to failure in any event. Human imagination is insufficient to conceive of all the possible things that could go wrong. Therefore contracts are always incomplete. We will always find surprises coming at us on dimensions we never thought to think about.

We hope we have not left the impression that managers and stockholders always succumb to temptation unless restrained. Usually they refrain voluntarily, not only from a sense of fair play but also on pragmatic grounds: A firm or individual that makes a killing today at the expense of a creditor will be coldly received when the time comes to borrow again. Aggressive game playing is done only by out-and-out crooks and by firms in extreme financial distress. Firms limit borrowing precisely because they don’t wish to land in distress and be exposed to the temptation to play.

Costs of Distress Vary with Type of Asset

Suppose your firm’s only asset is a large downtown hotel, mortgaged to the hilt. The recession hits, occupancy rates fall, and the mortgage payments cannot be met. The lender takes over and sells the hotel to a new owner and operator. You use your firm’s stock certificates for wallpaper.

What is the cost of bankruptcy? In this example, probably very little. The value of the hotel is, of course, much less than you hoped, but that is due to the lack of guests, not to the bankruptcy. Bankruptcy doesn’t damage the hotel itself. The direct bankruptcy costs are restricted to items such as legal and court fees, real estate commissions, and the time the lender spends sorting things out.

Suppose we repeat the story of Heartbreak Hotel for Fledgling Electronics. Everything is the same, except for the underlying real assets—not real estate but a high-tech going concern, a growth company whose most valuable assets are technology, investment opportunities, and its employees’ human capital.

If Fledgling gets into trouble, the stockholders may be reluctant to put up money to cash in on its growth opportunities. Failure to invest is likely to be much more serious for Fledgling than for the Heartbreak Hotel.

If Fledgling finally defaults on its debt, the lender will find it much more difficult to cash in by selling off the assets. Many of them are intangibles that have value only as a part of a going concern.

Could Fledgling be kept as a going concern through default and reorganization? It may not be as hopeless as putting a wedding cake through a car wash, but there are a number of serious difficulties. First, the odds of defections by key employees are higher than they would be if the firm had never gotten into financial trouble. Special guarantees may have to be given to customers who have doubts about whether the firm will be around to service its products. Aggressive investment in new products and technology will be difficult; each class of creditors will have to be convinced that it is in its interest for the firm to invest new money in risky ventures.

Some assets, like good commercial real estate, can pass through bankruptcy and reorganization largely unscathed;¹⁹ the values of other assets are likely to be considerably diminished. The losses are greatest for the intangible assets that are linked to the health of the firm as a going concern—for example, technology, human capital, and brand image. That may be why debt ratios are low in the pharmaceutical industry, where value depends on continued success in research and development, and in many service industries where value depends on human capital. We can also understand why highly profitable growth companies, such as Microsoft or Google, use mostly equity finance.

The moral of these examples is this: Do not think only about the probability that borrowing will bring trouble. Think also of the value that may be lost if trouble comes.

Heartbreak Hotel for Enron? Enron was one of the most glamorous, fast-growing, and (apparently) profitable companies of the 1990s. It played a lead role in the deregulation of electric power markets, both in the United States and internationally. It invested in electric power generation and distribution, gas pipelines, telecommunications networks, and various other ventures. It also built up an active energy trading business. At its peak the aggregate market value of Enron’s common stock exceeded $60 billion. By the end of 2001, Enron was in bankruptcy and its shares were worthless.

With hindsight we see that Enron was playing many of the games that we described earlier in this section. It was borrowing aggressively and hiding the debt in “special-purpose entities” (SPEs). The SPEs also allowed it to pump up its reported earnings, playing for time while making more and more risky investments. When the bubble burst, there was hardly any value left.

The collapse of Enron didn’t really destroy $60 billion in value, because that $60 billion wasn’t there in the first place. But there were genuine costs of financial distress. Let’s focus on Enron’s energy trading business. That business was not as profitable as it appeared, but it was nevertheless a valuable asset. It provided an important service for wholesale energy customers and suppliers who wanted to buy or sell contracts that locked in the future prices and quantities of electricity, natural gas, and other commodities.

What happened to this business when it became clear that Enron was in financial distress and probably headed for bankruptcy? It disappeared. Trading volume went to zero immediately. None of its customers was willing to make a new trade with Enron, because it was far from clear that Enron would be around to honor its side of the bargain. With no trading volume, there was no trading business. As it turned out, Enron’s trading business more resembled Fledgling Electronics than a tangible asset like Heartbreak Hotel.

The value of Enron’s trading business depended on Enron’s creditworthiness. The value should have been protected by conservative financing. Most of the lost value can be traced back to Enron’s aggressive borrowing. This loss of value was therefore a cost of financial distress.

The Trade-Off Theory of Capital Structure

BEYOND THE PAGE

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Do firms have a debt target?

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Financial managers often think of the firm’s debt–equity decision as a trade-off between interest tax shields and the costs of financial distress. Of course, there is controversy about how valuable interest tax shields are and what kinds of financial trouble are most threatening, but these disagreements are only variations on a theme. Thus, Figure 18.2 illustrates the debt–equity trade-off.

This trade-off theory of capital structure recognizes that target debt ratios may vary from firm to firm. Companies with safe, tangible assets and plenty of taxable income to shield ought to have high target ratios. Unprofitable companies with risky, intangible assets ought to rely primarily on equity financing.

If there were no costs of adjusting capital structure, then each firm should always be at its target debt ratio. However, there are costs, and therefore delays, in adjusting to the optimum. Firms cannot immediately offset the random events that bump them away from their capital structure targets, so we should see random differences in actual debt ratios among firms having the same target debt ratio.

All in all, this trade-off theory of capital structure choice tells a comforting story. Unlike MM’s theory, which seemed to say that firms should take on as much debt as possible, it avoids extreme predictions and rationalizes moderate debt ratios. Also, if you ask financial managers whether their firms have target debt ratios, they will usually say yes—although the target is often specified not as a debt ratio but as a debt rating. For example, the firm might manage its capital structure to maintain a single-A bond rating. Ratio or rating, a target is consistent with the trade-off theory.²⁰

But what are the facts? Can the trade-off theory of capital structure explain how companies actually behave?

The answer is “yes and no.” On the “yes” side, the trade-off theory successfully explains many industry differences in capital structure. High-tech growth companies, whose assets are risky and mostly intangible, normally use relatively little debt. Airlines can and do borrow heavily because their assets are tangible and relatively safe.²¹

On the “no” side, there are some things the trade-off theory cannot explain. It cannot explain why some of the most successful companies thrive with little debt. Think of Johnson & Johnson, which, as Table 18.4a shows, has little debt. Granted, Johnson & Johnson’s most valuable assets are intangible, the fruits of its research and development. We know that intangible assets and conservative capital structures go together. But Johnson & Johnson also has a very large corporate income tax bill (about $2.6 billion in 2011) and the highest possible credit rating. It could borrow enough to save tens of millions of dollars without raising a whisker of concern about possible financial distress.

Johnson & Johnson illustrates an odd fact about real-life capital structures: The most profitable companies commonly borrow the least.²² Here the trade-off theory fails, for it predicts exactly the reverse. Under the trade-off theory, high profits should mean more debt-servicing capacity and more taxable income to shield and so should give a higher target debt ratio.²³

In general it appears that public companies rarely make major shifts in capital structure just because of taxes,²⁴ and it is hard to detect the present value of interest tax shields in firms’ market values.²⁵ Also, there are large, long-lived differences between debt ratios of firms in the same industry, even after controlling for attributes that the trade-off theory says should be important.²⁶

A final point on the “no” side for the trade-off theory: Debt ratios today are no higher than they were in the early 1900s, when income tax rates were low (or zero). Debt ratios in other industrialized countries are equal to or higher than those in the U.S. Many of these countries have imputation tax systems, which should eliminate the value of the interest tax shields.²⁷

None of this disproves the trade-off theory. As George Stigler emphasized, theories are not rejected by circumstantial evidence; it takes a theory to beat a theory. So we now turn to a completely different theory of financing.

 18-4   The Pecking Order of Financing Choices

The pecking-order theory starts with asymmetric information—a fancy term indicating that managers know more about their companies’ prospects, risks, and values than do outside investors.

Managers obviously know more than investors. We can prove that by observing stock price changes caused by announcements by managers. For example, when a company announces an increased regular dividend, stock price typically rises, because investors interpret the increase as a sign of management’s confidence in future earnings. In other words, the dividend increase transfers information from managers to investors. This can happen only if managers know more in the first place.

Asymmetric information affects the choice between internal and external financing and between new issues of debt and equity securities. This leads to a pecking order, in which investment is financed first with internal funds, reinvested earnings primarily; then by new issues of debt, and finally with new issues of equity. New equity issues are a last resort when the company runs out of debt capacity, that is, when the threat of costs of financial distress brings regular insomnia to existing creditors and to the financial manager.

We will take a closer look at the pecking order in a moment. First, you must appreciate how asymmetric information can force the financial manager to issue debt rather than common stock.

Debt and Equity Issues with Asymmetric Information

To the outside world Smith & Company and Jones, Inc., our two example companies, are identical. Each runs a successful business with good growth opportunities. The two businesses are risky, however, and investors have learned from experience that current expectations are frequently bettered or disappointed. Current expectations price each company’s stock at $100 per share, but the true values could be higher or lower:

Now suppose that both companies need to raise new money from investors to fund capital investment. They can do this either by issuing bonds or by issuing new shares of common stock. How would the choice be made? One financial manager—we will not tell you which one—might reason as follows:

Sell stock for $100 per share? Ridiculous! It’s worth at least $120. A stock issue now would hand a free gift to new investors. I just wish those skeptical shareholders would appreciate the true value of this company. Our new factories will make us the world’s lowest-cost producer. We’ve painted a rosy picture for the press and security analysts, but it just doesn’t seem to be working. Oh well, the decision is obvious: we’ll issue debt, not underpriced equity. A debt issue will save underwriting fees too.

The other financial manager is in a different mood:

Beefalo burgers were a hit for a while, but it looks like the fad is fading. The fast-food division’s gotta find some good new products or it’s all downhill from here. Export markets are OK for now, but how are we going to compete with those new Siberian ranches? Fortunately the stock price has held up pretty well—we’ve had some good short-run news for the press and security analysts. Now’s the time to issue stock. We have major investments underway, and why add increased debt service to my other worries?

Of course, outside investors can’t read the financial managers’ minds. If they could, one stock might trade at $120 and the other at $80.

Why doesn’t the optimistic financial manager simply educate investors? Then the company could sell stock on fair terms, and there would be no reason to favor debt over equity or vice versa.

This is not so easy. (Note that both companies are issuing upbeat press releases.) Investors can’t be told what to think; they have to be convinced. That takes a detailed layout of the company’s plans and prospects, including the inside scoop on new technology, product design, marketing plans, and so on. Getting this across is expensive for the company and also valuable to its competitors. Why go to the trouble? Investors will learn soon enough, as revenues and earnings evolve. In the meantime the optimistic financial manager can finance growth by issuing debt.

Now suppose there are two press releases:

Jones, Inc., will issue $120 million of five-year senior notes.

Smith & Co. announced plans today to issue 1.2 million new shares of common stock. The company expects to raise $120 million.

As a rational investor, you immediately learn two things. First, Jones’s financial manager is optimistic and Smith’s is pessimistic. Second, Smith’s financial manager is also naive to think that investors would pay $100 per share. The attempt to sell stock shows that it must be worth less. Smith might sell stock at $80 per share, but certainly not at $100.²⁸

Smart financial managers think this through ahead of time. The end result? Both Smith and Jones end up issuing debt. Jones, Inc., issues debt because its financial manager is optimistic and doesn’t want to issue undervalued equity. A smart, but pessimistic, financial manager at Smith issues debt because an attempt to issue equity would force the stock price down and eliminate any advantage from doing so. (Issuing equity also reveals the manager’s pessimism immediately. Most managers prefer to wait. A debt issue lets bad news come out later through other channels.)

The story of Smith and Jones illustrates how asymmetric information favors debt issues over equity issues. If managers are better informed than investors and both groups are rational, then any company that can borrow will do so rather than issuing fresh equity. In other words, debt issues will be higher in the pecking order.

Taken literally this reasoning seems to rule out any issue of equity. That’s not right, because asymmetric information is not always important and there are other forces at work. For example, if Smith had already borrowed heavily, and would risk financial distress by borrowing more, then it would have a good reason to issue common stock. In this case announcement of a stock issue would not be entirely bad news. The announcement would still depress the stock price—it would highlight managers’ concerns about financial distress—but the fall in price would not necessarily make the issue unwise or infeasible.

High-tech, high-growth companies can also be credible issuers of common stock. Such companies’ assets are mostly intangible, and bankruptcy or financial distress would be especially costly. This calls for conservative financing. The only way to grow rapidly and keep a conservative debt ratio is to issue equity. If investors see equity issued for these reasons, problems of the sort encountered by Smith’s financial manager become much less serious.

With such exceptions noted, asymmetric information can explain the dominance of debt financing over new equity issues, at least for mature public corporations. Debt issues are frequent; equity issues, rare. The bulk of external financing comes from debt, even in the United States, where equity markets are highly information-efficient. Equity issues are even more difficult in countries with less well developed stock markets.

None of this says that firms ought to strive for high debt ratios—just that it’s better to raise equity by plowing back earnings than issuing stock. In fact, a firm with ample internally generated funds doesn’t have to sell any kind of security and thus avoids issue costs and information problems completely.

Implications of the Pecking Order

The pecking-order theory of corporate financing goes like this.

1.  Firms prefer internal finance.

2.  They adapt their target dividend payout ratios to their investment opportunities, while trying to avoid sudden changes in dividends.

3.  Sticky dividend policies, plus unpredictable fluctuations in profitability and investment opportunities, mean that internally generated cash flow is sometimes more than capital expenditures and other times less. If it is more, the firm pays off debt or invests in marketable securities. If it is less, the firm first draws down its cash balance or sells its marketable securities.

4.  If external finance is required, firms issue the safest security first. That is, they start with debt, then possibly hybrid securities such as convertible bonds, then perhaps equity as a last resort.

In this theory, there is no well-defined target debt–equity mix, because there are two kinds of equity, internal and external, one at the top of the pecking order and one at the bottom. Each firm’s observed debt ratio reflects its cumulative requirements for external finance.

The pecking order explains why the most profitable firms generally borrow less—not because they have low target debt ratios but because they don’t need outside money. Less profitable firms issue debt because they do not have internal funds sufficient for their capital investment programs and because debt financing is first on the pecking order of external financing.

In the pecking-order theory, the attraction of interest tax shields is assumed to be second-order. Debt ratios change when there is an imbalance of internal cash flow, net of dividends, and real investment opportunities. Highly profitable firms with limited investment opportunities work down to low debt ratios. Firms whose investment opportunities outrun internally generated funds are driven to borrow more and more.

This theory explains the inverse intraindustry relationship between profitability and financial leverage. Suppose firms generally invest to keep up with the growth of their industries. Then rates of investment will be similar within an industry. Given sticky dividend payouts, the least profitable firms will have less internal funds and will end up borrowing more.

The Trade-Off Theory vs. the Pecking-Order Theory—Some Evidence

In 1995 Rajan and Zingales published a study of debt versus equity choices by large firms in Canada, France, Germany, Italy, Japan, the UK, and the U.S. Rajan and Zingales found that the debt ratios of individual companies seemed to depend on four main factors:²⁹

1.  Size. Large firms tend to have higher debt ratios.

2.  Tangible assets. Firms with high ratios of fixed assets to total assets have higher debt ratios.

3.  Profitability. More profitable firms have lower debt ratios.

4.  Market to book. Firms with higher ratios of market-to-book value have lower debt ratios.

These results convey good news for both the trade-off and pecking-order theories. Trade-off enthusiasts note that large companies with tangible assets are less exposed to costs of financial distress and would be expected to borrow more. They interpret the market-to-book ratio as a measure of growth opportunities and argue that growth companies could face high costs of financial distress and would be expected to borrow less. Pecking-order advocates stress the importance of profitability, arguing that profitable firms use less debt because they can rely on internal financing. They interpret the market-to-book ratio as just another measure of profitability.

It seems that we have two competing theories, and they’re both right! That’s not a comfortable conclusion. So recent research has tried to run horse races between the two theories in order to find the circumstances in which one or the other wins. It seems that the pecking order works best for large, mature firms that have access to public bond markets. These firms rarely issue equity. They prefer internal financing, but turn to debt markets if needed to finance investment. Smaller, younger, growth firms are more likely to rely on equity issues when external financing is required.³⁰

There is also some evidence that debt ratios incorporate the cumulative effects of market timing.³¹ Market timing is an example of behavioral corporate finance. Suppose that investors are sometimes irrationally exuberant (as in the late 1990s) and sometimes irrationally despondent. If the financial manager’s views are more stable than investors’, then he or she can take advantage by issuing shares when the stock price is too high and switching to debt when the price is too low. Thus lucky companies with a history of buoyant stock prices will issue less debt and more shares, ending up with low debt ratios. Unfortunate and unpopular companies will avoid share issues and end up with high debt ratios.

Market timing could explain why companies tend to issue shares after run-ups in stock prices and also why aggregate stock issues are concentrated in bull markets and fall sharply in bear markets.

There are other behavioral explanations for corporate financing policies. For example, Bertrand and Schoar tracked the careers of individual CEOs, CFOs, and other top managers. Their individual “styles” persisted as they moved from firm to firm.³² For example, older CEOs tended to be more conservative and pushed their firms to lower debt. CEOs with MBA degrees tended to be more aggressive. In general, financial decisions depended not just on the nature of the firm and its economic environment, but also on the personalities of the firm’s top management.

The Bright Side and the Dark Side of Financial Slack

Other things equal, it’s better to be at the top of the pecking order than at the bottom. Firms that have worked down the pecking order and need external equity may end up living with excessive debt or passing by good investments because shares can’t be sold at what managers consider a fair price.

In other words, financial slack is valuable. Having financial slack means having cash, marketable securities, readily salable real assets, and ready access to debt markets or to bank financing. Ready access basically requires conservative financing so that potential lenders see the company’s debt as a safe investment.

In the long run, a company’s value rests more on its capital investment and operating decisions than on financing. Therefore, you want to make sure your firm has sufficient financial slack so that financing is quickly available for good investments. Financial slack is most valuable to firms with plenty of positive-NPV growth opportunities. That is another reason why growth companies usually aspire to conservative capital structures.

Of course financial slack is only valuable if you’re willing to use it. Take a look at the nearby box, which describes how Ford used up all of its financial slack in one enormous debt issue.

There is also a dark side to financial slack. Too much of it may encourage managers to take it easy, expand their perks, or empire-build with cash that should be paid back to stockholders. In other words, slack can make agency problems worse.

Michael Jensen has stressed the tendency of managers with ample free cash flow (or unnecessary financial slack) to plow too much cash into mature businesses or ill-advised acquisitions. “The problem,” Jensen says, “is how to motivate managers to disgorge the cash rather than investing it below the cost of capital or wasting it in organizational inefficiencies.”³³

If that’s the problem, then maybe debt is an answer. Scheduled interest and principal

BEYOND THE PAGE

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Sealed Air’s recapitalization

brealey.mhhe.com/c18

payments are contractual obligations of the firm. Debt forces the firm to pay out cash. Perhaps the best debt level would leave just enough cash in the bank, after debt service, to finance all positive-NPV projects, with not a penny left over.

We do not recommend this degree of fine-tuning, but the idea is valid and important. Debt can discipline managers who are tempted to invest too much. It can also provide the pressure to force improvements in operating efficiency. We pick up this theme again in Chapter 32.

FINANCE IN PRACTICE

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Ford Cashes in All of its Financial Slack

  In 2006, Ford Motor Company brought in a new CEO, Alan Mulally, who launched a thorough restructuring of the company. The company had to cut costs, improve efficiency, and renew its products. This was a massive investment, but debt financing was available. The company decided to borrow as much as it could, to maximize the amount of cash on hand to pay for the restructuring.

In December 2006, Ford issued $5 billion of senior convertible notes. It also arranged a $7 billion, seven-year term loan and an $11.5 billion, five-year revolving credit facility. The total was $23.5 billion.

Ford was able to get this money by pledging almost all of its assets as collateral, including its U.S. property, plant, and equipment; its equity investments in Ford Credit and Ford’s foreign subsidiaries; and its trademarks, including the Ford brand name and logo.

Why did Ford decide to use up all of its financial slack in one gigantic gulp? First, debt financing was available on relatively easy terms in 2006. Second, Mulally must have been aware of the history of restructuring programs in the U.S. auto industry. Some of these initiatives were failures, some partial successes, but none solved Ford, GM, or Chrysler’s competitive problems. The companies shrank but did not improve significantly.

So Mulally was in effect sending a wake-up call to Ford’s managers and employees: “We’ve raised all the cash that we can get. This is our last chance to reform the company. If we don’t make it, Ford is gone.”

Ford did not follow GM and Chrysler into bankruptcy. It lost money in the recession of 2008, but then recovered quickly. It looks as if Ford is a survivor.

Is There a Theory of Optimal Capital Structure?

No. That is, there is no one theory that can capture everything that drives thousands of corporations’ debt versus equity choices. Instead there are several theories, each more or less helpful, depending on each particular corporation’s assets, operations, and circumstances.

In other words, relax: Don’t waste time searching for a magic formula for the optimal debt ratio. Remember too that most value comes from the left side of the balance sheet, that is, from the firm’s operations, assets, and growth opportunities. Financing is less important. Of course, financing can subtract value rapidly if you screw it up, but you won’t do that.

In practice, financing choices depend on the relative importance of the factors discussed in this chapter. In some cases, reducing taxes will be the primary objective. Thus high debt ratios are found in the lease-financing business (see Chapter 25). Long-term leases are often tax-driven transactions. High debt ratios are also found in developed commercial real estate. For example, modern downtown office buildings can be safe, cash-cow assets if the office space is rented to creditworthy tenants. Bankruptcy costs are small, so it makes sense to lever up and save taxes.

For smaller growth companies, interest tax shields are less important than preserving financial slack. Profitable growth opportunities are valuable only if financing is available when it comes time to invest. Costs of financial distress are high, so it’s no surprise that growth companies try to use mostly equity financing.

Mature public corporations often end up following the pecking order. Information problems deter large equity issues, so such firms prefer to finance investment with retained earnings. They issue more debt when investments outrun retained earnings, and pay down debt when earnings outpace investment.

Sooner or later a corporation’s operations age to the point where growth opportunities evaporate. In that case, the firm may issue large amounts of debt and retire equity, to constrain investment and force payout of cash to investors. The higher debt ratio may come voluntarily or be forced by a takeover.

These examples are not exhaustive, but they give some flavor of how a thoughtful CEO can set financing strategy.

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SUMMARY

Our task in this chapter was to show why capital structure matters. We did not throw away MM’s proposition that capital structure is irrelevant; we added to it. However, we did not arrive at any simple, universal theory of optimal capital structure.

The trade-off theory emphasizes interest tax shields and the costs of financial distress. The value of the firm is broken down as

According to this theory, the firm should increase debt until the value from PV(tax shield) is just offset, at the margin, by increases in PV(costs of financial distress).

The costs of financial distress are:

1.  Bankruptcy costs

 a.  Direct costs such as legal and accounting fees.

 b.  Indirect costs reflecting the difficulty of managing a company undergoing liquidation or reorganization.

2.  Costs of financial distress short of bankruptcy

 a.  Doubts about a firm’s creditworthiness can hobble its operations. Customers and suppliers will be reluctant to deal with a firm that may not be around next year. Key employees will be tempted to leave. Highly leveraged firms seem to be less vigorous product-market competitors.

 b.  Conflicts of interest between bondholders and stockholders of firms in financial distress may lead to poor operating and investment decisions. Stockholders acting in their narrow self-interest can gain at the expense of creditors by playing “games” that reduce the overall value of the firm.

 c.  The fine print in debt contracts is designed to prevent these games. But fine print increases the costs of writing, monitoring, and enforcing the debt contract.

The value of the interest tax shield would be easy to compute if we had only corporate taxes to worry about. In that case the net tax saving from borrowing would be just the marginal corporate tax rate Tc times rDD, the interest payment. If debt is fixed, the tax shield can be valued by discounting at the borrowing rate rD. In the special case of fixed, permanent debt

However, corporate taxes are only part of the story. If investors pay higher taxes on interest income than on equity income (dividends and capital gains), then interest tax shields to the corporation will be partly offset by higher taxes paid by investors. The low (15% maximum) U.S. tax rates on dividends and capital gains have reduced the tax advantage to corporate borrowing.

The trade-off theory balances the tax advantages of borrowing against the costs of financial distress. Corporations are supposed to pick a target capital structure that maximizes firm value. Firms with safe, tangible assets and plenty of taxable income to shield ought to have high targets. Unprofitable companies with risky, intangible assets ought to rely more on equity financing.

This theory of capital structure successfully explains many industry differences in capital structure, but it does not explain why the most profitable firms within an industry generally have the most conservative capital structures. Under the trade-off theory, high profitability should mean high debt capacity and a strong tax incentive to use that capacity.

There is a competing, pecking-order theory, which states that firms use internal financing when available and choose debt over equity when external financing is required. This explains why the less profitable firms in an industry borrow more—not because they have higher target debt ratios but because they need more external financing and because debt is next on the pecking order when internal funds are exhausted.

The pecking order is a consequence of asymmetric information. Managers know more about their firms than outside investors do, and they are reluctant to issue stock when they believe the price is too low. They try to time issues when shares are fairly priced or overpriced. Investors understand this, and interpret a decision to issue shares as bad news. That explains why stock price usually falls when a stock issue is announced.

Debt is better than equity when these information problems are important. Optimistic managers will prefer debt to undervalued equity, and pessimistic managers will be pressed to follow suit. The pecking-order theory says that equity will be issued only when debt capacity is running out and financial distress threatens.

The pecking-order theory stresses the value of financial slack. Without sufficient slack, the firm may be caught at the bottom of the pecking order and be forced to choose between issuing undervalued shares, borrowing and risking financial distress, or passing up positive-NPV investment opportunities.

There is, however, a dark side to financial slack. Surplus cash or credit tempts managers to overinvest or to indulge an easy and glamorous corporate lifestyle. When temptation wins, or threatens to win, a high debt ratio can help: It forces the company to disgorge cash and prods managers and organizations to try harder to be more efficient.

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FURTHER READING

The research literature on capital structure is enormous. We cite only a few of the most important and interesting articles. The following review articles give broader surveys.

M. Harris and A. Raviv, “The Theory of Capital Structure,” Journal of Finance 46 (March 1991), pp. 297–355.

S. C. Myers, “Financing of Corporations,” in G. M. Constantinides, M. Harris, and R. Stulz (eds.), Handbook of the Economics of Finance (Amsterdam: Elsevier North-Holland, 2003).

The Winter 2005 issue of the Journal of Applied Corporate Finance contains several articles on capital structure decisions in practice.

The following paper surveys chief financial officers’ views about capital structure:

J. Graham and C. Harvey, “How Do CFOs Make Capital Budgeting and Capital Structure Decisions?” Journal of Applied Corporate Finance 15 (Spring 2002), pp. 8–23.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Tax shield The present value of interest tax shields is often written as TcD, where D is the amount of debt and Tc is the marginal corporate tax rate. Under what assumptions is this present value correct?

2.  Tax shield Here are book and market value balance sheets of the United Frypan Company (UF):

Assume that MM’s theory holds with taxes. There is no growth, and the $40 of debt is expected to be permanent. Assume a 40% corporate tax rate.

a.  How much of the firm’s value is accounted for by the debt-generated tax shield?

b.  How much better off will UF’s shareholders be if the firm borrows $20 more and uses it to repurchase stock?

3.  Tax shields What is the relative tax advantage of corporate debt if the corporate tax rate is Tc = .35, the personal tax rate is Tp = .35, but all equity income is received as capital gains and escapes tax entirely (TpE = 0)? How does the relative tax advantage change if the company decides to pay out all equity income as cash dividends that are taxed at 15%?

4.  Tax shields “The firm can’t use interest tax shields unless it has (taxable) income to shield.” What does this statement imply for debt policy? Explain briefly.

5.  Financial distress This question tests your understanding of financial distress.

a.  What are the costs of going bankrupt? Define these costs carefully.

b.  “A company can incur costs of financial distress without ever going bankrupt.” Explain how this can happen.

c.  Explain how conflicts of interest between bondholders and stockholders can lead to costs of financial distress.

6.  Bankruptcy On February 29, 2013, when PDQ Computers announced bankruptcy, its share price fell from $3.00 to $.50 per share. There were 10 million shares outstanding. Does that imply bankruptcy costs of 10 × (3.00 – .50) = $25 million? Explain.

7.  Trade-off theory The traditional theory of optimal capital structure states that firms trade off corporate interest tax shields against the possible costs of financial distress due to borrowing. What does this theory predict about the relationship between book profitability and target book debt ratios? Is the theory’s prediction consistent with the facts?

8.  Debt ratios Rajan and Zingales identified four variables that seemed to explain differences in debt ratios in several countries. What are the four variables?

9.  Pecking-order theory Why does asymmetric information push companies to raise external funds by borrowing rather than by issuing common stock?

10.  Pecking-order theory Fill in the blanks: According to the pecking-order theory,

a.  The firm’s debt ratio is determined by ___________ .

b.  Debt ratios depend on past profitability, because ___________ .

11.  Financial slack For what kinds of companies is financial slack most valuable? Are there situations in which financial slack should be reduced by borrowing and paying out the proceeds to the stockholders? Explain.

INTERMEDIATE

12.  Tax shields Compute the present value of interest tax shields generated by these three debt issues. Consider corporate taxes only. The marginal tax rate is Tc = .35.

a.  A $1,000, one-year loan at 8%.

b.  A five-year loan of $1,000 at 8%. Assume no principal is repaid until maturity.

c.  A $1,000 perpetuity at 7%.

13.  Tax shields Suppose that, in an effort to reduce the federal deficit, Congress increases the top personal tax rate on interest and dividends to 35% but retains a 15% tax rate on realized capital gains. The corporate tax rate stays at 35%. Compute the total corporate plus personal taxes paid on debt versus equity income if (a) all capital gains are realized immediately and (b) capital gains are deferred forever. Assume capital gains are half of equity income.

14.  Tax shields “The trouble with MM’s argument is that it ignores the fact that individuals cannot deduct interest for personal income tax.” Show why this is not an objection if personal tax rates on interest and equity income are the same.

15.  Tax shields Look back at the Johnson & Johnson example in Section 18-1. Suppose Johnson & Johnson increases its long-term debt to $30 billion. It uses the additional debt to repurchase shares. Reconstruct Table 18.4b with the new capital structure. How much additional value is added for Johnson & Johnson shareholders if the table’s assumptions are correct?

16.  Agency costs In Section 18-3, we briefly referred to three games: Playing for time, cash in and run, and bait and switch.

For each game, construct a simple numerical example (like the example for the risk-shifting game) showing how shareholders can gain at the expense of creditors. Then explain how the temptation to play these games could lead to costs of financial distress.

17.  Bankruptcy cost Look at some real companies with different types of assets. What operating problems would each encounter in the event of financial distress? How well would the assets keep their value?

18.  Agency costs Let us go back to Circular File’s market value balance sheet:

Who gains and who loses from the following maneuvers?

a.  Circular scrapes up $5 in cash and pays a cash dividend.

b.  Circular halts operations, sells its fixed assets, and converts net working capital into $20 cash. Unfortunately the fixed assets fetch only $6 on the secondhand market. The $26 cash is invested in Treasury bills.

c.  Circular encounters an acceptable investment opportunity, NPV = 0, requiring an investment of $10. The firm borrows to finance the project. The new debt has the same security, seniority, etc., as the old.

d.  Suppose that the new project has NPV = +$2 and is financed by an issue of preferred stock.

e.  The lenders agree to extend the maturity of their loan from one year to two in order to give Circular a chance to recover.

19.  Agency costs The Salad Oil Storage (SOS) Company has financed a large part of its facilities with long-term debt. There is a significant risk of default, but the company is not on the ropes yet. Explain:

a.  Why SOS stockholders could lose by investing in a positive-NPV project financed by an equity issue.

b.  Why SOS stockholders could gain by investing in a negative-NPV project financed by cash.

c.  Why SOS stockholders could gain from paying out a large cash dividend.

20.  Covenants

a.  Who benefits from the fine print in bond contracts when the firm gets into financial trouble? Give a one-sentence answer.

b.  Who benefits from the fine print when the bonds are issued? Suppose the firm is offered the choice of issuing (i) a bond with standard restrictions on dividend payout, additional borrowing, etc., and (ii) a bond with minimal restrictions but a much higher interest rate? Suppose the interest rates on both (i) and (ii) are fair from the viewpoint of lenders. Which bond would you expect the firm to issue? Why?

21.  Pecking-order theory “I was amazed to find that the announcement of a stock issue drives down the value of the issuing firm by 30%, on average, of the proceeds of the issue. That issue cost dwarfs the underwriter’s spread and the administrative costs of the issue. It makes common stock issues prohibitively expensive.”

a.  You are contemplating a $100 million stock issue. On past evidence, you anticipate that announcement of this issue will drive down stock price by 3% and that the market value of your firm will fall by 30% of the amount to be raised. On the other hand, additional equity financing is required to fund an investment project that you believe has a positive NPV of $40 million. Should you proceed with the issue?

b.  Is the fall in market value on announcement of a stock issue an issue cost in the same sense as an underwriter’s spread? Respond to the quote that begins this question.

Use your answer to (a) as a numerical example to explain your response to (b).

22.  Exchange offers Ronald Masulis analyzed the stock price impact of exchange offers of debt for equity or vice versa.³⁴ In an exchange offer, the firm offers to trade freshly issued securities for seasoned securities in the hands of investors. Thus, a firm that wanted to move to a higher debt ratio could offer to trade new debt for outstanding shares. A firm that wanted to move to a more conservative capital structure could offer to trade new shares for outstanding debt securities.

Masulis found that debt for equity exchanges were good news (stock price increased on announcement) and equity for debt exchanges were bad news.

a.  Are these results consistent with the trade-off theory of capital structure?

b.  Are the results consistent with the evidence that investors regard announcements of (i) stock issues as bad news, (ii) stock repurchases as good news, and (iii) debt issues as no news, or at most trifling disappointments?

c.  How could Masulis’s results be explained?

23.  Agency costs The possible payoffs from Ms. Ketchup’s projects (see Example 18.1, page 463) have not changed but there is now a 40% chance that Project 2 will pay off $24 and a 60% chance that it will pay off $0.

a.  Recalculate the expected payoffs to the bank and Ms. Ketchup if the bank lends the present value of $10. Which project would Ms. Ketchup undertake?

b.  What is the maximum amount the bank could lend that would induce Ms. Ketchup to take Project 1?

24.  Leverage targets Some corporations’ debt–equity targets are expressed not as a debt ratio but as a target debt rating on the firm’s outstanding bonds. What are the pros and cons of setting a target rating rather than a target ratio?

CHALLENGE

25.  Leverage measures Most financial managers measure debt ratios from their companies’ book balance sheets. Many financial economists emphasize ratios from market-value balance sheets. Which is the right measure in principle? Does the trade-off theory propose to explain book or market leverage? How about the pecking-order theory?

26.  Trade-off theory The trade-off theory relies on the threat of financial distress. But why should a public corporation ever have to land in financial distress? According to the theory, the firm should operate at the top of the curve in Figure 18.2. Of course market movements or business setbacks could bump it up to a higher debt ratio and put it on the declining, right-hand side of the curve. But in that case, why doesn’t the firm just issue equity, retire debt, and move back up to the optimal debt ratio?

What are the reasons why companies don’t issue stock—or enough stock—quickly enough to avoid financial distress?

27.  Debt and incentives The Bahia Corporation has fallen on hard times. It successfully issued 80 million Brazilian reals of zero coupon bonds four years ago, but since then its business has gone from bad to worse. The debt is due one year from now. Its only remaining asset is 20 million reals in cash. If Bahia’s managers do nothing, the bondholders will receive all of this cash, which is earning interest at the risk-free rate of 15%. Bahia can undertake the following projects.

Project X: Cost now is 20 million reals. Payoff one year from now is 160 million reals with 5% probability and zero reals (complete wipe-out) with 95% probability. Beta is zero (βX = 0), so the opportunity cost of capital is the risk-free rate.

Project Y: Cost now is 20 million reals. Payoff one year from now is 30 million reals with 100% probability.

Project Z: Cost now is 20 million reals. Payoff one year from now is 140 million reals with 5% probability and 50 million reals with 95% probability. Beta: βZ = 0.

a.  What are the NPVs of projects X and Y?

b.  What are today’s present values of the debt and equity of Bahia if it rejects both projects X and Y and leaves the 20 million reals in the bank at 15%? What if it accepts project X and rejects Y or accepts Y and rejects X?

c.  If the firm operates strictly in the interests of the shareholders, which strategy will it choose?

d.  How do your answers change if Project X is replaced with Project Z?

28.  Taxes and capital structure In Chapter 16 we described imputation tax systems, using Australia as an example. Imagine a simple imputation tax system in which stockholders who receive a dividend also receive a full income tax credit for the corporation tax that has been paid. Assume that companies distribute all their earnings as dividends. How would value be affected by capital structure? Suppose that, when valuing a project, you pretended that the corporate tax rate was zero. Would you correctly value the project?

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FINANCE ON THE WEB

You can download data for the following questions from the Yahoo! Finance website (www.finance.yahoo.com).

1.  Look up Johnson & Johnson on Yahoo! Finance.

a.  Recalculate book- and market-value balance sheets using the most recent available financial information. Use the same format as for Table 18.4.

b.  Track Johnson & Johnson’s long-term debt and debt ratio over the last five years (you will need to go to the company’s website to do this). How have they changed? Does it appear that the company has a stable target debt ratio? Do you see any evidence of pecking-order financing?

c.  How much has the company spent to repurchase its own shares? Would the trade-off theory predict share repurchases for a conservatively financed company like Johnson & Johnson?

2.  Select three or four companies from the Yahoo! Finance database. Estimate how much more these companies could borrow before they would exhaust taxable profits.

___________

¹Always use the marginal corporate tax rate, not the average rate. Average rates are often much lower than marginal rates because of accelerated depreciation and other tax adjustments. For large corporations, the marginal rate is usually taken as the statutory rate, which was 35% when this chapter was written (2012). However, effective marginal rates can be less than the statutory rate, especially for smaller, riskier companies that cannot be sure that they will earn taxable income in the future.

²In this example, we assume that the amount of debt is fixed and stable over time. The natural alternative assumption is a fixed ratio of debt to firm value. If the ratio is fixed, then the level of debt and the amount of interest tax shields will fluctuate as firm value fluctuates. In that case projected interest tax shields can’t be discounted at the cost of debt. We cover this point in detail in the next chapter.

³If the income of L does not cover interest in some future year, the tax shield is not necessarily lost. L can carry back the loss and receive a tax refund up to the amount of taxes paid in the previous two years. If L has a string of losses, and thus no prior tax payments that can be refunded, then losses can be carried forward and used to shield income in later years.

⁴Notice that as long as the bonds are sold at a fair price, all the benefits from the tax shield must go to the shareholders.

⁵Interest tax shields are recognized in MM’s original article, F. Modigliani and M. H. Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review 48 (June 1958), pp. 261–296. The valuation procedure used in Table 18.4b is presented in their 1963 article “Corporate Income Taxes and the Cost of Capital: A Correction,” American Economic Review 53 (June 1963), pp. 433–443.

⁶Personal taxes reduce the dollar amount of corporate interest tax shields, but the appropriate discount rate for cash flows after personal tax is also lower. If investors are willing to lend at a prospective return before personal taxes of rD, then they must also be willing to accept a return after personal taxes of rD(1 – Tp), where Tp is the marginal rate of personal tax. Thus we can compute the value after personal taxes of the tax shield on permanent debt:

This brings us back to our previous formula for firm value:

⁷M. H. Miller, “Debt and Taxes,” Journal of Finance 32 (May 1977), pp. 261–276.

⁸Graham’s estimates for individual firms recognize both the uncertainty in future profits and the existence of noninterest tax shields. See J. R. Graham, “How Big Are the Tax Benefits of Debt?” Journal of Finance 55 (October 2000), pp. 1901–1941.

⁹Ace Unlimited could be a partnership or sole proprietorship, which do not provide limited liability.

¹⁰The pioneering study of bankruptcy costs is J. B. Warner, “Bankruptcy Costs: Some Evidence,” Journal of Finance 26 (May 1977), pp. 337–348. See also L. A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of Financial Economics 27 (October 1990), pp. 285–314; E. I. Altman, “A Further Investigation of the Bankruptcy Cost Question,” Journal of Finance 39 (September 1984), pp. 1067–1089; and G. Andrade and S. N. Kaplan, “How Costly Is Financial (not Economic) Distress? Evidence from Highly Leveraged Transactions That Became Distressed,” Journal of Finance 53 (October 1998), pp. 1443–1493.

¹¹J. Franks and O. Sussman, “Financial Distress and Bank Restructuring of Small to Medium Size UK Companies,” Review of Finance 9 (2005), pp. 65–96. Karin Thornburg found that the Swedish bankruptcy system is reasonably efficient for smaller firms, however. See “Bankruptcy Auctions: Costs, Debt Recovery and Firm Survival,” Journal of Financial Economics 58 (December 2000), pp. 337–368.

¹²See L. A. Weiss and K. H. Wruck, “Information Problems, Conflicts of Interest, and Asset Stripping: Chapter 11’s Failure in the Case of Eastern Airlines,” Journal of Financial Economics 48 (1998), pp. 55–97.

¹³L. Zingales, “Survival of the Fittest or the Fattest? Exit and Financing in the Trucking Industry,” Journal of Finance 53 (June 1998), pp. 905–938.

¹⁴We are not concerned here with how to work out whether $5 is a fair price for stockholders to pay for the bet. We will come to that in Chapter 23 when we discuss risky debt.

¹⁵We are not calculating this $5 drop. We are simply using it as a plausible assumption. The tools necessary for a calculation come in Chapters 21 and 23.

¹⁶If stockholders or managers take money out of the firm in anticipation of financial distress or bankruptcy, the bankruptcy court can treat the payout as fraudulent conveyance and claw back the money to the firm and its creditors.

¹⁷We thank Paul Asquith for these figures. RJR Nabisco was finally taken private not by its management but by another LBO partnership. We discuss this LBO in Chapter 32.

¹⁸You might think that, if the bank suspects Ms. Ketchup will undertake project 2, it should just raise the interest rate on its loan. In this case Ms. Ketchup will not want to take on project 2 (they can’t both be happy with a lousy project). But Ms. Ketchup also would not want to pay a high rate of interest if she is going to take on project 1 (she would do better to borrow less money at the risk-free rate). So simply raising the interest rate is not the answer.

¹⁹In 1989 the Rockefeller family sold 80% of Rockefeller Center—several acres of extremely valuable Manhattan real estate—to Mitsubishi Estate Company for $1.4 billion. A REIT, Rockefeller Center Properties, held a $1.3 billion mortgage loan (the REIT’s only asset) secured by this real estate. But rents and occupancy rates did not meet forecasts, and by 1995 Mitsubishi had incurred losses of about $600 million. Then Mitsubishi quit, and Rockefeller Center was bankrupt. That triggered a complicated series of maneuvers and negotiations. But did this damage the value of the Rockefeller Center properties? Was Radio City Music Hall, one of the properties, any less valuable because of the bankruptcy? We doubt it.

²⁰See J. Graham and C. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 60 (May/June 2001), pp. 187–244.

²¹We are not suggesting that all airline companies are safe; many are not. But aircraft can support debt where airlines cannot. If Fly-by-Night Airlines fails, its planes retain their value in another airline’s operations. There’s a good secondary market in used aircraft, so a loan secured by aircraft can be well protected even if made to an airline flying on thin ice (and in the dark).

²²For example, in an international comparison Wald found that profitability was the single largest determinant of firm capital structure. See J. K. Wald, “How Firm Characteristics Affect Capital Structure: An International Comparison,” Journal of Financial Research 22 (Summer 1999), pp. 161–187.

²³Here we mean debt as a fraction of the book or replacement value of the company’s assets. Profitable companies might not borrow a greater fraction of their market value. Higher profits imply higher market value as well as stronger incentives to borrow.

²⁴Mackie-Mason found that taxpaying companies are more likely to issue debt (vs. equity) than nontaxpaying companies. This shows that taxes do affect financing choices. However, it is not necessarily evidence for the trade-off theory. Look back to Section 18-2, and note the special case where corporate and personal taxes cancel to make debt policy irrelevant. In that case, taxpaying firms would see no net tax advantage to debt: corporate interest tax shields would be offset by the taxes paid by investors in the firm’s debt. But the balance would tip in favor of equity for a firm that was losing money and reaping no benefits from interest tax shields. See J. Mackie-Mason, “Do Taxes Affect Corporate Financing Decisions?” Journal of Finance 45 (December 1990), pp. 1471–1493.

²⁵A study by E. F. Fama and K. R. French, covering over 2,000 firms from 1965 to 1992, failed to find any evidence that interest tax shields contributed to firm value. See “Taxes, Financing Decisions and Firm Value,” Journal of Finance 53 (June 1998), pp. 819–843.

²⁶M. L. Lemmon, M. R. Roberts, and J. F. Zender, “Back to the Beginning: Persistence and the Cross-Section of Corporate Capital Structure,” Journal of Finance 63 (August 2008), pp. 1575–1608.

²⁷We described the Australian imputation tax system in Section 16-5. Look again at Table 16.2, supposing that an Australian corporation pays A$10 of interest. This reduces the corporate tax by A$3.00; it also reduces the tax credit taken by the shareholders by A$3.00. The final tax does not depend on whether the corporation or the shareholder borrows.

You can check this by redrawing Figure 18.2 for the Australian system. The corporate tax rate Tc will cancel out. Since income after all taxes depends only on investors’ tax rates, there is no special advantage to corporate borrowing.

²⁸A Smith stock issue might not succeed even at $80. Persistence in trying to sell at $80 could convince investors that the stock is worth even less!

²⁹R. G. Rajan and L. Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data,” Journal of Finance 50 (December 1995), pp. 1421–1460. The same four factors seem to work in developing economies. See L. Booth, V. Aivazian, A. Demirguc-Kunt, and V. Maksimovic, “Capital Structure in Developing Countries,” Journal of Finance 56 (February 2001), pp. 87–130.

³⁰L. Shyam-Sunder and S. C. Myers found that the pecking-order hypothesis outperformed the trade-off hypothesis for a sample of large companies in the 1980s. See “Testing Static Trade-off against Pecking-Order Theories of Capital Structure,” Journal of Financial Economics 51 (February 1999), pp. 219–244. M. Frank and V. Goyal found that the performance of the pecking-order hypothesis deteriorated in the 1990s, especially for small growth firms. See “Testing the Pecking Order Theory of Capital Structure,” Journal of Financial Economics 67 (February 2003), pp. 217–248. See also E. Fama and K. French, “Testing Trade-off and Pecking Order Predictions about Dividends and Debt,” Review of Financial Studies 15 (Spring 2002), pp. 1–33; and M. L. Lemmon and J. F. Zender, “Debt Capacity and Tests of Capital Structure Theories,” Journal of Financial and Quantitative Analysis 45 (2010), pp. 1161–1187.

³¹M. Baker and J. Wurgler, “Market Timing and Capital Structure,” Journal of Finance 57 (February 2002), pp. 1–32.

³²M. Bertrand and A. Schoar, “Managing with Style: The Effect of Managers on Firm Policies,” Quarterly Journal of Economics 118 (November 2003), pp. 1169–1208.

³³M. C. Jensen, “Agency Costs of Free Cash Flow, Corporate Finance and Takeovers,” American Economic Review 26 (May 1986), pp. 323–329.

³⁴R. W. Masulis, “The Effects of Capital Structure Change on Security Prices: A Study of Exchange Offers,” Journal of Financial Economics 8 (June 1980), pp. 139–177, and “The Impact of Capital Structure Change on Firm Value,” Journal of Finance 38 (March 1983), pp. 107–126.

Part 5 Payout Policy and Capital Structure

Financing and Valuation

In Chapters 5 and 6 we showed how to value a capital investment project by a four-step procedure:

1.  Forecast after-tax cash flows, assuming all-equity financing.

2.  Assess the project’s risk.

3.  Estimate the opportunity cost of capital.

4.  Calculate NPV, using the opportunity cost of capital as the discount rate.

There’s nothing wrong with this procedure, but now we’re going to extend it to include value contributed by financing decisions. There are two ways to do this:

1.  Adjust the discount rate. The adjustment is typically downward, to account for the value of interest tax shields. This is the most common approach, which is usually implemented via the after-tax weighted-average cost of capital (WACC). We introduced the after-tax WACC in Chapters 9 and 17, but here we provide a lot more guidance on how it is calculated and used.

2.  Adjust the present value. That is, start by estimating the base-case value of the firm or project, assuming it is all-equity-financed, and then adjust this base-case value to account for financing.

Once you identify and value the financing side effects, calculating APV is no more than addition or subtraction.

This is a how-to-do-it chapter. In the first section, we explain and derive the after-tax WACC and use it to value a project and business. Then in Section 19-2 we work through a more complex and realistic valuation problem. Section 19-3 covers some tricks of the trade: helpful hints on how to estimate inputs and on how to adjust WACC when business risk or capital structure changes. Section 19-4 turns to the APV method. The idea behind APV is simple enough, but tracing through all the financing side effects can be tricky. We conclude the chapter with a question-and-answer section designed to clarify points that managers and students often find confusing. The Appendix covers an important special case, namely, the after-tax valuation of safe cash flows.

 19-1   The After-Tax Weighted-Average Cost of Capital

We first addressed problems of valuation and capital budgeting in Chapters 5 and 6. In those early chapters we said hardly a word about financing decisions. We separated investment from financing decisions. If the investment project was positive-NPV, we assumed that the firm would go ahead, without asking whether financing the project would add or subtract additional value. We were really assuming a Modigliani–Miller (MM) world in which all financing decisions are irrelevant. In a strict MM world, firms can analyze real investments as if they are all-equity-financed; the actual financing plan is a mere detail to be worked out later.

Under MM assumptions, decisions to spend money can be separated from decisions to raise money. Now we reconsider the capital budgeting decision when investment and financing decisions interact and cannot be wholly separated.

One reason that financing and investment decisions interact is taxes. Interest is a tax-deductible expense. Think back to Chapters 9 and 17 where we introduced the after-tax weighted-average cost of capital:

Here D and E are the market values of the firm’s debt and equity, V = D + E is the total market value of the firm, rD and rE are the costs of debt and equity, and Tc is the marginal corporate tax rate.

Notice that the WACC formula uses the after-tax cost of debt rD (1 – Tc). That is how the after-tax WACC captures the value of interest tax shields. Notice too that all the variables in the WACC formula refer to the firm as a whole. As a result, the formula gives the right discount rate only for projects that are just like the firm undertaking them. The formula works for the “average” project. It is incorrect for projects that are safer or riskier than the average of the firm’s existing assets. It is incorrect for projects whose acceptance would lead to an increase or decrease in the firm’s target debt ratio.

The WACC is based on the firm’s current characteristics, but managers use it to discount future cash flows. That’s fine as long as the firm’s business risk and debt ratio are expected to remain constant, but when the business risk and debt ratio are expected to change, discounting cash flows by the WACC is only approximately correct.

Many firms set a single, companywide WACC and keep it constant unless there are major changes in risk and interest rates. The WACC is a common reference point that avoids divisional squabbles about discount rates.¹ But all financial managers need to know how to adjust WACC when business risks and financing assumptions change. We show how to make these adjustments later in this chapter.

EXAMPLE 19.1 • Calculating Sangria’s WACC

Sangria is a U.S.-based company whose products aim to promote happy, low-stress lifestyles. Let’s calculate Sangria’s WACC. Its book and market-value balance sheets are

We calculated the market value of equity on Sangria’s balance sheet by multiplying its current stock price ($7.50) by 100 million, the number of its outstanding shares. The company’s future prospects are good, so the stock is trading above book value ($7.50 vs. $5.00 per share). However, interest rates have been stable since the firm’s debt was issued and the book and market values of debt are in this case equal.

Sangria’s cost of debt (the market interest rate on its existing debt and on any new borrowing)² is 6%. Its cost of equity (the expected rate of return demanded by investors in Sangria’s stock) is 12.4%.

The market-value balance sheet shows assets worth $1,250 million. Of course we can’t observe this value directly, because the assets themselves are not traded. But we know what they are worth to debt and equity investors ($500 + 750 = $1,250 million). This value is entered on the left of the market-value balance sheet.

Why did we show the book balance sheet? Only so you could draw a big X through it. Do so now.

Think of the WACC as the expected rate of return on a portfolio of the firm’s outstanding debt and equity. The portfolio weights depend on market values. The expected rate of return on the market-value portfolio reveals the expected rate of return demanded by investors for committing their hard-earned money to the firm’s assets and operations.

When estimating the weighted-average cost of capital, you are not interested in past investments but in current values and expectations for the future. Sangria’s true debt ratio is not 50%, the book ratio, but 40%, because its assets are worth $1,250 million. The cost of equity, rE = .124, is the expected rate of return from purchase of stock at $7.50 per share, the current market price. It is not the return on book value per share. You can’t buy shares in Sangria for $5 anymore.

Sangria is consistently profitable and pays taxes at the marginal rate of 35%. This tax rate is the final input for Sangria’s WACC. The inputs are summarized here:

The company’s after-tax WACC is

That’s how you calculate the weighted-average cost of capital. Now let’s see how Sangria would use it.

EXAMPLE 19.2 • Using Sangria’s WACC to value a project

Sangria’s enologists have proposed investing $12.5 million in the construction of a perpetual crushing machine, which (conveniently for us) never depreciates and generates a perpetual stream of earnings and cash flow of $1.731 million per year pretax. The project is average risk, so we can use WACC. The after-tax cash flow is:

Notice: This after-tax cash flow takes no account of interest tax shields on debt supported by the perpetual crusher project. As we explained in Chapter 6, standard capital budgeting practice separates investment from financing decisions and calculates after-tax cash flows as if the project were all-equity-financed. However, the interest tax shields will not be ignored: We are about to discount the project’s cash flows by Sangria’s WACC, in which the cost of debt is entered after tax. The value of interest tax shields is picked up not as higher after-tax cash flows, but in a lower discount rate.

The crusher generates a perpetual after-tax cash flow of C = $1.125 million, so NPV is

NPV = 0 means a barely acceptable investment. The annual cash flow of $1.125 million per year amounts to a 9% rate of return on investment (1.125/12.5 = .09), exactly equal to Sangria’s WACC.

If project NPV is exactly zero, the return to equity investors must exactly equal the cost of equity, 12.4%. Let’s confirm that Sangria shareholders can actually look forward to a 12.4% return on their investment in the perpetual crusher project.

Suppose Sangria sets up this project as a mini-firm. Its market-value balance sheet looks like this:

Calculate the expected dollar return to shareholders:

The project’s earnings are level and perpetual, so the expected rate of return on equity is equal to the expected equity income divided by the equity value:

The expected return on equity equals the cost of equity, so it makes sense that the project’s NPV is zero.

Review of Assumptions

When discounting the perpetual crusher’s cash flows at Sangria’s WACC, we assume that

•  The project’s business risks are the same as those of Sangria’s other assets and remain so for the life of the project.

•  The project supports the same fraction of debt to value as in Sangria’s overall capital structure, which remains constant for the life of the project.

You can see the importance of these two assumptions: If the perpetual crusher had greater business risk than Sangria’s other assets, or if the acceptance of the project would lead to a permanent, material change in Sangria’s debt ratio, then Sangria’s shareholders would not be content with a 12.4% expected return on their equity investment in the project.

But users of WACC need not worry about small or temporary fluctuations in debt ratios. Nor should they be misled by the immediate source of financing. Suppose that Sangria decides to borrow $12.5 million to get a quick start on construction of the crusher. This does not necessarily change Sangria’s long-term financing targets. The crusher’s debt capacity is only $5 million. If Sangria decides for convenience to borrow $12.5 million for the crusher, then sooner or later it will have to borrow $12.5 – $5 = $7.5 million less for other projects.

We have illustrated the WACC formula only for a project offering perpetual cash flows. But the formula works for any cash-flow pattern if the firm adjusts its borrowing to maintain a constant debt ratio over time.³ When the firm departs from this borrowing policy, WACC is only approximately correct.

 19-2   Valuing Businesses

On most workdays the financial manager concentrates on valuing projects, arranging financing, and helping run the firm more effectively. The valuation of the business as a whole is left to investors and financial markets. But on some days the financial manager has to take a stand on what an entire business is worth. When this happens, a big decision is typically in the offing. For example:

•  If firm A is about to make a takeover offer for firm B, then A’s financial managers have to decide how much the combined business A + B is worth under A’s management. This task is particularly difficult if B is a private company with no observable share price.

•  If firm C is considering the sale of one of its divisions, it has to decide what the division is worth in order to negotiate with potential buyers.

•  When a firm goes public, the investment bank must evaluate how much the firm is worth in order to set the issue price.

•  If a mutual fund owns shares in a company that is not traded, then the fund’s directors are obliged to estimate a fair value for those shares. If the directors do a sloppy job of coming up with a value, they are liable to find themselves in court.

In addition, thousands of analysts in stockbrokers’ offices and investment firms spend every workday burrowing away in the hope of finding undervalued firms. Many of these analysts use the valuation tools we are about to cover.

In Chapter 4 we took a first pass at valuing free cash flows from an entire business. We assumed then that the business was financed solely by equity. Now we will show how WACC can be used to value a company that is financed by a mixture of debt and equity. You just treat the company as if it were one big project. You forecast the company’s free cash flows (the hardest part of the exercise) and discount back to present value. But be sure to remember three important points:

1.  If you discount at WACC, cash flows have to be projected just as you would for a capital investment project. Do not deduct interest. Calculate taxes as if the company were all-equity-financed. (The value of interest tax shields is not ignored, because the after-tax cost of debt is used in the WACC formula.)

2.  Unlike most projects, companies are potentially immortal. But that does not mean that you need to forecast every year’s cash flow from now to eternity. Financial managers usually forecast to a medium-term horizon and add a terminal value to the cash flows in the horizon year. The terminal value is the present value at the horizon of all subsequent cash flows. Estimating the terminal value requires careful attention because it often accounts for the majority of the company’s value.

3.  Discounting at WACC values the assets and operations of the company. If the object is to value the company’s equity, that is, its common stock, don’t forget to subtract the value of the company’s outstanding debt.

Here’s an example.

Valuing Rio Corporation

Sangria is tempted to acquire the Rio Corporation, which is also in the business of promoting relaxed, happy lifestyles. Rio has developed a special weight-loss program called the Brazil Diet, based on barbecues, red wine, and sunshine. The firm guarantees that within three months you will have a figure that will allow you to fit right in at Ipanema or Copacabana beach in Rio de Janeiro. But before you head for the beach, you’ve got the job of working out how much Sangria should pay for Rio.

Rio is a U.S. company. It is privately held, so Sangria has no stock market price to rely on. Rio has 1.5 million shares outstanding and debt with a market and book value of $36 million. Rio is in the same line of business as Sangria, so we will assume that it has the same business risk as Sangria and can support the same proportion of debt. Therefore we can use Sangria’s WACC.

Your first task is to forecast Rio’s free cash flow (FCF). Free cash flow is the amount of cash that the firm can pay out to investors after making all investments necessary for growth. Free cash flow is calculated assuming the firm is all-equity-financed. Discounting the free cash flows at the after-tax WACC gives the total value of Rio (debt plus equity). To find the value of its equity, you will need to subtract the $36 million of debt.

We will forecast each year’s free cash flow out to a valuation horizon (H) and predict the business’s value at that horizon (PVH). The cash flows and horizon value are then discounted back to the present:

Of course, the business will continue after the horizon, but it’s not practical to forecast free cash flow year by year to infinity. PVH stands in for the value in year H of free cash flow in periods H + 1, H + 2, etc.

Free cash flow and net income are not the same. They differ in several important ways:

•  Income is the return to shareholders, calculated after interest expense. Free cash flow is calculated before interest.

•  Income is calculated after various noncash expenses, including depreciation. Therefore we will add back depreciation when we calculate free cash flow.

•  Capital expenditures and investments in working capital do not appear as expenses on the income statement, but they do reduce free cash flow.

Free cash flow can be negative for rapidly growing firms, even if the firms are profitable, because investment exceeds cash flow from operations. Negative free cash flow is normally temporary, fortunately for the firm and its stockholders. Free cash flow turns positive as growth slows down and the payoffs from prior investments start to roll in.

Table 19.1 sets out the information that you need to forecast Rio’s free cash flows. We will follow common practice and start with a projection of sales. In the year just ended Rio had sales of $83.6 million. In recent years sales have grown by between 5% and 8% a year. You forecast that sales will grow by about 7% a year for the next three years. Growth will then slow to 4% for years 4 to 6 and to 3% starting in year 7.

The other components of cash flow in Table 19.1 are driven by these sales forecasts. For example, you can see that costs are forecasted at 74% of sales in the first year with a gradual increase to 76% of sales in later years, reflecting increased marketing costs as Rio’s competitors gradually catch up.

BEYOND THE PAGE

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Try It! Rio’s spreadsheet

brealey.mhhe.com/c19

Increasing sales are likely to require further investment in fixed assets and working capital. Rio’s net fixed assets are currently about $.79 for each dollar of sales. Unless Rio has surplus capacity or can squeeze more output from its existing plant and equipment, its investment in fixed assets will need to grow along with sales. Therefore we assume that every dollar of sales growth requires an increase of $.79 in net fixed assets. We also assume that working capital grows in proportion to sales.

Rio’s free cash flow is calculated in Table 19.1 as profit after tax, plus depreciation, minus investment. Investment is the change in the stock of (gross) fixed assets and working capital from the previous year. For example, in year 1:

   TABLE 19.1 Free-cash-flow projections and company value for Rio Corporation ($ millions).

Estimating Horizon Value

We will forecast cash flows for each of the first six years. After that, Rio’s sales are expected to settle down to stable, long-term growth starting in year 7. To find the present value of the cash flows in years 1 to 6, we discount at the 9% WACC:

Now we need to find the value of the cash flows from year 7 onward. In Chapter 4 we looked at several ways to estimate horizon value. Here we will use the constant-growth DCF formula. This requires a forecast of the free cash flow for year 7, which we have worked out in the final column of Table 19.1, assuming a long-run growth rate of 3% per year.⁴ The free cash flow is $6.8 million, so

We now have all we need to value the business:

This is the total value of Rio. To find the value of the equity, we simply subtract the value of the debt:

And to find the value per share, we divide by the total number of shares outstanding:

Thus Sangria could afford to pay up to $34.60 per share for Rio.

You now have an estimate of the value of Rio Corporation. But how confident can you be in this figure? Notice that less than a quarter of Rio’s value comes from cash flows in the first six years. The rest comes from the horizon value. Moreover, this horizon value can change in response to only minor changes in assumptions. For example, if the long-run growth rate is 4% rather than 3%, Rio needs to invest more to support this higher growth, but firm value increases from $87.9 million to $89.9 million.

In Chapter 4 we stressed that wise managers won’t stop at this point. They will check their calculations by identifying comparable companies and comparing their price–earnings multiples and ratios of market to book value.⁵

When you forecast cash flows, it is easy to become mesmerized by the numbers and just do it mechanically. As we pointed out in Chapter 11, it is important to take a strategic view. Are the revenue figures consistent with what you expect your competitors to do? Are the costs you have predicted realistic? Probe the assumptions behind the numbers to make sure they are sensible. Be particularly careful about the growth rates and profitability assumptions that drive horizon values. Don’t assume that the business you are valuing will grow and earn more than the cost of capital in perpetuity.⁶ This would be a nice outcome for the business, but not an outcome that competition will tolerate.

You should also check whether the business is worth more dead than alive. Sometimes a company’s liquidation value exceeds its value as a going concern. Smart financial analysts sometimes ferret out idle or underexploited assets that would be worth much more if sold to someone else. You may end up counting these assets at their likely sale price and valuing the rest of the business without them.

WACC vs. the Flow-to-Equity Method

When valuing Rio, we forecasted the cash flows assuming all-equity financing and we used the WACC to discount these cash flows. The WACC formula picked up the value of the interest tax shields. Then, to find the equity value, we subtracted the value of debt from the total value of the firm.

If our task is to value a firm’s equity, there’s an obvious alternative to discounting cash flows at the firm’s WACC: Discount cash flows to equity after interest and after taxes, at the cost of equity capital. This is called the flow-to-equity method. If the company’s debt ratio is constant over time, the flow-to-equity method should give the same answer as discounting total cash flows at the WACC and then subtracting the value of the debt.

Suppose that you are asked to value Rio by the flow-to-equity method, assuming that the company adjusts its debt each year to maintain a constant debt ratio. You are given as a starter an estimate of Rio’s horizon value at the end of year 6. Perhaps this value was obtained by discounting subsequent cash flows by Rio’s WACC, or perhaps it was estimated by looking at how investors value comparable, publicly traded companies. You decide to expand the spreadsheet in Table 19.1 by calculating each year’s interest payments and issues or repayments of debt. You recompute taxes, recognizing that the interest payments are a tax-deductible expense. Finally, you discount the free cash flow to equity at the cost of equity, which in our example is rE = 12.4%.

BEYOND THE PAGE

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Try It! Cash-flow-to-equity model

brealey.mhhe.com/c19

It sounds straightforward, but in practice it can be tricky to do it right. The problem arises because each year’s interest payment depends on the amount of debt at the start of the year, and this depends in turn on Rio’s value at the start of the year (remember Rio’s debt is a constant proportion of value). So you seem to have a catch-22 situation in which you first need to know Rio’s value each year before you can go on to calculate and discount the cash flows to equity. Fortunately, a simple formula allows you to solve simultaneously for the company’s value and the cash flow in each year. We won’t get into that here, but if you would like to see how the flow-to-equity method can be used to value Rio, click on the worked example on our website, mhhe.com/bma.

 19-3   Using WACC In Practice

Some Tricks of the Trade

Sangria had just one asset and two sources of financing. A real company’s market-value balance sheet has many more entries, for example:⁷

Several questions immediately arise:

How does the formula change when there are more than two sources of financing? Easy: There is one cost for each element. The weight for each element is proportional to its market value. For example, if the capital structure includes both preferred and common shares,

where rP is investors’ expected rate of return on the preferred stock, P is the amount of preferred stock outstanding, and V = D + P + E.

What about short-term debt? Many companies consider only long-term financing when calculating WACC. They leave out the cost of short-term debt. In principle this is incorrect. The lenders who hold short-term debt are investors who can claim their share of operating earnings. A company that ignores this claim will misstate the required return on capital investments.

But “zeroing out” short-term debt is not a serious error if the debt is only temporary, seasonal, or incidental financing or if it is offset by holdings of cash and marketable securities. Suppose, for example, that one of your foreign subsidiaries takes out a six-month loan to finance its inventory and accounts receivable. The dollar equivalent of this loan will show up as a short-term debt. At the same time headquarters may be lending money by investing surplus dollars in short-term securities. If this lending and borrowing offset, there is no point in including the cost of short-term debt in the weighted-average cost of capital, because the company is not a net short-term borrower.

What about other current liabilities? Current liabilities are usually “netted out” by subtracting them from current assets. The difference is entered as net working capital on the left-hand side of the balance sheet. The sum of long-term financing on the right is called total capitalization.

When net working capital is treated as an asset, forecasts of cash flows for capital investment projects must treat increases in net working capital as a cash outflow and decreases as an inflow. This is standard practice, which we followed in Section 6-2. We also did so when we estimated the future investments that Rio would need to make in working capital.

Since current liabilities include short-term debt, netting them out against current assets excludes the cost of short-term debt from the weighted-average cost of capital. We have just explained why this can be an acceptable approximation. But when short-term debt is an important, permanent source of financing—as is common for small firms and firms outside the United States—it should be shown explicitly on the right-hand side of the balance sheet, not netted out against current assets.⁸ The interest cost of short-term debt is then one element of the weighted-average cost of capital.

How are the costs of financing calculated? You can often use stock market data to get an estimate of rE, the expected rate of return demanded by investors in the company’s stock. With that estimate, WACC is not too hard to calculate, because the borrowing rate rD and the debt and equity ratios D/V and E/V can be directly observed or estimated without too much trouble.⁹ Estimating the value and required return for preferred shares is likewise usually not too complicated.

Estimating the required return on other security types can be troublesome. Convertible debt, where the investors’ return comes partly from an option to exchange the debt for the company’s stock, is one example. We leave convertibles to Chapter 24.

Junk debt, where the risk of default is high, is likewise difficult. The higher the odds of default, the lower the market price of the debt, and the higher is the promised rate of interest. But the weighted-average cost of capital is an expected, that is average, rate of return, not a promised one. For example, in March 2012, the four-year bonds issued by the house builder Hovnanian Enterprises sold at only 57% of face value and offered a 24% promised yield, over 20 percentage points above yields on the highest-quality debt issues maturing at the same time. The price and yield on the Hovnanian bond demonstrated investors’ concern about the company’s chronic financial ill-health. But the 24% yield was not an expected return, because it did not average in the losses to be incurred if Hovnanian were to default. Including 24% as a “cost of debt” in a calculation of WACC would therefore have overstated Hovnanian’s true cost of capital.

This is bad news: There is no easy way of estimating the expected rate of return on most junk debt issues. The good news is that for most debt the odds of default are small. That means the promised and expected rates of return are close, and the promised rate can be used as an approximation in the weighted-average cost of capital.

Company vs. Industry WACCs Of course you want to know what your company’s WACC is. Yet industry WACCs are sometimes more useful. Here’s an example. Kansas City Southern used to be a portfolio of (1) the Kansas City Southern Railroad, with operations running from the U.S. Midwest south to Texas and Mexico, and (2) Stillwell Financial, an investment-management business that included the Janus mutual funds. It’s hard to think of two more dissimilar businesses. Kansas City Southern’s overall WACC was not right for either of them. The company would have been well advised to use a railroad industry WACC for its railroad operations and an investment management WACC for Stillwell.

Kansas City Southern spun off Stillwell in 2000 and is now a pure-play railroad. But even now the company would be wise to check its WACC against a railroad industry WACC. Industry WACCs are less exposed to random noise and estimation errors. Fortunately for Kansas City Southern, there are four large, pure-play railroads (including Canadian Pacific) that the company could use to calculate an industry WACC. Of course, use of an industry WACC for a particular company’s investments assumes that the company and industry have approximately the same business risk and financing.¹⁰

Mistakes People Make in Using the Weighted-Average Formula

The weighted-average formula is very useful but also dangerous. It tempts people to make logical errors. For example, manager Q, who is campaigning for a pet project, might look at the formula

and think, “Aha! My firm has a good credit rating. It could borrow, say, 90% of the project’s cost if it likes. That means D/V = .9 and E/V = .1. My firm’s borrowing rate rD is 8%, and the required return on equity, rE, is 15%. Therefore

or 6.2%. When I discount at that rate, my project looks great.”

Manager Q is wrong on several counts. First, the weighted-average formula works only for projects that are carbon copies of the firm. The firm isn’t 90% debt-financed.

Second, the immediate source of funds for a project has no necessary connection with the hurdle rate for the project. What matters is the project’s overall contribution to the firm’s borrowing power. A dollar invested in Q’s pet project will not increase the firm’s debt capacity by $.90. If the firm borrows 90% of the project’s cost, it is really borrowing in part against its existing assets. Any advantage from financing the new project with more debt than normal should be attributed to the old projects, not to the new one.

Third, even if the firm were willing and able to lever up to 90% debt, its cost of capital would not decline to 6.2%, as Q’s naive calculation predicts. You cannot increase the debt ratio without creating financial risk for stockholders and thereby increasing rE, the expected rate of return they demand from the firm’s common stock. Going to 90% debt would certainly increase the borrowing rate, too.

Adjusting WACC when Debt Ratios and Business Risks Differ

The WACC formula assumes that the project or business to be valued will be financed in the same debt–equity proportions as the company (or industry) as a whole. What if that is not true? For example, what if Sangria’s perpetual crusher project supports only 20% debt, versus 40% for Sangria overall?

Moving from 40% to 20% debt may change all the inputs to the WACC formula.¹¹ Obviously the financing weights change. But the cost of equity rE is less, because financial risk is reduced. The cost of debt may be lower too.

Take a look at Figure 19.1, which plots WACC and the costs of debt and equity as a function of the debt–equity ratio. The flat line is r, the opportunity cost of capital. Remember, this is the expected rate of return that investors would want from the company if it were all-equity-financed. The opportunity cost of capital depends only on business risk and is the natural reference point.

Suppose Sangria or the perpetual crusher project were all-equity-financed (D/V = 0). At that point WACC equals cost of equity, and both equal the opportunity cost of capital. Start from that point in Figure 19.1. As the debt ratio increases, the cost of equity increases, because of financial risk, but notice that WACC declines. The decline is not caused by use of “cheap” debt in place of “expensive” equity. It falls because of the tax shields on debt interest payments. If there were no corporate income taxes, the weighted-average cost of capital would be constant, and equal to the opportunity cost of capital, at all debt ratios. We showed this in Chapter 17.

Figure 19.1 shows the shape of the relationship between financing and WACC, but initially we have numbers only for Sangria’s current 40% debt ratio. We want to recalculate WACC at a 20% ratio.

Here is the simplest way to do it. There are three steps.

Step 1 Calculate the opportunity cost of capital. In other words, calculate WACC and the cost of equity at zero debt. This step is called unlevering the WACC. The simplest unlevering formula is

This formula comes directly from Modigliani and Miller’s proposition 1 (see Section 17-1). If taxes are left out, the weighted-average cost of capital equals the opportunity cost of capital and is independent of leverage.

   FIGURE 19.1 This plot shows WACC for the Sangria Corporation at debt-to-equity ratios of 25% and 67%. The corresponding debt-to-value ratios are 20% and 40%.

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Step 2 Estimate the cost of debt, rD, at the new debt ratio, and calculate the new cost of equity.

This formula is Modigliani and Miller’s proposition 2 (see Section 17-2). It calls for D/E, the ratio of debt to equity, not debt to value.

Step 3 Recalculate the weighted-average cost of capital at the new financing weights.

Let’s do the numbers for Sangria at D/V = .20, or 20%.

Step 1. Sangria’s current debt ratio is D/V = .4. So

Step 2. We will assume that the debt cost stays at 6% when the debt ratio is 20%. Then

Note that the debt–equity ratio is .2/.8 = .25.

Step 3. Recalculate WACC.

Figure 19.1 enters these numbers on the plot of WACC versus the debt–equity ratio.

Unlevering and Relevering Betas

Our three-step procedure (1) unlevers and then (2) relevers the cost of equity. Some financial managers find it convenient to (1) unlever and then (2) relever the equity beta. Given the beta of equity at the new debt ratio, the cost of equity is determined from the capital asset pricing model. Then WACC is recalculated.

The formula for unlevering beta was given in Section 17-2.

This equation says that the beta of a firm’s assets is revealed by the beta of a portfolio of all of the firm’s outstanding debt and equity securities. An investor who bought such a portfolio would own the assets free and clear and absorb only business risks.

The formula for relevering beta closely resembles MM’s proposition 2, except that betas are substituted for rates of return:

Use this formula to recalculate βE when D/E changes.

Suppose the debt and equity betas in our example are βD = .135 and βE = 1.06.¹² The risk-free rate is 5%, and the market risk premium is 7.0%. The cost of equity is

This matches the cost of equity in our example at a 40/60 debt–equity ratio. Let’s calculate the equity beta and cost of equity at a 20/80 ratio. The asset beta is

Now recalculate the equity beta and cost of equity at D/E = .2/.8 = .25:

This cost of equity gives the WACC of 9.4% calculated above and plotted in Figure 19.1.

The Importance of Rebalancing

The formulas for WACC and for unlevering and relevering expected returns are simple, but we must be careful to remember the underlying assumptions. The most important point is rebalancing.

Calculating WACC for a company at its existing capital structure requires that the capital structure not change; in other words, the company must rebalance its capital structure to maintain the same market-value debt ratio for the relevant future. Take Sangria Corporation as an example. It starts with a debt-to-value ratio of 40% and a market value of $1,250 million. Suppose that Sangria’s products do unexpectedly well in the marketplace and that market value increases to $1,500 million. Rebalancing means that it will then increase debt to .4 × 1,500 = $600 million, thus regaining a 40% ratio. The proceeds of the additional borrowing could be used to finance other investments or it could be paid out to the stockholders. If market value instead falls, Sangria would have to pay down debt proportionally.

Of course real companies do not rebalance capital structure in such a mechanical and compulsive way. For practical purposes, it’s sufficient to assume gradual but steady adjustment toward a long-run target.¹³ But if the firm plans significant changes in capital structure (for example, if it plans to pay off its debt), the WACC formula won’t work. In such cases, you should turn to the APV method, which we describe in the next section.

Our three-step procedure for recalculating WACC with a different debt ratio makes a similar rebalancing assumption.¹⁴ Whatever the starting debt ratio, the firm is assumed to rebalance to maintain that ratio in the future.¹⁵

The Modigliani–Miller Formula, Plus Some Final Advice

What if the firm does not rebalance to keep its debt ratio constant? In this case the only general approach is adjusted present value, which we cover in the next section. But sometimes financial managers turn to other discount-rate formulas, including one derived by Modigliani and Miller (MM). MM considered a company or project generating a level, perpetual stream of cash flows financed with fixed, perpetual debt, and derived a simple after-tax discount rate:¹⁶

Here it’s easy to unlever: just set the debt-capacity parameter (D/V) equal to zero.¹⁷

MM’s formula is still used in practice, but the formula is exact only in the special case where there is a level, perpetual stream of cash flows and fixed, perpetual debt. However, the formula is not a bad approximation for shorter-lived projects as long as debt is issued in a fixed amount.¹⁸

So which team do you want to play with, the fixed-debt team or the rebalancers? If you join the fixed-debt team you will be outnumbered. Most financial managers use the plain, after-tax WACC, which assumes constant market-value debt ratios and therefore assumes rebalancing. That makes sense, because the debt capacity of a firm or project must depend on its future value, which will fluctuate.

At the same time, we must admit that the typical financial manager doesn’t care much if his or her firm’s debt ratio drifts up or down within a reasonable range of moderate financial leverage. The typical financial manager acts as if a plot of WACC against the debt ratio is “flat” (constant) over this range. This too makes sense, if we just remember that interest tax shields are the only reason why the after-tax WACC declines in Figure 17.4 or 19.1. The WACC formula doesn’t explicitly capture costs of financial distress or any of the other nontax complications discussed in Chapter 18.¹⁹ All these complications may roughly cancel the value added by interest tax shields (within a range of moderate leverage). If so, the financial manager is wise to focus on the firm’s operating and investment decisions, rather than on fine-tuning its debt ratio.

 19-4   Adjusted Present Value

The idea behind adjusted present value (APV) is to divide and conquer. APV does not attempt to capture taxes or other effects of financing in a WACC or adjusted discount rate. A series of present value calculations is made instead. The first establishes a base-case value for the project or firm: its value as a separate, all-equity-financed venture. The discount rate for the base-case value is just the opportunity cost of capital. Once the base-case value is set, then each financing side effect is traced out, and the present value of its cost or benefit to the firm is calculated. Finally, all the present values are added together to estimate the project’s total contribution to the value of the firm:

The most important financing side effect is the interest tax shield on the debt supported by the project (a plus). Other possible side effects are the issue costs of securities (a minus) or financing packages subsidized by a supplier or government (a plus).

APV gives the financial manager an explicit view of the factors that are adding or subtracting value. APV can prompt the manager to ask the right follow-up questions. For example, suppose that base-case NPV is positive but less than the costs of issuing shares to finance the project. That should prompt the manager to look around to see if the project can be rescued by an alternative financing plan.

APV for the Perpetual Crusher

APV is easiest to understand in simple numerical examples. Let’s apply it to Sangria’s perpetual crusher project. We start by showing that APV is equivalent to discounting at WACC if we make the same assumptions about debt policy.

We used Sangria’s WACC (9%) as the discount rate for the crusher’s projected cash flows. The WACC calculation assumed that debt will be maintained at a constant 40% of the future value of the project or firm. In this case, the risk of interest tax shields is the same as the risk of the project.²¹ Therefore we will discount the tax shields at the opportunity cost of capital (r). We calculated the opportunity cost of capital in the last section by unlevering Sangria’s WACC to obtain r = 9.84%.

The first step is to calculate base-case NPV. We discount after-tax project cash flows of $1.125 million at the opportunity cost of capital of 9.84% and subtract the $12.5 million outlay. The cash flows are perpetual, so

Thus the project would not be worthwhile with all-equity financing. But it actually supports debt of $5 million. At a 6% borrowing rate (rD = .06) and a 35% tax rate (Tc = .35), annual tax shields are .35 × .06 × 5 = .105, or $105,000.

What are those tax shields worth? If the firm is constantly rebalancing its debt, we discount at r = 9.84%:

APV is the sum of base-case value and PV(interest tax shields):

This is exactly the same as we obtained by one-step discounting with WACC. The perpetual crusher is a break-even project by either valuation method.

But with APV, we don’t have to hold debt at a constant proportion of value. Suppose Sangria plans to keep project debt fixed at $5 million. In this case we assume the risk of the tax shields is the same as the risk of the debt and we discount at the 6% rate on debt:

Now the project is more attractive. With fixed debt, the interest tax shields are safe and therefore worth more. (Whether the fixed debt is safer for Sangria is another matter. If the perpetual crusher project fails, the $5 million of fixed debt may end up as a burden on Sangria’s other assets.)

Other Financing Side Effects

Suppose Sangria has to finance the perpetual crusher by issuing debt and equity. It issues $7.5 million of equity with issue costs of 7% ($525,000) and $5 million of debt with issue costs of 2% ($100,000, or $.10 million). Assume the debt is fixed once issued, so that interest tax shields are worth $1.75 million. Now we can recalculate APV, taking care to subtract the issue costs:

The issue costs would reduce APV to nearly zero.

Sometimes there are favorable financing side effects that have nothing to do with taxes. For example, suppose that a potential manufacturer of crusher machinery offers to sweeten the deal by leasing it to Sangria on favorable terms. Then you could calculate APV as the sum of base-case NPV plus the NPV of the lease. Or suppose that a local government offers to lend Sangria $5 million at a very low interest rate if the crusher is built and operated locally. The NPV of the subsidized loan could be added in to APV. (We cover leases in Chapter 25 and subsidized loans in the Appendix to this chapter.)

   TABLE 19.2 APV valuation of Rio Corporation ($ millions).

APV for Businesses

APV can also be used to value businesses. Let’s take another look at the valuation of Rio. In Table 19.1, we assumed a constant 40% debt ratio and discounted free cash flow at Sangria’s WACC. Table 19.2 runs the same analysis, but with a fixed debt schedule.

We’ll suppose that Sangria has decided to make an offer for Rio. If successful, it plans to finance the purchase with $51 million of debt. It intends to pay down the debt to $45 million in year 6. Recall Rio’s horizon value of $113.4 million, which is calculated in Table 19.1 and shown again in Table 19.2. The debt ratio at the horizon is therefore projected at 45/113.4 = .397, about 40%. Thus Sangria plans to take Rio back to a normal 40% debt ratio at the horizon.²² But Rio will be carrying a heavier debt load before the horizon. For example, the $51 million of initial debt is about 58% of company value as calculated in Table 19.1.

Let’s see how Rio’s APV is affected by this more aggressive borrowing schedule. Table 19.2 shows projections of free cash flows from Table 19.1.²³ Now we need Rio’s base-case value, so we discount these flows at the opportunity cost of capital (9.84%), not at WACC. The resulting base-case value for Rio is $84.3 million. Table 19.2 also projects debt levels, interest payments, and interest tax shields. If the debt levels are taken as fixed, then the tax shields should be discounted back at the 6% borrowing rate. The resulting PV of interest tax shields is $5.0 million. Thus,

an increase of $1.4 million from NPV in Table 19.1. The increase can be traced to the higher early debt levels and to the assumption that the debt levels and interest tax shields are fixed and relatively safe.²⁴

Now a difference of $1.4 million is not a big deal, considering all the lurking risks and pitfalls in forecasting Rio’s free cash flows. But you can see the advantage of the flexibility that APV provides. The APV spreadsheet allows you to explore the implications of different financing strategies without locking into a fixed debt ratio or having to calculate a new WACC for every scenario.

APV is particularly useful when the debt for a project or business is tied to book value or has to be repaid on a fixed schedule. For example, Kaplan and Ruback used APV to analyze the prices paid for a sample of leveraged buyouts (LBOs). LBOs are takeovers, typically of mature companies, financed almost entirely with debt. However, the new debt is not intended to be permanent. LBO business plans call for generating extra cash by selling assets, shaving costs, and improving profit margins. The extra cash is used to pay down the LBO debt. Therefore you can’t use WACC as a discount rate to evaluate an LBO because its debt ratio will not be constant.

APV works fine for LBOs. The company is first evaluated as if it were all-equity-financed. That means that cash flows are projected after tax, but without any interest tax shields generated by the LBO’s debt. The tax shields are then valued separately and added to the all-equity value. Any other financing side effects are added also. The result is an APV valuation for the company.²⁵ Kaplan and Ruback found that APV did a pretty good job explaining prices paid in these hotly contested takeovers, considering that not all the information available to bidders had percolated into the public domain. Kaplan and Ruback were restricted to publicly available data.

APV for International Investments

APV is most useful when financing side effects are numerous and important. This is frequently the case for large international investments, which may have custom-tailored project financing and special contracts with suppliers, customers, and governments. Here are a few examples of financing side effects resulting from a project finance.

We explain project finance in Chapter 24. It typically means very high debt ratios to start, with most or all of a project’s early cash flows committed to debt service. Equity investors have to wait. Since the debt ratio will not be constant, you have to turn to APV.

Project financing may include debt available at favorable interest rates. Most governments subsidize exports by making special financing packages available, and manufacturers of industrial equipment may stand ready to lend money to help close a sale. Suppose, for example, that your project requires construction of an on-site electricity generating plant. You solicit bids from suppliers in various countries. Don’t be surprised if the competing suppliers sweeten their bids with offers of low interest rate project loans or if they offer to lease the plant on favorable terms. You should then calculate the NPVs of these loans or leases and include them in your project analysis.

Sometimes international projects are supported by contracts with suppliers or customers. Suppose a manufacturer wants to line up a reliable supply of a crucial raw material—powdered magnoosium, say. The manufacturer could subsidize a new magnoosium smelter by agreeing to buy 75% of production and guaranteeing a minimum purchase price. The guarantee is clearly a valuable addition to the smelter’s APV: if the world price of powdered magnoosium falls below the minimum, the project doesn’t suffer. You would calculate the value of this guarantee (by the methods explained in Chapters 20 to 22) and add it to APV.

Sometimes local governments impose costs or restrictions on investment or disinvestment. For example, Chile, in an attempt to slow down a flood of short-term capital inflows in the 1990s, required investors to “park” part of their incoming money in non-interest-bearing accounts for a period of two years. An investor in Chile during this period could have calculated the cost of this requirement and subtracted it from APV.²⁶

 19-5   Your Questions Answered

Question: All these cost of capital formulas—which ones do financial managers actually use?

Answer: The after-tax weighted-average cost of capital, most of the time. WACC is estimated for the company, or sometimes for an industry. We recommend industry WACCs when data are available for firms with similar assets, operations, business risks, and growth opportunities.

Of course, conglomerate companies, with divisions operating in two or more unrelated industries, should not use a single company or industry WACC. Such firms should try to estimate a different industry WACC for each operating division.

Question: But WACC is the correct discount rate only for “average” projects. What if the project’s financing differs from the company’s or industry’s?

Answer: Remember, investment projects are usually not separately financed. Even when they are, you should focus on the project’s contribution to the firm’s overall debt capacity, not on its immediate financing. (Suppose it’s convenient to raise all the money for a particular project with a bank loan. That doesn’t mean the project itself supports 100% debt financing. The company is borrowing against its existing assets as well as the project.)

But if the project’s debt capacity is materially different from the company’s existing assets, or if the company’s overall debt policy changes, WACC should be adjusted. The adjustment can be done by the three-step procedure explained in Section 19-3.

Question: Could we do one more numerical example?

Answer: Sure. Suppose that WACC has been estimated as follows at a 30% debt ratio:

What is the correct discount rate at a 50% debt ratio?

Step 1. Calculate the opportunity cost of capital.

Step 2. Calculate the new costs of debt and equity. The cost of debt will be higher at 50% debt than 30%. Say it is rD = .095. The new cost of equity is

Step 3. Recalculate WACC.

Question: How do I use the capital asset pricing model to calculate the after-tax weighted-average cost of capital?

Answer: First plug the equity beta into the capital asset pricing formula to calculate rE, the expected return to equity. Then use this figure, along with the after-tax cost of debt and the debt-to-value and equity-to-value ratios, in the WACC formula.

Of course the CAPM is not the only way to estimate the cost of equity. For example, you might be able to use the dividend-discount model (see Section 4-3).

Question: But suppose I do use the CAPM? What if I have to recalculate the equity beta for a different debt ratio?

Answer: The formula for the equity beta is

where βE is the equity beta, βA is the asset beta, and βD is the beta of the company’s debt. The asset beta is a weighted average of the debt and equity betas:

Suppose you needed the opportunity cost of capital r. You could calculate βA and then r from the capital asset pricing model.

Question: I think I understand how to adjust for differences in debt capacity or debt policy. How about differences in business risk?

Answer: If business risk is different, then r, the opportunity cost of capital, is different.

Figuring out the right r for an unusually safe or risky project is never easy. Sometimes the financial manager can use estimates of risk and expected return for companies similar to the project. Suppose, for example, that a traditional pharmaceutical company is considering a major commitment to biotech research. The financial manager could pick a sample of biotech companies, estimate their average beta and cost of capital, and use these estimates as benchmarks for the biotech investment.

But in many cases it’s difficult to find a good sample of matching companies for an unusually safe or risky project. Then the financial manager has to adjust the opportunity cost of capital by judgment. Section 9-3 may be helpful in such cases.

Question: When do I need adjusted present value (APV)?

Answer: The WACC formula picks up only one financing side effect: the value of interest tax shields on debt supported by a project. If there are other side effects—subsidized financing tied to a project, for example—you should use APV.

You can also use APV to break out the value of interest tax shields:

Suppose, for example, that you are analyzing a company just after a leveraged buyout. The company has a very high initial debt level but plans to pay down the debt as rapidly as possible. APV could be used to obtain an accurate valuation.

Question: When should personal taxes be incorporated into the analysis?

Answer: Always use Tc, the marginal corporate tax rate, when calculating WACC as a weighted average of the costs of debt and equity. The discount rate is adjusted only for corporate taxes.

In principle, APV can be adjusted for personal taxes by replacing the marginal corporate rate Tc with an effective tax rate that combines corporate and personal taxes and reflects the net tax advantage per dollar of interest paid by the firm. We provided back-of-the-envelope calculations of this advantage in Section 18-2. The effective tax rate is almost surely less than Tc, but it is very difficult to pin down the numerical difference. Therefore, in practice Tc is almost always used as an approximation.

Question: Are taxes really that important? Do financial managers really fine-tune the debt ratio to minimize WACC?

Answer: As we saw in Chapter 18, financing decisions reflect many forces beyond taxes, including costs of financial distress, differences in information, and incentives for managers. There may not be a sharply defined optimal capital structure. Therefore most financial managers don’t fine-tune their companies’ debt ratios, and they don’t rebalance financing to keep debt ratios strictly constant. In effect they assume that a plot of WACC for different debt ratios is “flat” over a reasonable range of moderate leverage.

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SUMMARY

In this chapter we considered how financing can be incorporated into the valuation of projects and ongoing businesses. There are two ways to take financing into account. The first is to calculate NPV by discounting at an adjusted discount rate, usually the after-tax weighted-average cost of capital (WACC). The second approach discounts at the opportunity cost of capital and then adds or subtracts the present values of financing side effects. The second approach is called adjusted present value, or APV.

The formula for the after-tax WACC is

where rD and rE are the expected rates of return demanded by investors in the firm’s debt and equity securities, D and E are the current market values of debt and equity, and V is the total market value of the firm (V = D + E). Of course, the WACC formula expands if there are other sources of financing, for example, preferred stock.

Strictly speaking, discounting at WACC works only for projects that are carbon copies of the existing firm—projects with the same business risk that will be financed to maintain the firm’s current, market debt ratio. But firms can use WACC as a benchmark rate to be adjusted for differences in business risk or financing. We gave a three-step procedure for adjusting WACC for different debt ratios.

Discounting cash flows at the WACC assumes that debt is rebalanced to keep a constant ratio of debt to market value. The amount of debt supported by a project is assumed to rise or fall with the project’s after-the-fact success or failure. The WACC formula also assumes that financing matters only because of interest tax shields. When this or other assumptions are violated, only APV will give an absolutely correct answer.

APV is, in concept at least, simple. First calculate the base-case NPV of the project or business on the assumption that financing doesn’t matter. (The discount rate is not WACC, but the opportunity cost of capital.) Then calculate the present values of any relevant financing side effects and add or subtract from base-case value. A capital investment project is worthwhile if

is positive. Common financing side effects include interest tax shields, issue costs, and special financing packages offered by suppliers or governments.

For firms or going-concern businesses, value depends on free cash flow. Free cash flow is the amount of cash that can be paid out to all investors, debt as well as equity, after deducting cash needed for new investment or increases in working capital. Free cash flow does not include the value of interest tax shields, however. The WACC formula accounts for interest tax shields by using the after-tax cost of debt. APV adds PV(interest tax shields) to base-case value.

Businesses are usually valued in two steps. First free cash flow is forecasted out to a valuation horizon and discounted back to present value. Then a horizon value is calculated and also discounted back. Be particularly careful to avoid unrealistically high horizon values. By the time the horizon arrives, competitors will have had several years to catch up. Also, when you are done valuing the business, don’t forget to subtract its debt to get the value of the firm’s equity.

All of this chapter’s examples reflect assumptions about the amount of debt supported by a project or business. Remember not to confuse “supported by” with the immediate source of funds for investment. For example, a firm might, as a matter of convenience, borrow $1 million for a $1 million research program. But the research is unlikely to contribute $1 million in debt capacity; a large part of the $1 million new debt would be supported by the firm’s other assets.

Also remember that debt capacity is not meant to imply an absolute limit on how much the firm can borrow. The phrase refers to how much it chooses to borrow against a project or ongoing business.

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FURTHER READING

The Harvard Business Review has published a popular account of APV:

T. A. Luehrman, “Using APV: A Better Tool for Valuing Operations,” Harvard Business Review 75 (May–June 1997), pp. 145–154.

There have been dozens of articles on the weighted-average cost of capital and other issues discussed in this chapter. Here are three:

J. Miles and R. Ezzell, “The Weighted Average Cost of Capital, Perfect Capital Markets, and Project Life: A Clarification,” Journal of Financial and Quantitative Analysis 15 (September 1980), pp. 719–730.

R. A. Taggart, Jr., “Consistent Valuation and Cost of Capital Expressions with Corporate and Personal Taxes,” Financial Management 20 (Autumn 1991), pp. 8–20.

R. S. Ruback, “Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows,” Financial Management 31 (Summer 2002), pp. 85–103.

The valuation rule for safe, nominal cash flows is developed in:

R. S. Ruback, “Calculating the Market Value of Risk-Free Cash Flows,” Journal of Financial Economics 15 (March 1986), pp. 323–339.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  WACC Calculate the weighted-average cost of capital (WACC) for Federated Junkyards of America, using the following information:

•  Debt: $75,000,000 book value outstanding. The debt is trading at 90% of book value. The yield to maturity is 9%.

•  Equity: 2,500,000 shares selling at $42 per share. Assume the expected rate of return on Federated’s stock is 18%.

•  Taxes: Federated’s marginal tax rate is Tc = .35.

2.  WACC Suppose Federated Junkyards decides to move to a more conservative debt policy. A year later its debt ratio is down to 15% (D/V = .15). The interest rate has dropped to 8.6%. Recalculate Federated’s WACC under these new assumptions. The company’s business risk, opportunity cost of capital, and tax rate have not changed. Use the three-step procedure explained in Section 19-3.

3.  WACC True or false? Use of the WACC formula assumes

a.  A project supports a fixed amount of debt over the project’s economic life.

b.  The ratio of the debt supported by a project to project value is constant over the project’s economic life.

c.  The firm rebalances debt each period, keeping the debt-to-value ratio constant.

4.  Flow-to-equity valuation What is meant by the flow-to-equity valuation method? What discount rate is used in this method? What assumptions are necessary for this method to give an accurate valuation?

5.  APV True or false? The APV method

a.  Starts with a base-case value for the project.

b.  Calculates the base-case value by discounting project cash flows, forecasted assuming all-equity financing, at the WACC for the project.

c.  Is especially useful when debt is to be paid down on a fixed schedule.

6.  APV A project costs $1 million and has a base-case NPV of exactly zero (NPV = 0). What is the project’s APV in the following cases?

a.  If the firm invests, it has to raise $500,000 by a stock issue. Issue costs are 15% of net proceeds.

b.  If the firm invests, its debt capacity increases by $500,000. The present value of interest tax shields on this debt is $76,000.

7.  WACC Whispering Pines, Inc., is all-equity-financed. The expected rate of return on the company’s shares is 12%.

a.  What is the opportunity cost of capital for an average-risk Whispering Pines investment?

b.  Suppose the company issues debt, repurchases shares, and moves to a 30% debt-to-value ratio (D/V = .30). What will the company’s weighted-average cost of capital be at the new capital structure? The borrowing rate is 7.5% and the tax rate is 35%.

8.  APV Consider a project lasting one year only. The initial outlay is $1,000 and the expected inflow is $1,200. The opportunity cost of capital is r = .20. The borrowing rate is rD = .10, and the tax shield per dollar of interest is Tc = .35.

a.  What is the project’s base-case NPV?

b.  What is its APV if the firm borrows 30% of the project’s required investment?

9.  WACC The WACC formula seems to imply that debt is “cheaper” than equity—that is, that a firm with more debt could use a lower discount rate. Does this make sense? Explain briefly.

10.  APV and debt capacity Suppose KCS Corp. buys out Patagonia Trucking, a privately owned business, for $50 million. KCS has only $5 million cash in hand, so it arranges a $45 million bank loan. A normal debt-to-value ratio for a trucking company would be 50% at most, but the bank is satisfied with KCS’s credit rating.

Suppose you were valuing Patagonia by APV in the same format as Table 19.2. How much debt would you include? Explain briefly.

INTERMEDIATE

11.  WACC Table 19.3 shows a book balance sheet for the Wishing Well Motel chain. The company’s long-term debt is secured by its real estate assets, but it also uses short-term bank loans as a permanent source of financing. It pays 10% interest on the bank debt and 9% interest on the secured debt. Wishing Well has 10 million shares of stock outstanding, trading at $90 per share. The expected return on Wishing Well’s common stock is 18%.

Calculate Wishing Well’s WACC. Assume that the book and market values of Wishing Well’s debt are the same. The marginal tax rate is 35%.

12.  Forecasting cash flow Suppose Wishing Well is evaluating a new motel and resort on a romantic site in Madison County, Wisconsin. Explain how you would forecast the after-tax cash flows for this project. (Hints: How would you treat taxes? Interest expense? Changes in working capital?)

13.  APV To finance the Madison County project, Wishing Well will have to arrange an additional $80 million of long-term debt and make a $20 million equity issue. Underwriting fees, spreads, and other costs of this financing will total $4 million. How would you take this into account in valuing the proposed investment?

14.  WACC Table 19.4 shows a simplified balance sheet for Rensselaer Felt. Calculate this company’s weighted-average cost of capital. The debt has just been refinanced at an interest rate of 6% (short term) and 8% (long term). The expected rate of return on the company’s shares is 15%. There are 7.46 million shares outstanding, and the shares are trading at $46. The tax rate is 35%.

15.  WACC How will Rensselaer Felt’s WACC and cost of equity change if it issues $50 million in new equity and uses the proceeds to retire long-term debt? Assume the company’s borrowing rates are unchanged. Use the three-step procedure from Section 19-3.

16.  APV Bergwerk Rheingold a.g. has the opportunity to invest €1 million now (t = 0) and expects after-tax returns of €600,000 in t = 1 and €700,000 in t = 2. The project will last for two years only. The appropriate cost of capital is 12% with all-equity financing, the borrowing rate is 8%, and BR will borrow €300,000 against the project. This debt must be repaid in two equal installments. Assume debt tax shields have a net value of €.30 per dollar of interest paid. Calculate the project’s APV using the procedure followed in Table 19.2.

17.  APV Consider another perpetual project like the crusher described in Section 19-1. Its initial investment is $1,000,000, and the expected cash inflow is $95,000 a year in perpetuity. The opportunity cost of capital with all-equity financing is 10%, and the project allows the firm to borrow at 7%. The tax rate is 35%.

   TABLE 19.3 Book balance sheet for Wishing Well, Inc. (figures in $ millions).

   TABLE 19.4 Simplified book balance sheet for Rensselaer Felt (figures in $ thousands).

Use APV to calculate this project’s value.

a.  Assume first that the project will be partly financed with $400,000 of debt and that the debt amount is to be fixed and perpetual.

b.  Then assume that the initial borrowing will be increased or reduced in proportion to changes in the market value of this project.

Explain the difference between your answers to (a) and (b).

18.  Opportunity cost of capital Suppose the project described in Problem 17 is to be undertaken by a university. Funds for the project will be withdrawn from the university’s endowment, which is invested in a widely diversified portfolio of stocks and bonds. However, the university can also borrow at 7%. The university is tax exempt.

The university treasurer proposes to finance the project by issuing $400,000 of perpetual bonds at 7% and by selling $600,000 worth of common stocks from the endowment. The expected return on the common stocks is 10%. He therefore proposes to evaluate the project by discounting at a weighted-average cost of capital, calculated as

What’s right or wrong with the treasurer’s approach? Should the university invest? Should it borrow? Would the project’s value to the university change if the treasurer financed the project entirely by selling common stocks from the endowment?

19.  APV Consider a project to produce solar water heaters. It requires a $10 million investment and offers a level after-tax cash flow of $1.75 million per year for 10 years. The opportunity cost of capital is 12%, which reflects the project’s business risk.

a.  Suppose the project is financed with $5 million of debt and $5 million of equity. The interest rate is 8% and the marginal tax rate is 35%. The debt will be paid off in equal annual installments over the project’s 10-year life. Calculate APV.

b.  How does APV change if the firm incurs issue costs of $400,000 to raise the $5 million of required equity?

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

20.  WACC and APV Take another look at the valuations of Rio in Tables 19.1 and 19.2. Now use the live spreadsheets on this book’s website (www.mcgraw-hill.co.uk/textbooks/brealey) to show how the valuations depend on

a.  The forecasted long-term growth rate.

b.  The required amounts of investment in fixed assets and working capital.

c.  The opportunity cost of capital. Note you can also vary the opportunity cost of capital in Table 19.1.

d.  Profitability, that is, cost of goods sold as a percentage of sales.

e.  The assumed amount of debt financing.

21.  Issue costs and APV Melbourne Chemicals is currently at its target debt ratio of 40%. It is contemplating a A$1 million expansion of its existing business. This expansion is expected to produce a cash inflow of A$130,000 a year in perpetuity.

The company is uncertain whether to undertake this expansion and how to finance it. The two options are a A$1 million issue of common stock or a A$1 million issue of 20-year debt. The flotation costs of a stock issue would be around 5% of the amount raised, and the flotation costs of a debt issue would be around 1½%.

Melbourne’s financial manager, Ms. Polly Ethylene, estimates that the required return on the company’s equity is 14%, but she argues that the flotation costs increase the cost of new equity to 19%. On this basis, the project does not appear viable.

On the other hand, she points out that the company can raise new debt on a 7% yield, which would make the cost of new debt 8½%. She therefore recommends that Melbourne should go ahead with the project and finance it with an issue of long-term debt.

Is Ms. Ethylene right? How would you evaluate the project?

22.  WACC Nevada Hydro is 40% debt-financed and has a weighted-average cost of capital of 9.7%:

Goldensacks Company is advising Nevada Hydro to issue $75 million of preferred stock at a dividend yield of 9%. The proceeds would be used to repurchase and retire common stock. The preferred issue would account for 10% of the pre-issue market value of the firm.

Goldensacks argues that these transactions would reduce Nevada Hydro’s WACC to 9.4%:

Do you agree with this calculation? Explain.

23.  Company valuation The management of Chiara della Palma has made the projections shown in Table 19.5. Use this table as a starting point to value the company as a whole. The WACC for Chiara is 12% and the long-run growth rate after year 5 is 4%. The company has €5 million debt and 865,000 shares outstanding. What is the value per share?

   TABLE 19.5 Cash flow projections for Chiara. (€ thousands).

CHALLENGE

24.  Miles-Ezzell formula In footnote 15 we referred to the Miles–Ezzell discount rate formula, which assumes that debt is not rebalanced continuously, but at one-year intervals. Derive this formula. Then use it to unlever Sangria’s WACC and calculate Sangria’s opportunity cost of capital. Your answer will be slightly different from the opportunity cost that we calculated in Section 19-3. Can you explain why?

25.  Rebalancing The WACC formula assumes that debt is rebalanced to maintain a constant debt ratio D/V. Rebalancing ties the level of future interest tax shields to the future value of the company. This makes the tax shields risky. Does that mean that fixed debt levels (no rebalancing) are better for stockholders?

26.  Horizon value Modify Table 19.1 on the assumption that competition eliminates any opportunities to earn more than WACC on new investment after year 7 (PVGO = 0). How does the valuation of Rio change?

27.  APV vs. WACC A project to produce diatomaceous semiconductors is expected to cost HK$100 million and generate level real cash flows of HK$17.5 million for 10 years. Nominal cash flows should increase with inflation at 4% per year. The real opportunity cost of capital is 8%.

a.  Suppose the project is partly financed with HK$50 million debt and HK$50 million from retained earnings. The (nominal) interest rate is 7.5% and the marginal corporate tax rate is 30%. The debt will be paid off in equal annual installments. What is the project’s APV?

b.  Can you design a debt repayment schedule that better fits the total principal and interest payments to the time-pattern of project cash flows? Set out the alternative schedule and recalculate APV.

c.  Value the project by discounting at an after-tax WACC. What time pattern of borrowing does this valuation imply?

d.  How do the values calculated in (a), (b) and (c) change if the firm incurs issue costs of HK$4 million to raise the HK$50 million of equity needed for the project?

28.  APV and subsidized borrowing There is a long-running dispute between the European aircraft company Airbus and its U.S. competitor Boeing. Boeing claims that Airbus has received subsidies in the form of government loans with long maturities, easy terms and below-market interest rates. Airbus claims that Boeing has received government subsidies through other channels. March 2010 saw more flare-ups in this dispute, when the German and French governments announced loans of €2.5 billion to help Airbus finance development of its new A350. Also the World Trade Organization issued a report saying that past loans to Airbus “contained a certain element of subsidy.”

We don’t have to take sides in this dispute, but for this question assume that the German and French loans for the A350 will carry significantly lower interest rates than Airbus could get from private lenders, given the terms and maturities of the loans. Assume you are a financial analyst for Airbus. How would you value the loans and include them in a capital-investment analysis of the A350 program? Explain.

● ● ● ● ●

FINANCE ON THE WEB

Table 19.6 is a simplified book balance sheet for Apache Corp. at year-end 2011. Here is some further information:

a.  Calculate Apache’s WACC. Use the capital asset pricing model and the additional information given above. Make additional assumptions and approximations as necessary.

b.  What is Apache’s opportunity cost of capital?

c.  Finally, go to finance.yahoo.com and update your answers to questions (a) and (b).

   TABLE 19.6 Simplified book balance sheet for Apache, year-end 2011 (figures in $ millions).

APPENDIX ● ● ● ● ●

Discounting Safe, Nominal Cash Flows

Suppose you’re considering purchase of a $100,000 machine. The manufacturer sweetens the deal by offering to finance the purchase by lending you $100,000 for five years, with annual interest payments of 5%. You would have to pay 13% to borrow from a bank. Your marginal tax rate is 35% (Tc = .35).

How much is this loan worth? If you take it, the cash flows, in thousands of dollars, are

What is the right discount rate?

Here you are discounting safe, nominal cash flows—safe because your company must commit to pay if it takes the loan,²⁷ and nominal because the payments would be fixed regardless of future inflation. Now, the correct discount rate for safe, nominal cash flows is your company’s after-tax, unsubsidized borrowing rate,²⁸ which is rD(1 – Tc) = .13(1 – .35) = .0845. Therefore,

The manufacturer has effectively cut the machine’s purchase price from $100,000 to $100,000 – $20,520 = $79,480. You can now go back and recalculate the machine’s NPV using this fire-sale price, or you can use the NPV of the subsidized loan as one element of the machine’s adjusted present value.

A General Rule

Clearly, we owe an explanation of why rD(1 – Tc) is the right discount rate for safe, nominal cash flows. It’s no surprise that the rate depends on rD, the unsubsidized borrowing rate, for that is investors’ opportunity cost of capital, the rate they would demand from your company’s debt. But why should rD be converted to an after-tax figure?

Let’s simplify by taking a one-year subsidized loan of $100,000 at 5%. The cash flows, in thousands of dollars, are

Now ask, What is the maximum amount X that could be borrowed for one year through regular channels if $103,250 is set aside to service the loan?

“Regular channels” means borrowing at 13% pretax and 8.45% after tax. Therefore you will need 108.45% of the amount borrowed to pay back principal plus after-tax interest charges. If 1.0845X = 103,250, then X = 95,205. Now if you can borrow $100,000 by a subsidized loan, but only $95,205 through normal channels, the difference ($4,795) is money in the bank. Therefore, it must also be the NPV of this one-period subsidized loan.

When you discount a safe, nominal cash flow at an after-tax borrowing rate, you are implicitly calculating the equivalent loan, the amount you could borrow through normal channels, using the cash flow as debt service. Note that

In some cases, it may be easier to think of taking the lender’s side of the equivalent loan rather than the borrower’s. For example, you could ask, How much would my company have to invest today to cover next year’s debt service on the subsidized loan? The answer is $95,205: If you lend that amount at 13%, you will earn 8.45% after tax, and therefore have 95,205(1.0845) = $103,250. By this transaction, you can in effect cancel, or “zero out,” the future obligation. If you can borrow $100,000 and then set aside only $95,205 to cover all the required debt service, you clearly have $4,795 to spend as you please. That amount is the NPV of the subsidized loan.

Therefore, regardless of whether it’s easier to think of borrowing or lending, the correct discount rate for safe, nominal cash flows is an after-tax interest rate.²⁹

In some ways, this is an obvious result once you think about it. Companies are free to borrow or lend money. If they lend, they receive the after-tax interest rate on their investment; if they borrow in the capital market, they pay the after-tax interest rate. Thus, the opportunity cost to companies of investing in debt-equivalent cash flows is the after-tax interest rate. This is the adjusted cost of capital for debt-equivalent cash flows.³⁰

Some Further Examples

Here are some further examples of debt-equivalent cash flows.

Payout Fixed by Contract

Suppose you sign a maintenance contract with a truck leasing firm, which agrees to keep your leased trucks in good working order for the next two years in exchange for 24 fixed monthly payments. These payments are debt-equivalent flows.

Depreciation Tax Shields

Capital projects are normally valued by discounting the total after-tax cash flows they are expected to generate. Depreciation tax shields contribute to project cash flow, but they are not valued separately; they are just folded into project cash flows along with dozens, or hundreds, of other specific inflows and outflows. The project’s opportunity cost of capital reflects the average risk of the resulting aggregate.

However, suppose we ask what depreciation tax shields are worth by themselves. For a firm that’s sure to pay taxes, depreciation tax shields are a safe, nominal flow. Therefore, they should be discounted at the firm’s after-tax borrowing rate.

Suppose we buy an asset with a depreciable basis of $200,000, which can be depreciated by the five-year tax depreciation schedule (see Table 6.4). The resulting tax shields are

The after-tax discount rate is rD(1 – Tc) = .13(1 – .35) = .0845. (We continue to assume a 13% pretax borrowing rate and a 35% marginal tax rate.) The present value of these shields is

A Consistency Check

You may have wondered whether our procedure for valuing debt-equivalent cash flows is consistent with the WACC and APV approaches presented earlier in this chapter. Yes, it is consistent, as we will now illustrate.

Let’s look at another very simple numerical example. You are asked to value a $1 million payment to be received from a blue-chip company one year hence. After taxes at 35%, the cash inflow is $650,000. The payment is fixed by contract.

Since the contract generates a debt-equivalent flow, the opportunity cost of capital is the rate investors would demand on a one-year note issued by the blue-chip company, which happens to be 8%. For simplicity, we’ll assume this is your company’s borrowing rate too. Our valuation rule for debt-equivalent flows is therefore to discount at rD(1 – Tc) = .08(1 – .35) = .052:

What is the debt capacity of this $650,000 payment? Exactly $617,900. Your company could borrow that amount and pay off the loan completely—principal and after-tax interest—with the $650,000 cash inflow. The debt capacity is 100% of the PV of the debt-equivalent cash flow.

If you think of it that way, our discount rate rD (1 – Tc) is just a special case of WACC with a 100% debt ratio (D/V = 1).

Now let’s try an APV calculation. This is a two-part valuation. First, the $650,000 inflow is discounted at the opportunity cost of capital, 8%. Second, we add the present value of interest tax shields on debt supported by the project. Since the firm can borrow 100% of the cash flow’s value, the tax shield is rD Tc APV, and APV is:

Solving for APV, we get $617,900, the same answer we obtained by discounting at the after-tax borrowing rate. Thus our valuation rule for debt-equivalent flows is a special case of APV.

QUESTIONS

1.  The U.S. government has settled a dispute with your company for $16 million. It is committed to pay this amount in exactly 12 months. However, your company will have to pay tax on the award at a marginal tax rate of 35%. What is the award worth? The one-year Treasury rate is 5.5%.

2.  You are considering a five-year lease of office space for R&D personnel. Once signed, the lease cannot be canceled. It would commit your firm to six annual $100,000 payments, with the first payment due immediately. What is the present value of the lease if your company’s borrowing rate is 9% and its tax rate is 35%? The lease payments would be tax-deductible.

___________

¹See Section 9-1 under “Perfect Pitch and the Cost of Capital.”

²Always use an up-to-date interest rate (yield to maturity), not the interest rate when the firm’s debt was first issued and not the coupon rate on the debt’s book value.

³We can prove this statement as follows. Denote expected after-tax cash flows (assuming all-equity financing) as C1, C2, . . ., CT. With all-equity financing, these flows would be discounted at the opportunity cost of capital r. But we need to value the cash flows for a firm that is financed partly with debt.

Start with value in the next to last period: VT – 1 = DT – 1 + ET – 1. The total cash payoff to debt and equity investors is the cash flow plus the interest tax shield. The expected total return to debt and equity investors is

Assume the debt ratio is constant at L = D/V. Equate (1) and (2) and solve for VT – 1:

The logic repeats for VT – 2. Note that the next period’s payoff includes VT – 1:

We can continue all the way back to date 0:

⁴Notice that expected free cash flow increases by about 13.3% from year 6 to year 7 because the transition from 4% to 3% sales growth reduces required investment. But sales, investment, and free cash flow will all increase at 3% once the company settles into stable growth. Recall that the first cash flow in the constant-growth DCF formula occurs in the next year, year 7 in this case. Growth progresses at a steady-state 3% from year 7 onward. Therefore it’s OK to use the 3% growth rate in the horizon-value formula.

⁵See Section 4-5.

⁶Table 19.1 is too optimistic in this respect, because the horizon value increases with the assumed long-run growth rate. This implies that Rio has valuable growth opportunities (PVGO) even after the horizon in year 6. A more sophisticated spreadsheet would add an intermediate growth stage, say from years 7 through 10, and gradually reduce profitability to competitive levels. See Problem 26 at the end of this chapter.

⁷This balance sheet is for exposition and should not be confused with a real company’s books. It includes the value of growth opportunities, which accountants do not recognize, though investors do. It excludes certain accounting entries, for example, deferred taxes.

Deferred taxes arise when a company uses faster depreciation for tax purposes than it uses in reports to investors. That means the company reports more in taxes than it pays. The difference is accumulated as a liability for deferred taxes. In a sense there is a liability, because the Internal Revenue Service “catches up,” collecting extra taxes, as assets age. But this is irrelevant in capital investment analysis, which focuses on actual after-tax cash flows and uses accelerated tax depreciation.

Deferred taxes should not be regarded as a source of financing or an element of the weighted-average cost of capital formula. The liability for deferred taxes is not a security held by investors. It is a balance sheet entry created for accounting purposes.

Deferred taxes can be important in regulated industries, however. Regulators take deferred taxes into account in calculating allowed rates of return and the time patterns of revenues and consumer prices.

⁸Financial practitioners have rules of thumb for deciding whether short-term debt is worth including in WACC. One rule checks whether short-term debt is at least 10% of total liabilities and net working capital is negative. If so, then short-term debt is almost surely being used to finance long-term assets and is explicitly included in WACC.

⁹Most corporate debt is not actively traded, so its market value cannot be observed directly. But you can usually value a nontraded debt security by looking to securities that are traded and that have approximately the same default risk and maturity. See Chapter 23.

For healthy firms the market value of debt is usually not too far from book value, so many managers and analysts use book value for D in the weighted-average cost of capital formula. However, be sure to use market, not book, values for E.

¹⁰We noted the difficulty of estimating expected rates of return on junk debt. This problem largely disappears for industry WACCs, provided that most or all of the companies in the industry sample are not relying on junk-debt financing.

¹¹Even the tax rate could change. For example, Sangria might have enough taxable income to cover interest payments at 20% debt but not at 40% debt. In that case the effective marginal tax rate would be higher at 20% than 40% debt.

¹²Debt betas are generally small, and many managers simplify and assume βD = 0. Junk-debt betas can be well above zero, however.

¹³Here’s another way to interpret the WACC formula’s assumption of a constant debt ratio. Assume that the debt capacity of a project is a constant fraction of the project’s value. (“Capacity” does not mean the maximum amount that could be borrowed against the project, but the amount that managers would optimally choose to borrow.) Discounting at WACC gives the project credit for interest tax shields on the project’s debt capacity, even if the firm does not rebalance its capital structure and ends up borrowing more or less than the total capacity of all its projects.

¹⁴Similar, but not identical. The basic WACC formula is correct whether rebalancing occurs at the end of each period or continuously. The unlevering and relevering formulas used in steps 1 and 2 of our three-step procedure are exact only if rebalancing is continuous so that the debt ratio stays constant day-to-day and week-to-week. However, the errors introduced from annual rebalancing are very small and can be ignored for practical purposes.

¹⁵Here’s why the formulas work with continuous rebalancing. Think of a market-value balance sheet with assets and interest tax shields on the left and debt and equity on the right, with D + E = PV(assets) + PV(tax shield). The total risk (beta) of the firm’s debt and equity equals the blended risk of PV(assets) and PV(tax shield):

where α is the proportion of the total firm value from its assets and 1 – α is the proportion from interest tax shields. If the firm readjusts its capital structure to keep D/V constant, then the beta of the tax shield must be the same as the beta of the assets. With rebalancing, an x% change in firm value V changes debt D by x%. So the interest tax shield Tc rD D will change by x% as well. Thus the risk of the tax shield must be the same as the risk of the firm as a whole:

This is our unlevering formula expressed in terms of beta. Since expected returns depend on beta:

Rearrange formulas (2) and (3) to get the relevering formulas for βE and rE. (Notice that the tax rate Tc has dropped out.)

All this assumes continuous rebalancing. Suppose instead that the firm rebalances once a year, so that the next year’s interest tax shield, which depends on this year’s debt, is known. Then you can use a formula developed by Miles and Ezzell:

See J. Miles and J. Ezzell, “The Weighted Average Cost of Capital, Perfect Capital Markets, and Project Life: A Clarification,” Journal of Financial and Quantitative Analysis 15 (September 1980), pp. 719–730.

¹⁶The formula first appeared in F. Modigliani and M. H. Miller, “Corporate Income Taxes and the Cost of Capital: A Correction,” American Economic Review 53 (June 1963), pp. 433–443. It is explained more fully in M. H. Miller and F. Modigliani: “Some Estimates of the Cost of Capital to the Electric Utility Industry: 1954–1957,” American Economic Review 56 (June 1966), pp. 333–391.

Given perpetual fixed debt,

¹⁷In this case the relevering formula for the cost of equity is

The unlevering and relevering formulas for betas are

and

See R. Hamada, “The Effect of a Firm’s Capital Structure on the Systematic Risk of Common Stocks,” Journal of Finance 27 (May 1972), pp. 435–452.

¹⁸See S. C. Myers, “Interactions of Corporate Financing and Investment Decisions—Implications for Capital Budgeting,” Journal of Finance 29 (March 1974), pp. 1–25.

¹⁹Costs of financial distress can show up as rapidly increasing costs of debt and equity, especially at high debt ratios. The costs of financial distress could “flatten out” the WACC curve in Figures 17.4 and 19.1, and finally increase WACC as leverage climbs. Thus some practitioners calculate an industry WACC and take it as constant, at least within the range of debt ratios observed for healthy companies in the industry.

Personal taxes could also generate a flatter curve for after-tax WACC as a function of leverage. See Section 18-2.

²⁰“The adjusted-present-value rule was developed in S. C. Myers, “Interactions of Corporate Financing and Investment Decisions—Implications for Capital Budgeting,” Journal of Finance 29 (March 1974), pp. 1–25.

²¹That is, βA = βtax shields. See footnote 15, above.

²²Therefore we still calculate the horizon value in year 6 by discounting subsequent free cash flows at WACC. The horizon value in year 6 is discounted back to year 0 at the opportunity cost of capital, however.

²³Many of the assumptions and calculations in Table 19.1 have been hidden in Table 19.2. The hidden rows can be recalled in the “live” version of Table 19.2, which is available on this book’s website (www.mcgraw-hill.co.uk/textbooks/brealey).

²⁴But will Rio really support debt at the levels shown in Table 19.2? If not, then the debt must be partly supported by Sangria’s other assets, and only part of the $5 million in PV(interest tax shields) can be attributed to Rio itself.

²⁵Kaplan and Ruback actually used “compressed” APV, in which all cash flows, including interest tax shields, are discounted at the opportunity cost of capital. S. N. Kaplan and R. S. Ruback, “The Valuation of Cash Flow Forecasts: An Empirical Analysis,” Journal of Finance 50 (September 1995), pp. 1059–1093.

²⁶Such capital controls have been described as financial roach motels: Money can get in, but it can’t get out.

²⁷In theory, safe means literally “risk-free,” like the cash returns on a Treasury bond. In practice, it means that the risk of not paying or receiving a cash flow is small.

²⁸In Section 13-1 we calculated the NPV of subsidized financing using the pretax borrowing rate. Now you can see that was a mistake. Using the pretax rate implicitly defines the loan in terms of its pretax cash flows, violating a rule promulgated way back in Section 6-1: Always estimate cash flows on an after-tax basis.

²⁹Borrowing and lending rates should not differ by much if the cash flows are truly safe, that is, if the chance of default is small. Usually your decision will not hinge on the rate used. If it does, ask which offsetting transaction—borrowing or lending—seems most natural and reasonable for the problem at hand. Then use the corresponding interest rate.

³⁰All the examples in this section are forward-looking; they call for the value today of a stream of future debt-equivalent cash flows. But similar issues arise in legal and contractual disputes when a past cash flow has to be brought forward in time to a present value today. Suppose it’s determined that company A should have paid B $1 million 10 years ago. B clearly deserves more than $1 million today, because it has lost the time value of money. The time value of money should be expressed as an after-tax borrowing or lending rate, or if no risk enters, as the after-tax risk-free rate. The time value of money is not equal to B’s overall cost of capital. Allowing B to “earn” its overall cost of capital on the payment allows it to earn a risk premium without bearing risk. For a broader discussion of these issues, see F. Fisher and C. Romaine, “Janis Joplin’s Yearbook and the Theory of Damages,” Journal of Accounting, Auditing & Finance 5 (Winter/Spring 1990), pp. 145–157.

Part 6 Options

Understanding Options

Pop quiz: What do the following events have in common?

• The German airline, Lufthansa, buys options that help to put a ceiling on the price that it will pay for purchases of jet fuel.

• Flatiron offers its president a bonus if the company’s stock price exceeds $120.

• Blitzen Computer dips a toe in the water and enters a new market.

• Malted Herring postpones investment in a positive-NPV plant.

• Hewlett-Packard exports partially assembled printers even though it would be cheaper to ship the finished product.

• Didcot A power station in England operates three dual fired units that can use either natural gas or coal.

• Mobile phone maker Nokia announces plans to issue €750 million of bonds that are convertible into shares.

• In February 2010 China Solar Energy announces plans to sell up to 1.13 billion warrants. Each warrant can be used to buy a share in the company for HK$0.14 at any time before February 2012.

Answers: (1) Each of these events involves an option, and (2) they illustrate why the financial manager of an industrial company needs to understand options.

Companies regularly use commodity, currency, and interest-rate options to reduce risk. For example, a meatpacking company that wishes to put a ceiling on the cost of beef might take out an option to buy live cattle at a fixed price. A company that wishes to limit its future borrowing costs might take out an option to sell long-term bonds at a fixed price. And so on. In Chapter 26 we explain how firms employ options to limit their risk.

Many capital investments include an embedded option to expand in the future. For instance, the company may invest in a patent that allows it to exploit a new technology or it may purchase adjoining land that gives it the option in the future to increase capacity. In each case the company is paying money today for the opportunity to make a further investment. To put it another way, the company is acquiring growth opportunities.

Here is another disguised option to invest: You are considering the purchase of a tract of desert land that is known to contain gold deposits. Unfortunately, the cost of extraction is higher than the current price of gold. Does this mean the land is almost worthless? Not at all. You are not obliged to mine the gold, but ownership of the land gives you the option to do so. Of course, if you know that the gold price will remain below the extraction cost, then the option is worthless. But if there is uncertainty about future gold prices, you could be lucky and make a killing.¹

If the option to expand has value, what about the option to bail out? Projects don’t usually go on until the equipment disintegrates. The decision to terminate a project is usually taken by management, not by nature. Once the project is no longer profitable, the company will cut its losses and exercise its option to abandon the project. Some projects have higher abandonment value than others. Those that use standardized equipment may offer a valuable abandonment option. Others may actually cost money to discontinue. For example, it is very costly to decommission an offshore oil platform.

We took a peek at investment options in Chapter 10, and we showed there how to use decision trees to analyze a pharmaceutical company’s options to discontinue trials of a new drug. In Chapter 22 we take a more thorough look at these real options.

Another important reason why financial managers need to understand options is that they are often tacked on to an issue of corporate securities and so provide the investor or the company with the flexibility to change the terms of the issue. For example, in Chapter 24 we show how warrants or convertibles give their holders an option to buy common stock in exchange for cash or bonds.

In fact, we see in Chapter 23 that whenever a company borrows, it gains an option to walk away from its debts and surrender its assets to the bondholders. If the value of the company’s assets is less than the amount of the debt, the company will choose to default on the payment and the bondholders will get to keep the company’s assets. Thus, when the firm borrows, the lender effectively acquires the company and the shareholders obtain the option to buy it back by paying off the debt. This is an extremely important insight. It means that anything that we can learn about traded options applies equally to corporate liabilities.

In this chapter we use traded stock options to explain how options work, but we hope that our brief survey has convinced you that the interest of financial managers in options goes far beyond traded stock options. That is why we are asking you to invest here to acquire several important ideas for use later.

If you are unfamiliar with the wonderful world of options, it may seem baffling on first encounter. We therefore divide this chapter into three bite-sized pieces. Our first task is to introduce you to call and put options and to show you how the payoff on these options depends on the price of the underlying asset. We then show how financial alchemists can combine options to produce a variety of interesting strategies.

We conclude the chapter by identifying the variables that determine option values. There you encounter some surprising and counterintuitive effects. For example, investors are used to thinking that increased risk reduces present value. But for options it is the other way around.

 20-1   Calls, Puts, and Shares

Investors regularly trade options on common stocks.² For example, Table 20.1 reproduces quotes for options on the stock of Apple. You can see that there are two types of option—calls and puts. We explain each in turn.

BEYOND THE PAGE

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Option volume, 1973–2011

brealey.mhhe.com/c20

Call Options and Position Diagrams

A call option gives its owner the right to buy stock at a specified exercise or strike price on or before a specified maturity date. If the option can be exercised only at maturity, it is conventionally known as a European call; in other cases (such as the Apple options shown in Table 20.1), the option can be exercised on or at any time before maturity, and it is then known as an American call.

The third column of Table 20.1 sets out the prices of Apple call options with different exercise prices and exercise dates. Look at the quotes for options maturing in December 2011. The first entry says that for $69.30 you could acquire an option to buy one share³ of Apple stock for $340 on or before December 2011. Moving down to the next row, you can see that an option to buy for $30 more ($370 vs. $340) costs $25 less, that is $44.30. In general, the value of a call option goes down as the exercise price goes up.

   TABLE 20.1 Selected prices of put and call options on Apple stock in October 2011, when the closing stock price was about $400.

aLong-term options are called “LEAPS.”

Source: Yahoo! Finance, finance.yahoo.com

Now look at the quotes for options maturing in April 2012 and January 2013. Notice how the option price increases as option maturity is extended. For example, at an exercise price of $400, the December 2011 call option costs $24.30, the April 2012 option costs $44.05, and the January 2013 option costs $70.00.

In Chapter 13 we met Louis Bachelier, who in 1900 first suggested that security prices follow a random walk. Bachelier also devised a very convenient shorthand to illustrate the effects of investing in different options. We use this shorthand to compare a call option and a put option on Apple stock.

The position diagram in Figure 20.1(a) shows the possible consequences of investing in Apple April 2012 call options with an exercise price of $400 (boldfaced in Table 20.1). The outcome from investing in Apple calls depends on what happens to the stock price. If the stock price at the end of this six-month period turns out to be less than the $400 exercise price, nobody will pay $400 to obtain the share via the call option. Your call will in that case be valueless. On the other hand, if the stock price turns out to be greater than $400, it will pay to exercise your option to buy the share. In this case, when the call expires, it will be worth the market price of the share minus the $400 that you must pay to acquire it. For example, suppose that the price of Apple stock rises to $470. Your call will then be worth $470 – $400 = $70. That is your payoff, but of course it is not all profit. Table 20.1 shows that you had to pay $44.05 to buy the call.

   FIGURE 20.1 Position diagrams show how payoffs to owners of Apple calls and puts (shown by the colored lines) depend on the share price. (a) Result of buying Apple call exercisable at $400. (b) Result of buying Apple put exercisable at $400.

Put Options

Now let us look at the Apple put options in the right-hand column of Table 20.1. Whereas a call option gives you the right to buy a share for a specified exercise price, a put gives you the right to sell the share. For example, the boldfaced entry in the right-hand column of Table 20.1 shows that for $37.15 you could acquire an option to sell Apple stock for a price of $400 anytime before April 2012. The circumstances in which the put turns out to be profitable are just the opposite of those in which the call is profitable. You can see this from the position diagram in Figure 20.1(b). If Apple’s share price immediately before expiration turns out to be greater than $400, you won’t want to sell stock at that price. You would do better to sell the share in the market, and your put option will be worthless. Conversely, if the share price turns out to be less than $400, it will pay to buy stock at the low price and then take advantage of the option to sell it for $400. In this case, the value of the put option on the exercise date is the difference between the $400 proceeds of the sale and the market price of the share. For example, if the share is worth $310, the put is worth $90:

Selling Calls, Puts, and Shares

Let us now look at the position of an investor who sells these investments. If you sell, or “write,” a call, you promise to deliver shares if asked to do so by the call buyer. In other words, the buyer’s asset is the seller’s liability. If the share price is below the exercise price when the option matures, the buyer will not exercise the call and the seller’s liability will be zero. If it rises above the exercise price, the buyer will exercise and the seller must give up the shares. The seller loses the difference between the share price and the exercise price received from the buyer. Notice that it is the buyer who always has the option to exercise; option sellers simply do as they are told.

Suppose that the price of Apple stock turns out to be $470, which is above the option’s exercise price of $400. In this case the buyer will exercise the call. The seller is forced to sell stock worth $470 for only $400 and so has a payoff of – $70.⁴ Of course, that $70 loss is the buyer’s gain. Figure 20.2(a) shows how the payoffs to the seller of the Apple call option vary with the stock price. Notice that for every dollar the buyer makes, the seller loses a dollar. Figure 20.2(a) is just Figure 20.1(a) drawn upside down.

In just the same way we can depict the position of an investor who sells, or writes, a put by standing Figure 20.1(b) on its head. The seller of the put has agreed to pay $400 for the share if the buyer of the put should request it. Clearly the seller will be safe as long as the share price remains above $400 but will lose money if the share price falls below this figure. The worst thing that can happen is that the stock becomes worthless. The seller would then be obliged to pay $400 for a stock worth $0. The payoff to the option position would be – $400.

   FIGURE 20.2 Payoffs to sellers of Apple calls and puts (shown by the colored lines) depend on the share price. (a) Result of selling Apple call exercisable at $400. (b) Result of selling Apple put exercisable at $400.

Position Diagrams Are Not Profit Diagrams

Position diagrams show only the payoffs at option exercise; they do not account for the initial cost of buying the option or the initial proceeds from selling it.

This is a common point of confusion. For example, the position diagram in Figure 20.1(a) makes purchase of a call look like a sure thing—the payoff is at worst zero, with plenty of upside if Apple’s stock price goes above $400 by April 2012. But compare the profit diagram in Figure 20.3(a), which subtracts the $44.05 cost of the call in October 2011 from the payoff at maturity. The call buyer loses money at all share prices less than $400 + 44.05 = $444.05. Take another example: The position diagram in Figure 20.2(b) makes selling a put look like a sure loss—the best payoff is zero. But the profit diagram in Figure 20.3(b), which recognizes the $37.15 received by the seller, shows that the seller gains at all prices above $400 – 37.15 = $362.85.⁵

   FIGURE 20.3 Profit diagrams incorporate the costs of buying an option or the proceeds from selling one. In panel (a), we subtract the $44.05 cost of the Apple call from the payoffs plotted in Figure 20.1(a). In panel (b), we add the $37.15 proceeds from selling the Apple put to the payoffs in Figure 20.2(b).

Profit diagrams like those in Figure 20.3 may be helpful to the options beginner, but options experts rarely draw them.⁶ Now that you’ve graduated from the first options class we won’t draw them either. We stick to position diagrams, because you have to focus on payoffs at exercise to understand options and to value them properly.

 20-2   Financial Alchemy with Options

Look now at Figure 20.4(a), which shows the payoff if you buy Apple stock at $400. You gain dollar-for-dollar if the stock price goes up and you lose dollar-for-dollar if it falls. That’s trite; it doesn’t take a genius to draw a 45-degree line.

Look now at panel (b), which shows the payoffs from an investment strategy that retains the upside potential of Apple stock but gives complete downside protection. In this case your payoff stays at $400 even if the Apple stock price falls to $300, $100, or zero. Panel (b)’s payoffs are clearly better than panel (a)’s. If a financial alchemist could turn panel (a) into panel (b), you’d be willing to pay for the service.

Of course alchemy has its dark side. Panel (c) shows an investment strategy for masochists. You lose if the stock price falls, but you give up any chance of profiting from a rise in the stock price. If you like to lose, or if someone pays you enough to take the strategy on, this is the investment for you.

   FIGURE 20.4 Payoffs at the end of six months to three investment strategies for Apple stock. (a) You buy one share for $400. (b) No downside. If stock price falls, your payoff stays at $400. (c) A strategy for masochists? You lose if stock price falls, but you don’t gain if it rises.

Now, as you have probably suspected, all this financial alchemy is for real. You can do both the transmutations shown in Figure 20.4. You do them with options, and we will show you how.

Consider first the strategy for masochists. The first diagram in Figure 20.5 shows the payoffs from buying a share of Apple stock, while the second shows the payoffs from selling a call option with a $400 exercise price. The third diagram shows what happens if you combine these two positions. The result is the no-win strategy that we depicted in panel (c) of Figure 20.4. You lose if the stock price declines below $400, but, if the stock price rises above $400, the owner of the call will demand that you hand over your stock for the $400 exercise price. So you lose on the downside and give up any chance of a profit. That’s the bad news. The good news is that you get paid for taking on this liability. In October 2011 you would have been paid $44.05, the price of a six-month call option.

Now, we’ll create the downside protection shown in Figure 20.4(b). Look at row 1 of Figure 20.6. The first diagram again shows the payoff from buying a share of Apple stock, while the next diagram in row 1 shows the payoffs from buying an Apple put option with an exercise price of $400. The third diagram shows the effect of combining these two positions. You can see that, if Apple’s stock price rises above $400, your put option is valueless, so you simply receive the gains from your investment in the share. However, if the stock price falls below $400, you can exercise your put option and sell your stock for $400. Thus, by adding a put option to your investment in the stock, you have protected yourself against loss.⁷ This is the strategy that we depicted in panel (b) of Figure 20.4. Of course, there is no gain without pain. The cost of insuring yourself against loss is the amount that you pay for a put option on Apple stock with an exercise price of $400. In October 2011 the price of this put was $37.15. This was the going rate for financial alchemists.

We have just seen how put options can be used to provide downside protection. We now show you how call options can be used to get the same result. This is illustrated in row 2 of Figure 20.6. The first diagram shows the payoff from placing the present value of $400 in a bank deposit. Regardless of what happens to the price of Apple stock, your bank deposit will pay off $400. The second diagram in row 2 shows the payoff from a call option on Apple stock with an exercise price of $400, and the third diagram shows the effect of combining these two positions. Notice that, if the price of Apple stock falls, your call is worthless, but you still have your $400 in the bank. For every dollar that Apple stock price rises above $400, your investment in the call option pays off an extra dollar. For example, if the stock price rises to $470, you will have $400 in the bank and a call worth $70. Thus you participate fully in any rise in the price of the stock, while being fully protected against any fall. So we have just found another way to provide the downside protection depicted in panel (b) of Figure 20.4.

   FIGURE 20.5 You can use options to create a strategy where you lose if the stock price falls but do not gain if it rises (strategy [c] in Figure 20.4).

   FIGURE 20.6 Each row in the figure shows a different way to create a strategy where you gain if the stock price rises but are protected on the downside (strategy [b] in Figure 20.4).

These two rows of Figure 20.6 tell us something about the relationship between a call option and a put option. Regardless of the future stock price, both investment strategies provide identical payoffs. In other words, if you buy the share and a put option to sell it for $400, you receive the same payoff as from buying a call option and setting enough money aside to pay the $400 exercise price. Therefore, if you are committed to holding the two packages until the options expire, the two packages should sell for the same price today. This gives us a fundamental relationship for European options:

To repeat, this relationship holds because the payoff of

is identical to the payoff from

This basic relationship among share price, call and put values, and the present value of the exercise price is called put–call parity.⁹

Put–call parity can be expressed in several ways. Each expression implies two investment strategies that give identical results. For example, suppose that you want to solve for the value of a put. You simply need to twist the put–call parity formula around to give

From this expression you can deduce that

is identical to

In other words, if puts are not available, you can get exactly the same payoff by buying calls, putting cash in the bank, and selling shares.

   FIGURE 20.7 A strategy of buying a call, depositing the present value of the exercise price in the bank, and selling the stock is equivalent to buying a put.

If you find this difficult to believe, look at Figure 20.7, which shows the possible payoffs from each position. The diagram on the left shows the payoffs from a call option on Apple stock with an exercise price of $400. The second diagram shows the payoffs from placing the present value of $400 in the bank. Regardless of what happens to the share price, this investment will pay off $400. The third diagram shows the payoffs from selling Apple stock. When you sell a share that you don’t own, you have a liability—you must sometime buy it back. As they say on Wall Street:

He who sells what isn’t his’n
Buys it back or goes to pris’n

Therefore the best that can happen to you is that the share price falls to zero. In that case it costs you nothing to buy the share back. But for every extra dollar on the future share price, you will need to spend an extra dollar to buy the share. The final diagram in Figure 20.7 shows that the total payoff from these three positions is the same as if you had bought a put option. For example, suppose that when the option matures the stock price is $370. Your call will be worthless, your bank deposit will be worth $400, and it will cost you $370 to repurchase the share. Your total payoff is 0 + 400 – 370 = $30, exactly the same as the payoff from the put.

If two investments offer identical payoffs, then they should sell for the same price today. If the law of one price is violated, you have a potential arbitrage opportunity. So let’s check whether there are any arbitrage profits to be made from our Apple calls and puts. In October 2011 the price of a six-month call with a $400 exercise price was $44.05, the interest rate was 3.5%, and the price of Apple stock was $400. Therefore the cost of a homemade put was

This is almost exactly the same as it would have cost you to buy a put directly.

Spotting the Option

Options rarely come with a large label attached. Often the trickiest part of the problem is to identify the option. When you are not sure whether you are dealing with a put or a call or a complicated blend of the two, it is a good precaution to draw a position diagram. Here is an example.

The Flatiron and Mangle Corporation has offered its president, Ms. Higden, the following incentive scheme: At the end of the year Ms. Higden will be paid a bonus of $50,000 for every dollar that the price of Flatiron stock exceeds its current figure of $120. However, the maximum bonus that she can receive is set at $2 million.

You can think of Ms. Higden as owning 50,000 tickets, each of which pays nothing if the stock price fails to beat $120. The value of each ticket then rises by $1 for each dollar rise in the stock price up to the maximum of $2,000,000/50,000 = $40. Figure 20.8 shows the payoffs from just one of these tickets. The payoffs are not the same as those of the simple put and call options that we drew in Figure 20.1, but it is possible to find a combination of options that exactly replicates Figure 20.8. Before going on to read the answer, see if you can spot it yourself. (If you are someone who enjoys puzzles of the make-a-triangle-from-just-two-matchsticks type, this one should be a walkover.)

The answer is in Figure 20.9. The solid black line represents the purchase of a call option with an exercise price of $120, and the dotted line shows the sale of another call option with an exercise price of $160. The colored line shows the payoffs from a combination of the purchase and the sale—exactly the same as the payoffs from one of Ms. Higden’s tickets.

Thus, if we wish to know how much the incentive scheme is costing the company, we need to calculate the difference between the value of 50,000 call options with an exercise price of $120 and the value of 50,000 calls with an exercise price of $160.

   FIGURE 20.8 The payoff from one of Ms. Higden’s “tickets” depends on Flatiron’s stock price.

   FIGURE 20.9 The solid black line shows the payoff from buying a call with an exercise price of $120. The dotted line shows the sale of a call with an exercise price of $160. The combined purchase and sale (shown by the colored line) is identical to one of Ms. Higden’s “tickets.”

We could have made the incentive scheme depend in a much more complicated way on the stock price. For example, the bonus could peak at $2 million and then fall steadily back to zero as the stock price climbs above $160.¹⁰ You could still have represented this scheme as a combination of options. In fact, we can state a general theorem:

Any set of contingent payoffs—that is, payoffs that depend on the value of some other asset—can be constructed with a mixture of simple options on that asset.

In other words, you can create any position diagram—with as many ups and downs or peaks and valleys as your imagination allows—by buying or selling the right combinations of puts and calls with different exercise prices.¹¹

Finance pros often talk about financial engineering, which is the practice of packaging different investments to create new tailor-made instruments. Perhaps a German company would like to set a minimum and maximum cost at which it can buy dollars in six-months’ time. Or perhaps an oil company would like to pay a lower rate of interest on its debt if the price of oil falls. Options provide the building blocks that financial engineers use to create these interesting payoff structures.

 20-3   What Determines Option Values?

So far we have said nothing about how the market value of an option is determined. We do know what an option is worth when it matures, however. Consider, for instance, our earlier example of an option to buy Apple stock at $400. If Apple’s stock price is below $400 on the exercise date, the call will be worthless; if the stock price is above $400, the call will be worth $400 less than the value of the stock. This relationship is depicted by the heavy, lower line in Figure 20.10.

Even before maturity the price of the option can never remain below the heavy, lower-bound line in Figure 20.10. For example, if our option were priced at $10 and the stock were priced at $430, it would pay any investor to sell the stock and then buy it back by purchasing the option and exercising it for an additional $400. That would give an arbitrage opportunity with a profit of $20. The demand for options from investors seeking to exploit this opportunity would quickly force the option price up, at least to the heavy line in the figure. For options that still have some time to run, the heavy line is therefore a lower bound on the market price of the option. Option geeks express the same idea more concisely when they write Lower bound = max(stock price – exercise price, 0).

The diagonal line in Figure 20.10 is the upper bound to the option price. Why? Because the option cannot give a higher ultimate payoff than the stock. If at the option’s expiration the stock price ends up above the exercise price, the option is worth the stock price less the exercise price. If the stock price ends up below the exercise price, the option is worthless, but the stock’s owner still has a valuable security. For example, if the option’s exercise price is $400, then the extra dollar returns realized by stockholders are shown in the following table:

   FIGURE 20.10 Value of a call before its expiration date (dashed line). The value depends on the stock price. It is always worth more than its value if exercised now (heavy line). It is never worth more than the stock price itself.

If the stock and the option have the same price, everyone will rush to sell the option and buy the stock. Therefore, the option price must be somewhere in the shaded region of Figure 20.10. In fact, it will lie on a curved, upward-sloping line like the dashed curve shown in the figure. This line begins its travels where the upper and lower bounds meet (at zero). Then it rises, gradually becoming parallel to the upward-sloping part of the lower bound.

But let us look more carefully at the shape and location of the dashed line. Three points, A, B, and C, are marked on the dashed line. As we explain each point you will see why the option price has to behave as the dashed line predicts.

Point A When the stock is worthless, the option is worthless. A stock price of zero means that there is no possibility the stock will ever have any future value.¹² If so, the option is sure to expire unexercised and worthless, and it is worthless today.

That brings us to our first important point about option value:

The value of an option increases as stock price increases, if the exercise price is held constant.

That should be no surprise. Owners of call options clearly hope for the stock price to rise and are happy when it does.

Point B When the stock price becomes large, the option price approaches the stock price less the present value of the exercise price. Notice that the dashed line representing the option price in Figure 20.10 eventually becomes parallel to the ascending heavy line representing the lower bound on the option price. The reason is as follows: The higher the stock price, the higher is the probability that the option will eventually be exercised. If the stock price is high enough, exercise becomes a virtual certainty; the probability that the stock price will fall below the exercise price before the option expires becomes trivially small.

If you own an option that you know will be exchanged for a share of stock, you effectively own the stock now. The only difference is that you don’t have to pay for the stock (by handing over the exercise price) until later, when formal exercise occurs. In these circumstances, buying the call is equivalent to buying the stock but financing part of the purchase by borrowing. The amount implicitly borrowed is the present value of the exercise price. The value of the call is therefore equal to the stock price less the present value of the exercise price.

This brings us to another important point about options. Investors who acquire stock by way of a call option are buying on credit. They pay the purchase price of the option today, but they do not pay the exercise price until they actually take up the option. The delay in payment is particularly valuable if interest rates are high and the option has a long maturity.

Thus, the value of an option increases with both the rate of interest and the time to maturity.

Point C The option price always exceeds its minimum value (except when stock price is zero). We have seen that the dashed and heavy lines in Figure 20.10 coincide when stock price is zero (point A), but elsewhere the lines diverge; that is, the option price must exceed the minimum value given by the heavy line. The reason for this can be understood by examining point C.

At point C, the stock price exactly equals the exercise price. The option is therefore worthless if exercised today. However, suppose that the option will not expire until three months hence. Of course we do not know what the stock price will be at the expiration date. There is roughly a 50% chance that it will be higher than the exercise price and a 50% chance that it will be lower. The possible payoffs to the option are therefore

If there is a positive probability of a positive payoff, and if the worst payoff is zero, then the option must be valuable. That means the option price at point C exceeds its lower bound, which at point C is zero. In general, the option prices will exceed their lower-bound values as long as there is time left before expiration.

One of the most important determinants of the height of the dashed curve (i.e., of the difference between actual and lower-bound value) is the likelihood of substantial movements in the stock price. An option on a stock whose price is unlikely to change by more than 1% or 2% is not worth much; an option on a stock whose price may halve or double is very valuable.

As an option holder, you gain from volatility because the payoffs are not symmetric. If the stock price falls below the exercise price, your call option will be worthless, regardless of whether the shortfall is a few cents or many dollars. On the other hand, for every dollar that the stock price rises above the exercise price, your call will be worth an extra dollar. Therefore, the option holder gains from the increased volatility on the upside, but does not lose on the downside.

A simple example may help to illustrate the point. Consider two stocks, X and Y, each of which is priced at $100. The only difference is that the outlook for Y is much less easy to predict. There is a 50% chance that the price of Y will rise to $150 and a similar chance that it will fall to $70. By contrast, there is a 50-50 chance that the price of X will either rise to $130 or fall to $90.

Suppose that you are offered a call option on each of these stocks with an exercise price of $100. The following table compares the possible payoffs from these options:

In both cases there is a 50% chance that the stock price will decline and make the option worthless but, if the stock price rises, the option on Y will give the larger payoff. Since the chance of a zero payoff is the same, the option on Y is worth more than the option on X.

Of course, in practice future stock prices may take on a range of different values. We have recognized this in Figure 20.11, where the uncertain outlook for Y’s stock price shows up in the wider probability distribution of future prices.¹³ The greater spread of outcomes for stock Y again provides more upside potential and therefore increases the chance of a large payoff on the option.

   FIGURE 20.11 Call options on the shares of (a) firm X and (b) firm Y. In each case, the current share price equals the exercise price, so each option has a 50% chance of ending up worthless (if the share price falls) and a 50% chance of ending up “in the money” (if the share price rises). However, the chance of a large payoff is greater for the option on firm Y’s shares because Y’s stock price is more volatile and therefore has more upside potential.

Figure 20.12 shows how volatility affects the value of an option. The upper curved line depicts the value of the Apple call option assuming that Apple’s stock price, like that of stock Y, is highly variable. The lower curved line assumes a lower (and more realistic) degree of volatility.¹⁴

The probability of large stock price changes during the remaining life of an option depends on two things: (1) the variance (i.e., volatility) of the stock price per period and (2) the number of periods until the option expires. If there are t remaining periods, and the variance per period is σ2, the value of the option should depend on cumulative variability σ2t.¹⁵ Other things equal, you would like to hold an option on a volatile stock (high σ2). Given volatility, you would like to hold an option with a long life ahead of it (large t).

   FIGURE 20.12 How the value of the Apple call option increases with the volatility of the stock price. Each of the curved lines shows the value of the option for different initial stock prices. The only difference is that the upper line assumes a much higher level of uncertainty about Apple’s future stock price.

Thus the value of an option increases with both the volatility of the share price and the time to maturity.

It’s a rare person who can keep all these properties straight at first reading. Therefore, we have summed them up in Table 20.2.

Risk and Option Values

In most financial settings, risk is a bad thing; you have to be paid to bear it. Investors in risky (high-beta) stocks demand higher expected rates of return. High-risk capital investment projects have correspondingly high costs of capital and have to beat higher hurdle rates to achieve positive NPV.

For options it’s the other way around. As we have just seen, options written on volatile assets are worth more than options written on safe assets. If you can understand and remember that one fact about options, you’ve come a long way.

   TABLE 20.2 What the price of a call option depends on.

*The direct effect of increases in rf or σ on option price, given the stock price. There may also be indirect effects. For example, an increase in rf could reduce stock price P. This in turn could affect option price.

EXAMPLE 20.1 • Volatility and Executive Stock Options

Suppose you have to choose between two job offers, as CFO of either Establishment Industries or Digital Organics. Establishment Industries’ compensation package includes a grant of the stock options described on the left side of Table 20.3. You demand a similar package from Digital Organics, and they comply. In fact they match the Establishment Industries options in every respect, as you can see on the right side of Table 20.3. (The two companies’ current stock prices just happen to be the same.) The only difference is that Digital Organics’ stock is 50% more volatile than Establishment Industries’ stock (36% annual standard deviation versus 24% for Establishment Industries).

If your job choice hinges on the value of the executive stock options, you should take the Digital Organics offer. The Digital Organics options are written on the more volatile asset and therefore are worth more.

We value the two stock-option packages in the next chapter.

   TABLE 20.3 Which package of executive stock options would you choose? The package offered by Digital Organics is more valuable, because the volatility of that company’s stock is higher.

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SUMMARY

If you have managed to reach this point, you are probably in need of a rest and a stiff gin and tonic. So we will summarize what we have learned so far and take up the subject of options again in the next chapter when you are rested (or drunk).

There are two types of option. An American call is an option to buy an asset at a specified exercise price on or before a specified maturity date. Similarly, an American put is an option to sell the asset at a specified price on or before a specified date. European calls and puts are exactly the same except that they cannot be exercised before the specified maturity date. Calls and puts are the basic building blocks that can be combined to give any pattern of payoffs.

What determines the value of a call option? Common sense tells us that it ought to depend on three things:

1.  To exercise an option you have to pay the exercise price. Other things being equal, the less you are obliged to pay, the better. Therefore, the value of a call option increases with the ratio of the asset price to the exercise price.

2.  You do not have to pay the exercise price until you decide to exercise the option. Therefore, a call option gives you a free loan. The higher the rate of interest and the longer the time to maturity, the more this free loan is worth. So the value of a call option increases with the interest rate and time to maturity.

3.  If the price of the asset falls short of the exercise price, you won’t exercise the call option. You will, therefore, lose 100% of your investment in the option no matter how far the asset depreciates below the exercise price. On the other hand, the more the price rises above the exercise price, the more profit you will make. Therefore the option holder does not lose from increased volatility if things go wrong, but gains if they go right. The value of an option increases with the variance per period of the stock return multiplied by the number of periods to maturity.

Always remember that an option written on a risky (high-variance) asset is worth more than an option on a safe asset. It’s easy to forget, because in most other financial contexts increases in risk reduce present value.

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FURTHER READING

See Further Readings for Chapter 21.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Vocabulary Complete the following passage:

A _________ option gives its owner the opportunity to buy a stock at a specified price that is generally called the _________ price. A _________ option gives its owner the opportunity to sell stock at a specified price. Options that can be exercised only at maturity are called _________ options.

2.  Option payoffs Note Figure 20.13 below. Match each diagram, (a) and (b), with one of the following positions:

• Call buyer

• Call seller

• Put buyer

• Put seller

   FIGURE 20.13 See Problem 2.

3.  Option payoffs Suppose that you hold a share of stock and a put option on that share. What is the payoff when the option expires if (a) the stock price is below the exercise price? (b) the stock price is above the exercise price?

4.  Put–call parity What is put–call parity and why does it hold? Could you apply the parity formula to a call and put with different exercise prices?

5.  Put–call parity There is another strategy involving calls and borrowing or lending that gives the same payoffs as the strategy described in Problem 3. What is the alternative strategy?

6.  Option payoffs Dr. Livingstone I. Presume holds £600,000 in East African gold stocks. Bullish as he is on gold mining, he requires absolute assurance that at least £500,000 will be available in six months to fund an expedition. Describe two ways for Dr. Presume to achieve this goal. There is an active market for puts and calls on East African gold stocks, and the rate of interest is 6% per year.

7.  Option payoffs Suppose you buy a one-year European call option on Wombat stock with an exercise price of $100 and sell a one-year European put option with the same exercise price. The current stock price is $100, and the interest rate is 10%.

a.  Draw a position diagram showing the payoffs from your investments.

b.  How much will the combined position cost you? Explain.

8.  Option payoffs Look again at Figure 20.13. It appears that the investor in panel (b) can’t lose and the investor in panel (a) can’t win. Is that correct? Explain. (Hint: Draw a profit diagram for each panel.)

9.  Option payoffs What is a call option worth if (a) the stock price is zero? (b) the stock price is extremely high relative to the exercise price?

10.  Option values How does the price of a call option respond to the following changes, other things equal? Does the call price go up or down?

a.  Stock price increases.

b.  Exercise price is increased.

c.  Risk-free rate increases.

d.  Expiration date of the option is extended.

e.  Volatility of the stock price falls.

f.  Time passes, so the option’s expiration date comes closer.

11.  Option values Respond to the following statements.

a.  “I’m a conservative investor. I’d much rather hold a call option on a safe stock like Exxon Mobil than a volatile stock like Apple.”

b.  “I bought an American call option on Fava Farms stock, with an exercise price of $45 per share and three more months to maturity. Fava Farms’ stock has skyrocketed from $35 to $55 per share, but I’m afraid it will fall back below $45. I’m going to lock in my gain and exercise my call right now.”

INTERMEDIATE

12.  Option payoffs Discuss briefly the risks and payoffs of the following positions:

a.  Buy stock and a put option on the stock.

b.  Buy stock.

c.  Buy call.

d.  Buy stock and sell call option on the stock.

e.  Buy bond.

f.  Buy stock, buy put, and sell call.

g.  Sell put.

13.  Option payoffs “The buyer of the call and the seller of the put both hope that the stock price will rise. Therefore the two positions are identical.” Is the speaker correct? Illustrate with a position diagram.

14.  Option bounds Atacama Autos stock price is currently 200 pesos. A one-year American call option has an exercise price of 50 pesos and is priced at 75 pesos. How would you take advantage of this great opportunity? Now suppose the option is a European call. What would you do?

15.  Put–call parity It is possible to buy three-month call options and three-month puts on stock Q. Both options have an exercise price of $60 and both are worth $10. If the interest rate is 5% a year, what is the stock price? (Hint: Use put–call parity.)

16.  Put–call parity In October 2011, a 15-month call on the stock of Amazon.com, with an exercise price of $230, sold for $46.97. The stock price was $230. The risk-free interest rate was 3%. How much would you be willing to pay for a put on Amazon stock with the same maturity and exercise price? Assume that the Amazon options are European options. (Note: Amazon does not pay a dividend.)

17.  Option values FX Bank has succeeded in hiring ace foreign exchange trader Lucinda Cable for its London office. Her remuneration package reportedly includes an annual bonus of 20% of the profits that she generates in excess of £100 million. Does Ms. Cable have an option? Does it provide her with the appropriate incentives?

18.  Option payoffs Suppose that Enrico Colleoni borrows the present value of €100, buys a six-month put option on stock Y with an exercise price of €150, and sells a six-month put option on Y with an exercise price of €50.

a.  Draw a position diagram showing the payoffs when the options expire.

b.  Suggest two other combinations of loans, options, and the underlying stock that would give S. Colleoni the same payoffs.

19.  Put–call parity Which one of the following statements is correct?

a.  Value of put + present value of exercise price = value of call + share price

b.  Value of put + share price = value of call + present value of exercise price

c.  Value of put – share price = present value of exercise price – value of call

d.  Value of put + value of call = share price – present value of exercise price

The correct statement equates the value of two investment strategies. Plot the payoffs to each strategy as a function of the stock price. Show that the two strategies give identical payoffs.

20.  Put–call parity Test the formula linking put and call prices by using it to explain the relative prices of actual traded puts and calls. (Note: The formula is exact only for European options. Most traded puts and calls are American.)

21.  Put–call parity

a.  If you can’t sell a share short, you can achieve exactly the same final payoff by a combination of options and borrowing or lending. What is this combination?

b.  Now work out the mixture of stock and options that gives the same final payoff as investment in a risk-free loan.

22.  Put–call parity The common stock of Triangular File Company is selling at $90. A 26-week call option written on Triangular File’s stock is selling for $8. The call’s exercise price is $100. The risk-free interest rate is 10% per year.

a.  Suppose that puts on Triangular stock are not traded, but you want to buy one. How would you do it?

b.  Suppose that puts are traded. What should a 26-week put with an exercise price of $100 sell for?

23.  Option payoffs Ms. Higden has been offered yet another incentive scheme (see Section 20-2). She will receive a bonus of $500,000 if the stock price at the end of the year is $120 or more; otherwise she will receive nothing. (Don’t ask why anyone should want to offer such an arrangement. Maybe there’s some tax angle.)

a.  Draw a position diagram illustrating the payoffs from such a scheme.

b.  What combination of options would provide these payoffs? (Hint: You need to buy a large number of options with one exercise price and sell a similar number with a different exercise price.)

24.  Option payoffs Option traders often refer to “straddles” and “butterflies.” Here is an example of each:

• Straddle: Buy one call with exercise price of $100 and simultaneously buy one put with exercise price of $100.

• Butterfly: Simultaneously buy one call with exercise price of $100, sell two calls with exercise price of $110, and buy one call with exercise price of $120.

Draw position diagrams for the straddle and butterfly, showing the payoffs from the investor’s net position. Each strategy is a bet on variability. Explain briefly the nature of each bet.

25.  Option values Look at actual trading prices of call options on stocks to check whether they behave as the theory presented in this chapter predicts. For example,

a.  Follow several options as they approach maturity. How would you expect their prices to behave? Do they actually behave that way?

b.  Compare two call options written on the same stock with the same maturity but different exercise prices.

c.  Compare two call options written on the same stock with the same exercise price but different maturities.

26.  Option values Is it more valuable to own an option to buy a portfolio of stocks or to own a portfolio of options to buy each of the individual stocks? Say briefly why.

27.  Option values Table 20.4 lists some prices of options on common stocks (prices are quoted to the nearest dollar). The interest rate is 10% a year. Can you spot any mispricing? What would you do to take advantage of it?

28.  Option values You’ve just completed a month-long study of energy markets and conclude that energy prices will be much more volatile in the next year than historically. Assuming you’re right, what types of option strategies should you undertake? (Note: You can buy or sell options on oil-company stocks or on the price of future deliveries of crude oil, natural gas, fuel oil, etc.)

29.  Put-call parity In November 2012 the stock of Australia and New Zealand Banking Group (ANZ) was trading at A$23.50. Suppose you buy a one-year European call option on the stock and sell a one-year European put. The put and call have the same exercise price of A$22 and the one-year interest rate is 6.5%. What is the net cost of buying the call and selling the put? How does your answer change (other things equal) if the interest rate increases to 7.5% or the stock price increases to A$25?

   TABLE 20.4 Prices of options on common stocks (in dollars). See Problem 27.

30.  Index calls Almost every country that has a stock market has a stock-market index and call options traded on the index. What factors should make index calls more expensive in some countries versus others? Assume the calls are at the money (exercise price = index level) and for six-month maturities.

CHALLENGE

31.  Option payoffs Figure 20.14 on the next page shows some complicated position diagrams. Work out the combination of stocks, bonds, and options that produces each of these positions.

32.  Option payoffs Some years ago the Australian firm Bond Corporation sold a share in some land that it owned near Rome for $110 million and as a result boosted its annual earnings by $74 million. A television program subsequently revealed that the buyer was given a put option to sell its share in the land back to Bond for $110 million and that Bond had paid $20 million for a call option to repurchase the share in the land for the same price.

a.  What happens if the land is worth more than $110 million when the options expire? What if it is worth less than $110 million?

b.  Use position diagrams to show the net effect of the land sale and the option transactions.

c.  Assume a one-year maturity on the options. Can you deduce the interest rate?

d.  The television program argued that it was misleading to record a profit on the sale of land. What do you think?

33.  Option values Three six-month call options are traded on Hogswill stock:

How would you make money by trading in Hogswill options? (Hint: Draw a graph with the option price on the vertical axis and the ratio of stock price to exercise price on the horizontal axis. Plot the three Hogswill options on your graph. Does this fit with what you know about how option prices should vary with the ratio of stock price to exercise price?) Now look in the newspaper at options with the same maturity but different exercise prices. Can you find any money-making opportunities?

   FIGURE 20.14 Some complicated position diagrams. See Problem 29.

34.  Option payoffs Digital Organics has 10 million outstanding shares trading at $25 per share. It also has a large amount of debt outstanding, all coming due in one year. The debt pays interest at 8%. It has a par (face) value of $350 million, but is trading at a market value of only $280 million. The one-year risk-free interest rate is 6%.

a.  Write out the put–call parity formula for Digital Organics’ stock, debt, and assets.

b.  What is the value of the company’s option to default on its debt?

35.  Short sales and options pricing During the financial crisis of 2007–2009, some European companies argued strenuously that short-selling should be restricted in order to prevent speculators from driving down stock prices. Would restrictions on short-selling cause problems for trading in options? Hint: Suppose that investors want to sell calls to option dealers. How will the dealers hedge their positions?

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FINANCE ON THE WEB

Go to finance.yahoo.com. Check out the delayed quotes for Apple for different exercise prices and maturities.

a.  Confirm that higher exercise prices mean lower call prices and higher put prices.

b.  Confirm that longer maturity means higher prices for both puts and calls.

c.  Choose an Apple put and call with the same exercise price and maturity. Confirm that put–call parity holds (approximately). (Note: You will have to use an up-to-date risk-free interest rate.)

___________

¹In Chapter 11 we valued Kingsley Solomon’s gold mine by calculating the value of the gold in the ground and then subtracting the value of the extraction costs. That is correct only if we know that the gold will be mined. Otherwise, the value of the mine is increased by the value of the option to leave the gold in the ground if its price is less than the extraction cost.

²The two principal options exchanges in the United States are the International Securities Exchange (ISE) and the Chicago Board Options Exchange (CBOE).

³You can’t actually buy an option on a single share. Trades are in multiples of 100. The minimum order would be for 100 options on 100 Apple shares.

⁴The seller has some consolation, for he or she was paid $44.05 in October for selling the call.

⁵The fact that you have made a profit on your position is not necessarily a cause for rejoicing. The profit needs to compensate you for the time value of money and the risk that you took.

⁶Profit diagrams such as Figure 20.3 deduct the initial cost of the option from the final payoff. They therefore ignore the first lesson of finance—“A dollar today is worth more than a dollar in the future.”

⁷This combination of a stock and a put option is known as a protective put.

⁸The present value is calculated at the risk-free rate of interest. It is the amount that you would have to invest today in a bank deposit or Treasury bills to realize the exercise price on the option’s expiration date.

⁹Put–call parity holds only if you are committed to holding the options until the final exercise date. It therefore does not hold for American options, which you can exercise before the final date. We discuss possible reasons for early exercise in Chapter 21. Also if the stock makes a dividend payment before the final exercise date, you need to recognize that the investor who buys the call misses out on this dividend. In this case the relationship is

¹⁰This is not as nutty a bonus scheme as it may sound. Maybe Ms. Higden’s hard work can lift the value of the stock by so much and the only way she can hope to increase it further is by taking on extra risk. You can deter her from doing this by making her bonus start to decline beyond some point. Too bad that the bonus schemes for some bank CEOs did not contain this feature.

¹¹In some cases you may also have to borrow or lend money to generate a position diagram with your desired pattern. Lending raises the payoff line in position diagrams, as in the bottom row of Figure 20.6. Borrowing lowers the payoff line.

¹²If a stock can be worth something in the future, then investors will pay something for it today, although possibly a very small amount.

¹³Figure 20.11 continues to assume that the exercise price on both options is equal to the current stock price. This is not a necessary assumption. Also in drawing Figure 20.11 we have assumed that the distribution of stock prices is symmetric. This also is not a necessary assumption, and we will look more carefully at the distribution of stock prices in the next chapter.

¹⁴The option values shown in Figure 20.12 were calculated by using the Black-Scholes option-valuation model. We explain this model in Chapter 21 and use it to value the Apple option.

¹⁵Here is an intuitive explanation: If the stock price follows a random walk (see Section 13-2), successive price changes are statistically independent. The cumulative price change before expiration is the sum of t random variables. The variance of a sum of independent random variables is the sum of the variances of those variables. Thus, if σ2 is the variance of the daily price change, and there are t days until expiration, the variance of the cumulative price change is σ2t.

Part 6 Options

Valuing Options

In the last chapter we introduced you to call and put options. Call options give the owner the right to buy an asset at a specified exercise price; put options give the right to sell. We also took the first step toward understanding how options are valued. The value of a call option depends on five variables:

1.  The higher the price of the asset, the more valuable an option to buy it.

2.  The lower the price that you must pay to exercise the call, the more valuable the option.

3.  You do not need to pay the exercise price until the option expires. This delay is most valuable when the interest rate is high.

4.  If the stock price is below the exercise price at maturity, the call is valueless regardless of whether the price is $1 below or $100 below. However, for every dollar that the stock price rises above the exercise price, the option holder gains an additional dollar. Thus, the value of the call option increases with the volatility of the stock price.

5.  Finally, a long-term option is more valuable than a short-term option. A distant maturity delays the point at which the holder needs to pay the exercise price and increases the chance of a large jump in the stock price before the option matures.

In this chapter we show how these variables can be combined into an exact option-valuation model—a formula we can plug numbers into to get a definite answer. We first describe a simple way to value options, known as the binomial model. We then introduce the Black–Scholes formula for valuing options. Finally, we provide a checklist showing how these two methods can be used to solve a number of practical option problems.

The most efficient way to value most options is to use a computer. But in this chapter we will work through some simple examples by hand. We do so because unless you understand the basic principles behind option valuation, you are likely to make mistakes in setting up an option problem and you won’t know how to interpret the computer’s answer and explain it to others.

In the last chapter we looked at the put and call options on Apple stock. In this chapter we stick with that example and show you how to value the Apple options. But remember why you need to understand option valuation. It is not to make a quick buck trading on an options exchange. It is because many capital budgeting and financing decisions have options embedded in them. We discuss a variety of these options in subsequent chapters.

 21-1   A Simple Option-Valuation Model

Why Discounted Cash Flow Won’t Work for Options

For many years economists searched for a practical formula to value options until Fischer Black and Myron Scholes finally hit upon the solution. Later we will show you what they found, but first we should explain why the search was so difficult.

Our standard procedure for valuing an asset is to (1) figure out expected cash flows and (2) discount them at the opportunity cost of capital. Unfortunately, this is not practical for options. The first step is messy but feasible, but finding the opportunity cost of capital is impossible, because the risk of an option changes every time the stock price moves.

When you buy a call, you are taking a position in the stock but putting up less of your own money than if you had bought the stock directly. Thus, an option is always riskier than the underlying stock. It has a higher beta and a higher standard deviation of returns.

How much riskier the option is depends on the stock price relative to the exercise price. A call option that is in the money (stock price greater than exercise price) is safer than one that is out of the money (stock price less than exercise price). Thus a stock price increase raises the option’s price and reduces its risk. When the stock price falls, the option’s price falls and its risk increases. That is why the expected rate of return investors demand from an option changes day by day, or hour by hour, every time the stock price moves.

We repeat the general rule: The higher the stock price is relative to the exercise price, the safer is the call option, although the option is always riskier than the stock. The option’s risk changes every time the stock price changes.

Constructing Option Equivalents from Common Stocks and Borrowing

If you’ve digested what we’ve said so far, you can appreciate why options are hard to value by standard discounted-cash-flow formulas and why a rigorous option-valuation technique eluded economists for many years. The breakthrough came when Black and Scholes exclaimed, “Eureka! We have found it!¹ The trick is to set up an option equivalent by combining common stock investment and borrowing. The net cost of buying the option equivalent must equal the value of the option.”

We’ll show you how this works with a simple numerical example. We’ll travel back to October 2011 and consider a six-month call option on Apple stock with an exercise price of $400. We’ll pick a day when Apple stock was also trading at $400, so that this option is at the money. The short-term, risk-free interest rate was 3% per year.

To keep the example as simple as possible, we assume that Apple stock can do only two things over the option’s six-month life: either the price will fall by a fifth to $320 or rise by a quarter to $500.

If Apple’s stock price falls to $320, the call option will be worthless, but if the price rises to $500, the option will be worth $500 – 400 = $100. The possible payoffs to the option are therefore as follows:

Now compare these payoffs with what you would get if you bought .556 Apple shares and borrowed the present value of $177.80 from the bank:²

Notice that the payoffs from the levered investment in the stock are identical to the payoffs from the call option. Therefore, the law of one price tells us that both investments must have the same value:

Presto! You’ve valued a call option.

To value the Apple option, we borrowed money and bought stock in such a way that we exactly replicated the payoff from a call option. This is called a replicating portfolio. The number of shares needed to replicate one call is called the hedge ratio or option delta. In our Apple example one call is replicated by a levered position in .556 shares. The option delta is, therefore, .556.

How did we know that Apple’s call option was equivalent to a levered position in .556 shares? We used a simple formula that says:

You have learned not only to value a simple option but also that you can replicate an investment in the option by a levered investment in the underlying asset. Thus, if you can’t buy or sell a call option on an asset, you can create a homemade option by a replicating strategy—that is, you buy or sell delta shares and borrow or lend the balance.

Risk-Neutral Valuation Notice why the Apple call option should sell for $47.48. If the option price is higher than $47.48, you could make a certain profit by buying .556 shares of stock, selling a call option, and borrowing the present value of $177.78. Similarly, if the option price is less than $47.48, you could make an equally certain profit by selling .556 shares, buying a call, and lending the balance. In either case there would be an arbitrage opportunity.³

If there’s a possible arbitrage profit, everyone scurries to take advantage of it. So when we said that the option price had to be $47.48 or there would be an arbitrage opportunity, we did not have to know anything about investor attitudes to risk. The option price cannot depend on whether investors detest risk or do not care a jot.

This suggests an alternative way to value the option. We can pretend that all investors are indifferent about risk, work out the expected future value of the option in such a world, and discount it back at the risk-free interest rate to give the current value. Let us check that this method gives the same answer.

If investors are indifferent to risk, the expected return on the stock must be equal to the risk-free rate of interest:

We know that Apple stock can either rise by 25% to $500 or fall by 20% to $320. We can, therefore, calculate the probability of a price rise in our hypothetical risk-neutral world:

Therefore,

Notice that this is not the true probability that Apple stock will rise. Since investors dislike risk, they will almost surely require a higher expected return than the risk-free interest rate from Apple stock. Therefore the true probability is greater than .4830.

The general formula for calculating the risk-neutral probability of a rise in value is

In the case of Apple stock:

We know that if the stock price rises, the call option will be worth $100; if it falls, the call will be worth nothing. Therefore, if investors are risk-neutral, the expected value of the call option is

And the current value of the call is

Exactly the same answer that we got earlier!

We now have two ways to calculate the value of an option:

1.  Find the combination of stock and loan that replicates an investment in the option. Since the two strategies give identical payoffs in the future, they must sell for the same price today.

2.  Pretend that investors do not care about risk, so that the expected return on the stock is equal to the interest rate. Calculate the expected future value of the option in this hypothetical risk-neutral world and discount it at the risk-free interest rate. This idea may seem familiar to you. In Chapter 9 we showed how you can value an investment either by discounting the expected cash flows at a risk-adjusted discount rate or by adjusting the expected cash flows for risk and then discounting these certainty-equivalent flows at the risk-free interest rate. We have just used this second method to value the Apple option. The certainty-equivalent cash flows on the stock and option are the cash flows that would be expected in a risk-neutral world.

Valuing the Apple Put Option

Valuing the Apple call option may well have seemed like pulling a rabbit out of a hat. To give you a second chance to watch how it is done, we will use the same method to value another option—this time, the six-month Apple put option with a $400 exercise price.⁴ We continue to assume that the stock price will either rise to $500 or fall to $320.

If Apple’s stock price rises to $500, the option to sell for $400 will be worthless. If the price falls to $320, the put option will be worth $400 – 320 = $80. Thus the payoffs to the put are

We start by calculating the option delta using the formula that we presented above:⁵

Notice that the delta of a put option is always negative; that is, you need to sell delta shares of stock to replicate the put. In the case of the Apple put you can replicate the option payoffs by selling .444 Apple shares and lending the present value of $222.22. Since you have sold the share short, you will need to lay out money at the end of six months to buy it back, but you will have money coming in from the loan. Your net payoffs are exactly the same as the payoffs you would get if you bought the put option:

Since the two investments have the same payoffs, they must have the same value:

Valuing the Put Option by the Risk-Neutral Method Valuing the Apple put option with the risk-neutral method is a cinch. We already know that the probability of a rise in the stock price is .4830. Therefore the expected value of the put option in a risk-neutral world is

And therefore the current value of the put is

The Relationship between Call and Put Prices We pointed out earlier that for European options there is a simple relationship between the values of the call and the put.⁶

Since we had already calculated the value of the Apple call, we could also have used this relationship to find the value of the put:

Everything checks.

 21-2   The Binomial Method for Valuing Options

The essential trick in pricing any option is to set up a package of investments in the stock and the loan that will exactly replicate the payoffs from the option. If we can price the stock and the loan, then we can also price the option. Equivalently, we can pretend that investors are risk-neutral, calculate the expected payoff on the option in this fictitious risk-neutral world, and discount by the rate of interest to find the option’s present value.

These concepts are completely general, but the example in the last section used a simplified version of what is known as the binomial method. The method starts by reducing the possible changes in the next period’s stock price to two, an “up” move and a “down” move. This assumption that there are just two possible prices for Apple stock at the end of six months is clearly fanciful.

We could make the Apple problem a trifle more realistic by assuming that there are two possible price changes in each three-month period. This would give a wider variety of six-month prices. And there is no reason to stop at three-month periods. We could go on to take shorter and shorter intervals, with each interval showing two possible changes in Apple’s stock price and giving an even wider selection of six-month prices.

We illustrate this in Figure 21.1. The top diagram shows our starting assumption: just two possible prices at the end of six months. Moving down, you can see what happens when there are two possible price changes every three months. This gives three possible stock prices when the option matures. In Figure 21.1(c) we have gone on to divide the six-month period into 26 weekly periods, in each of which the price can make one of two small moves. The distribution of prices at the end of six months is now looking much more realistic.

We could continue in this way to chop the period into shorter and shorter intervals, until eventually we would reach a situation in which the stock price is changing continuously and there is a continuum of possible future stock prices. We demonstrate first with our simple two-step case in Figure 21.1(b). Then we work up to the situation where the stock price is changing continuously.

   FIGURE 21.1 This figure shows the possible six-month price changes for Apple stock assuming that the stock makes a single up or down move each six months (Fig. 21.1[a]), 2 moves, one every three months (Fig. 21.1[b]), or 26 moves, one every week (Fig. 21.1[c]). Beside each tree we show a histogram of the possible six-month price changes, assuming investors are risk-neutral.

Example: The Two-Step Binomial Method

Dividing the period into shorter intervals doesn’t alter the basic approach for valuing a call option. We can still find at each point a levered investment in the stock that gives exactly the same payoffs as the option. The value of the option must therefore be equal to the value of this replicating portfolio. Alternatively, we can pretend that investors are risk-neutral and expect to earn the interest rate on all their investments. We then calculate at each point the expected future value of the option and discount it at the risk-free interest rate. Both methods give the same answer.

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Try It! The two-step binomial model

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If we use the replicating-portfolio method, we must recalculate the investment in the stock at each point, using the formula for the option delta:

Recalculating the option delta is not difficult, but it can become a bit of a chore. It is simpler in this case to use the risk-neutral method, and that is what we will do.

Figure 21.2 is taken from Figure 21.1(b) and shows the possible prices of Apple stock, assuming that in each three-month period the price will either rise by 17.09% or fall by 14.60%.⁷ We show in parentheses the possible values at maturity of a six-month call option with an exercise price of $400. For example, if Apple’s stock price turns out to be $291.75 in month 6, the call option will be worthless; at the other extreme, if the stock value is $548.42, the call will be worth $548.42 – $400 = $148.42. We haven’t worked out yet what the option will be worth before maturity, so we will just put question marks there for now.

We continue to assume an interest rate of 3.5% a year, which is equivalent to .86% a quarter. We now ask: If investors demand a return of .86% a quarter, what is the probability (p) at each stage that the stock price will rise? The answer is given by our simple formula:

We can check that if there is a 48.79% chance of a rise of 17.09% and a 51.21% chance of a fall of 14.60%, then the expected return must be equal to the .86% risk-free rate:

Option Value in Month 3 Now we can find the possible option values in month 3. Suppose that at the end of three months the stock price is $468.37. In that case investors know that, when the option finally matures in month 6, the option value will be either $0 or $148.42. We can therefore use our risk-neutral probabilities to calculate the expected option value at month 6:

   FIGURE 21.2 Present and possible future prices of Apple stock assuming that in each three-month period the price will either rise by 17.09% or fall by 14.60%. Figures in parentheses show the corresponding values of a six-month call option with an exercise price of $400. The interest rate is .86% a quarter.

   FIGURE 21.3 Present and possible future prices of Apple stock. Figures in parentheses show the corresponding values of a six-month call option with an exercise price of $400.

And the value in month 3 is 72.41/1.0086 = $71.79.

What if the stock price falls to $341.61 by month 3? In that case the option is bound to be worthless at maturity. Its expected value is zero, and its value at month 3 is also zero.

Option Value Today We can now get rid of two of the question marks in Figure 21.2. Figure 21.3 shows that if the stock price in month 3 is $468.37, the option value is $71.79 and if the stock price is $341.61, the option value is zero. It only remains to work back to the option value today.

There is a 48.79% chance that the option will be worth $71.79 and a 51.21% chance that it will be valueless. So the expected value in month 3 is

And the value today is 35.03/1.0086 = $34.73.

The General Binomial Method

Moving to two steps when valuing the Apple call probably added extra realism. But there is no reason to stop there. We could go on, as in Figure 21.1, to chop the period into smaller and smaller intervals. We could still use the binomial method to work back from the final date to the present. Of course, it would be tedious to do the calculations by hand, but simple to do so with a computer.

Since a stock can usually take on an almost limitless number of future values, the binomial method gives a more realistic and accurate measure of the option’s value if we work with a large number of subperiods. But that raises an important question. How do we pick sensible figures for the up and down changes in value? For example, why did we pick figures of +17.09% and –14.6% when we revalued Apple’s option with two subperiods? Fortunately, there is a neat little formula that relates the up and down changes to the standard deviation of stock returns:

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Try It! Binomial model

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where

e = base for natural logarithms = 2.718

σ = standard deviation of (continuously compounded) stock returns

h = interval as fraction of a year

When we said that Apple’s stock price could either rise by 25% or fall by 20% over six months (h = .5), our figures were consistent with a figure of 31.56% for the standard deviation of annual returns:⁸

To work out the equivalent upside and downside changes when we divide the period into two three-month intervals (h = .25), we use the same formula:

The center columns in Table 21.1 show the equivalent up and down moves in the value of the firm if we chop the period into six monthly or 26 weekly periods, and the final column shows the effect on the estimated option value. (We explain the Black–Scholes value shortly.)

The Binomial Method and Decision Trees

Calculating option values by the binomial method is basically a process of solving decision trees. You start at some future date and work back through the tree to the present. Eventually the possible cash flows generated by future events and actions are folded back to a present value.

Is the binomial method merely another application of decision trees, a tool of analysis that you learned about in Chapter 10? The answer is no, for at least two reasons. First, option pricing theory is absolutely essential for discounting within decision trees. Discounting expected cash flows doesn’t work within decision trees for the same reason that it doesn’t work for puts and calls. As we pointed out in Section 21-1, there is no single, constant discount rate for options because the risk of the option changes as time and the price of the underlying asset change. There is no single discount rate inside a decision tree, because if the tree contains meaningful future decisions, it also contains options. The market value of the future cash flows described by the decision tree has to be calculated by option pricing methods.

   TABLE 21.1 As the number of steps is increased, you must adjust the range of possible changes in the value of the asset to keep the same standard deviation. But you will get increasingly close to the Black–Scholes value of the Apple call option.

Note: The standard deviation is σ = .3156.

Second, option theory gives a simple, powerful framework for describing complex decision trees. For example, suppose that you have the option to abandon an investment. The complete decision tree would overflow the largest classroom chalkboard. But now that you know about options, the opportunity to abandon can be summarized as “an American put.” Of course, not all real problems have such easy option analogies, but we can often approximate complex decision trees by some simple package of assets and options. A custom decision tree may get closer to reality, but the time and expense may not be worth it. Most men buy their suits off the rack even though a custom-made Armani suit would fit better and look nicer.

 21-3   The Black–Scholes Formula

Look back at Figure 21.1, which showed what happens to the distribution of possible Apple stock price changes as we divide the option’s life into a larger and larger number of increasingly small subperiods. You can see that the distribution of price changes becomes increasingly smooth.

If we continued to chop up the option’s life in this way, we would eventually reach the situation shown in Figure 21.4, where there is a continuum of possible stock price changes at maturity. Figure 21.4 is an example of a lognormal distribution. The lognormal distribution is often used to summarize the probability of different stock price changes.⁹ It has a number of good commonsense features. For example, it recognizes the fact that the stock price can never fall by more than 100%, but that there is some, perhaps small, chance that it could rise by much more than 100%.

   FIGURE 21.4 As the option’s life is divided into more and more subperiods, the distribution of possible stock price changes approaches a lognormal distribution.

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Black-Scholes assumptions

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Subdividing the option life into indefinitely small slices does not affect the principle of option valuation. We could still replicate the call option by a levered investment in the stock, but we would need to adjust the degree of leverage continuously as time went by. Calculating option value when there is an infinite number of subperiods may sound a hopeless task. Fortunately, Black and Scholes derived a formula that does the trick.¹⁰ It is an unpleasant-looking formula, but on closer acquaintance you will find it exceptionally elegant and useful. The formula is

where

Notice that the value of the call in the Black–Scholes formula has the same properties that we identified earlier. It increases with the level of the stock price P and decreases with the present value of the exercise price PV(EX), which in turn depends on the interest rate and time to maturity. It also increases with the time to maturity and the stock’s variability

To derive their formula Black and Scholes assumed that there is a continuum of stock prices, and therefore to replicate an option investors must continuously adjust their holding in the stock.¹² Of course this is not literally possible, but even so the formula performs remarkably well in the real world, where stocks trade only intermittently and prices jump from one level to another. The Black–Scholes model has also proved very flexible; it can be adapted to value options on a variety of assets such as foreign currencies, bonds, and commodities. It is not surprising, therefore, that it has been extremely influential and has become the standard model for valuing options. Every day dealers on the options exchanges use this formula to make huge trades. These dealers are not for the most part trained in the formula’s mathematical derivation; they just use a computer or a specially programmed calculator to find the value of the option.

Using the Black–Scholes Formula

The Black–Scholes formula may look difficult, but it is very straightforward to apply. Let us practice using it to value the Apple call.

Here are the data that you need:

•  Price of stock now = P = 400

•  Exercise price = EX = 400

•  Standard deviation of continuously compounded annual returns = σ = .3156

•  Years to maturity = t = .5

•  Interest rate per annum = rf = 3.5% (or 1.73% for six months)¹³

Remember that the Black–Scholes formula for the value of a call is

where

There are three steps to using the formula to value the Apple call:

Step 1 Calculate d1 and d2. This is just a matter of plugging numbers into the formula (noting that “log” means natural log):

Step 2 Find N(d1) and N(d2). N(d1) is the probability that a normally distributed variable will be less than d1 standard deviations above the mean. If d1 is large, N(d1) is close to 1.0 (i.e., you can be almost certain that the variable will be less than d1 standard deviations above the mean). If d1 is zero, N(d1) is .5 (i.e., there is a 50% chance that a normally distributed variable will be below the average).

The simplest way to find N(d1) is to use the Excel function NORMSDIST. For example, if you enter NORMSDIST(.1887) into an Excel spreadsheet, you will see that there is a .5748 probability that a normally distributed variable will be less than .1887 standard deviations above the mean.

Again you can use the Excel function to find N(d2). If you enter NORMSDIST(–.0345) into an Excel spreadsheet, you should get the answer .4862. In other words, there is a probability of .4862 that a normally distributed variable will be less than .0345 standard deviations below the mean.

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Try It! The two-step binomial model

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Step 3 Plug these numbers into the Black–Scholes formula. You can now calculate the value of the Apple call:

In other words, you can replicate the Apple call option by investing $229.92 in the company’s stock and borrowing $191.17. Subsequently, as time passes and the stock price changes, you may need to borrow a little more to invest in the stock or you may need to sell some of your stock to reduce your borrowing.

The Risk of an Option

How risky is the Apple call option? We have seen that you can exactly replicate a call by a combination of risk-free borrowing and an investment in the stock. So the risk of the option must be the same as the risk of this replicating portfolio. We know that the beta of any portfolio is simply a weighted average of the betas of the separate holdings. So the risk of the option is just a weighted average of the betas of the investments in the loan and the stock.

On past evidence the beta of Apple stock is βstock = 1.28; the beta of a risk-free loan is βloan = 0. You are investing $229.92 in the stock and –$191.17 in the loan. (Notice that the investment in the loan is negative—you are borrowing money.) Therefore the beta of the option is βoption = (–191.17 × 0 + 229.92 × 1.28)/(–191.17 + 229.92) = 7.59. Notice that, because a call option is equivalent to a levered position in the stock, it is always riskier than the stock itself. In Apple’s case the option is nearly eight times as risky as the stock. As time passes and the price of Apple stock changes, the risk of the option will also change.

Some More Practice Suppose you repeat the calculations for the Apple call for a wide range of stock prices. The result is shown in Figure 21.5. You can see that the option values lie along an upward-sloping curve that starts its travels in the bottom left-hand corner of the diagram. As the stock price increases, the option value rises and gradually becomes parallel to the lower bound for the option value. This is exactly the shape we deduced in Chapter 20 (see Figure 20.10).

The height of this curve of course depends on risk and time to maturity. For example, if the risk of Apple stock had suddenly decreased, the curve shown in Figure 21.5 would drop at every possible stock price.

   FIGURE 21.5 The curved line shows how the value of the Apple call option changes as the price of Apple stock changes.

The Black–Scholes Formula and the Binomial Method

Look back at Table 21.1 where we used the binomial method to calculate the value of the Apple call. Notice that, as the number of intervals is increased, the values that you obtain from the binomial method begin to snuggle up to the Black–Scholes value of $38.75.

The Black–Scholes formula recognizes a continuum of possible outcomes. This is usually more realistic than the limited number of outcomes assumed in the binomial method. The formula is also more accurate and quicker to use than the binomial method. So why use the binomial method at all? The answer is that there are many circumstances in which you cannot use the Black–Scholes formula but the binomial method will still give you a good measure of the option’s value. We will look at several such cases in Section 21-5.

 21-4   Black–Scholes in Action

To illustrate the principles of option valuation, we focused on the example of Apple’s options. But financial managers turn to the Black–Scholes model to estimate the value of a variety of different options. Here are four examples.

Executive Stock Options

In fiscal year 2011 Larry Ellison, the CEO of Oracle Corporation, received a salary of $1 million, but he also pocketed another $63 million in the form of stock options.

The example highlights that executive stock options are often an important part of compensation. For many years companies were able to avoid reporting the cost of these options in their annual statements. However, they must now treat options as an expense just like salaries and wages, so they need to estimate the value of all new options that they have granted. For example, Oracle’s financial statements show that in fiscal 2011 the company issued a total of 110 million options with an average life of five years and an exercise price of $22.58. Oracle calculated that the average value of these options was $6.61. How did it come up with this figure? It just used the Black–Scholes model assuming a standard deviation of 33% and an interest rate of 1.8%.¹⁴

Some companies have disguised how much their management is paid by backdating the grant of an option. Suppose, for example, that a firm’s stock price has risen from $20 to $40. At that point the firm awards its CEO options exercisable at $20. That is generous but not illegal. However, if the firm pretends that the options were actually awarded when the stock price was $20 and values them on that basis, it will substantially understate the CEO’s compensation.¹⁵ The nearby box discusses the backdating scandal.

Speaking of executive stock options, we can now use the Black–Scholes formula to value the option packages you were offered in Section 20-3 (see Table 20.3). Table 21.2 calculates the value of the options from the safe-and-stodgy Establishment Industries at $5.26 each. The options from risky-and-glamorous Digital Organics are worth $7.40 each. Congratulations.

   TABLE 21.2 Using the Black–Scholes formula to value the executive stock options for Establishment Industries and Digital Organics (see Table 20.3).

Warrants

In October 2009 the Chinese company, Longwei Petroleum, needed to raise money for a 70,000 ton oil storage facility in the city of Gujiao. As part of the financing, Longwei issued 14.8 million warrants. Each warrant gave its owner the right to buy a share in the company for $2.255 at any point during the following three years. When the warrants were issued, the stock price was $2.05. So the price needed to appreciate by only 10% by the end of the three years for the warrants to be worth exercising. The warrants clearly provided a valuable option. The company used an option pricing model to estimate a value of $.495 for each warrant, but you can be sure that investors also used their own estimates of volatility to value the warrants.

You won’t often find warrants whose prices are obviously out of line with the values provided by option valuation models, but there are exceptions. The box on page 552 provides an extraordinary example.

Portfolio Insurance

Your company’s pension fund owns an $800 million diversified portfolio of common stocks that moves closely in line with the market index. The pension fund is currently fully funded, but you are concerned that if it falls by more than 20% it will start to be underfunded. Suppose that your bank offers to insure you for one year against this possibility. What would you be prepared to pay for this insurance? Think back to Section 20-2 (Figure 20.6), where we showed that you can shield against a fall in asset prices by buying a protective put option. In the present case the bank would be selling you a one-year put option on U.S. stock prices with an exercise price 20% below their current level. You can get the value of that option in two steps. First use the Black–Scholes formula to value a call with the same exercise price and maturity. Then back out the put value from put–call parity. (You will have to adjust for dividends, but we’ll leave that to the next section.)

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VIX—USA, Europe, and Japan

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Calculating Implied Volatilities

So far we have used our option pricing model to calculate the value of an option given the standard deviation of the asset’s returns. Sometimes it is useful to turn the problem around and ask what the option price is telling us about the asset’s volatility. For example, the Chicago Board Options Exchange trades options on several market indexes. As we write this, the Standard and Poor’s 500 Index is about 1250, while a one-year at-the-money call on the index is priced at 126. If the Black–Scholes formula is correct, then an option value of 126 makes sense only if investors believe that the standard deviation of index returns is about 25% a year.¹⁶

The Chicago Board Options Exchange regularly publishes the implied volatility on the Standard and Poor’s index, which it terms the VIX (see the box on page 551). There is an active market in the VIX. For example, suppose you feel that the implied volatility is implausibly low. Then you can “buy” the VIX at the current low price and hope to “sell” it at a profit when implied volatility has increased.

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The Perfect Payday*

  On an October day in 1999 the shares of the giant insurer United Health Group sank to their lowest level of the year. That may have been bad news for investors but it was good news for William McGuire, the chief executive, for the company granted him options to buy the stock in the future at that low price. If the options had been dated a month later when the stock price was 40% higher, those options would have been far less valuable. Lucky coincidence? Possibly, but the following year Mr. McGuire was also granted options on the day that the stock price hit the year’s low. And in 2001 the grant came near the bottom of a sharp dip in the stock price.

Over the following years evidence began to accumulate that in other companies too executives were being granted options at unusually favorable prices. It seemed that these firms were using hindsight to choose the date on which the options were granted. Such backdating is not necessarily illegal, but most options are granted under a shareholder-approved plan that typically requires the exercise price to be equal to the fair market value of the company’s stock at the time of the grant. Also backdating may result in an underestimate of the amount of compensation paid and therefore to a misstatement of earnings and an underpayment of taxes.

Investigations by the SEC and prosecutions by disgruntled shareholders led to the resignation of a number of directors and officers of major corporations that were found to have backdated options. William McGuire was among those who fell on their sword. He subsequently agreed to pay $39 million and forfeit another 3.7 million compensatory stock options to settle a class-action suit headed by the California Public Employee Retirement System (Calpers).

*“The Perfect Payday” is the title of an article in The Wall Street Journal that drew attention to the practice of backdating. See C. Forelle and J. Bandler, “The Perfect Payday; Some CEOs Reap Millions by Landing Stock Options When They Are Most Valuable; Luck—or Something Else?” The Wall Street Journal, March 18, 2006, p. A1. Earlier evidence of backdating appeared in D. Yermack, “Good Timing: CEO Stock Option Awards and Company News Announcements,” Journal of Finance 52 (1997), pp. 449–476, and in E. Lie, “On the Timing of CEO Stock Option Awards,” Management Science 51 (2005), pp. 802–812.

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An uncertainty index

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You may be interested to compare the current implied volatility that we calculated earlier with Figure 21.6, which shows past measures of implied volatility for the Standard and Poor’s index and for the Nasdaq index (VXN). Notice the sharp increase in investor uncertainty at the height of the credit crunch in 2008. This uncertainty showed up in the price that investors were prepared to pay for options.

   FIGURE 21.6 Standard deviations of market returns implied by prices of options on stock indexes.

Source: Chicago Board Options Exchange, www.cboe.com.

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The Chinese Warrants Bubble

Most warrants give the holder the option to buy stock in the company. A less common warrant is the put warrant that allows the holder to sell stock back to the company.

In April 2006 the Chinese liquor producer WuLiangYe Corporation issued 313 million put warrants on the Shenzhen Stock Exchange. The maturity date for the warrants was April 2, 2008, and the last date for trading was March 26, 2008. The exercise price for the warrants was 5.63 yuan, and the stock price at the time of issue was 5.03 yuan.

After the warrants were issued, the price of WuLiangYe stock rose steadily to touch a high of 71.56 yuan in October 2007. By that point there was almost no chance that the stock price would fall below 5.63 yuan by April 2008, so the put warrants were almost certain to expire unexercised. By that stage the Black–Scholes formula showed that the warrants were effectively worthless. Yet, as the price of the stock rose, so did that of the warrants. By June 2007 the warrant price had reached a high of 8.15 yuan, before falling to one penny in the last minute of the last trading day.

The WuLiangYe put warrants were not an isolated case of mispricing. Another 15 Chinese put warrants were similarly overvalued during this period. So why didn’t smart investors arbitrage the mispricing by selling the warrants and buying delta shares of stock? If short sales of the put warrants had been allowed, this arbitrage would have been very profitable. However, in China investors were prohibited by law from short-selling stocks or warrants. In addition, China limits the amount by which a share price may change in a single day to 10%. During the final few days of trading, the price of WuLiangYe stock was sufficiently high that the 10% limit meant that the put warrant would inevitably expire worthless. Yet the warrants traded for significant amounts of money.

How could the price of an option depart so dramatically from any reasonable estimate of its value? Did the investors who bought the warrants at 8.15 yuan mistakenly believe that they were getting an option to buy WuLiangYe stock for 5.63 yuan? Perhaps wise investors, who were unable to sell the warrants short, decided instead to join the bandwagon by buying the warrants to resell them later to a greater fool at an even higher price. If so, the Chinese put–warrant episode is another example of the bubbles that we discussed in Chapter 13.

Source: Wei Xiong and Jialin Yu, “The Chinese Warrants Bubble,” American Economic Review, 101(6): 2723–2753.

 21-5   Option Values at a Glance

So far our discussion of option values has assumed that investors hold the option until maturity. That is certainly the case with European options that cannot be exercised before maturity but may not be the case with American options that can be exercised at any time. Also, when we valued the Apple call, we could ignore dividends, because Apple did not pay any. Can the same valuation methods be extended to American options and to stocks that pay dividends?

Another question concerns dilution. When investors buy and then exercise traded options, there is no effect on the number of shares issued by the company. But sometimes the company itself may give options to key employees or sell them to investors. When these options are exercised, the number of outstanding shares does increase, and therefore the stake of existing stockholders is diluted. Option valuation models need to be able to cope with the effect of dilution.

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Dilution

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In this section we look at how the possibility of early exercise and dividends affect option value.

American Calls—No Dividends Unlike European options, American options can be exercised anytime. However, we know that in the absence of dividends the value of a call option increases with time to maturity. So, if you exercised an American call option early, you would needlessly reduce its value. Since an American call should not be exercised before maturity, its value is the same as that of a European call, and the Black–Scholes model applies to both options.

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The Fear Index*

  The Market Volatility Index or VIX measures the volatility that is implied by near-term Standard & Poor’s 500 Index options and is therefore an estimate of expected future market volatility over the next 30 calendar days. Implied market volatilities have been calculated by the Chicago Board Options Exchange (CBOE) since January 1986, though in its current form the VIX dates back only to 2003.

Investors regularly trade volatility. They do so by buying or selling VIX futures and options contracts. Since these were introduced by the Chicago Board Options Exchange (CBOE), combined trading activity in the two contracts has grown to more than 100,000 contracts per day, making them two of the most successful innovations ever introduced by the exchange.

Because VIX measures investor uncertainty, it has been dubbed the “fear index.” The market for index options tends to be dominated by equity investors who buy index puts when they are concerned about a potential drop in the stock market. Any subsequent decline in the value of their portfolio is then offset by the increase in the value of the put option. The more that investors demand such insurance, the higher the price of index put options. Thus VIX is an indicator that reflects the price of portfolio insurance.

Between January 1986 and March 2012 the VIX has averaged 20.9%, almost identical to the long-term level of market volatility that we cited in Chapter 7. The high point for the index was in October 1987 when the VIX closed the month at 61%,** but there have been several other short-lived spikes, for example, at the time of Iraq’s invasion of Kuwait and the subsequent response by U.N. forces.

Although the VIX is the most widely quoted measure of volatility, volatility measures are also available for several other U.S. and overseas stock market indexes (such as the FTSE 100 Index in the UK and the CAC 40 in France), as well as for gold, oil, and the euro.

*For a review of the VIX index see R. E. Whaley, “Understanding the VIX,” Journal of Portfolio Management 35 (Spring 2009), pp. 98–105.

**On October 19, 1987 (Black Monday), the VIX closed at 150. Fortunately, the market volatility returned fairly rapidly to less exciting levels.

European Puts—No Dividends If we wish to value a European put, we can use the put–call parity formula from Chapter 20:

American Puts—No Dividends It can sometimes pay to exercise an American put before maturity in order to reinvest the exercise price. For example, suppose that immediately after you buy an American put, the stock price falls to zero. In this case there is no advantage to holding onto the option since it cannot become more valuable. It is better to exercise the put and invest the exercise money. Thus an American put is always more valuable than a European put. In our extreme example, the difference is equal to the present value of the interest that you could earn on the exercise price. In all other cases the difference is less.

Because the Black–Scholes formula does not allow for early exercise, it cannot be used to value an American put exactly. But you can use the step-by-step binomial method as long as you check at each point whether the option is worth more dead than alive and then use the higher of the two values.

European Calls and Puts on Dividend-Paying Stocks Part of the share value comprises the present value of dividends. The option holder is not entitled to dividends. Therefore, when using the Black–Scholes model to value a European option on a dividend-paying stock, you should reduce the price of the stock by the present value of the dividends to be paid before the option’s maturity.

Dividends don’t always come with a big label attached, so look out for instances where the asset holder gets a benefit and the option holder does not. For example, when you buy foreign currency, you can invest it to earn interest; but if you own an option to buy foreign currency, you miss out on this income. Therefore, when valuing an option to buy foreign currency, you need to deduct the present value of this foreign interest from the current price of the currency.¹⁷

American Calls on Dividend-Paying Stocks We have seen that when the stock does not pay dividends, an American call option is always worth more alive than dead. By holding on to the option, you not only keep your option open but also earn interest on the exercise money. Even when there are dividends, you should never exercise early if the dividend you gain is less than the interest you lose by having to pay the exercise price early. However, if the dividend is sufficiently large, you might want to capture it by exercising the option just before the ex-dividend date.

The only general method for valuing an American call on a dividend-paying stock is to use the step-by-step binomial method. In this case you must check at each stage to see whether the option is more valuable if exercised just before the ex-dividend date than if held for at least one more period.

 21-6   The Option Menagerie

Our focus in the past two chapters has been on plain-vanilla puts and calls or combinations of them. An understanding of these options and how they are valued will allow you to handle most of the option problems that you are likely to encounter in corporate finance. However, you may occasionally encounter some more unusual options. We are not going to be looking at them in this book, but just for fun and to help you hold your own in conversations with your investment banker friends, here is a crib sheet that summarizes a few of these exotic options:

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SUMMARY

In this chapter we introduced the basic principles of option valuation by considering a call option on a stock that could take on one of two possible values at the option’s maturity. We showed that it is possible to construct a package of the stock and a loan that would provide exactly the same payoff as the option regardless of whether the stock price rises or falls. Therefore the value of the option must be the same as the value of this replicating portfolio.

We arrived at the same answer by pretending that investors are risk-neutral, so that the expected return on every asset is equal to the interest rate. We calculated the expected future value of the option in this imaginary risk-neutral world and then discounted this figure at the interest rate to find the option’s present value.

The general binomial method adds realism by dividing the option’s life into a number of subperiods in each of which the stock price can make one of two possible moves. Chopping the period into these shorter intervals doesn’t alter the basic method for valuing a call option. We can still replicate the call by a package of the stock and a loan, but the package changes at each stage.

Finally, we introduced the Black–Scholes formula. This calculates the option’s value when the stock price is constantly changing and takes on a continuum of possible future values.

An option can be replicated by a package of the underlying asset and a risk-free loan. Therefore, we can measure the risk of any option by calculating the risk of this portfolio. Naked options are often substantially more risky than the asset itself.

When valuing options in practical situations there are a number of features to look out for. For example, you may need to recognize that the option value is reduced by the fact that the holder is not entitled to any dividends.

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FURTHER READING

Three readable articles about the Black–Scholes model are:

F. Black, “How We Came up with the Option Formula,” Journal of Portfolio Management 15 (1989), pp. 4–8.

F. Black, “The Holes in Black–Scholes,” RISK Magazine 1 (1988), pp. 27–29.

F. Black, “How to Use the Holes in Black–Scholes,” Journal of Applied Corporate Finance 1 (Winter 1989), pp. 67–73.

There are a number of good books on option valuation. They include:

J. Hull, Options, Futures and Other Derivatives, 7th ed. (Englewood Cliffs, NJ: Prentice-Hall, Inc., 2008).

R. L. McDonald, Derivatives Markets, 2nd ed. (Reading, MA: Pearson Addison Wesley, 2005).

P. Wilmott, Paul Wilmott on Quantitative Finance, 2nd ed. (New York: John Wiley & Sons, 2006).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Binomial model The stock price of Heavy Metal (HM) changes only once a month: either it goes up by 20% or it falls by 16.7%. Its price now is $40. The interest rate is 12.7% per year, or about 1% per month.

a.  What is the value of a one-month call option with an exercise price of $40?

b.  What is the option delta?

c.  Show how the payoffs of this call option can be replicated by buying HM’s stock and borrowing.

d.  What is the value of a two-month call option with an exercise price of $40?

e.  What is the option delta of the two-month call over the first one-month period?

2.  Option delta

a.  Can the delta of a call option be greater than 1.0? Explain.

b.  Can it be less than zero?

c.  How does the delta of a call change if the stock price rises?

d.  How does it change if the risk of the stock increases?

3.  Binomial model Take another look at our two-step binomial trees for Apple, for example, in Figure 21.2. Use the replicating-portfolio or risk-neutral method to value six-month call and put options with an exercise price of $370. Assume the Apple stock price is $400.

4.  Binomial model Imagine that Apple’s stock price will either rise by 33.3% or fall by 25% over the next six months (see Section 21-1). Recalculate the value of the call option (exercise price = $400) using (a) the replicating portfolio method and (b) the risk-neutral method. Explain intuitively why the option value rises from the value computed in Section 21-1.

5.  Binomial model Over the coming year Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.

a.  What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?

b.  Use the replicating-portfolio method to value this call.

c.  In a risk-neutral world what is the probability that Ragwort stock will rise in price?

d.  Use the risk-neutral method to check your valuation of the Ragwort option.

e.  If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.

6.  Black–Scholes model Use the Black–Scholes formula to value the following options:

a.  A call option written on a stock selling for $60 per share with a $60 exercise price. The stock’s standard deviation is 6% per month. The option matures in three months. The risk-free interest rate is 1% per month.

b.  A put option written on the same stock at the same time, with the same exercise price and expiration date.

Now for each of these options find the combination of stock and risk-free asset that would replicate the option.

7.  Option risk “An option is always riskier than the stock it is written on.” True or false? How does the risk of an option change when the stock price changes?

8.  Option exercise For which of the following options might it be rational to exercise before maturity? Explain briefly why or why not.

a.  American put on a non-dividend-paying stock.

b.  American call—the dividend payment is $5 per annum, the exercise price is $100, and the interest rate is 10%.

c.  American call—the interest rate is 10%, and the dividend payment is 5% of future stock price. (Hint: The dividend depends on the stock price, which could either rise or fall.)

INTERMEDIATE

9.  Binomial trees Johnny Jones’s high school derivatives homework asks for a binomial valuation of a 12-month call option on the common stock of the Overland Railroad. The stock is now selling for $45 per share and has an annual standard deviation of 24%. Johnny first constructs a binomial tree like Figure 21.2, in which stock price moves up or down every six months. Then he constructs a more realistic tree, assuming that the stock price moves up or down once every three months, or four times per year.

a.  Construct these two binomial trees.

b.  How would these trees change if Overland’s standard deviation were 30%? (Hint: Make sure to specify the right up and down percentage changes.)

10.  Binomial model Suppose a stock price can go up by 15% or down by 13% over the next year. You own a one-year put on the stock. The interest rate is 10%, and the current stock price is $60.

a.  What exercise price leaves you indifferent between holding the put or exercising it now?

b.  How does this break-even exercise price change if the interest rate is increased?

11.  Dividends The price of Moria Mining stock on the Australian Securities Exchange is A$100. During each of the next two six-month periods the price may either rise by 25% or fall by 20% (equivalent to a standard deviation of 31.5% a year). At month 6 the company will pay a dividend of A$20. The interest rate is 10% per six-month period. What is the value of a one-year American call option with an exercise price of A$80? Now recalculate the option value, assuming that the dividend is equal to 20% of the with-dividend stock price.

12.  Binomial model Buffelhead’s stock price is $220 and could halve or double in each six-month period (equivalent to a standard deviation of 98%). A one-year call option on Buffelhead has an exercise price of $165. The interest rate is 21% a year.

a.  What is the value of the Buffelhead call?

b.  Now calculate the option delta for the second six months if (i) the stock price rises to $440 and (ii) the stock price falls to $110.

c.  How does the call option delta vary with the level of the stock price? Explain intuitively why.

d.  Suppose that in month 6 the Buffelhead stock price is $110. How at that point could you replicate an investment in the stock by a combination of call options and risk-free lending? Show that your strategy does indeed produce the same returns as those from an investment in the stock.

13.  American puts Suppose that you own an American put option on Buffelhead stock (see Problem 12) with an exercise price of $220.

a.  Would you ever want to exercise the put early?

b.  Calculate the value of the put.

c.  Now compare the value with that of an equivalent European put option.

14.  Dividends Recalculate the value of the Buffelhead call option (see Problem 12), assuming that the option is American and that at the end of the first six months the company pays a dividend of $25. (Thus the price at the end of the year is either double or half the ex-dividend price in month 6.) How would your answer change if the option were European?

15.  Binomial model Suppose that you have an option that allows you to sell Buffelhead stock (see Problem 12) in month 6 for $165 or to buy it in month 12 for $165. What is the value of this unusual option?

16.  American puts The current price of the stock of Mont Tremblant Air is C$100. During each six-month period it will either rise by 11.1% or fall by 10% (equivalent to an annual standard deviation of 14.9%). The interest rate is 5% per six-month period.

a.  Calculate the value of a one-year European put option on Mont Tremblant’s stock with an exercise price of C$102.

b.  Recalculate the value of the Mont Tremblant put option, assuming that it is an American option.

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17.  Binomial and Black–Scholes models The current price of United Carbon (UC) stock is $200. The standard deviation is 22.3% a year, and the interest rate is 21% a year. A one-year call option on UC has an exercise price of $180.

a.  Use the Black–Scholes model to value the call option on UC. You may find it helpful to use the spreadsheet in Table 21.2 on the book’s website, www.mcgraw-hill.co.uk/textbooks/brealey.

b.  Use the formula given in Section 21-2 to calculate the up and down moves that you would use if you valued the UC option with the one-period binomial method. Now value the option by using that method.

c.  Recalculate the up and down moves and revalue the option by using the two-period binomial method.

d.  Use your answer to part (c) to calculate the option delta (i) today; (ii) next period if the stock price rises; and (iii) next period if the stock price falls. Show at each point how you would replicate a call option with a levered investment in the company’s stock.

18.  Option delta Suppose you construct an option hedge by buying a levered position in delta shares of stock and selling one call option. As the share price changes, the option delta changes, and you will need to adjust your hedge. You can minimize the cost of adjustments if changes in the stock price have only a small effect on the option delta. Construct an example to show whether the option delta is likely to vary more if you hedge with an in-the-money option, an at-the-money option, or an out-of-the-money option.

19.  Option risk

a.  In Section 21-3 we calculated the risk (beta) of a six-month call option on Apple stock with an exercise price of $400. Now repeat the exercise for a similar option with an exercise price of $370. Does the risk rise or fall as the exercise price is reduced?

b.  Now calculate the risk of a one-year call on Apple stock with an exercise price of $400. Does the risk rise or fall as the maturity of the option lengthens?

20.  Option exercise Other things equal, which of these American options are you most likely to want to exercise early?

a.  A put option on a stock with a large dividend or a call on the same stock.

b.  A put option on a stock that is selling below exercise price or a call on the same stock.

c.  A put option when the interest rate is high or the same put option when the interest rate is low.

Illustrate your answer with examples.

21.  Option exercise Is it better to exercise a call option on the with-dividend date or on the ex-dividend date? How about a put option? Explain.

22.  Warrants In Section 21-4 we showed how Longwei Petroleum used the Black-Scholes formula to value its warrants. You can use the Black–Scholes program on this book’s website, www.mcgraw-hill.co.uk/textbooks/brealey, to estimate the volatility that Longwei assumed in its estimates. The interest rate was 1.5% and Longwei did not pay a dividend. Ignore the problem of dilution.

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23.  Pension fund insurance Use the Black–Scholes program at www.mcgraw-hill.co.uk/textbooks/brealey to estimate how much you should be prepared to pay to insure the value of your pension fund portfolio for the coming year. Make reasonable assumptions about the volatility of the market and use current interest rates. Remember to subtract the present value of likely dividend payments from the current level of the market index.

CHALLENGE

24.  Option delta Use the formula that relates the value of the call and the put (see Section 20-2) and the one-period binomial model to show that the option delta for a put option is equal to the option delta for a call option minus 1.

25.  Option delta Show how the option delta changes as the stock price rises relative to the exercise price. Explain intuitively why this is the case. (What happens to the option delta if the exercise price of an option is zero? What happens if the exercise price becomes indefinitely large?)

26.  Dividends Your company has just awarded you a generous stock option scheme. You suspect that the board will either decide to increase the dividend or announce a stock repurchase program. Which do you secretly hope they will decide? Explain. (You may find it helpful to refer back to Chapter 16.)

27.  Option risk Calculate and compare the risk (betas) of the following investments: (a) a share of Apple stock; (b) a one-year call option on Apple; (c) a one-year put option; (d) a portfolio consisting of a share of Apple stock and a one-year put option; (e) a portfolio consisting of a share of Apple stock, a one-year put option, and the sale of a one-year call. In each case assume that the exercise price of the option is $400, which is also the current price of Apple stock.

28.  Option maturity Some corporations have issued perpetual warrants. Warrants are call options issued by a firm, allowing the warrant holder to buy the firm’s stock.

a.  What does the Black–Scholes formula predict for the value of an infinite-lived call option on a non-dividend-paying stock? Explain the value you obtain. (Hint: What happens to the present value of the exercise price of a long-maturity option?)

b.  Do you think this prediction is realistic? If not, explain carefully why. (Hints: What about dividends? What about bankruptcy?)

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FINANCE ON THE WEB

Look back at the stocks listed in Table 7.3. Pick at least three stocks and find call option prices for each of them on finance.yahoo.com. Now find monthly adjusted prices and calculate the standard deviation from the monthly returns using the Excel function STDEV. Convert the standard deviation from monthly to annual units by multiplying by the square root of 12.

a.  For each stock pick a traded option with a maturity of about six months and an exercise price equal to the current stock price. Use the Black–Scholes formula and your estimate of standard deviation to value each option. If the stock pays dividends, remember to subtract from the stock price the present value of any dividends that the option holder will miss out on. How close is your calculated value to the traded price of the option?

b.  Your answer to part (a) will not exactly match the traded price. Experiment with different values for the standard deviation until your calculated values match the prices of the traded options as closely as possible. What are these implied volatilities? What do the implied volatilities say about investors’ forecasts of future volatility?

MINI-CASE ● ● ● ● ●

Bruce Honiball’s Invention

It was another disappointing year for Bruce Honiball, the manager of retail services at the Gibb River Bank. Sure, the retail side of Gibb River was making money, but it didn’t grow at all in 2009. Gibb River had plenty of loyal depositors, but few new ones. Bruce had to figure out some new product or financial service—something that would generate some excitement and attention.

Bruce had been musing on one idea for some time. How about making it easy and safe for Gibb River’s customers to put money in the stock market? How about giving them the upside of investing in equities—at least some of the upside—but none of the downside?

Bruce could see the advertisements now:

How would you like to invest in Australian stocks completely risk-free? You can with the new Gibb River Bank Equity-Linked Deposit. You share in the good years; we take care of the bad ones.

Here’s how it works. Deposit A$100 with us for one year. At the end of that period you get back your A$100 plus A$5 for every 10% rise in the value of the Australian All Ordinaries stock index. But, if the market index falls during this period, the Bank will still refund your A$100 deposit in full.

There’s no risk of loss. Gibb River Bank is your safety net.

Bruce had floated the idea before and encountered immediate skepticism, even derision: “Heads they win, tails we lose—is that what you’re proposing, Mr. Honiball?” Bruce had no ready answer. Could the bank really afford to make such an attractive offer? How should it invest the money that would come in from customers? The bank had no appetite for major new risks.

Bruce has puzzled over these questions for the past two weeks but has been unable to come up with a satisfactory answer. He believes that the Australian equity market is currently fully valued, but he realizes that some of his colleagues are more bullish than he is about equity prices.

Fortunately, the bank had just recruited a smart new MBA graduate, Sheila Liu. Sheila was sure that she could find the answers to Bruce Honiball’s questions. First she collected data on the Australian market to get a preliminary idea of whether equity-linked deposits could work. These data are shown in Table 21.3. She was just about to undertake some quick calculations when she received the following further memo from Bruce:

Sheila, I’ve got another idea. A lot of our customers probably share my view that the market is overvalued. Why don’t we also give them a chance to make some money by offering a “bear market deposit”? If the market goes up, they would just get back their A$100 deposit. If it goes down, they get their A$100 back plus $5 for each 10% that the market falls. Can you figure out whether we could do something like this? Bruce.

QUESTION

1.  What kinds of options is Bruce proposing? How much would the options be worth? Would the equity-linked and bear-market deposits generate positive NPV for Gibb River Bank?

   TABLE 21.3 Australian interest rates and equity returns, 1989–2008.

___________

¹We do not know whether Black and Scholes, like Archimedes, were sitting in bathtubs at the time.

²The exact number of shares to buy is 100/180 = .55555… as explained below. You will encounter some rounding errors if you replicate the calculations below with .556.

³Of course, you don’t get seriously rich by dealing in .556 shares. But if you multiply each of our transactions by a million, it begins to look like real money.

⁴When valuing American put options, you need to recognize the possibility that it will pay to exercise early. We discuss this complication later in the chapter, but it is unimportant for valuing the Apple put and we ignore it here.

⁵The delta of a put option is always equal to the delta of a call option with the same exercise price minus one. In our example, delta of put = .556 – 1 = –.444.

⁶Reminder: This formula applies only when the two options have the same exercise price and exercise date.

⁷We explain shortly why we picked these figures.

⁸To find the standard deviation given u, we turn the formula around:

where log = natural logarithm. In our example,

⁹When we first looked at the distribution of stock price changes in Chapter 8, we depicted these changes as normally distributed. We pointed out at the time that this is an acceptable approximation for very short intervals, but the distribution of changes over longer intervals is better approximated by the lognormal.

¹⁰The pioneering articles on options are F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81 (May–June 1973), pp. 637–654; and R. C. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science 4 (Spring 1973), pp. 141–183.

¹¹That is, N(d) is the probability that a normally distributed random variable will be less than or equal to d. N(d1) in the Black–Scholes formula is the option delta. Thus the formula tells us that the value of a call is equal to an investment of N(d1) in the common stock less borrowing of N(d2) × PV(EX).

¹²The important assumptions of the Black–Scholes formula are that (a) the price of the underlying asset follows a lognormal random walk, (b) investors can adjust their hedge continuously and costlessly, (c) the risk-free rate is known, and (d) the underlying asset does not pay dividends.

¹³When valuing options, it is more common to use continuously compounded rates (see Section 2-4). If the annually compounded rate is 3.5%, the equivalent continuously compounded rate is 3.44%. (The natural log of 1.035 is .0344 and e.0344 = 1.035.) Using continuous compounding, PV(EX) = 400 × e–.0344 × .5 = 393.18.

If both methods give the same answer, why do we bother to mention the subject here? It is simply because most computer programs for valuing options call for a continuously compounded rate. If you enter an annually compounded rate by mistake, the error will usually be small, but you can waste a lot of time trying to trace it.

¹⁴Many of the recipients of these options may not have agreed with Oracle’s valuation. First, the options were less valuable to their owners if they created substantial undiversifiable risk. Second, if the holders planned to quit the company in the next few years, they were liable to forfeit the options. For a discussion of these issues see J. I. Bulow and J. B. Shoven, “Accounting for Stock Options,” Journal of Economic Perspectives 19 (Fall 2005), pp. 115–134.

¹⁵Until 2005 companies were obliged to record as an expense any difference between the stock price when the options were granted and the exercise price. Thus, as long as the options were granted at-the-money (exercise price equals stock price), the company was not obliged to show any expense.

¹⁶In calculating the implied volatility we need to allow for the dividends paid on the shares. We explain how to take these into account in the next section.

¹⁷For example, suppose that it currently costs $2 to buy £1 and that this pound can be invested to earn interest of 5%. The option holder misses out on interest of .05 × $2 = $.10. So, before using the Black–Scholes formula to value an option to buy sterling, you must adjust the current price of sterling:

Part 6 Options

Real Options

When you use discounted cash flow (DCF) to value a project, you implicitly assume that your firm will hold the project passively. In other words, you are ignoring the real options attached to the project—options that sophisticated managers can take advantage of. You could say that DCF does not reflect the value of management. Managers who hold real options do not have to be passive; they can make decisions to capitalize on good fortune or to mitigate loss. The opportunity to make such decisions clearly adds value whenever project outcomes are uncertain.

Chapter 10 introduced the four main types of real options:

•  The option to expand if the immediate investment project succeeds.

•  The option to wait (and learn) before investing.

•  The option to shrink or abandon a project.

•  The option to vary the mix of output or the firm’s production methods.

Chapter 10 gave several simple examples of real options. We also showed you how to use decision trees to set out possible future outcomes and decisions. But we did not show you how to value real options. That is our task in this chapter. We apply the concepts and valuation principles you learned in Chapter 21.

For the most part we work with simple numerical examples. The art and science of valuing real options are illustrated just as well with simple calculations as complex ones. But we also describe several more realistic examples, including

•  A strategic investment in the computer business.

•  The option to develop commercial real estate.

•  The decision to operate or mothball an oil tanker.

•  Purchase options on aircraft.

•  Investment in pharmaceutical R&D.

These examples show how financial managers can value real options in real life. We also show how managers can create real options, adding value by adding flexibility to the firm’s investments and operations.

We should start with a warning. Setting out the possible future choices that the firm may encounter usually calls for a strong dose of judgment. Therefore, do not expect precision when valuing real options. Often managers do not even try to put a figure on the value of the option, but simply draw on their experience to decide whether it is worth paying for additional flexibility. Thus they might say, “We just don’t know whether gargle blasters will catch on, but it probably makes sense to spend an extra $200,000 now to allow for an extra production line in the future.”

 22-1   The Value of Follow-On Investment Opportunities

It is 1982. You are assistant to the chief financial officer (CFO) of Blitzen Computers, an established computer manufacturer casting a profit-hungry eye on the rapidly developing personal computer market. You are helping the CFO evaluate the proposed introduction of the Blitzen Mark I Micro.

   TABLE 22.1 Summary of cash flows and financial analysis of the Mark I microcomputer ($ millions).

The Mark I’s forecasted cash flows and NPV are shown in Table 22.1. Unfortunately the Mark I can’t meet Blitzen’s customary 20% hurdle rate and has a $46 million negative NPV, contrary to top management’s strong gut feeling that Blitzen ought to be in the personal computer market.

The CFO has called you in to discuss the project:

“The Mark I just can’t make it on financial grounds,” the CFO says. “But we’ve got to do it for strategic reasons. I’m recommending we go ahead.”

“But you’re missing the all-important financial advantage, Chief,” you reply.

“Don’t call me ‘Chief.’ What financial advantage?”

“If we don’t launch the Mark I, it will probably be too expensive to enter the micro market later, when Apple, IBM, and others are firmly established. If we go ahead, we have the opportunity to make follow-on investments that could be extremely profitable. The Mark I gives not only its own cash flows but also a call option to go on with a Mark II micro. That call option is the real source of strategic value.”

“So it’s strategic value by another name. That doesn’t tell me what the Mark II investment’s worth. The Mark II could be a great investment or a lousy one—we haven’t got a clue.”

“That’s exactly when a call option is worth the most,” you point out perceptively. “The call lets us invest in the Mark II if it’s great and walk away from it if it’s lousy.”

“So what’s it worth?”

“Hard to say precisely, but I’ve done a back-of-the-envelope calculation, which suggests that the value of the option to invest in the Mark II could more than offset the Mark I’s $46 million negative NPV. [The calculations are shown in Table 22.2.] If the option to invest is worth $55 million, the total value of the Mark I is its own NPV, – $46 million, plus the $55 million option attached to it, or +$9 million.”

“You’re just overestimating the Mark II,” the CFO says gruffly. “It’s easy to be optimistic when an investment is three years away.”

“No, no,” you reply patiently. “The Mark II is expected to be no more profitable than the Mark I—just twice as big and therefore twice as bad in terms of discounted cash flow. I’m forecasting it to have a negative NPV of about $100 million. But there’s a chance the Mark II could be extremely valuable. The call option allows Blitzen to cash in on those upside outcomes. The chance to cash in could be worth $55 million.”

“Of course, the $55 million is only a trial calculation, but it illustrates how valuable follow-on investment opportunities can be, especially when uncertainty is high and the product market is growing rapidly. Moreover, the Mark II will give us a call on the Mark III, the Mark III on the Mark IV, and so on. My calculations don’t take subsequent calls into account.”

“I think I’m beginning to understand a little bit of corporate strategy,” mumbles the CFO.

   TABLE 22.2 Valuing the option to invest in the Mark II microcomputer.

Questions and Answers about Blitzen’s Mark II

Question: I know how to use the Black–Scholes formula to value traded call options, but this case seems harder. What number do I use for the stock price? I don’t see any traded shares.

Answer: With traded call options, you can see the value of the underlying asset that the call is written on. Here the option is to buy a nontraded real asset, the Mark II. We can’t observe the Mark II’s value; we have to compute it.

The Mark II’s forecasted cash flows are set out in Table 22.3. The project involves an initial outlay of $900 million in 1985. The cash inflows start in the following year and have a present value of $807 million in 1985, equivalent to $467 million in 1982 as shown in Table 22.3. So the real option to invest in the Mark II amounts to a three-year call on an underlying asset worth $467 million, with a $900 million exercise price.

   TABLE 22.3 Cash flows of the Mark II microcomputer, as forecasted from 1982 ($ millions).

Notice that real options analysis does not replace DCF. You typically need DCF to value the underlying asset.

Question: Table 22.2 uses a standard deviation of 35% per year. Where does that number come from?

Answer: We recommend you look for comparables, that is, traded stocks with business risks similar to the investment opportunity.¹ For the Mark II, the ideal comparables would be growth stocks in the personal computer business, or perhaps a broader sample of high-tech growth stocks. Use the average standard deviation of the comparable companies’ returns as the benchmark for judging the risk of the investment opportunity.²

Question: Table 22.3 discounts the Mark II’s cash flows at 20%. I understand the high discount rate, because the Mark II is risky. But why is the $900 million investment discounted at the risk-free interest rate of 10%? Table 22.3 shows the present value of the investment in 1982 of $676 million.

Answer: Black and Scholes assumed that the exercise price is a fixed, certain amount. We wanted to stick with their basic formula. If the exercise price is uncertain, you can switch to a slightly more complicated valuation formula.³

Question: Nevertheless, if I had to decide in 1982, once and for all, whether to invest in the Mark II, I wouldn’t do it. Right?

Answer: Right. The NPV of a commitment to invest in the Mark II is negative:

The option to invest in the Mark II is “out of the money” because the Mark II’s value is far less than the required investment. Nevertheless, the option is worth +$55 million. It is especially valuable because the Mark II is a risky project with lots of upside potential. Figure 22.1 shows the probability distribution of the possible present values of the Mark II in 1985. The expected (mean or average) outcome is our forecast of $807,⁴ but the actual value could exceed $2 billion.

Question: Could it also be far below $807 million—$500 million or less?

Answer: The downside is irrelevant, because Blitzen won’t invest unless the Mark II’s actual value turns out higher than $900 million. The net option payoffs for all values less than $900 million are zero.

In a DCF analysis, you discount the expected outcome ($807 million), which averages the downside against the upside, the bad outcomes against the good. The value of a call option depends only on the upside. You can see the danger of trying to value a future investment option with DCF.

   FIGURE 22.1 This distribution shows the range of possible present values for the Mark II project in 1985. The expected value is about $800 million, less than the required investment of $900 million. The option to invest pays off in the shaded area above $900 million.

Question: What’s the decision rule?

Answer: Adjusted present value. The best-case NPV of the Mark I project is –$46 million, but accepting it creates the expansion option for the Mark II. The expansion option is worth $55 million, so

Of course we haven’t counted other follow-on opportunities. If the Mark I and Mark II are successes, there will be an option to invest in the Mark III, possibly the Mark IV, and so on.

Other Expansion Options

You can probably think of many other cases where companies spend money today to create opportunities to expand in the future. A mining company may acquire rights to an ore body that is not worth developing today but could be very profitable if product prices increase. A real estate developer may invest in worn-out farmland that could be turned into a shopping mall if a new highway is built. A pharmaceutical company may acquire a patent that gives the right but not the obligation to market a new drug. In each case the company is acquiring a real option to expand.

 22-2   The Timing Option

The fact that a project has a positive NPV does not mean that you should go ahead today. It may be better to wait and see how the market develops.

As CFO of Zeebanket Nederlands you are contemplating a now-or-never opportunity to build a malted herring factory. In this case you have an about-to-expire call option on the present value of the factory’s future cash flows. If the present value exceeds the cost of the factory, the call option’s payoff is the project’s NPV. But if NPV is negative, the call option’s payoff is zero, because in that case the firm will not make the investment.

Now suppose that you can delay construction of the plant. You still have the call option, but you face a trade-off. If the outlook is highly uncertain, it is tempting to wait and see whether the malted herring market takes off or decays. On the other hand, if the project is truly profitable, the sooner you can capture the project’s cash flows, the better. If the cash flows are high enough, you will want to exercise your option right away.

The cash flows from an investment project play the same role as dividend payments on a stock. When a stock pays no dividends, an American call is always worth more alive than dead and should never be exercised early. But payment of a dividend before the option matures reduces the ex-dividend price and the possible payoffs to the call option at maturity. Think of the extreme case: If a company pays out all its assets in one bumper dividend, the stock price must be zero and the call worthless. Therefore, any in-the-money call would be exercised just before this liquidating dividend.

Dividends do not always prompt early exercise, but if they are sufficiently large, call option holders capture them by exercising just before the ex-dividend date. We see managers acting in the same way: When a project’s forecasted cash flows are sufficiently large, managers capture the cash flows by investing right away. But when forecasted cash flows are small, managers are inclined to hold on to their call rather than to invest, even when project NPV is positive.⁵ This explains why managers are sometimes reluctant to commit to positive-NPV projects. This caution is rational as long as the option to wait is open and sufficiently valuable.

Valuing the Malted Herring Option

Figure 22.2 shows the possible cash flows and end-of-year values for the malted herring project. If you commit and invest €180 million, you have a project worth €200 million. If demand turns out to be low in year 1, the cash flow is only €16 million and the value of the project falls to €160 million. But if demand is high in year 1, the cash flow is €25 million and value rises to €250 million. Although the project lasts indefinitely, we assume that investment cannot be postponed beyond the end of the first year, and therefore we show only the cash flows for the first year and the possible values at the end of the year. Notice that if you undertake the investment right away, you capture the first year’s cash flow (€16 million or €25 million); if you delay, you miss out on this cash flow, but you will have more information on how the project is likely to work out.

We can use the binomial method to value this option. The first step is to pretend that investors are risk neutral and to calculate the probabilities of high and low demand in this risk-neutral world. If demand is high in the first year, the malted herring plant has a cash flow of €25 million and a year-end value of €250 million. The total return is (25 + 250)/200 – 1 = .375, or 37.5%. If demand is low, the plant has a cash flow of €16 million and a year-end value of €160 million. Total return is (16 + 160)/200 – 1 = –.12, or –12%. In a risk-neutral world, the expected return would be equal to the interest rate, which we assume is 5%:

   FIGURE 22.2 Possible cash flows and end-of-period values for the malted herring project are shown in black. The project costs €180 million, either now or later. The red figures in parentheses show payoffs from the option to wait and to invest later if the project is positive NPV at year 1. Waiting means loss of the first year’s cash flows. The problem is to figure out the current value of the option.

Therefore the risk-neutral probability of high demand is 34.3%. This is the probability that would generate the risk-free return of 5%.

We want to value a call option on the malted herring project with an exercise price of €180 million. We begin as usual at the end and work backward. The bottom row of Figure 22.2 shows the possible values of this option at the end of the year. If project value is €160 million, the option to invest is worthless. At the other extreme, if project value is €250 million, option value is €250 – 180 = €70 million.

To calculate the value of the option today, we work out the expected payoffs in a risk-neutral world and discount at the interest rate of 5%. Thus, the value of your option to invest in the malted herring plant is

But here is where we need to recognize the opportunity to exercise the option immediately. The option is worth €22.9 million if you keep it open, and it is worth the project’s immediate NPV (200 – 180 = €20 million) if exercised now. Therefore we decide to wait, and then to invest next year only if demand turns out high.

We have of course simplified the malted herring calculations. You won’t find many actual investment-timing problems that fit into a one-step binomial tree. But the example delivers an important practical point: A positive NPV is not a sufficient reason for investing. It may be better to wait and see.

Optimal Timing for Real Estate Development

Sometimes it pays to wait for a long time, even for projects with large positive NPVs. Suppose you own a plot of vacant land in the suburbs.⁶ The land can be used for a hotel or an office building, but not for both. A hotel could be later converted to an office building, or an office building to a hotel, but only at significant cost. You are therefore reluctant to invest, even if both investments have positive NPVs.

In this case you have two options to invest, but only one can be exercised. You therefore learn two things by waiting. First, you learn about the general level of cash flows from development, for example, by observing changes in the value of developed properties near your land. Second, you can update your estimates of the relative size of the hotel’s future cash flows versus the office building’s.

Figure 22.3 shows the conditions in which you would finally commit to build either the hotel or the office building. The horizontal axis shows the current cash flows that a hotel would generate. The vertical axis shows current cash flows for an office building. For simplicity, we assume that each investment would have an NPV of exactly zero at a current cash flow of 100. Thus, if you were forced to invest today, you would choose the building with the higher cash flow, assuming the cash flow is greater than 100. (What if you were forced to decide today and each building could generate the same cash flow, say, 150? You would flip a coin.)

   FIGURE 22.3 Development option for vacant land, assuming two mutually exclusive uses, either hotel or office building. The developer should “wait and see” unless the hotel’s or office building’s cash flows end up in one of the shaded areas.

Source: Adapted from Figure 1 in P. D. Childs, T. J. Riddiough, and A. J. Triantis, “Mixed Uses and the Redevelopment Option,” Real Estate Economics 24 (Fall 1996), pp. 317–339. Used with permission of John Wiley and Sons, via Copyright Clearance Center.

If the two buildings’ cash flows plot in the colored area at the lower right of Figure 22.3, you build the hotel. To fall in this area, the hotel’s cash flows have to beat two hurdles. First, they must exceed a minimum level of about 240. Second, they must exceed the office building’s cash flows by a sufficient amount. If the situation is reversed, with office building cash flows above the minimum level of 240, and also sufficiently above the hotel’s, then you build the office building. In this case, the cash flows plot in the colored area at the top left of the figure.

Notice how the “wait and see” region extends upward along the 45-degree line in Figure 22.3. When the cash flows from the hotel and office building are nearly the same, you become very cautious before choosing one over the other.

You may be surprised at how high cash flows have to be in Figure 22.3 to justify investment. There are three reasons. First, building the office building means not building the hotel, and vice versa. Second, the calculations underlying Figure 22.3 assumed cash flows that were small, but growing; therefore, the costs of waiting to invest were small. Third, the calculations did not consider the threat that someone might build a competing hotel or office building right next door. In that case the “relax and wait” area of Figure 22.3 would shrink dramatically.

 22-3   The Abandonment Option

Expansion value is important. When investments turn out well, the quicker and easier the business can be expanded, the better. But suppose bad news arrives, and cash flows are far below expectations. In that case it is useful to have the option to bail out and recover the value of the project’s plant, equipment, or other assets. The option to abandon is equivalent to a put option. You exercise that abandonment option if the value recovered from the project’s assets is greater than the present value of continuing the project for at least one more period.

Bad News for the Perpetual Crusher

We introduced the perpetual crusher project in Chapter 19 to illustrate the use of the weighted average cost of capital (WACC). The project cost $12.5 million and generated expected perpetual cash flows of $1.125 million per year. With WACC = .09, the project was worth PV = 1.125/.09 = $12.5 million. Subtracting the investment of $12.5 million gave NPV = 0.

Several years later, the crusher has not panned out. Cash flows are still expected to be perpetual but are now running at only $450,000 a year. The crusher is now worth only $450,000/.09 = $5 million. Is this bad news terminal?

Suppose the crusher project can be abandoned, with recovery of $5.5 million from the sale of machinery and real estate. Does abandonment make sense? The immediate gain from abandonment is of course $5.5 – 5 = $.5 million. But what if you can wait and reconsider abandonment later? In this case you have an abandonment option that does not have to be exercised immediately.

We can value the abandonment option as a put. Assume for simplicity that the put lasts one year only (abandon now or at year 1) and that the one-year standard deviation of the crusher project is 30%. The risk-free interest rate is 4%. We value the one-year abandonment put using the Black–Scholes formula and put–call parity. The asset value is $5 million and the exercise price is $5.5 million. (See Table 22.2 if you need a refresher on using the Black–Scholes formula.)

Therefore you decide not to abandon now. The project, if alive, is worth $5 + .768 = $5.768 million when the abandonment put is included but only $5.5 million if it is abandoned immediately.

You are keeping the project alive not out of stubbornness or loyalty to the crusher, but because there is a chance that cash flows will recover. The abandonment put still protects on the downside if the crusher project deals up further disappointments.

Of course we have made simplifying assumptions. For example, the recovery value of the crusher is likely to decline as you wait to abandon. So perhaps we are using too high an exercise price. On the other hand, we have considered only a one-year European put. In fact you have an American put with a potentially long maturity. A long-lived American put is worth more than a one-year European put because you can abandon in year 2, 3, or later if you wish.

Abandonment Value and Project Life

A project’s economic life can be just as hard to predict as its cash flows. Yet NPVs for capital-investment projects usually assume fixed economic lives. For example, in Chapter 6 we assumed that the guano project would operate for exactly seven years. Real-option techniques allow us to relax such fixed-life assumptions. Here is the procedure:⁷

1.   Forecast cash flows well beyond the project’s expected economic life. For example, you might forecast guano production and sales out to year 15.

2.   Value the project, including the value of your abandonment put, which allows, but does not require, abandonment before year 15. The actual timing of abandonment will depend on project performance. In the best upside scenarios, project life will be 15 years—it will make sense to continue in the guano business as long as possible. In the worst downside scenarios, project life will be much shorter than seven years. In intermediate scenarios where actual cash flows match original expectations, abandonment will occur around year 7.

This procedure links project life to the performance of the project. It does not impose an arbitrary ending date, except in the far distant future.

Temporary Abandonment

Companies are often faced with complex options that allow them to abandon a project temporarily, that is, to mothball it until conditions improve. Suppose you own an oil tanker operating in the short-term spot market. (In other words, you charter the tanker voyage by voyage, at whatever short-term charter rates prevail at the start of the voyage.) The tanker costs $50 million a year to operate and at current tanker rates it produces charter revenues of $52.5 million per year. The tanker is therefore profitable but scarcely cause for celebration. Now tanker rates dip by 10%, forcing revenues down to $47.5 million. Do you immediately lay off the crew and mothball the tanker until prices recover? The answer is clearly yes if the tanker operation can be turned on and off like a faucet. But that is unrealistic. There is a fixed cost to mothballing the tanker. You don’t want to incur this cost only to regret your decision next month if rates rebound to their earlier level. The higher the costs of mothballing and the more variable the level of charter rates, the greater the loss that you will be prepared to bear before you call it quits and lay up the boat.

Suppose that eventually you do decide to take the boat off the market. You lay up the tanker temporarily.⁸ Two years later your faith is rewarded; charter rates rise, and the revenues from operating the tanker creep above the operating cost of $50 million. Do you reactivate immediately? Not if there are costs to doing so. It makes more sense to wait until the project is well in the black and you can be fairly confident that you will not regret the cost of bringing the tanker back into operation.

These choices are illustrated in Figure 22.4. The teal line shows how the value of an operating tanker varies with the level of charter rates. The black line shows the value of the tanker when mothballed.⁹ The level of rates at which it pays to mothball is given by M and the level at which it pays to reactivate is given by R. The higher the costs of mothballing and reactivating and the greater the variability in tanker rates, the further apart these points will be. You can see that it will pay for you to mothball as soon as the value of a mothballed tanker reaches the value of an operating tanker plus the costs of mothballing. It will pay to reactivate as soon as the value of a tanker that is operating in the spot market reaches the value of a mothballed tanker plus the costs of reactivating. If the level of rates falls below M, the value of the tanker is given by the black line; if the level is greater than R, value is given by the teal line. If rates lie between M and R, the tanker’s value depends on whether it happens to be mothballed or operating.

   FIGURE 22.4 An oil tanker should be mothballed when tanker rates fall to M, where the tanker’s value if mothballed is enough above its value in operation to cover mothballing costs. The tanker is reactivated when rates recover to R.

 22-4   Flexible Production and Procurement

Flexible production means the ability to vary production inputs or outputs in response to fluctuating demand or prices. Take the case of CT (combustion-turbine) generating plants, which are designed to deliver short bursts of peak-load electrical power. CTs can’t match the thermal efficiency of coal or nuclear power plants, but CTs can be turned on or off on short notice. The coal plants and “nukes” are efficient only if operated on “base load” for long periods.

The profits from operating a CT depend on the spark spread, that is, on the difference between the price of electricity and the cost of the natural gas used as fuel. CTs are money-losers at average spark spreads, but the spreads are volatile and can spike to very high levels when demand is high and generating capacity tight. Thus a CT delivers a series of call options that can be exercised day by day (even hour by hour) when spark spreads are sufficiently high. The call options are normally out-of-the-money (CTs typically operate only about 5% of the time), but the money made at peak prices makes investment in the CTs worthwhile.¹⁰

The volatility of spark spreads depends on the correlation between the price of electricity and the price of natural gas used as fuel. If the correlation were 1.0, so that electricity and natural gas prices moved together dollar for dollar, the spark spread would barely move from its average value, and the options to operate the gas turbine would be worthless. But in fact the correlation is less than 1.0, so the options are valuable. In addition, some CTs are set up to give a further option, because they can be run on oil as well as natural gas.¹¹

The top panel of Figure 22.5 shows a histogram of electricity prices for the UK in 2011. Prices are set every half hour, so there are about 17,500 prices plotted. Prices are quoted as pounds per megawatt-hour (£/MWH). Notice how strongly the histogram is skewed to the right. Although most prices fall between £40 and £60/MWH, prices above £100/MWH crop up regularly when electricity demand peaks. The highest price in 2011 was £333/MWH. The occasional high prices are hardly visible in the top panel of Figure 22.5. The bottom panel plots only the prices above £60/MWH on a smaller vertical scale.

Suppose you have a CT generating plant in the UK that is only profitable at prices above £60/MWH. Of course you will exercise your option to operate only if prices are above £60 and leave the plant idle otherwise. The payoff from operating equals the price minus £60. The possible payoffs are plotted in the bottom panel of Figure 22.5. The payoff line exactly matches the payoff diagrams for call options with an exercise price of £60. The only difference is that your plant has about 17,500 options, one for each half hour in the year.

The payoff line in Figure 22.5 assumes that the plant’s operating cost is constant at £60. This is accurate only if the cost of natural gas is constant. Otherwise the payoff to the option to operate depends on the spark spread. Often the cost of gas is locked in by contract between the generator and the gas supplier. But if the cost of gas is sufficiently volatile, you would replot Figure 22.5 in spark spreads rather than electricity prices. You would operate when the spark spread is positive.

In this example, the output is the same (electricity); option value comes from the ability to vary output. In other cases, option value comes from the flexibility to switch from product to product using the same production facilities. For example, textile firms have invested heavily in computer-controlled knitting machines, which allow production to shift from product to product, or from design to design, as demand and fashion dictate.

   FIGURE 22.5 In the UK electricity prices are set every half hour. The top panel is a histogram of prices (£/MWH) for 2011. Note how the histogram is skewed to the right. Many prices exceeded £100/MWH and a few (not visible in the plot) exceeded £200/MWH. The bottom panel shows the payoff to a plant that costs £60/MWH to run. The plant operator has an option to produce with an exercise price of £60.

Flexibility in procurement can also have option value. For example, a computer manufacturer planning next year’s production must also plan to buy components, such as disk drives and microprocessors, in large quantities. Should it strike a deal today with the component manufacturer? This locks in the quantity, price, and delivery dates. But it also gives up flexibility, for example, the ability to switch suppliers next year or buy at a “spot” price if next year’s prices are lower.

The Finance in Practice box features another example of the value of flexibility in production or procurement.

FINANCE IN PRACTICE

● ● ● ● ●

Valuing Flexibility

  With the help of faculty from Stanford University, Hewlett-Packard has experimented with real options since the beginning of the 1990s. Example: In the ’80s, HP customized inkjet printers for foreign markets at the factory, then shipped them in finished form to warehouses. Customizing at the factory is cheaper than customizing in the field. But HP kept guessing wrong on demand and ending up with, say, too many printers configured for French customers but not enough for Germans.

Executives realized that it would be smarter to ship partially assembled printers and then customize them at the warehouse, once it had firm orders. True, local customization costs more. But even though production costs rose, HP saved $3 million a month by more effectively matching supply to demand, says Corey A. Billington, a former Stanford professor who directs HP’s Strategic Planning & Modeling group.

Common sense? Sure. But you can also view it as a neat solution of a real-options problem. Increasing the cost of production—anathema to your average engineer—was in effect the price HP paid for the option to delay configuration choices until the optimal time.

Source: P. Coy, “Exploiting Uncertainty.” Reprinted from June 7, 1999, issue of Business Week. Used with permission of Bloomberg L.P. Copyright © 2012. All rights reserved.

Aircraft Purchase Options

For our final example, we turn to the problem confronting airlines that order new airplanes for future use. In this industry lead times between an order and delivery can extend to several years. Long lead times mean that airlines that order planes today may end up not needing them. You can see why an airline might negotiate for an aircraft purchase option.

In Section 10-4, we used aircraft purchase options to illustrate the option to expand. What we said there was the truth, but not the whole truth. Let’s take another look. Suppose an airline forecasts a need for a new Airbus A320 four years hence.¹¹ It has at least three choices.

•   Commit now. It can commit now to buy the plane, in exchange for Airbus’s offer of locked-in price and delivery date.

•   Acquire option. It can seek a purchase option from Airbus, allowing the airline to decide later whether to buy. A purchase option fixes the price and delivery date if the option is exercised.

•   Wait and decide later. Airbus will be happy to sell another A320 at any time in the future if the airline wants to buy one. However, the airline may have to pay a higher price and wait longer for delivery, especially if the airline industry is flying high and many planes are on order.

The top half of Figure 22.6 shows the terms of a typical purchase option for an Airbus A320. The option must be exercised at year 3, when final assembly of the plane will begin. The option fixes the purchase price and the delivery date in year 4. The bottom half of the figure shows the consequences of “wait and decide later.” We assume that the decision will come at year 3. If the decision is “buy,” the airline pays the year-3 price and joins the queue for delivery in year 5 or later.

The payoffs from “wait and decide later” can never be better than the payoffs from an aircraft purchase option, since the airline can discard the option and negotiate afresh with Airbus if it wishes. In most cases, however, the airline will be better off in the future with the option than without it; the airline is at least guaranteed a place in the production line, and it may have locked in a favorable purchase price. But how much are these advantages worth today, compared to the wait-and-see strategy?

   FIGURE 22.6 This aircraft purchase option, if exercised at year 3, guarantees delivery at year 4 at a fixed price. Without the option, the airline can still order the plane at year 3, but the price is uncertain and the wait for delivery longer.

Source: Adapted from Figure 17–17 in J. Stonier, “What Is an Aircraft Purchase Option Worth? Quantifying Asset Flexibility Created through Manufacturer Lead-Time Reductions and Product Commonality,” Handbook of Airline Finance, ed. G. F. Butler and M. R. Keller. Copyright 1999 Aviation Week Books; Reprinted with permission from The McGraw-Hill Companies, Inc.

Figure 22.7 illustrates Airbus’s answers to this problem. It assumes a three-year purchase option with an exercise price equal to an A320 price of $45 million. The present value of the purchase option depends on both the NPV of purchasing an A320 at that price and on the forecasted wait for delivery if the airline does not have a purchase option but nevertheless decides to place an order in year 3. The longer the wait in year 3, the more valuable it is to have the purchase option today. (Remember that the purchase option holds a place in the A320 production line and guarantees delivery in year 4.)

If the NPV of buying an A320 today is very high (the right-hand side of Figure 22.7), future NPV will probably be high as well, and the airline will want to buy regardless of whether it has a purchase option. In this case the value of the purchase option comes mostly from the value of guaranteed delivery in year 4.¹² If the NPV is very low, then the option has low value because the airline is unlikely to exercise it. (Low NPV today probably means low NPV in year 3.) The purchase option is worth the most, compared to the wait-and-decide-later strategy, when NPV is around zero. In this case the airline can exercise the option, getting a good price and early delivery, if future NPV is higher than expected; alternatively, it can walk away from the option if NPV disappoints. Of course, if it walks away, it may still wish to negotiate with Airbus for delivery at a price lower than the option’s exercise price.

   FIGURE 22.7 Value of aircraft purchase option—the extra value of the option versus waiting and possibly negotiating a purchase later. (See Figure 22.6.) The purchase option is worth most when NPV of purchase now is about zero and the forecasted wait for delivery is long.

Source: Adapted from Fig. 17–20 in J. Stonier, “What Is an Aircraft Purchase Option Worth? Quantifying Asset Flexibility Created Through Manufacturer Lead-Time Reductions and Product Commonality,” in Handbook of Aviation Finance., ed. G. F. Butler and M. R. Keller. © 1999 Aviation Week Books; Reprinted with permission from The McGraw-Hill Companies, Inc.

We have cruised by many of the technical details of Airbus’s valuation model for purchase options. But the example does illustrate how real-options models are being built and used. By the way, Airbus offers more than just plain-vanilla purchase options. Airlines can negotiate “rolling options,” which lock in price but do not guarantee a place on the production line. (Exercise of the rolling option means that the airline joins the end of the queue.) Airbus also offers a purchase option that includes the right to switch from delivery of an A320 to an A319, a somewhat smaller plane.

 22-5   Investment in Pharmaceutical R&D

An investment in research and development (R&D) is really an investment in real options. When your research engineers invent a better mousetrap, they hand you an option to manufacture and sell it. New and improved mousetraps can be engineering triumphs but commercial failures. You will make the investment to manufacture and launch the better mousetrap only if the PV of expected cash inflows is greater than the required investment.

The pharmaceutical industry spends massive amounts for R&D to develop options to produce and sell new drugs. We described pharmaceutical R&D in Example 10.2 and in Figure 10.6, which is a simplified decision tree. After you have reviewed that example and figure, take a look at Figure 22.8, which recasts the decision tree as a real option.

   FIGURE 22.8 The decision tree from Figure 10.6 recast as a real option. If phase II trials are successful, the company has a real call option to invest $130 million. If the option is exercised, the company gets an 80% chance of launching an approved drug. The PV of the drug, which is forecasted at $350 million in year 5, is the underlying asset for the call option.

The drug candidate in Figure 22.8 requires an immediate investment of $18 million. That investment buys a real option to invest $130 million at year 2 to pay for phase III trials and costs incurred during the prelaunch period. Of course the real option exists only if phase II trials are successful. There is a 56% probability of failure. So after we value the real option, we will have to multiply its value by the 44% probability of success.

The exercise price of the real option is $130 million. The underlying asset is the PV of the drug, assuming that it passes phase II successfully. Figure 10.6 forecasts the expected PV of the drug at launch at $350 million in year 5. We multiply this value by .8, because the decision whether to exercise the option must be taken in year 2, before the company knows whether the drug will succeed or fail in phase III and prelaunch. Then we must discount this value back to year 0, because the Black–Scholes formula calls for the value of the underlying asset on the date when the option is valued. The cost of capital is 9.6%, so the PV today is

To value the real option, we need a risk-free rate (assume 4%) and a volatility of the value of the drug once launched (assume 20%). With these inputs, the Black–Scholes value of a two-year call on an asset worth $177 million with an exercise price of $130 million is $58.4 million. (Refer to Table 22.2 if you need a refresher on how to use the Black–Scholes formula.)

But there’s only a 44% chance that the drug will pass phase II trials. So the company must compare an initial investment of $18 million with a 44% chance of receiving an option worth $58.4 million. The NPV of the drug at year 0 is

This NPV is less than the $19 million NPV computed from Figure 10.6.¹³ Nevertheless, the R&D project is still a “go.”

Of course Figure 22.8 assumes only one decision point, and only one real option, between the start of phase II and the product launch. In practice there would be other decision points, including a Go/No Go decision after phase III trials but before prelaunch investment. In this case, the payoff to the first option at the end of phase II is the value at that date of the second option. This is an example of a compound call.

With two sequential options, you could look up the formula for a compound call in an option pricing manual or you could build a binomial tree for the R&D project. Suppose you take the binomial route. Once you set up the tree, using risk-neutral probabilities for changes in the value of the underlying asset, you solve the tree as you would solve any decision tree. You work back from the end of the tree, always choosing the decision that gives the highest value at each decision point. NPV is positive if the PV at the start of the tree is higher than the $18 million initial investment.

Despite its simplifying assumptions, our example explains why investors demand higher expected returns from R&D investments than from the products that the R&D may generate. R&D invests in real call options.¹⁴ A call option is always riskier (higher beta) than the underlying asset that is acquired when the option is exercised. Thus the opportunity cost of capital for R&D is higher than for a new product after the product is launched successfully.¹⁵

R&D is also risky because it may fail. But the risk of failure is not usually a market or macroeconomic risk. The drug’s beta or cost of capital does not depend on the probabilities that a drug will fail in phase II or III. If the drug fails, it will be because of medical or clinical problems not because the stock market is down. We take account of medical or clinical risks by multiplying future outcomes by the probability of success, not by adding a fudge factor to the discount rate.

 22-6   A Conceptual Problem?

In this chapter we have shown how option pricing models can help to value the real options in capital investment decisions. But that raises a question.

When we introduced option pricing models in Chapter 21, we showed that the trick is to construct a package of the underlying asset and a loan that would give exactly the same payoffs as the option. If the two investments do not sell for the same price, then there are arbitrage possibilities. But many assets are not freely traded. This means that we can no longer rely on arbitrage arguments to justify the use of option models.

The risk-neutral method still makes practical sense, however. It’s really just an application of the certainty-equivalent method introduced in Chapter 9.¹⁶ The key assumption—implicit till now—is that the company’s shareholders have access to assets with the same risk characteristics (e.g., the same beta) as the capital investments being evaluated by the firm.

Think of each real investment opportunity as having a “double,” a security or portfolio with identical risk. Then the expected rate of return offered by the double is also the cost of capital for the real investment and the discount rate for a DCF valuation of the investment project. Now what would investors pay for a real option based on the project? The same as for an identical traded option written on the double. This traded option does not have to exist; it is enough to know how it would be valued by investors, who could employ either the arbitrage or the risk-neutral method. The two methods give the same answer, of course.

When we value a real option by the risk-neutral method, we are calculating the option’s value if it could be traded. This exactly parallels standard capital budgeting. Shareholders would vote unanimously to accept any capital investment whose market value if traded exceeds its cost, as long as they can buy traded securities with the same risk characteristics as the project. This key assumption supports the use of both DCF and real-option valuation methods.

Practical Challenges

The challenges in applying real-options analysis are not conceptual but practical. It isn’t always easy. We can tick off some of the reasons why.

First, real options can be complex, and valuing them can absorb a lot of analytical and computational horsepower. Whether you want to invest in that horsepower is a matter for business judgment. Sometimes an approximate answer now is more useful than a “perfect” answer later, particularly if the perfect answer comes from a complicated model that other managers will regard as a black box. One advantage of real-options analysis, if you keep it simple, is that it’s relatively easy to explain. Complex decision trees can often be described as the payoffs to one or two simple call or put options.

The second problem is lack of structure. To quantify the value of a real option, you have to specify its possible payoffs, which depend on the range of possible values of the underlying asset, exercise prices, timing of exercise, etc. In this chapter we have taken well-structured examples where it is easy to see the road map of possible outcomes. For example, investments in pharmaceutical R&D are well-structured because all new drugs have to go through the same series of clinical trials to get approved by the U.S. Food and Drug Administration. Outcomes may be uncertain, but the road map is clear. In other cases you may not have a road map. For example, reading this book can enhance your personal call option to work in financial management, yet we suspect that you would find it hard to write down how that option would change the binomial tree of your entire future career.

A third problem can arise when your competitors have real options. This is not a problem in industries where products are standardized and no single competitor can shift demand and prices. But when you face just a few key competitors, all with real options, then the options can interact. If so, you can’t value your options without thinking of your competitors’ moves. Your competitors will be thinking in the same fashion.

An analysis of competitive interactions would take us into other branches of economics, including game theory. But you can see the danger of assuming passive competitors. Think of the timing option. A simple real-options analysis will often tell you to wait and learn before investing in a new market. Be careful that you don’t wait and learn that a competitor has moved first.¹⁷

Given these hurdles, you can understand why systematic, quantitative valuation of real options is restricted mostly to well-structured problems like the examples in this chapter. The qualitative implications of real options are widely appreciated, however. Real options give the financial manager a conceptual framework for strategic planning and thinking about capital investments. If you can identify and understand real options, you will be a more sophisticated consumer of DCF analysis and better equipped to invest your company’s money wisely.

Understanding real options also pays off when you can create real options, adding value by adding flexibility to the company’s investments and operations. For example, it may be better to design and build a series of modular production plants, each with capacity of 50,000 tons per year of magnoosium alloy, than to commit to one large plant with capacity of 150,000 tons per year. The larger plant will probably be more efficient because of economies of scale. But with the smaller plants, you retain the flexibility to expand in step with demand and to defer investment when demand growth is disappointing.

Sometimes valuable options can be created simply by “overbuilding” in the initial round of investment. For example, oil-production platforms are typically built with vacant deck space to reduce the cost of adding equipment later. Undersea oil pipelines from the platforms to shore are often built with larger diameters and capacity than production from the platform will require. The additional capacity is then available at low cost if additional oil is found nearby. The extra cost of a larger-diameter pipeline is much less than the cost of building a second pipeline later.

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SUMMARY

In Chapter 21 you learned the basics of option valuation. In this chapter we described four important real options:

1.   The option to make follow-on investments. Companies often cite “strategic” value when taking on negative-NPV projects. A close look at the projects’ payoffs reveals call options on follow-on projects in addition to the immediate projects’ cash flows. Today’s investments can generate tomorrow’s opportunities.

2.   The option to wait (and learn) before investing. This is equivalent to owning a call option on the investment project. The call is exercised when the firm commits to the project. But rather than exercising the call immediately, it’s often better to defer a positive-NPV project in order to keep the call alive. Deferral is most attractive when uncertainty is great and immediate project cash flows—which are lost or postponed by waiting—are small.

3.   The option to abandon. The option to abandon a project provides partial insurance against failure. This is a put option; the put’s exercise price is the value of the project’s assets if sold or shifted to a more valuable use.

4.   The option to vary the firm’s output or its production methods. Firms often build flexibility into their production facilities so that they can use the cheapest raw materials or produce the most valuable set of outputs. In this case they effectively acquire the option to exchange one asset for another.

We should offer here a healthy warning: The real options encountered in practice are often complex. Each real option brings its own issues and trade-offs. Nevertheless the tools that you have learned in this and previous chapters can be used in practice. The Black–Scholes formula often suffices to value one-time expansion and abandonment options. For more complex options, it’s sometimes easier to switch to binomial trees.

Binomial trees are cousins of decision trees. You work back through binomial trees from future payoffs to present value. Whenever a future decision needs to be made, you figure out the value-maximizing choice, using the principles of option pricing theory, and record the resulting value at the appropriate node of the tree.

Don’t jump to the conclusion that real-option valuation methods can replace discounted cash flow (DCF). First, DCF works fine for safe cash flows. It also works for “cash cow” assets—that is, for assets or businesses whose value depends primarily on forecasted cash flows, not on real options. Second, the starting point in most real-option analyses is the present value of an underlying asset. To value the underlying asset, you typically have to use DCF.

Real options are rarely traded assets. When we value a real option, we are estimating its value if it could be traded. This is the standard approach in corporate finance, the same approach taken in DCF valuations. The key assumption is that shareholders can buy traded securities or portfolios with the same risk characteristics as the real investments being evaluated by the firm. If so, they would vote unanimously for any real investment whose market value if traded would exceed the investment required. This key assumption supports the use of both DCF and real-option valuation methods.

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FURTHER READING

The Further Reading for Chapter 10 lists several introductory articles on real options. The Spring 2005 and 2007 issues of the Journal of Applied Corporate Finance contain additional articles.

The Spring 2006 issue contains two further articles:

R. L. McDonald, “The Role of Real Options in Capital Budgeting: Theory and Practice,” Journal of Applied Corporate Finance 18 (Spring 2006), pp. 28–39.

M. Amram, F. Li, and C. A. Perkins, “How Kimberly-Clark Uses Real Options,” Journal of Applied Corporate Finance 18 (Spring 2006), pp. 40–47.

The standard texts on real options include:

M. Amran and N. Kulatilaka, Real Options: Managing Strategic Investments in an Uncertain World (Boston: Harvard Business School Press, 1999).

T. Copeland and V. Antikarov, Real Options: A Practitioner’s Guide (New York: Texere, 2001).

A. K. Dixit and R. S. Pindyck, Investment under Uncertainty (Princeton, NJ: Princeton University Press, 1994).

H. Smit and L. Trigeorgis, Strategic Investment, Real Options and Games (Princeton, NJ: Princeton University Press, 2004).

L. Trigeorgis, Real Options (Cambridge, MA: MIT Press, 1996).

Mason and Merton review a range of option applications to corporate finance:

S. P. Mason and R. C. Merton, “The Role of Contingent Claims Analysis in Corporate Finance,” in E. I. Altman and M. G. Subrahmanyan (eds.), Recent Advances in Corporate Finance (Homewood, IL: Richard D. Irwin, Inc., 1985).

Brennan and Schwartz have worked out an interesting application to natural resource investments:

M. J. Brennan and E. S. Schwartz, “Evaluating Natural Resource Investments,” Journal of Business 58 (April 1985), pp. 135–157.

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PROBLEM SETS

ch23conSelect problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Expansion options Look again at the valuation in Table 22.2 of the option to invest in the Mark II project. Consider a change in each of the following inputs. Would the change increase or decrease the value of the expansion option?

 a.  Increased uncertainty (higher standard deviation).

 b.  More optimistic forecast (higher expected value) of the Mark II in 1985.

 c.  Increase in the required investment in 1985.

2.  Abandonment options A start-up company is moving into its first offices and needs desks, chairs, filing cabinets, and other furniture. It can buy the furniture for $25,000 or rent it for $1,500 per month. The founders are of course confident in their new venture, but nevertheless they rent. Why? What’s the option?

3.  Abandonment options Flip back to Tables 6.2 and 6.6, where we assumed an economic life of seven years for IM&C’s guano plant. What’s wrong with that assumption? How would you undertake a more complete analysis?

4.  Timing options You own a parcel of vacant land. You can develop it now, or wait.

 a.  What is the advantage of waiting?

 b.  Why might you decide to develop the property immediately?

5.  Operating options Gas turbines are among the least efficient ways to produce electricity, much less thermally efficient than coal or nuclear plants. Why do gas-turbine generating stations exist? What’s the option?

6.  Real options Why is quantitative valuation of real options often difficult in practice? List the reasons briefly.

7.  Real options True or false?

 a.  Real-options analysis sometimes tells firms to make negative-NPV investments to secure future growth opportunities.

 b.  Using the Black–Scholes formula to value options to invest is dangerous when the investment project would generate significant immediate cash flows.

 c.  Binomial trees can be used to evaluate options to acquire or abandon an asset. It’s OK to use risk-neutral probabilities in the trees even when the asset beta is 1.0 or higher.

 d.  It’s OK to use the Black–Scholes formula or binomial trees to value real options, even though the options are not traded.

 e.  A real-options valuation will sometimes reveal that it’s better to invest in a single large plant than a series of smaller plants.

8.  Real options Alert financial managers can create real options. Give three or four possible examples.

INTERMEDIATE

9.  Real options Describe each of the following situations in the language of options:

a.  Drilling rights to undeveloped heavy crude oil in Northern Alberta. Development and production of the oil is a negative-NPV endeavor. (Assume a break-even oil price is C$90 per barrel, versus a spot price of C$80.) However, the decision to develop can be put off for up to five years. Development costs are expected to increase by 5% per year.

b.  A Singapore restaurant is producing net cash flows, after all out-of-pocket expenses, of S$700,000 per year. There is no upward or downward trend in the cash flows, but they fluctuate as a random walk, with an annual standard deviation of 15%. The real estate occupied by the restaurant is owned, not leased, and could be sold for S$5 million. Ignore taxes.

c.  A variation on part (b): Assume the restaurant faces known fixed costs of S$300,000 per year, incurred as long as the restaurant is operating. Thus,

The annual standard deviation of the forecast error of revenue less variable costs is 10.5%. The interest rate is 10%. Ignore taxes.

d.  A paper mill in Finland can be shut down in periods of low demand and restarted if demand improves sufficiently. The costs of closing and reopening the mill are fixed.

e.  A real estate developer uses a parcel of urban land as a parking lot, although construction of either a hotel or an apartment building on the land would be a positive-NPV investment.

f.  Air France negotiates a purchase option for 10 Boeing 787s. Air France must confirm the order by 2014. Otherwise Boeing will be free to sell the aircraft to other airlines.

10.  Expansion options Look again at Table 22.2. How does the value in 1982 of the option to invest in the Mark II change if

a.  The investment required for the Mark II is $800 million (vs. $900 million)?

b.  The present value of the Mark II in 1982 is $500 million (vs. $467 million)?

c.  The standard deviation of the Mark II’s present value is only 20% (vs. 35%)?

11.  Option valuation You own a one-year call option to buy one acre of Los Angeles real estate. The exercise price is $2 million, and the current, appraised market value of the land is $1.7 million. The land is currently used as a parking lot, generating just enough money to cover real estate taxes. The annual standard deviation is 15% and the interest rate 12%. How much is your call worth? Use the Black–Scholes formula. You may find it helpful to go to the spreadsheet for Chapter 21, which calculates Black–Scholes values (visit this book’s website, www.mcgraw-hill.co.uk/textbooks/brealey).

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

12.  Option valuation A variation on Problem 11: Suppose the land is occupied by a warehouse generating rents of $150,000 after real estate taxes and all other out-of-pocket costs. The present value of the land plus warehouse is again $1.7 million. Other facts are as in Problem 11. You have a European call option. What is it worth?

13.  Abandonment value Take another look at the perpetual crusher example in Section 22-3. Construct a sensitivity analysis showing how the value of the abandonment put changes depending on the standard deviation of the project and the exercise price.

14.  R&D Construct a sensitivity analysis of the value of the pharmaceutical R&D project described in Figure 22.8. What input assumptions are most critical for the NPV of the project? Be sure to check the inputs to valuing the real option to invest at year 2.

15.  Binomial valuation You have an option to purchase all of the assets of the Overland Railroad for $2.5 billion. The option expires in nine months. You estimate Overland’s current (month 0) present value (PV) as $2.7 billion. Overland generates after-tax free cash flow (FCF) of $50 million at the end of each quarter (i.e., at the end of each three-month period). If you exercise your option at the start of the quarter, that quarter’s cash flow is paid out to you. If you do not exercise, the cash flow goes to Overland’s current owners.

In each quarter, Overland’s PV either increases by 10% or decreases by 9.09%. This PV includes the quarterly FCF of $50 million. After the $50 million is paid out, PV drops by $50 million. Thus the binomial tree for the first quarter is (figures in millions):

The risk-free interest rate is 2% per quarter.

a.  Build a binomial tree for Overland, with one up or down change for each three-month period (three steps to cover your nine-month option).

b.  Suppose you can only exercise your option now, or after nine months (not at month 3 or 6). Would you exercise now?

c.  Suppose you can exercise now, or at month 3, 6, or 9. What is your option worth today? Should you exercise today, or wait?

16.  Abandonment options In Section 10-4 we considered two production technologies for a new Wankel-engined outboard motor. Technology A was the most efficient but had no salvage value if the new outboards failed to sell. Technology B was less efficient but offered a salvage value of $17 million.

         Figure 10.5 shows the present value of the project as either $24 or $16 million in year 1 if Technology A is used. Assume that the present value of these payoffs is $18 million at year 0.

a.  With Technology B, the payoffs at year 1 are $22.5 or $15 million. What is the present value of these payoffs in year 0 if Technology B is used? (Hint: The payoffs with Technology B are 93.75% of the payoffs from Technology A.)

b.  Technology B allows abandonment in year 1 for $17 million salvage value. You also get cash flow of $1.5 million, for a total of $18.5 million. Calculate abandonment value, assuming a risk-free rate of 7%.

17.  Real options Respond to the following comments.

a.  “You don’t need option pricing theories to value flexibility. Just use a decision tree. Discount the cash flows in the tree at the company cost of capital.”

b.  “These option pricing methods are just plain nutty. They say that real options on risky assets are worth more than options on safe assets.”

c.  “Real-options methods eliminate the need for DCF valuation of investment projects.”

18.  Option valuation Josh Kidding, who has only read part of Chapter 10, decides to value a real option by (1) setting out a decision tree, with cash flows and probabilities forecasted for each future outcome; (2) deciding what to do at each decision point in the tree; and (3) discounting the resulting expected cash flows at the company cost of capital. Will this procedure give the right answer? Why or why not?

19.  Option valuation In binomial trees, risk-neutral probabilities are set to generate an expected rate of return equal to the risk-free interest rate in each branch of the tree. What do you think of the following statement: “The value of an option to acquire an asset increases with the difference between the risk-free rate of interest and the weighted-average cost of capital for the asset”?

20.  Put–call parity and real options Redo the example in Figure 22.8, assuming that the real option is a put option allowing the company to abandon the R&D program if commercial prospects are sufficiently poor at year 2. Use put–call parity. The NPV of the drug at date 0 should again be +$7.7 million.

CHALLENGE

21.  Complex real options Suppose you expect to need a new plant that will be ready to produce turbo-encabulators in 36 months. If design A is chosen, construction must begin immediately. Design B is more expensive, but you can wait 12 months before breaking ground. Figure 22.9 below shows the cumulative present value of construction costs for the two designs up to the 36-month deadline. Assume that the designs, once built, will be equally efficient and have equal production capacity.

A standard DCF analysis ranks design A ahead of design B. But suppose the demand for turbo-encabulators falls and the new factory is not needed; then, as Figure 22.9 shows, the firm is better off with design B, provided the project is abandoned before month 24.

Describe this situation as the choice between two (complex) call options. Then describe the same situation in terms of (complex) abandonment options. The two descriptions should imply identical payoffs, given optimal exercise strategies.

   FIGURE 22.9 Cumulative construction cost of the two plant designs. Plant A takes 36 months to build; plant B, only 24. But plant B costs more.

22.  Options and growth In Chapter 4, we expressed the value of a share of stock as

where EPS1 is earnings per share from existing assets, r is the expected rate of return required by investors, and PVGO is the present value of growth opportunities. PVGO really consists of a portfolio of expansion options.¹⁸

a.  What is the effect of an increase in PVGO on the standard deviation or beta of the stock’s rate of return?

b.  Suppose the CAPM is used to calculate the cost of capital for a growth (high-PVGO) firm. Assume all-equity financing. Will this cost of capital be the correct hurdle rate for investments to expand the firm’s plant and equipment, or to introduce new products?

23.  Real options cases Go to the website of the Real Options Group (www.rogroup.com). Under “Publications/Resources — Applications” you should find three case studies in the pharmaceutical industry, including real-options analyses at the U.K. company GlaxoSmithKline and the German company MediGene AG. Review these case studies. Have the analysts “done it right,” given the concepts and procedures discussed in this chapter? In what ways do the analyses extend these concepts and procedures? Discuss.

___________

¹You could also use scenario analysis, which we described in Chapter 10. Work out “best” and “worst” scenarios to establish a range of possible future values. Then find the annual standard deviation that would generate this range over the life of the option. For the Mark II, a range from $300 million to $2 billion would cover about 90% of the possible outcomes. This range, shown in Figure 22.1, is consistent with an annual standard deviation of 35%.

²Be sure to “unlever” the standard deviations, thereby eliminating volatility created by debt financing. Chapters 17 and 19 covered unlevering procedures for beta. The same principles apply for standard deviation: You want the standard deviation of a portfolio of all the debt and equity securities issued by the comparable firm.

³If the required investment is uncertain, you have, in effect, an option to exchange one risky asset (the future value of the exercise price) for another (the future value of the Mark II’s cash inflows). See W. Margrabe, “The Value of an Option to Exchange One Asset for Another,” Journal of Finance 33 (March 1978), pp. 177–186.

⁴We have drawn the future values of the Mark II as a lognormal distribution, consistent with the assumptions of the Black–Scholes formula. Lognormal distributions are skewed to the right, so the average outcome is greater than the most likely outcome. The most likely outcome is the highest point on the probability distribution.

⁵We have been a bit vague about forecasted project cash flows. If competitors can enter and take away cash that you could have earned, the meaning is clear. But what about the decision to, say, develop an oil well? Here delay doesn’t waste barrels of oil in the ground; it simply postpones production and the associated cash flow. The cost of waiting is the decline in today’s present value of revenues from production. Present value declines if the cash flow from production increases more slowly than the cost of capital.

⁶The following example is based on P. D. Childs, T. J. Riddiough, and A. J. Triantis, “Mixed Uses and the Redevelopment Option,” Real Estate Economics 24 (Fall 1996), pp. 317–339.

⁷See S. C. Myers and S. Majd, “Abandonment Value and Project Life,” in Advances in Futures and Options Research, ed. F. J. Fabozzi (Greenwich, CT: JAI Press, 1990).

⁸We assume it makes sense to keep the tanker in mothballs. If rates fall sufficiently, it will pay to scrap the tanker.

⁹Dixit and Pindyck estimate these thresholds for a medium-sized tanker and show how they depend on costs and the volatility of freight rates. See A. K. Dixit and R. S. Pindyck, Investment under Uncertainty (Princeton, NJ: Princeton University Press, 1994), Chapter 7. Brennan and Schwartz provide an analysis of a mining investment that also includes an option to shut down temporarily. See M. Brennan and E. Schwartz, “Evaluating Natural Resource Investments,” Journal of Business 58 (April 1985), pp. 135–157.

¹⁰Here we refer to simple CTs, which are just large gas turbines connected to generators. Combined-cycle CTs add a steam generator to capture exhaust heat from the turbine. The steam is used to generate additional electricity. Combined-cycle units are much more efficient than simple CTs.

¹¹Industrial steam and heating systems can also be designed to switch between fuels, depending on relative fuel costs. See N. Kulatilaka, “The Value of Flexibility: The Case of a Dual-Fuel Industrial Steam Boiler,” Financial Management 22 (Autumn 1993), pp. 271–280.

¹¹The following example is based on J. E. Stonier, “What Is an Aircraft Purchase Option Worth? Quantifying Asset Flexibility Created through Manufacturer Lead-Time Reductions and Product Commonality,” in Handbook of Airline Finance, ed. G. F. Butler and M. R. Keller. © 1999 Aviation Week Books.

¹²The Airbus real-options model assumes that future A320 prices will be increased when demand is high, but only to an upper bound. Thus the airline that waits and decides later may still have a positive-NPV investment opportunity if future demand and NPV are high. Figure 22.7 plots the difference between the value of the purchase option and this wait-and-see opportunity. This difference can shrink when NPV is high, especially if forecasted waiting times are short.

¹³Note that the Black–Scholes formula treats the exercise price of $130 million as a fixed amount and calculates its PV at a risk-free rate. In Chapter 10, we assumed this investment was just as risky as the drug’s postlaunch cash flows. We discounted the investment at the 9.6% overall cost of capital, reducing its PV and thus increasing NPV overall. This is one reason why the Black–Scholes formula gives a lower NPV than we calculated in Chapter 10. Of course the $130 million is only an estimate, so discounting at the risk-free rate may not be correct. You could move from Black–Scholes to the valuation formula for an exchange option, which allows for uncertain exercise prices (see footnote 3 above). On the other hand, the R&D investment is probably close to a fixed cost, because it is not exposed to the risks of the drug’s operating cash flows postlaunch. There is a good case for discounting R&D investment at a low rate, even in a decision tree analysis.

¹⁴You could also value the R&D example as (1) the PV of making all future investments, given success in clinical trials, plus (2) the value of an abandonment put, which will be exercised if clinical trials are successful but the PV of postlaunch cash flows is sufficiently low. NPV is identical because of put–call parity.

¹⁵The higher cost of capital for R&D is not revealed by the Black–Scholes formula, which discounts certainty-equivalent payoffs at the risk-free interest rate.

¹⁶Use of risk-neutral probabilities converts future cash flows to certainty equivalents, which are then discounted to present value at a risk-free rate.

¹⁷Being the first mover into a new market is not always the best strategy, of course. Sometimes later movers win. For a survey of real options and product-market competition, see H. Smit and L. Trigeorgis, Strategic Investment, Real Options and Games (Princeton, NJ: Princeton University Press, 2004).

¹⁸If this challenge problem intrigues you, check out two articles by Eduardo Schwartz and Mark Moon, who attempt to use real-options theory to value Internet companies: “Rational Valuation of Internet Companies,” Financial Analysts Journal 56 (May/June 2000), pp. 62–65, and “Rational Pricing of Internet Companies Revisited,” The Financial Review 36 (November 2001), pp. 7–25.

Part 7 Debt Financing

Credit Risk and the Value of Corporate Debt

We first looked at how to value bonds way back in Chapter 3. We explained in that chapter what bond dealers mean when they refer to spot rates of interest and yields to maturity. We discussed why long-term and short-term bonds may offer different rates of interest and why prices of long-term bonds are affected more by a change in rates. We looked at the difference between nominal and real (inflation-adjusted) interest rates, and we saw how interest rates respond to changes in the prospects for inflation.

All the lessons of Chapter 3 hold good for both government and corporate bonds, but there is also a fundamental distinction between government and corporate issues. When a government borrows money, you can be fairly confident that the debt will be repaid in full and on time. This is not true of corporate borrowing. Look, for example, at Figure 23.1. You can see that in 2009, following the financial crisis, companies defaulted on a record $628 billion of debt. Bondholders are aware of the danger that they will not get their money back and so demand a higher yield.

We begin our review of corporate bonds by looking at how yields vary with the likelihood of default. Then in Section 23-2 we look more carefully at the company’s decision to default. We show that default is an option; if the going becomes too tough, the company has the option to stop payments on its bonds and hand over the business to the debtholders. We know what determines the value of options; therefore, we know the basic variables that must enter into the valuation of corporate bonds.

Our next step is to look at bond ratings and some of the techniques that are used by banks and bond investors to estimate the probability that the borrower will not be able to repay its debts. As a company’s prospects deteriorate, bondholders worry increasingly about this risk, and their worries are reflected in lower bond prices. Therefore, in the final section we describe some of the ways that financial managers measure the risk of loss from investment in corporate bonds.

 23-1   Yields on Corporate Debt

In August 2005 LifeCare Holdings issued $150 million of eight-year 9.25% senior notes. By the start of 2012 these notes were trading at only 74% of face value and offered a yield to maturity of 39%. A naïve investor who compared this figure with the 2% yield on Treasury bonds might have concluded that the LifeCare notes were a wonderful investment. But the owner would earn a 39% return only if the company repaid the debt in full. By 2012 that was looking increasingly doubtful. The company was itself on life support; it had recorded a series of losses and had over $400 million of debt and negative book equity. Because there was a considerable risk that the company would default on its bonds, the expected yield was much less than 39%.

BEYOND THE PAGE

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U.S. bond default rate, 1980–2011

brealey.mhhe.com/c23

   FIGURE 23.1 Global face value of defaulting debt, 1990–2010, in billions of dollars.

Source: Standard & Poor’s, Default, Transition and Recovery: 2010 Annual Global Corporate Default Study and Rating Transitions, February 2011.

Corporate bonds, such as the LifeCare bond, offer a higher promised yield than government bonds, but do they necessarily offer a higher expected yield? We can answer this question with a simple numerical example. Suppose that the interest rate on one-year risk-free bonds is 5%. Backwoods Chemical Company has issued 5% notes, maturing in one year. What will the Backwoods notes sell for?

If the notes are risk-free, the answer is easy—just discount principal and interest at 5%:

Suppose, however, that there is a 20% chance that Backwoods will default and that, if default does occur, holders of its notes receive half the face value of the notes, or $500. In this case, the possible payoffs to the noteholders are

The expected payment is .8($105) + .2($50) = $94.

We can value the Backwoods notes like any other risky asset, by discounting their expected payoff ($94) at the appropriate opportunity cost of capital. We might discount at the risk-free interest rate (5%) if Backwoods’s possible default is totally unrelated to other events in the economy. In this case default risk is wholly diversifiable, and the beta of the notes is zero. The notes would sell for

An investor who purchased the notes for $89.5 would receive a promised yield of 17.3%:

That is, an investor who purchased the notes for $895 would earn a return of 17.3% if Backwoods does not default. Bond traders therefore might say that the Backwoods notes “yield 17.3%.” But the smart investor would realize that the notes’ expected yield is only 5%, the same as on risk-free bonds.

This of course assumes that the risk of default with these notes is wholly diversifiable, so that they have no market risk. In general, risky bonds do have market risk (that is, positive betas) because default is more likely to occur in recessions when all businesses are doing poorly. Suppose that investors demand a 3% risk premium and an 8% expected rate of return. Then the Backwoods notes will sell for 94/1.08 = 87 and offer a promised yield of (105/87) – 1 = .207, or 20.7%.

What Determines the Yield Spread?

Figure 23.2 shows how the yield spread on U.S. corporate bonds varies with the bond’s risk. Bonds rated Aaa by Moody’s are the highest-grade bonds and are issued only by blue-chip companies. The promised yield on these bonds has on average been about 1% higher than the yield on Treasuries. Baa bonds are rated three notches lower; the yield spread on these bonds has averaged over 2%. At the bottom of the heap are high-yield or “junk” bonds. There is considerable variation in the yield spreads on junk bonds; a typical spread might be about 5% over Treasuries, but, as we saw in the case of the LifeCare bond, spreads can go skyward as companies approach distress.

Remember these are promised yields and companies don’t always keep their promises. Many high-yielding bonds have defaulted, while some of the more successful issuers have called their debt, thus depriving their holders of the prospect of a continuing stream of high coupon payments. So while the promised yield on junk bonds has averaged 5% more than yields on Treasuries, the annual return since 1980 has been less than 3% higher.

Figure 23.2 also shows that yield spreads can vary quite sharply from one year to the next, particularly for low-rated bonds. For example, they were unusually high in 1990–1991, 2000–2002, and 2008. Why is this? The main reason is that these were periods when profits were poor and defaults more likely. However, the fluctuations in spreads appear to be too large to be due simply to changing probabilities of default. It seems that there are occasions when investors are particularly reluctant to bear the risk of low-grade bonds and so scurry to the safe haven of government debt.¹

   FIGURE 23.2 End-year yield spreads between corporate and 10-year Treasury bonds, 1980–2011.

Source: The Federal Reserve, www.federalreserve.gov, and Datastream.

To understand more precisely what the yield spread measures, compare these two strategies:

Strategy 1: Invest $1,000 in a floating-rate default-free bond yielding 9%.²

Strategy 2: Invest $1,000 in a comparable floating-rate corporate bond yielding 10%. At the same time take out an insurance policy to protect yourself against the possibility of default. You pay an insurance premium of 1% a year, but in the event of default you are compensated for any loss in the bond’s value.

Both strategies provide exactly the same payoff. In the case of Strategy 2 you gain a 1% higher yield but this is exactly offset by the 1% annual premium on the insurance policy. Why does the insurance premium have to be equal to the spread? Because, if it weren’t, one strategy would dominate the other and there would be an arbitrage opportunity. The law of one price tells us that two equivalent risk-free investments must cost the same.

Our example tells us how to interpret the spread on corporate bonds. It is equal to the annual premium that would be needed to insure the bond against default.³

By the way, you can insure corporate bonds; you do so with an arrangement called a credit default swap (CDS). If you buy a default swap, you commit to pay a regular insurance premium (or spread).⁴ In return, if the company subsequently defaults on its debt, the seller of the swap pays you the difference between the face value of the debt and its market value. For example, when American Airlines defaulted in 2011, its unsecured bonds were auctioned for 23.5% of face value. Thus sellers of default swaps had to pay out 76.5 cents on each dollar of American Airlines’s debt that they had insured. In the case of American Airlines, it was clear that the company was in default, but occasionally it is not so obvious, as the box on the next page explains.

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CDS volume

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CDSs have proved very popular, particularly with banks that need to reduce the risk of their loan books. From almost nothing in 2000, the notional value of default swaps and related products had mushroomed to $62 trillion in 2007 before falling sharply over the next two years.⁵

Figure 23.3 shows the annual cost of insuring the 10-year bonds of a sample of well-known European firms. Notice the sharp increase in the cost of the default swaps in 2009. By the end of February 2009 it cost €3.19 a year to insure €100 of UBS debt.

   FIGURE 23.3 Credit default swaps insure the holders of corporate bonds against default. This figure shows the cost of default swaps on the 10-year senior debt of four companies.

Source: Datastream

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What Exactly Is a Default?

  At the start of 2012, holders of $3.2 billion of Greek government debt had bought credit default swaps that insured them against default. Governments in Europe worried that if the insurance were triggered, the banks that had sold it would suffer significant losses. Could Greece somehow avoid paying its debts without defaulting?

The governments’ solution was to ask (or strong-arm) private bond holders to voluntarily exchange their existing bonds for a package of new securities worth about 30% of the value of their existing bonds. The decision as to whether this would trigger payment on the default swaps was the responsibility of the International Swaps and Derivatives Association (ISDA). In such cases, the ISDA arranges for a Determinations Committee to decide whether there has been a “credit event.” Once the committee acknowledges that a credit event has occurred, an auction is conducted to determine the value of the defaulted bonds; owners of default swaps are paid the difference between this auction value and the face value of the bonds.

The ISDA’s Determinations Committee has 15 members. Ten are dealers and five represent investors. The dealer representatives must be participating bidders in the auctions determining payouts, and the ones who are chosen are likely to have the biggest positions. The investor members must have at least $1 billion of assets under management and $1 billion of CDS exposure. Thus the people on the Determinations Committee are not disinterested parties, and this has the potential to cause problems.

The Determinations Committee initially ruled that if Greece’s proposed bond exchange was indeed voluntary, then it could not be regarded as a default. However, this decision was rapidly overtaken by events. Greece announced that it had persuaded a majority of its private-sector creditors to accept its proposal and that it would activate “collective action clauses” that had been retrospectively inserted into the bonds’ terms and conditions. These clauses would coerce the remaining reluctant bondholders to accept the deal and swap their old bonds for new. At that point in March 2012 the Determinations Committee formally ruled that Greece was in default and that payments were due on the default swaps.

Many of these default swaps were sold by monoline insurers, which specialize in providing services to the capital markets. The monolines had traditionally concentrated on insuring relatively safe municipal debt but had been increasingly prepared to underwrite corporate debt, as well as many securities that were backed by subprime mortgages. By 2008 insurance companies had sold protection on $2.4 trillion of bonds. As the outlook for many of these bonds deteriorated, investors began to question whether the insurance companies had sufficient capital to make good on their guarantees.

One of the largest providers of credit protection was AIG Financial Products, part of the giant insurance group, AIG, with a portfolio of over $440 billion of credit guarantees. AIG’s clients never dreamt that the company would be unable to pay up: not only was AIG triple-A rated, but it had promised to post generous collateral if the value of the insured securities dropped or if its own credit rating fell. So confident was AIG of its strategy that the head of its financial products group claimed that it was hard “to even see a scenario within any kind of realm of reason that would see us losing one dollar in any of these transactions.” But in September 2008 this unthinkable scenario occurred, when the credit rating agencies downgraded AIG’s debt, and the company found itself obliged to provide $32 billion of additional collateral within the next 15 days. Had AIG defaulted, everyone who had bought a CDS contract from the company would have suffered large losses on these contracts. To save AIG from imminent collapse, the Federal Reserve stepped in with an $85 billion rescue package.

 23-2   The Option to Default

The difference between a corporate bond and a comparable Treasury bond is that the company has the option to default whereas the government supposedly doesn’t.⁶ That is a valuable option. If you don’t believe us think about whether (other things equal) you would prefer to be a shareholder in a company with limited liability or in a company with unlimited liability. Of course, you would prefer to have the option to walk away from your company’s debts. Unfortunately, every silver lining has its cloud, and the drawback to having a default option is that corporate bondholders expect to be compensated for giving it to you. That is why corporate bonds sell at lower prices and offer higher yields than government bonds.

We can illustrate the nature of the default option by returning to the plight of Circular File Company, which we discussed in Chapter 18. Circular File borrowed $50 per share, but then the firm fell on hard times and the market value of its assets fell to $30. Circular’s bond and stock prices fell to $25 and $5, respectively. Thus Circular’s market-value balance sheet is:

If Circular’s debt were due and payable now, the firm could not repay the $50 it originally borrowed. It would default, leaving bondholders with assets worth $30 and shareholders with nothing. The reason that Circular stock has a market value of $5 is that the debt is not due now, but rather a year from now. A stroke of good fortune could increase firm value enough to pay off the bondholders in full, with something left over for the stockholders.

When Circular File borrowed, it acquired an option to default. In other words, it is not compelled to repay the debt at maturity. If the value of its assets is less than the $50 that it owes, it will choose to default on the debt and the bondholders will get to keep the assets. To put it another way, when Circular borrowed, the bondholders effectively acquired the company’s assets and the shareholders gained an option to buy them back by paying off the debt. In effect, the stockholders purchased a call option on the assets of the firm. Thus the balance sheet of Circular File can be expressed as follows:

Figure 23.4 shows the possible payoffs to Circular File’s shareholders when the bonds mature at the end of the year. If the future value of the assets is less than $50, Circular will default and the stock will be worthless. If the value of the assets exceeds $50, the stockholders will receive asset value less the $50 paid over to the bondholders. Does Figure 23.4 look familiar to you? It should if you have read Chapter 20 on options. The payoffs in Figure 23.4 are identical to those of a call option on the firm’s assets with an exercise price of $50.

   FIGURE 23.4 The value of Circular’s common stock is the value of a call option on the firm’s assets with an exercise price of $50.

In Chapter 20 we also set out the basic relationship between calls and puts:

To apply this to Circular File, we need to interpret “value of share” as “asset value,” because the common stock is a call option on the firm’s assets. Also “present value of exercise price” is the present value of receiving the promised payment of $50 to bondholders for sure next year. Thus,

Now we can solve for the value of Circular’s bonds. This is equal to the firm’s asset value less the value of the shareholders’ call option on these assets:

Circular’s bondholders have in effect bought a safe bond, but at the same time given the shareholders a put option to sell them the firm’s assets for the amount of the debt.

Now you can see why bond traders, investors, and financial managers refer to default puts. When a firm defaults, its stockholders are in effect exercising their default put. The put’s value is the value of limited liability—the value of the stockholders’ right to walk away from their firm’s debts in exchange for handing over the firm’s assets to its creditors. In the case of Circular File this option to default is extremely valuable because default is likely to occur. At the other extreme, the value of IBM’s option to default is trivial compared with the value of IBM’s assets. Default on IBM bonds is possible but extremely unlikely. Option traders would say that for Circular File the put option is “deep in the money” because today’s asset value ($30) is well below the exercise price ($50). For IBM the put option is far “out of the money” because the value of IBM’s assets substantially exceeds the amount of IBM’s debt.

Valuing corporate bonds should be a two-step process:

The first step is easy: Calculate the bond’s value assuming no default risk. (Discount promised interest and principal payments at the rates offered by Treasury issues.) Second, calculate the value of a put written on the firm’s assets, where the maturity of the put equals the maturity of the bond and the exercise price of the put equals the promised payment to bondholders.

Owning a corporate bond is also equivalent to owning the firm’s assets but giving a call option on these assets to the firm’s stockholders:

Thus you can also calculate a bond’s value, given the value of the firm’s assets, by valuing a call option on these assets and subtracting the value of this call from that of the assets. (Remember: The call value is just the value of the firm’s common stock.) Therefore, if you can value puts and calls on the firm’s assets, you can value its debt.⁷

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Try It! Valuing the default put

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How the Default Option Affects a Bond’s Risk and Yield

If the firm’s debt is risk-free, the equityholders bear all the risk of the underlying assets. But when the firm has limited liability, the debtholders share this risk with the equityholders. We have seen that the equity of a firm with limited liability is equivalent to a call option on the firm’s assets. So, if we can calculate the risk of this call, we can find how the firm’s risk is shared between the equityholders and the debtholders.⁸

Think back to Chapter 21 where you learned how to calculate the risk of a call option. This involved two steps:

 1.  Find the combination of the underlying asset and risk-free borrowing that provides the same payoffs as the call option (in the present case, the call option is the leveraged equity).

 2.  Calculate the beta of this replicating portfolio.

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Try It! Leverage and debt betas

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Figure 23.5 takes a hypothetical company whose underlying assets have a beta of 1.0 and shows how the beta of these assets is shared between the equityholders and the debtholders. If the company had unlimited liability, the equityholders would bear all the risk of the assets and the debt would be risk-free. But with limited liability, the debtholders bear part of the risk. The higher the leverage and the longer the maturity of the debt, the greater the proportion of the risk that is assumed by the debtholders. For example, suppose that our hypothetical company is financed 60% by 25-year debt. With unlimited liability the debt would have a beta of zero and the equity would have a beta of 2.5.⁹ But, when the risk of the assets is shared, the debt has a beta of .4 and the equity a beta of 1.4.

Figure 23.6 stays with the same hypothetical company and shows how the promised yield on its debt varies with leverage and bond maturity. For example, you can see that if a company has a 20% debt ratio and all its debt matures in 25 years, then it should pay about .50 percentage point above the government rate to compensate for default risk. Notice that just as risk increases with maturity, so generally does the promised yield. This makes sense, for the longer you have to wait for repayment, the greater the chance that things will go wrong.¹⁰

   FIGURE 23.5 How the betas of the debt and equity vary with the degree of leverage and the maturity of the debt. These curves are calculated using option pricing theory under the following simplified assumptions: (1) the risk-free interest rate is constant for all maturities; (2) the standard deviation of the returns on the company’s assets is 25% per annum; (3) the asset beta is 1.0; (4) debt is in the form of zero-coupon bonds; and (5) leverage is the ratio D/V, where D is the face value of the debt discounted at the risk-free interest rate and V is the market value of the assets.

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   FIGURE 23.6 How the interest rate on risky corporate debt changes with leverage and maturity.

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Notice that in constructing Figure 23.6 we made several artificial assumptions. One assumption is that the company does not pay dividends or repurchase stock. If it does regularly pay out part of its assets to stockholders, there will be fewer assets to protect the bondholder in the event of trouble. In this case, the market will justifiably require a higher yield on the company’s bonds.

There are other complications that make the valuation of corporate debt a good bit more difficult than it sounds. For example, Figure 23.6 assumes that the company makes only a single issue of zero-coupon debt. But suppose instead that it issues a 10-year bond that pays interest annually. We can still think of the company’s stock as a call option that can be exercised by making the promised payments. But in this case there are 10 payments rather than just one. To value the stock, we would need to value 10 sequential call options. The first option can be exercised by making the first interest payment when it comes due. By exercising, the stockholders obtain a second call option, which can be exercised by making the second interest payment. The reward to exercising is that the stockholders get a third call option, and so on. Finally, in year 10 the stockholders can exercise the tenth option. By paying off both the principal and the last year’s interest, the stockholders regain unencumbered ownership of the company’s assets.

Of course, if the firm does not make any of these payments when due, bondholders take over and stockholders are left with nothing. In other words, by not exercising one call option, stockholders give up all subsequent call options.

Valuing the equity when the 10-year bond is issued is equivalent to valuing the first of the 10 call options. But you cannot value the first option without valuing the nine that follow.¹¹ Even this example understates the practical difficulties, because large firms may have dozens of outstanding debt issues with different interest rates and maturities, and before the current debt matures they may make further issues. Consequently, when bond traders evaluate a corporate bond, they do not immediately reach for their option calculator. They are more likely to start by identifying bonds with a similar risk of default and look at the yield spreads offered by these bonds.

In practice, interest rate differentials tend to be much greater than those shown in Figure 23.6. The highest-grade corporate bonds typically offer promised yields about 1 percentage point higher than U.S. Treasury bonds. It is very difficult to justify differentials of this magnitude simply in terms of default risk.¹² So what is going on? It could be that companies are paying too much for their debt, but it seems likely that the high yields on corporate bonds stem in part from some other drawback. One possibility is that investors demand the additional yield to compensate for the lack of liquidity in corporate debt markets.¹³ There is little doubt that investors prefer bonds that are easily bought and sold. We can even see small yield differences in the Treasury bond market, where the latest bonds issued (known as “on-the-run” bonds) are traded much more heavily and typically yield a little less than more seasoned issues.

Another reason that corporate bond investors in the United States may require a higher yield is that interest payments are subject to both federal and state tax. Interest on Treasury bonds is exempt from state tax. Suppose, for example, that you hold a corporate bond with a 6% coupon and pay state tax of 5%. Then you would need an additional yield of about .05 × 6 = .3% simply to compensate for the additional tax.¹⁴

A Digression: Valuing Government Financial Guarantees

When American Airlines declared bankruptcy in 2011, its pension plan had liabilities of $18.5 billion and assets of just $8.3 billion. But the 130,000 workers and retirees did not face a destitute old age. Their pensions were largely guaranteed by the Pension Benefit Guaranty Corporation (PBGC).¹⁵

Pension promises don’t always appear on the company’s balance sheet, but they are a long-term liability just like the promises to bondholders. The guarantee by the PBGC changes the pension promises from a risky liability to a safe one. If the company goes belly-up and there are insufficient assets to cover the pensions, the PBGC makes up the difference.

The government recognizes that the guarantee provided by the PBGC is costly. Thus shortly after assuming the liability for the American Airlines plan, the PBGC calculated that the discounted value of payments on defaulted plans and those close to default amounted to $98 billion.

Unfortunately, these calculations ignore the risk that other firms in the future may fail and hand over their pension liability to the PBGC. To calculate the cost of the guarantee, we need to think about what the value of company pension promises would be without any guarantee:

With the guarantee the pensions are as safe as a promise by the U.S. government;¹⁶ without the guarantee the pensions are like an ordinary debt obligation of the firm. We already know what the difference is between the value of safe government debt and risky corporate debt. It is the value of the firm’s right to hand over the assets of the firm and to walk away from its obligations. Thus the value of the pension guarantee is the value of this put option.

In a paper prepared for the Congressional Budget Office, Wendy Kiska, Deborah Lucas, and Marvin Phaup show how option pricing models can help to give a better measure of the cost to the PBGC of pension guarantees.¹⁷ Their estimates suggest that the value of the PBGC’s guarantees was substantially higher than the published estimate.

The PBGC is not the only government body to provide financial guarantees. For example, the Federal Deposit Insurance Corporation (FDIC) guarantees bank deposit accounts; the Federal Family Education Loan (FFEL) program guarantees loans to students; the Small Business Administration (SBA) provides partial guarantees for loans to small businesses, and so on. The government’s liability under these programs is enormous. Fortunately, option pricing is leading to a better way to calculate their cost.

 23-3   Bond Ratings and the Probability of Default

Banks and other financial institutions not only want to know the value of the loans that they have made, but they also need to know the risk that they are incurring. Some rely on the judgments of specialized bond rating services. Others have developed their own models for measuring the probability that the borrower will default. We describe bond ratings first, and then discuss two models for predicting default.

The relative quality of most traded bonds can be judged by bond ratings. There are three principal rating services—Moody’s, Standard & Poor’s, and Fitch.¹⁸ Table 23.1 summarizes these ratings. For example, the highest-quality bonds are rated triple-A (Aaa) by Moody’s, then come double-A (Aa) bonds, and so on. Bonds rated Baa or above are known as investment-grade bonds.¹⁹ Commercial banks, many pension funds, and other financial institutions are not allowed to invest in bonds unless they are investment-grade.²⁰

Bonds rated below Baa are termed high-yield, or junk, bonds. Most junk bonds used to be fallen angels, that is, bonds of companies that had fallen on hard times. But during the 1980s new issues of junk bonds multiplied tenfold as more and more companies issued large quantities of low-grade debt to finance takeovers. The result was that for the first time corporate midgets were able to take control of corporate giants.

   TABLE 23.1 Key to bond ratings. The highest-quality bonds are rated triple-A. Investment-grade bonds have to be the equivalent of Baa or higher. Bonds that don’t make this cut are called “high-yield” or “junk” bonds.

Issuers of these junk bonds often had debt ratios of 90% to 95%. Many worried that this threatened the health of corporate America and, as default rates on corporate debt rose to 10% in the early 1990s, the market for new issues of junk bonds dried up. Since then the market for junk debt has had its ups and downs, but, as we write this in early 2012, new issues of junk bonds have just enjoyed a record year.

Bond ratings are judgments about firms’ financial and business prospects. There is no fixed formula by which ratings are calculated. Nevertheless, investment bankers, bond portfolio managers, and others who follow the bond market closely can get a fairly good idea of how a bond will be rated by looking at a few key numbers such as the firm’s debt ratio, the ratio of earnings to interest, and the return on assets. Table 23.2 shows how these ratios vary with the firm’s bond rating.

Figure 23.7 shows that bond ratings do reflect the probability of default. Since 1981 only 3 in 10,000 U.S. bonds that were initially rated triple-A by Standard & Poor’s have defaulted in the year after issue and only 55 in 10,000 have defaulted within 10 years of issue. (The AAA default rate is not plotted in Figure 23.7. It would be invisible.) At the other extreme, half of CCC bonds have defaulted by year 10. Of course, bonds do not usually fall suddenly from grace. As time passes and the company becomes progressively more shaky, the agencies revise downward the bond’s rating to reflect the increasing probability of default.

   TABLE 23.2 How financial ratios differ according to a firm’s bond rating. Two-year (2008–2009) median ratios for U.S. nonfinancial companies by bond rating.

a A debt ratio greater than 100% means that book equity is negative.

Source: Moody’s Financial Metrics: Key Ratios by Rating and Industry for Global Non-Financial Corporations, December 2009.

   FIGURE 23.7 Default rates of corporate bonds 1981–2010, by Standard & Poor’s rating at time of issue.

Source: Standard & Poor’s, “Default, Transition, and Recovery: 2010 Global Annual Corporate Default Study and Rating Transitions,” February 2011. www.standardandpoors.com.

Rating agencies don’t always get it right. When Enron went belly-up in 2001, investors protested that only two months earlier the company’s debt had an investment-grade rating. Rating agencies also did not win many friends during the financial crisis of 2007–2009, when many of the mortgage-backed assets that had been given a triple-A rating went belly-up. And when agencies do downgrade a company’s debt, they are often accused of precipitate action that increases the cost of borrowing.

 23-4   Predicting the Probability of Default

Credit Scoring

If you apply for a credit card or a bank loan, you will probably be asked to complete a questionnaire that provides details about your job, home, and financial health. This information is then used to calculate an overall credit score.²¹ If you do not make the grade on the score, you are likely to be refused credit or subjected to a more detailed analysis. In a similar way, mechanical credit scoring systems are used by banks to assess the risk of their corporate loans and by firms when they extend credit to customers.

Suppose that you are given the task of developing a credit scoring system that will help to decide whether to extend credit to businesses. You start by comparing the financial statements of companies that went bankrupt over a 40-year period with those of surviving firms. Figure 23.8 shows what you find. Panel (a) illustrates that, as early as four years before they went bankrupt, failing firms were earning a much lower return on assets (ROA) than firms that survived. Panel (b) shows that on average they also had a high ratio of liabilities to assets, and Panel (c) shows that EBITDA (earnings before interest, taxes, and depreciation) was low relative to the firms’ total liabilities. Thus bankrupt firms were less profitable (low ROA), were more highly leveraged (high ratio of liabilities to assets), and generated relatively little cash (low ratio of EBITDA to liabilities). In each case these indicators of the firms’ financial health steadily deteriorated as bankruptcy approached.

Rather than focusing on individual ratios, it makes more sense to combine the ratios into a single score that can separate the creditworthy sheep from the impecunious goats. For example, William Beaver, Maureen McNichols, and Jung-Wu Rhie, who studied these firms, concluded that the chance of failing during the next year relative to the chance of not failing was best estimated by the following equation:²²

   FIGURE 23.8 Financial ratios of 544 failing and nonfailing firms.

Source: W. H. Beaver, M. F. McNichols, and J-W. Rhie, “Have Financial Statements Become Less Informative? Evidence from the Ability of Financial Ratios to Predict Bankruptcy,” Review of Accounting Studies 10 (2005), pp. 93–122. Used with kind permission from Springer Science+Business Media.

Credit scoring systems should carry a health warning. When you construct a risk index, it is tempting to experiment with many different combinations of variables until you find the equation that would have worked best in the past. Unfortunately, if you “mine” the data in this way, you are likely to find that the system works less well in the future than it did previously. If you are misled by the past successes into placing too much faith in your model, you may refuse credit to a number of potentially good customers. The profits that you lose by turning away these customers could more than offset the gains that you make by avoiding a few bad eggs. As a result, you could be worse off than if you had pretended that you could not tell one would-be borrower from another and extended credit to all of them.

Does this mean that firms should not use credit scoring systems? Not a bit. It merely implies that it is not sufficient to have a good system; you also need to know how much to rely on it.

Market-Based Risk Models

Credit scoring systems rely primarily on the companies’ financial statements to estimate which firms are most likely to become bankrupt and default on their debts. For small businesses there may be little alternative to the use of accounting data, but for large, publicly traded firms it is also possible to take advantage of the information in security prices. These techniques build on the idea that stockholders will exercise their option to default if the market value of the assets falls below the payments that must be made on the debt.

Suppose that the assets of Phlogiston Chemical have a current market value of $100 and its debt has a face value of $60 (i.e., 60% leverage), all of which is due to be repaid at the end of five years. Figure 23.9 shows the range of possible values of Phlogiston’s assets when the loan becomes due. The expected value of the assets is $120, but this value is by no means certain. There is a probability of 20% that the asset value could fall below $60, in which case the company will default on its debt. This probability is shown by the shaded area in Figure 23.9.

To calculate the probability that Phlogiston will default, we need to know the expected growth in the market value of its assets, the face value and maturity of the debt, and the variability of future asset values. Real-world cases are likely to be more complex than our Phlogiston example. For example, firms may have several classes of debt maturing on different dates. If so, it may pay the stockholders to put up more money to pay off the short-term debt and thus keep alive the chance that the firm’s fortunes will recover before the rest of the debt becomes due.

   FIGURE 23.9 Phlogiston Chemical has issued five-year debt with a face value of $60. The shaded area shows that there is a 20% probability that the value of the company’s assets in year 5 will be less than $60, in which case the company will choose to default.

   FIGURE 23.10 The market value of the assets of Six Flags crept closer and closer to the point at which the firm would choose to default.

Source: Moody’s KMV.

   FIGURE 23.11 Estimates by Moody’s KMV of the probability that Six Flags would default on its debt within a year.

Note: The probabilities reported by Moody’s KMV are limited to a range from .01% to 35%.

However, banks and consulting firms are now finding that they can use these ideas to measure the risk of actual loans. For example, Six Flags is known for the roller-coaster rides at its theme parks, but the company itself has experienced a white-knuckle ride of its own. By early 2009 the price of its 9.625% bonds of 2014 had fallen to 19.5% of face value and offered a yield to maturity of 64%. In June 2009, Six Flags finally succumbed and filed for bankruptcy.

The teal line in Figure 23.10 shows the market value that investors placed on Six Flags’s assets, and the red line shows the asset value at which the company would choose to default on its debts. You can see how the value of the company’s assets crept closer and closer to the default point before finally hitting it.

Of course, nobody had a crystal ball that foretold the eventual outcome, but Moody’s KMV, which specializes in credit models, regularly estimates the probability that companies will default on their debts during the next year. Figure 23.11 shows how KMV progressively increased its estimate of the chances that the value of Six Flags’s assets would hit the default point. As the value of the company’s assets started to collapse, KMV’s assessment of the probability of default progressively increased. By July 2008 it had reached the maximum figure of 35%.²³

 23-5   Value at Risk

It is January 2012 and you own Starbucks 6.25% bonds maturing in 2017. The bonds are rated BBB by Standard & Poor’s and are currently priced at 119.4% to offer a promised yield to maturity of 2.5%. If you plan to hold the bonds for the next 12 months, how much risk are you taking?

You may be tempted to look back at past default rates for BBB-rated bonds and conclude that there is only a negligible chance that the bonds will default during the next year and therefore your investment is almost as safe as U.S. Treasuries. But of course this ignores the possibility that, although default is unlikely in the short term, Starbucks’s prospects may not be as good at the end of the year as they are now. If so, the bonds could be downrated and their value would fall.

Banks and consulting firms have developed a variety of ways to measure the risk of a deterioration in credit quality. For example, one of the most popular, the CreditMetrics system, looks at the possible impact of changes in the bond rating.²⁴ Table 23.3 shows how frequently bonds were rerated in the years 1981–2010. Since your Starbucks bonds are BBB-rated, we will focus on the fourth row of the table. You can see that in the past 84.55% of BBB bonds were still rated triple-B after one year and a few were even upgraded to A or better. However, the bad news is that after one year over 5% of BBB-rated bonds had moved into the junk bond category of BB or below.

If Starbucks debt were to be downgraded to BB, investors would undoubtedly demand a higher yield. For example, in 2012 the yield on BB bonds was about 1.3% higher than that on triple-Bs. If the yield on your Starbucks bonds rose by this amount, the price would fall by about 7%. In other words, there is more than a 5% chance that the value of your investment will fall 7% or more over the coming year. Bankers refer to this as the value at risk (or VAR) on the Starbucks bonds.

There are a number of ways to improve this back-of-the-envelope estimate of the value at risk. For example, we assumed that the yield spreads on corporate bonds are constant. But, if investors become more reluctant to take on credit risk, you could lose much more than 7% on your investment. Notice also that when we calculated the risk from investing in Starbucks debt, we looked only at how the price of the bonds would be affected by a change in credit rating. If we wanted a comprehensive measure of value at risk, we would need to recognize that risk-free interest rates, too, may change over the year.

   TABLE 23.3 Global average one-year transition rates, 1981–2010, showing the percentage of bonds changing from one rating to another.

Source: Standard & Poor’s, “Default, Transition, and Recovery: 2010 Annual Global Default Study and Rating Transitions,” February 2011.

Banks and bond investors are not just interested in the risk of individual loans; they would also like to know the risk of their entire portfolio. Therefore, specialists in credit risk need to worry about the correlation between the outcomes. A portfolio of loans, all of which are to factory outlets in suburban Hicksville, is likely to be more risky than a portfolio with a variety of different borrowers.

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SUMMARY

Corporations have limited liability. If companies are unable to pay their debts, they can file for bankruptcy. Lenders are aware that they may receive less than they are owed, and that the expected yield on a corporate bond is less than the promised yield.

Because of the possibility of default, the promised yield on a corporate bond is higher than on a government bond. You can think of this extra yield as the amount that you would need to pay to insure the bond against default. There is an active market for insurance policies that protect the debtholder against default. These policies are called credit default swaps. There are no free lunches in financial markets. So the extra yield you get for buying a corporate bond is eaten up by the cost of insuring against default.

The company’s option to default is equivalent to a put option. If the value of the firm’s assets is less than the amount of the debt, it will pay for the company to default and to allow the lenders to take over the assets in settlement of the debt. This insight tells us what we need to think about when valuing corporate debt—the current value of the firm relative to the point at which it would default, the volatility of the assets, the maturity of the debt payments, and the risk-free interest rate. Unfortunately, most companies have several loans outstanding with payments due at different times. This considerably complicates the task of valuing the put option.

Because of these complications, bond investors do not regularly use option models to value the default option that is attached to a corporate bond. More commonly, they rely on their experience to judge whether the spread between the yield on a corporate bond and the yield on a comparable government issue compensates for the possibility of default. Spreads can change rapidly as investors reassess the chances of default or become more or less risk-averse.

When investors want a measure of the risk of a company’s bonds, they usually look at the rating that has been assigned by Moody’s, Standard & Poor’s, or Fitch. They know that bonds with a triple-A rating are much less likely to default than bonds with a junk rating.

Banks, rating services, and consulting firms have also developed a number of models for estimating the likelihood of default. Credit scoring systems take accounting ratios or other indicators of corporate health and weight them to produce a single measure of default. Moody’s KMV takes a different tack and seeks to measure the probability that the market value of the firm’s assets will fall to the point at which the firm will choose to default rather than try to keep up with its debt payments.

Don’t assume that there is no risk just because there is no immediate prospect of default. If the quality of the bonds deteriorates, investors will demand a higher yield and the bond price will fall. One way to calculate the value at risk is to look at the probability of possible ratings changes and to estimate the likely effect of these changes for the bond’s price.

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FURTHER READING

The websites of the main credit rating agencies and of Moody’s KMV contain a variety of useful reports on credit risk. (See in particular www.moodys.com, www.standardandpoors.com, www.fitch.com, and www.moodyskmv.com.)

Altman and Hotchkiss provide a review of credit scoring models in:

E. I. Altman and E. Hotchkiss, Corporate Financial Distress and Bankruptcy, 3rd ed. (New York: John Wiley, 2006).

There are a number of books that discuss corporate bonds and credit risk. Look, for example, at:

A. Saunders and L. Allen, Credit Risk Measurement, 3rd ed. (New York: John Wiley, 2010).

J. B. Caouette, E. I. Altman, P. Narayanan, and R. Nimmo, Managing Credit Risk (New York: John Wiley, 2008).

D. Duffie, Measuring Corporate Default Risk (Cambridge, UK: Oxford University Press, 2011).

D. Duffie and K. J. Singleton, Credit Risk: Pricing, Measurement and Management (Princeton, NJ: Princeton University Press, 2003).

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PROBLEM SETS

ch23con Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

 1.  Expected yield You own a 5% bond maturing in two years and priced at 87%. Suppose that there is a 10% chance that at maturity the bond will default and you will receive only 40% of the promised payment. What is the bond’s promised yield to maturity? What is its expected yield?

 2.  Yield spreads Other things equal, would you expect the difference between the price of a Treasury bond and a corporate bond to increase or decrease with

 a.  The company’s business risk?

 b.  The degree of leverage?

 3.  Default option The difference between the value of a government bond and a simple corporate bond is equal to the value of an option. What is this option and what is its exercise price?

 4.  Default probability The following table shows some financial data for two companies:

Use the formula shown in Section 23-4 to calculate which has the higher probability of default.

 5. Default probability What variables are required to use a market-based approach to calculate the probability that a company will default on its debt?

 6. Ratings transition You have a B-rated bond. On past evidence, what is the probability that it will continue to be rated B in one year’s time? What is the probability that it will have a lower rating?

 7. Ratings transition You have an A-rated bond. Is a rise in rating more likely than a fall? Would your answer be the same if the bond were B-rated?

 8. Value at risk Why is it more difficult to estimate the value at risk for a portfolio of loans rather than for a single loan?

INTERMEDIATE

 9. Default option Company A has issued a single zero-coupon bond maturing in 10 years. Company B has issued a coupon bond maturing in 10 years. Explain why it is more complicated to value B’s debt than A’s.

 10. Default probability Company X has borrowed $150 maturing this year and $50 maturing in 10 years. Company Y has borrowed $200 maturing in five years. In both cases asset value is $140. Sketch a scenario in which X does not default but Y does.

 11. Credit scoring Discuss the problems with developing a numerical credit scoring system for evaluating personal loans. You can only test your system using data for applicants who have in the past been granted credit. Is this a potential problem?

 12. Default probability What problems are you likely to encounter when using a market-based approach for estimating the probability that a company will default?

 13. Default option How much would it cost you to insure the bonds of Backwoods Chemical against default? (See Section 23-1.)

CHALLENGE

 14. Default option valuation Look back to the first Backwoods Chemical example at the start of Section 23-1. Suppose that the firm’s book balance sheet is

The debt has a one-year maturity and a promised interest payment of 9%. Thus, the promised payment to Backwoods’s creditors is 1,090. The market value of the assets is 1,200 and the standard deviation of asset value is 45% per year. The risk-free interest rate is 9%. Calculate the value of Backwoods debt and equity.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

 15.  Default option valuation Use the Black–Scholes model and redraw Figures 23.5 and 23.6 assuming that the standard deviation of the return on the firm’s assets is 40% a year. Do the calculations for 60% leverage only. (Hint: It is simplest to assume that the risk-free interest rate is zero.) What does this tell you about the effect of changing risk on the spread between high-grade and low-grade corporate bonds? (You may find it helpful to use the Black–Scholes program on the spreadsheet for Chapter 21 at www.mcgraw-hill.co.uk/textbooks/brealey.)

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FINANCE ON THE WEB

 1.  Go to finance.yahoo.com and select three industrial companies that have been experiencing difficult times.

 a.  For each of them draw a figure similar to Figure 23.8. Are the companies’ troubles reflected in their financial ratios?

 b.  Calculate a default probability for each using the formula shown in Section 23-4.

 c.  Now look at the company’s bond rating. Do the two measures provide consistent messages?

 2.  Log in to www.moodysanalytics.com and find the sections on credit research. This site contains a number of case studies showing how the probability of default (termed the expected default frequency or EDF) changes as default comes closer. Compare the information provided by the EDFs with that provided by the credit ratings.

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¹For evidence on the effect of changing risk aversion on bond spreads, see A. Berndt, R. Douglas, D. Duffie, M. Ferguson, and D. Schranz, “Measuring Default Risk Premia from Default Swap Rates and EDFs,” BIS Working Paper No. 173; EFA 2004 Maastricht Meetings Paper No. 5121. Available at SSRN: http://ssrn.com/abstract=556080.

²The interest payment on floating-rate bonds goes up and down as the general level of interest rates changes. Thus a floating-rate default-free bond will sell at close to face value on each coupon date. Many governments issue “floaters.” The U.S. Treasury does not do so, though some U.S. government agencies do.

³For illustration, we have used the example of a floating-rate bond to demonstrate the equivalence between the yield spread and the cost of default insurance. But the spread on a fixed-rate corporate bond should be effectively identical to that on a floater.

⁴In the case of low-grade bonds, when the regular spread does not sufficiently protect the seller against the possibility of an early default, the buyer of the default swap may also be asked to pay an up-front fee.

⁵The International Swap Dealers Association (ISDA) publishes data on credit derivatives at www.isda.org.

⁶But governments cannot print the currencies of other countries. Therefore, they may be forced into default on their foreign currency debt. For example, we saw in Chapter 3 how Argentina defaulted on $95 billion of foreign currency debt. Very occasionally governments have even defaulted on their own currency’s debt. For example, in 1998 the Russian government defaulted on $36 billion of ruble debt.

⁷However, option-valuation procedures cannot value the assets of the firm. Puts and calls must be valued as a proportion of asset value. For example, note that the Black–Scholes formula (Section 21-3) requires stock price to compute the value of a call option.

⁸The classic paper on the valuation of the option to default is R. Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance 29 (May 1974), pp. 449–470.

⁹Remember that the beta of the assets is a weighted average of the beta of the debt and that of the equity:

If βassets = 1.0 and βdebt = 0, then with 60% leverage

¹⁰The price of the bond always declines with maturity and leverage. (Remember the value of a put option increases with maturity and with the exercise price.) However, with very long maturities and high leverage the bond’s yield per annum will start to decline.

¹¹The other approach to valuing the company’s debt (subtracting the value of a put option from risk-free bond value) is no easier. The analyst would be confronted by not one simple put option but a package of 10 sequential puts.

¹²See, for example, J. Huang and M. Huang, “How Much of the Corporate-Treasury Yield Spread Is Due to Credit Risk?” The Review of Asset Pricing Studies, forthcoming, http://sfsraps.org/addenda_viewpaper.php?id=21.

¹³For evidence that the more liquid corporate bonds have lower yields than less liquid bonds, see E. J. Elton, M. J. Gruber, D. Agrawal, and C. Mann, “Factors Affecting the Valuation of Corporate Bonds,” Journal of Banking and Finance 28 (November 2006), pp. 2747–2767.

¹⁴See E. J. Elton, M. J. Gruber, D. Agrawal, and C. Mann, “Explaining the Rate Spread on Corporate Bonds,” Journal of Finance 56 (February 2001), pp. 247–277. Since state taxes are deductible when calculating federal taxes, our calculation slightly overstates the effect of state tax.

¹⁵An even more costly failure occurred when United Airlines declared bankruptcy, leaving the PBGC with a liability of $6.6 billion.

¹⁶The pension guarantee is not ironclad. If the PBGC cannot meet its obligations, the government is not committed to providing the extra cash. But few doubt that it would do so.

¹⁷Congressional Budget Office, “The Risk Exposure of the Pension Benefit Guaranty Corporation,” Washington, DC, September 2005.

¹⁸The SEC has been concerned about the power wielded by the three bond-rating agencies. It has therefore approved six new nationally recognized statistical rating organizations (NRSOs): DBRS (2003), A.M. Best (2005), Egan-Jones Ratings (2007), Japan Credit Rating Agency (2007), Morningstar Credit Ratings (previously known as Realpoint, 2009) and Kroll Brand Ratings (2010).

¹⁹Rating services also provide a finer breakdown. Thus a bond might be rated A-1, A-2, or A-3 (the lowest A rating). In addition, the rating service may announce that it has put an issue on its watch list for a possible upgrade or downgrade.

²⁰Investment-grade bonds can usually be entered at face value on the books of banks and life insurance companies.

²¹The most commonly used consumer credit score is the FICO score developed by Fair Isaac & Co., which uses data provided by any one of three credit bureaus—Experian, TransUnion, or Equifax.

²²See W. H. Beaver, M. F. McNichols, and J.-W. Rhie, “Have Income Statements Become Less Informative? Evidence from the Ability of Financial Ratios to Predict Bankruptcy,” Review of Accounting Studies 10 (2005), pp. 93–122. Their model uses the technique of hazard analysis. Another popular model, the Z-score model, uses multiple discriminant analysis. This was originally suggested by Edward Altman and is described in E. I. Altman and E. Hotchkiss, Corporate Financial Distress and Bankruptcy, 3rd ed. (New York: John Wiley, 2006).

²³The probabilities provided by Moody’s KMV are kept within the range of .01% to 35%.

²⁴CreditMetrics was originally developed by JPMorgan Chase.

Part 7 Debt Financing

The Many Different Kinds of Debt

In Chapters 17 and 18 we discussed how much a company should borrow. But companies also need to think about what type of debt to issue. They can choose to issue short- or long-term debt, straight or convertible bonds; they can issue in their home country or in the international debt market; and they can either sell the debt publicly or place it privately with a few large investors.

As a financial manager, you need to choose the type of debt that makes sense for your company. For example, if a firm has only a temporary need for funds, it will generally issue short-term debt. Firms with a substantial overseas business may prefer to issue foreign currency debt. Sometimes competition between lenders opens a window of opportunity in a particular sector of the debt market. The effect may be only a few basis points reduction in yield, but on a large issue that can translate into savings of several million dollars. Remember the saying, “A million dollars here and a million there—pretty soon it begins to add up to real money.”¹

Figure 24.1 provides a road map through this chapter. Our initial focus is on the long-term bond market. In Section 24-1 we concentrate on the more standard bonds. We examine the differences between senior and junior bonds and between secured and unsecured bonds, including a special kind of secured bond called an asset-backed security. We describe how bonds may be repaid by means of a sinking fund and how the borrower or the lender may have an option for early repayment. As we review these different features of corporate debt, we try to explain why sinking funds, repayment options, and the like exist. They are not simply matters of custom or neutral mutations; there are generally good reasons for their use.

In Section 24-2 we look at some less common bonds, starting with convertible bonds and their close relative, the package of bonds and warrants. We also illustrate the enormous variety of bond designs by looking at a few unusual bonds and at some of the motives for innovation in the bond market.

In Section 24-3 we turn to shorter-term debt, much of which is supplied by banks. Often companies arrange a revolving line of credit with a bank that allows them to borrow up to an agreed amount whenever they need financing. This is often intended to tide the firm over when it has a temporary shortage of cash and is therefore repaid in only a few months. However, banks also make term loans that sometimes extend for five years or more. Some loans are too large to be made by a single bank. We describe how in these cases the loan is syndicated among a group of banks. We also look at how banks protect their loans by imposing restrictions on the borrower and by requiring security.

Rather than borrowing from a bank, large blue-chip companies sometimes bypass the banking system and issue their own short-term debt to investors. This is called commercial paper. Somewhat longer-term loans that are marketed on a regular basis are known as medium-term notes. We discuss both in turn in Section 24-4.

In the Appendix to the chapter, we discuss another form of private placement known as project finance. This is the glamorous part of the debt market. The words project finance conjure up images of multi-million-dollar loans to finance huge ventures in exotic parts of the world. You’ll find there’s something to the popular image, but it’s not the whole story.

We should point out that many debts are not shown on the company’s balance sheet. For example, companies have occasionally disguised the debt by establishing special-purpose entities (SPEs), which raise cash by a mixture of equity and debt and then use that cash to help fund the parent company. By making use of SPEs, Enron kept a large amount of its debt off-balance-sheet, but that did not stop the company from going bankrupt. Since the Enron scandal, accountants have moved to tighten up the rules on disclosing SPE debt.

   FIGURE 24.1 The principal species of corporate debt and the sections of this chapter in which they are discussed.

Companies have other important long-term liabilities that we do not discuss in this chapter. For instance, long-term leases are very similar to debt. The user of the equipment agrees to make a series of lease payments and, if it defaults, it may be forced into bankruptcy. We discuss leases in Chapter 25.

Postretirement health benefits and pension promises can also be huge liabilities. For example, in 2003 General Motors had a pension deficit of $19 billion. To reduce this deficit, GM made a large issue of bonds and invested the majority of the proceeds in its pension fund. You could say that the effect was to increase the company’s debt, but the economic reality was that it substituted one long-term obligation (the new debt) for another (its pension obligation). Management of pension plans is outside the scope of this book, but financial managers spend a good deal of time worrying about the pension “debt.”

 24-1   Long-Term Bonds

Bond Terms

To give you some feel for the bond contract (and for some of the language in which it is couched), we have summarized in Table 24.1 the terms of a bond issue by J.C. Penney. The bond was a plain vanilla issue; in other words, it was pretty well standard in every way. We will look in turn at its principal features.

The J.C. Penney bond was issued in 1992 and is due to mature 30 years later in 2022. It was issued in denominations of $1,000. So at maturity the company will repay the principal amount of $1,000 to the holder of each bond.

The annual interest or coupon payment on the bond is 8.25% of $1,000, or $82.50. This interest is payable semiannually, so every six months the bondholder receives interest of 82.50/2 = $41.25. Most U.S. bonds pay interest semiannually, but in many other countries it is common to pay interest annually.²

   TABLE 24.1 Summary of terms of bond issue by J.C. Penney.

The regular interest payment on a bond is a hurdle that the company must keep jumping. If J.C. Penney ever fails to make the payment, lenders can demand their money back instead of waiting until matters deteriorate further.³ Thus, interest payments provide added protection for lenders.

Sometimes bonds are sold with a lower coupon payment but at a significant discount on their face value, so investors receive much of their return in the form of capital appreciation.⁴ The ultimate is the zero-coupon bond, which pays no interest at all; in this case the entire return consists of capital appreciation.⁵

The J.C. Penney interest payment is fixed for the life of the bond, but in some issues the payment varies with the general level of interest rates. For example, the payment may be set at 1% over the U.S. Treasury bill rate or (more commonly) over the London interbank offered rate (LIBOR), which is the rate at which international banks borrow from one another. Sometimes these floating-rate notes specify a minimum (or floor) interest rate, or they may specify a maximum (or cap) on the rate.⁶ You may also come across “collars,” which stipulate both a maximum and a minimum payment.

BEYOND THE PAGE

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Accrued interest calculations

brealey.mhhe.com/c24

The J.C. Penney bonds have a face value of $1,000 and were sold to investors at 99.489% of face value. In addition, buyers had to pay any accrued interest. This is the amount of any future interest that has accumulated by the time of the purchase. For example, investors who bought bonds for delivery on (say) December 15, would have only two months to wait before receiving their first interest payment. Therefore, the four months of accrued interest would be (120/360) × 8.25 = 2.75%, and the investor would need to pay the purchase price of the bond plus 2.75%.⁷

Although the J.C. Penney bonds were offered to the public at a price of 99.489%, the company received only 98.614%. The difference represents the underwriters’ spread. Of the $248.7 million raised, $246.5 million went to the company and $2.2 million (or about .9%) went to the underwriters.

Moving down Table 24.1, you see that the J.C. Penney bonds are registered. This means that the company’s registrar records the ownership of each bond and the company pays the interest and final principal amount directly to each owner. Almost all bonds in the United States are issued in registered form, but in many countries companies may issue bearer bonds. In this case the bond certificate constitutes the primary evidence of ownership, so the bondholder must return the certificate to the company to claim the final repayment of principal.

The J.C. Penney bonds were sold publicly to investors in the United States. Before it could sell the bonds, it needed to file a registration statement for approval of the SEC and to prepare a prospectus. It also entered into a bond agreement in the form of an indenture, or trust deed, between the company and a trustee. Bank of America National Trust and Savings Association, which is the trust company for the issue, represents the bondholders. It must see that the terms of the indenture are observed and look after the bondholders in the event of default. The bond indenture is a turgid legal document,⁸ but the main provisions are described in the prospectus to the issue.

Security and Seniority

Sometimes a company sets aside particular assets for the protection of the bondholder. For example, utility company bonds are often secured. In this case, if the company defaults on its debt, the trustee or lender may take possession of the relevant assets. If these are insufficient to satisfy the claim, the remaining debt will have a general claim, alongside any unsecured debt, on the other assets of the firm.

Unsecured bonds maturing in 10 years or fewer are usually called notes, while longer-term issues are called debentures (though in some countries, such as the UK and Australia, “debenture” means a secured bond). Like most bond issues by industrial and financial companies, the J.C. Penney bonds are unsecured. However, the company has promised that it will not issue any secured bonds without offering the same security to its debentures.⁹

The majority of secured bonds are mortgage bonds. These sometimes provide a claim against a specific building, but they are more often secured on all of the firm’s property.¹⁰ Of course, the value of any mortgage depends on the extent to which the property has alternative uses. A custom-built machine for producing buggy whips will not be worth much when the market for buggy whips dries up.

Companies that own securities may use them as collateral for a loan. For example, holding companies are firms whose main assets consist of common stock in a number of subsidiaries. So, when holding companies wish to borrow, they generally use these investments as collateral. In such cases, the problem for the lender is that the stock is junior to all other claims on the assets of the subsidiaries, and so these collateral trust bonds usually include detailed restrictions on the freedom of the subsidiaries to issue debt or preferred stock.

A third form of secured debt is the equipment trust certificate. This is most frequently used to finance new railroad rolling stock but may also be used to finance trucks, aircraft, and ships. Under this arrangement a trustee obtains formal ownership of the equipment. The company makes a down payment on the cost of the equipment, and the balance is provided by a package of equipment trust certificates with different maturities that might typically run from 1 to 15 years. Only when all these debts have finally been paid off does the company become the formal owner of the equipment. Bond rating agencies such as Moody’s or Standard & Poor’s usually rate equipment trust certificates one grade higher than the company’s regular debt.

Bonds may be senior claims or they may be subordinated to the senior bonds or to all other creditors.¹¹ If the firm defaults, the senior bonds come first in the pecking order. The subordinated lender gets in line behind the general creditors but ahead of the preferred stockholders and the common stockholders.

As you can see from Figure 24.2, if default does occur, it pays to hold senior secured bonds. On average, investors in these bonds can expect to recover nearly two-thirds of the amount of the loan. At the other extreme, recovery rates for junior unsecured bondholders are only 15% of the face value of the debt.

   FIGURE 24.2 Ultimate percentage recovery rates on defaulting debt by seniority and security, 1987–2010.

Source: Moody’s “Moody’s Ultimate Recovery Database.”

Asset-Backed Securities

Instead of borrowing money directly, companies sometimes bundle up a group of assets and then sell the cash flows from these assets. This issue is known as an asset-backed security, or ABS. The debt is secured, or backed, by the underlying assets.

Suppose your company has made a large number of mortgage loans to buyers of homes or commercial real estate. However, you don’t want to wait until the loans are paid off; you would like to get your hands on the money now. Here is what you do. You establish a separate special-purpose company that buys a package of the mortgage loans. To finance this purchase, the company sells mortgage-backed securities. The holders of these bonds simply receive a share of the mortgage payments.¹² For example, if interest rates fall and the mortgages are repaid early, holders of the bonds are also repaid early. That is not generally popular with these holders, for they get their money back just when they don’t want it—when interest rates are low.

Instead of issuing one class of bonds, a pool of mortgages or of mortgage-backed bonds can be bundled and then split into different slices (or tranches), known as collateralized debt obligations or CDOs. For example, mortgage payments might be used first to pay off one class of security holders and only then will other classes start to be repaid. The senior tranches have first claim on the cash flows and therefore may be attractive to conservative investors such as insurance companies or pension funds. The riskiest (or equity) tranche can then be sold to hedge funds or mutual funds that specialize in low-quality debt.

Real estate lenders are not unique in wanting to turn future cash receipts into upfront cash. Automobile loans, student loans, and credit card receivables are also often bundled and remarketed as an asset-backed security. Indeed, investment bankers seem able to repackage any set of cash flows into a loan. In 1997 David Bowie, the British rock star, established a company that then purchased the royalties from his current albums. The company financed the purchase by selling $55 million of 10-year notes. The royalty receipts were used to make the principal and interest payments on the notes. When asked about the singer’s reaction to the idea, his manager replied, “He kind of looked at me cross-eyed and said ‘What?’ ”¹³

The process of bundling a number of future cash flows into a single security is called securitization. You can see the arguments for securitization. As long as the risks of the individual loans are not perfectly correlated, the risk of the package is less than that of any of the parts. In addition, securitization distributes the risk of the loans widely and, because the package can be traded, investors are not obliged to hold it to maturity.

In the years leading up to the financial crisis, the proportion of new mortgages that were securitized expanded sharply, while the quality of the mortgages declined. By 2007 over half of the new issues of CDOs involved exposure to subprime mortgages. Because the mortgages were packaged together, investors in these CDOs were protected against the risk of default on an individual mortgage. However, even the senior tranches were exposed to the risk of an economy-wide slump in the housing market. For this reason the debt has been termed “economic catastrophe debt.”¹⁴

Economic catastrophe struck in the summer of 2007, when the investment bank Bear Stearns revealed that two of its hedge funds had invested heavily in nearly worthless CDOs. Bear Stearns was rescued with help from the Federal Reserve, but it signaled the start of the credit crunch and the collapse of the CDO market. By 2009 issues of CDOs had effectively disappeared.¹⁵

Did this collapse reflect a fundamental flaw in the practice of securitization? A bank that packages and resells its mortgage loans spreads the risk of those loans. However, when a bank can earn juicy fees from securitization, it might not worry so much if the loans in the package are junk.¹⁶

Sinking Funds

Back to our J.C. Penney bond: Its maturity date is 2022, but the issue is repaid on a regular basis before maturity. To do this, the company makes a series of payments into a sinking fund. If the payment is in the form of cash, the trustee selects bonds by lottery and uses the cash to redeem them at their face value.¹⁷ Alternatively, the company can choose to buy bonds in the marketplace and pay these into the fund. This is a valuable option for the company. If the bond price is low, the firm will buy the bonds in the market and hand them to the sinking fund; if the price is high, it will call the bonds by lottery.

Generally, there is a mandatory fund that must be satisfied and an optional fund that can be satisfied if the borrower chooses. For example, J.C. Penney must contribute at least $12.5 million each year to the sinking fund but has the option to contribute a further $25 million. The J.C. Penney “sinker” begins to operate after about 10 years, and the payments on the fund are sufficient to redeem the entire issue over the bond’s life. We saw earlier that interest payments provide a regular test of solvency. A sinking fund provides an additional hurdle that the firm must keep jumping. If it cannot pay the cash into the sinking fund, the lenders can demand their money back. That is why long-dated, lower-quality issues involve larger sinking funds. Higher-quality bonds generally have a lighter sinking fund requirement if they have one at all.

Unfortunately, a sinking fund is a weak test of solvency if the firm is allowed to repurchase bonds in the market. Since the market value of the debt declines as the firm approaches financial distress, the sinking fund becomes a hurdle that gets progressively lower as the hurdler gets weaker.

Call Provisions

The J.C. Penney bond includes a call option that allows the company to repay the debt early. Sometimes you come across bonds that give the investor the repayment option. Retractable (or puttable) bonds give investors the right to demand early repayment; extendible bonds give them the option to extend the bond’s life.

For some companies callable bonds offer a natural form of insurance. For example, Fannie Mae and Freddie Mac offer fixed-rate mortgages to home buyers. When interest rates fall, home owners are likely to repay their fixed-rate mortgage and take out a new mortgage at the lower interest rate. This can severely dent the income of the two agencies. Therefore, to protect themselves against the effect of falling interest rates, they have issued large quantities of long-term callable debt. When interest rates fall, the agencies can reduce their funding costs by calling their bonds and replacing them with new bonds at a lower rate. Ideally, the fall in bond interest payments should exactly offset the reduction in mortgage income.

J.C. Penney’s bonds provide investors with 10 years of call protection. During this period the company is not permitted to call the bonds at all. Sometimes a company may not be allowed to call the bonds in the first few years if it then replaces the bonds with new debt at a lower interest rate. In some bond issues, the call provision is combined with an increasing coupon payment. For example, Bank of America has issued a 10-year step-up bond. The bond’s coupon starts out at 4.5% in the first year and then climbs progressively to 6.5% by the tenth year. Those higher interest rates may sound mouthwatering. The catch is that the company can call the bonds whenever the coupon is about to step up.

How does a company know when to call its bonds? The answer is simple: Other things equal, if it wishes to maximize the value of its stock, it must minimize the value of its bonds. Therefore, a company should never call the bonds if their market value is less than the call price, for that would just be giving a present to the bondholders. Equally, a company should call the bond if it is worth more than the call price.

Of course, investors take the call option into account when they buy or sell the bond. They know that the company will call the bond as soon as it is worth more than the call price, so no investor will be willing to pay more than the call price for the bond. The market price of the bond may, therefore, reach the call price, but it will not rise above it. This gives the company the following rule for calling its bonds: Call the bond when, and only when, the market price reaches the call price.¹⁸

If we know how bond prices behave over time, we can modify the basic option-valuation model of Chapter 21 to find the value of the callable bond, given that investors know that the company will call the issue as soon as the market price reaches the call price. For example, look at Figure 24.3. It illustrates the relationship between the value of a straight 8% five-year bond and the value of a comparable callable bond. Suppose that the value of the straight bond is very low. In this case there is little likelihood that the company will ever wish to call its bonds. (Remember that it will call the bonds only when their price equals the call price.) Therefore the value of the callable bond will be almost identical to the value of the straight bond. Now suppose that the straight bond is worth exactly 100. In this case there is a good chance that at some time the company will wish to call its bonds. Therefore the value of our callable bond will be slightly less than that of the straight bond. If interest rates decline further, the price of the straight bond will continue to rise, but nobody will ever pay more than the call price for the callable bond.

   FIGURE 24.3 Relationship between the value of a callable bond and that of a straight (noncallable) bond. Assumptions: (1) Both bonds have an 8% coupon and a five-year maturity; (2) the callable bond may be called at face value any time before maturity; (3) the short-term interest rate follows a random walk, and the expected returns on bonds of all maturities are equal.

Source: M. J. Brennan and E. S. Schwartz, “Savings Bonds, Retractable Bonds, and Callable Bonds,” Journal of Financial Economics 5 (1977), pp. 67–88. © 1977, with permission from Elsevier.

A call provision is not a free lunch. It provides the issuer with a valuable option, but that is recognized in a lower issue price. So why do companies bother with a call provision? One reason is that bond indentures often place a number of restrictions on what the company can do. Companies are happy to agree to these restrictions as long as they know that they can escape from them if the restrictions prove too inhibiting. The call provision provides the escape route.

We mentioned earlier that some bonds also provide the investor with an option to demand early repayment. Puttable bonds exist largely because bond indentures cannot anticipate every action the company may take that could harm the bondholder. If the value of the bonds is reduced, the put option allows the bondholders to demand repayment.

Puttable loans can sometimes get their issuers into BIG trouble. During the 1990s many loans to Asian companies gave their lenders a repayment option. Consequently, when the Asian crisis struck in 1997, these companies were faced by a flood of lenders demanding their money back.

Bond Covenants

Investors in corporate bonds know that there is a risk of default. But they still want to make sure that the company plays fair. They don’t want it to gamble with their money. Therefore, the loan agreement usually includes a number of debt covenants that prevent the company from purposely increasing the value of its default option.¹⁹ These covenants may be relatively light for blue-chip companies but more restrictive for smaller, riskier borrowers.

Lenders worry that after they have made the loan, the company may pile up more debt and so increase the chance of default. They protect themselves against this risk by prohibiting the company from making further debt issues unless the ratio of debt to equity is below a specified limit.

Not all debts are created equal. If the firm defaults, the senior debt comes first in the pecking order and must be paid off in full before the junior debtholders get a cent. Therefore, when a company issues senior debt, the lenders will place limits on further issues of senior debt. But they won’t restrict the amount of junior debt that the company can issue. Because the senior lenders are at the front of the queue, they view the junior debt in the same way that they view equity: They would be happy to see an issue of either. Of course, the converse is not true. Holders of the junior debt do care both about the total amount of debt and the proportion that is senior to their claim. As a result, an issue of junior debt generally includes a restriction on both total debt and senior debt.

All bondholders worry that the company may issue more secured debt. An issue of mortgage bonds often imposes a limit on the amount of secured debt. This is not necessary when you are issuing unsecured debentures. As long as the debenture holders are given an equal claim, they don’t care how much you mortgage your assets. Therefore, unsecured bonds usually include a so-called negative-pledge clause, in which the unsecured holders simply say, “Me too.”²⁰ We saw earlier that the J.C. Penney bonds include a negative pledge clause.

Instead of borrowing money to buy an asset, companies may enter into a long-term agreement to rent or lease it. For the debtholder this is very similar to secured borrowing. Therefore debt agreements also include limitations on leasing.

We have talked about how an unscrupulous borrower can try to increase the value of the default option by issuing more debt. But this is not the only way that such a company can exploit its existing bondholders. For example, we know that the value of an option is reduced when the company pays out some of its assets to stockholders. In the extreme case a company could sell all its assets and distribute the proceeds to shareholders as a bumper dividend. That would leave nothing for the lenders. To guard against such dangers, debt issues may restrict the amount that the company may pay out in the form of dividends or repurchases of stock.²¹

Take a look at Table 24.2, which summarizes the principal covenants in a large sample of senior bond issues. Notice that investment-grade bonds tend to have fewer restrictions than high-yield bonds. For example, restrictions on the amount of any dividends or repurchases are less common in the case of investment-grade bonds.

These debt covenants do matter. Asquith and Wizman, who studied the effect of leveraged buyouts on the value of the company’s debt, found that when there were no restrictions on further debt issues, dividend payments, or mergers, the buyout led to a 5.2% fall in the value of existing bonds.²² Those bonds that were protected by strong covenants against excessive borrowing increased in price by 2.6%.

Unfortunately, it is not always easy to cover all loopholes, as the bondholders of Marriott Corporation discovered in 1992. They hit the roof when the company announced plans to divide its operations into two separate businesses. One business, Marriott International, would manage Marriott’s hotel chain and receive most of the revenues, while the other, Host Marriott, would own all the company’s real estate and be responsible for servicing essentially all of the old company’s $3 billion of debt. As a result, the price of Marriott’s bonds plunged nearly 30%, and investors began to think about how they could protect themselves against such event risks. It is now more common for bondholders to insist on poison-put clauses that oblige the borrower to repay the debt if there is a change of control and the bonds are downrated.

However, there are always nasty surprises lurking around the next corner. The nearby box describes one such surprise for bond investors of U.S. Shoe.

   TABLE 24.2 Percentage of sample of bonds with covenant restrictions. Sample consists of 4,478 senior bonds issued between 1993 and 2007.

a For example, default on other loans, rating changes, or declining net worth.

Source: S. Chava, P. Kumar, and A. Warga, “Managerial Agency and Bond Covenants,” Review of Financial Studies 23 (2010), pp. 1120–1148, by permission of Oxford University Press.

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Luxottica Riles Bondholders with Its Debt Moves

  Imagine a company trying to push its bonds into technical default just so it can redeem them before maturity. Some bond analysts assert that this is exactly what Luxottica Group SpA of Italy—the new owner of U.S. Shoe Corp.—is doing with U.S. Shoe’s 8 ⅝% note issue.

Luxottica’s strategy, which the company asserts wasn’t deliberately designed to hurt bondholders, is shaping up to be the newest wrinkle in corporate America’s scramble to pry high-interest-bearing bonds from the hands of investors before they mature, some analysts say. As interest rates have fallen, a host of corporate issuers—from stodgy utilities to fleet-footed finance companies—have rushed to redeem their high-interest bonds with lower coupon issues. As long as the bonds are “callable,” or redeemable, there is usually no problem. Increasingly, however, corporate issuers are trying to redeem noncallable bonds—securities that can’t be wrested from investors before maturity—using unusual tactics.

Bond analysts say Luxottica has been trying to put U.S. Shoe’s 8 ⅝% note issue, maturing in 2002, in technical default by piling $1.4 billion of secured debt onto the company earlier this year. That’s because a little-noticed covenant in U.S. Shoe’s bond indenture says its bonds are in technical default if it adds secured debt to its financial ledger without simultaneously adding collateral to back the 8 ⅝% securities so they’re on the same level as the bank debt.

What’s riling bondholders is that Luxottica hasn’t been willing to secure its 8 ⅝% notes even though it took on a load of secured debt earlier this year. Now Luxottica is trying to redeem its bonds early, which the company says it can do under the covenants when the issue is in technical default.

“This action is 10 times worse than Marriott on its worst day, because Marriott never violated an explicit covenant,” contends Max Holmes, a securities analyst.

Source: Extracted from Anita Raghavan, “U.S. Shoe’s Owner Riles Bondholders with Its Debt Moves,” The Wall Street Journal, October 18, 1995, p. C1. Eastern Edition (Staff-produced copy only). Reprinted by permission of the The Wall Street Journal, copyright © 1995 Dow Jones & Company, Inc. All Rights Reserved Worldwide.

Privately Placed Bonds

The J.C. Penney debentures were registered with the SEC and sold publicly. However, bonds may also be placed privately with a few financial institutions, though the market for privately placed bonds is much smaller than the public market.²³

As we saw in Section 15-5, it costs less to arrange a private placement than to make a public debt issue. But there are other differences between a privately placed bond and its public counterpart.

First, if you place an issue privately with one or two financial institutions, it may be necessary to sign only a simple promissory note. This is just an IOU that lays down certain conditions that the borrower must observe. However, when you make a public issue of debt, you must worry about who is supposed to represent the bondholders in any subsequent negotiations and what procedures are needed for paying interest and principal. Therefore, the contract has to be somewhat more complicated.

The second characteristic of publicly issued bonds is that they are somewhat standardized products. They have to be—investors are constantly buying and selling without checking the fine print in the agreement. This is not so necessary in private placements and so the debt can be custom-tailored for firms with special problems or opportunities. The relationship between borrower and lender is much more intimate. Imagine a $200 million debt issue privately placed with an insurance company, and compare it with an equivalent public issue held by 200 anonymous investors. The insurance company can justify a more thorough investigation of the company’s prospects and therefore may be more willing to accept unusual terms or conditions.²⁴

These features of private placements give them a particular niche in the corporate debt market, namely, relatively low-grade loans to small- and medium-sized firms.²⁵ These are the firms that face the highest costs in public issues, that require the most detailed investigation, and that may require specialized, flexible loan arrangements.

Of course, the advantages of private placements are not free, for the lenders demand a higher rate of interest to compensate them for holding an illiquid asset. It is difficult to generalize about the difference in interest rates between private placements and public issues, but a typical differential is 50 basis points, or .50 percentage points.

Foreign Bonds, Eurobonds, and Global Bonds

J.C. Penney sold its bonds in the United States, but it could have issued debt in another country. For example, it could have sold sterling bonds in the UK or Swiss franc bonds in Switzerland. Foreign currency bonds that are sold to local investors in another country are known as foreign bonds. Many foreign companies issue their bonds in the United States, making it by far the largest market for foreign bonds. Japan and Switzerland are also substantial markets. Foreign bonds have a variety of nicknames. For example, a bond sold by a foreign company in the United States is known as a yankee bond; a bond sold by a foreign firm in Japan is a samurai, and one sold in Switzerland is an alpine.

Of course, any firm that raises money from local investors in a foreign country is subject to the rules of that country and oversight by its financial regulator. For example, when a foreign company issues publicly traded bonds in the United States it must first register the issue with the SEC. However, foreign firms borrowing in the United States can avoid registration by complying with the SEC’s Rule 144A. Rule 144A bonds can be bought and sold only by large financial institutions.²⁶

Instead of issuing a bond in a particular country’s market, a company may market a bond issue internationally. Issues that are denominated in one country’s currency but marketed internationally outside that country are known as eurobonds and are usually made in one of the major currencies, such as the U.S. dollar, the euro, or the yen. For example, J.C. Penney could have issued a dollar bond to investors around the world. As long as the issue is not marketed to U.S. investors, it does not need to be registered with the SEC.²⁷ Eurobond issues are marketed by international syndicates of underwriters, such as the London branches of large U.S., European, and Japanese banks and security dealers. Be careful not to confuse a eurobond (which is outside the oversight of any domestic regulator and may be in any currency) with a bond that is marketed in a European country and denominated in euros.²⁸

The eurobond market arose during the 1960s because the U.S. government imposed a tax on the purchase of foreign securities and discouraged American corporations from exporting capital. Consequently, both European and American multinationals were forced to tap an international market for capital. The tax was removed in 1974. Since firms can now choose whether to borrow in New York or London, the interest rates in the two markets are usually similar. However, the eurobond market is not directly subject to regulation by the U.S. authorities, and therefore the financial manager needs to be alert to small differences in the cost of borrowing in one market rather than another.

These days very large bond issues are often marketed both internationally (i.e., in the eurobond market) and in individual domestic markets. For example, J.C. Penney could have sold dollar bonds internationally and also registered the issue for sale in the United States. Such bonds are called global bonds.

 24-2   Convertible Securities and Some Unusual Bonds

Unlike the common or garden bond, a convertible security can change its spots. It starts life as a bond (or preferred stock), but subsequently may turn into common stock. For example, in October 2012 Nokia issued €750 million of 5% senior convertible notes due in 2017. Bonds with a face value of €1,000 can be converted at any time into 382.26 shares of common stock. Thus the owner has a five-year option to return the bond to the company and receive 382.26 shares of common stock in exchange. The number of shares into which each bond can be converted is called the bond’s conversion ratio. The conversion ratio of the Nokia bond is 382.26.

To receive these shares, the owner of the convertible must surrender bonds with a face value of €1,000. This means that to receive one share, the owner needs to surrender a face amount of €1,000/382.26 = €2.616. This is the bond’s conversion price. Anybody who bought the bond at €1,000 to convert it into stock paid the equivalent of €2.616 a share, 28% above the stock price at the time of the convertible issue.

You can think of a convertible bond as equivalent to a straight bond plus an option to acquire common stock. When convertible bondholders exercise this option, they do not pay cash; instead they give up their bonds in exchange for shares. If Nokia’s bonds had not been convertible, they would probably have been worth about €880 at the time of issue. The difference between the price of a convertible bond and the price of an equivalent straight bond represents the value that investors place on the conversion option. For example, an investor who paid €1,000 in 2012 for the Nokia convertible would have paid about €1,000 2 €880 5 €120 for the option to acquire 382.26 shares.

The Value of a Convertible at Maturity

By the time that the Nokia convertible matures, investors need to choose whether to stay with the bond or convert to common stock. Figure 24.4(a) shows the possible bond values at maturity.²⁹ Notice that the bond value is simply the face value as long as Nokia does not default. However, if the value of the company’s assets is sufficiently low, the bondholders will receive less than the face value and, in the extreme case that the assets are worthless, they will receive nothing. You can think of the bond value as a lower bound, or “floor,” to the price of the convertible. But that floor has a nasty slope and, when the company falls on hard times, the bond may not be worth much.

Figure 24.4(b) shows the value of the shares that investors receive if they choose to convert. If Nokia’s assets are worthless, the shares into which the convertible can be exchanged are also worthless. But, as the value of the assets rises, so does the conversion value.

   FIGURE 24.4

(a) The bond value when Nokia’s convertible bond matures. If firm value is at least equal to the face value of Nokia’s debt, the bond is paid off at face value.

(b) The conversion value at maturity. If converted, the value of the convertible rises in proportion to firm value.

(c) At maturity the convertible bondholder can choose to receive the payment on the bond or convert to common stock. The value of the convertible bond is therefore the higher of its bond value and its conversion value.

Nokia’s convertible cannot sell for less than its conversion value. If it did, investors would buy the convertible, exchange it rapidly for stock, and sell the stock. Their profit would be equal to the difference between the conversion value and the price of the convertible. Therefore, there are two lower bounds to the price of the convertible: its bond value and its conversion value. Investors will not convert if the convertible is worth more as a bond; they will do so if the conversion value at maturity exceeds the bond value. In other words, the price of the convertible at maturity is represented by the higher of the two lines in Figures 24.4(a) and (b). This is shown in Figure 24.4(c).

Forcing Conversion

Many issuers of convertible bonds have an option to buy (or call) the bonds back at their face value whenever its stock price is 30% or so above the bond’s conversion price.³⁰ If the company does announce that it will call the bonds, it makes sense for investors to convert immediately. Thus a call can force conversion.

As we saw earlier, calling a bond does not affect the total size of the company pie, but it can affect the size of the individual slices. If the convertible is callable, the company can minimize the value of the bondholder’s slice by forcing conversion and terminating the bondholder’s option.³¹

Why Do Companies Issue Convertibles?

You are approached by an investment banker who is anxious to persuade your company to issue a convertible bond with a conversion price set somewhat above the current stock price. She points out that investors would be prepared to accept a lower yield on the convertible, so that it is “cheaper” debt than a straight bond.³² You observe that if your company’s stock performs as well as you expect, investors will convert the bond. “Great,” she replies, “in that case you will have sold shares at a much better price than you could sell them for today. It’s a win-win opportunity.”

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Why companies issue convertibles

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Is the investment banker right? Are convertibles “cheap debt”? Of course not. They are a package of a straight bond and an option. The higher price that investors are prepared to pay for the convertible represents the value that they place on the option. The convertible is “cheap” only if this price overvalues the option.

What then of the other argument, that the issue represents a deferred sale of common stock at an attractive price? The convertible gives investors the right to buy stock by giving up a bond.³³ Bondholders may decide to do this, but then again they may not. Thus issue of a convertible bond may amount to a deferred stock issue. But if the firm needs equity capital, a convertible issue is an unreliable way of getting it.

John Graham and Campbell Harvey surveyed companies that had seriously considered issuing convertibles. In 58% of the cases management considered convertibles an inexpensive way to issue “delayed” common stock. Forty-two percent of the firms viewed convertibles as less expensive than straight debt.³⁴ Taken at their face value, these arguments don’t make sense. But we suspect that these phrases encapsulate some more complex and rational motives.

Notice that convertibles tend to be issued by the smaller and more speculative firms. These issues are almost invariably unsecured and generally subordinated. Now put yourself in the position of a potential investor. You are approached by a firm with an untried product line that wants to issue some junior unsecured debt. You know that if things go well, you will get your money back, but if they do not, you could easily be left with nothing. Since the firm is in a new line of business, it is difficult to assess the chances of trouble. Therefore you don’t know what the fair rate of interest is. Also, you may be worried that once you have made the loan, management will be tempted to run extra risks. It may take on additional senior debt, or it may decide to expand its operations and go for broke on your money. In fact, if you charge a very high rate of interest, you could be encouraging this to happen.

What can management do to protect you against a wrong estimate of the risk and to assure you that its intentions are honorable? In crude terms, it can give you a piece of the action. You don’t mind the company running unanticipated risks as long as you share in the gains as well as the losses.³⁵ Convertible securities make sense whenever it is unusually costly to assess the risk of debt or whenever investors are worried that management may not act in the bondholders’ interest.³⁶

The relatively low coupon rate on convertible bonds may also be a convenience for rapidly growing firms facing heavy capital expenditures.³⁷ They may be willing to provide the conversion option to reduce immediate cash requirements for debt service. Without that option, lenders might demand extremely high (promised) interest rates to compensate for the probability of default. This would not only force the firm to raise still more capital for debt service but also increase the risk of financial distress. Paradoxically, lenders’ attempts to protect themselves against default may actually increase the probability of financial distress by increasing the burden of debt service on the firm.

Valuing Convertible Bonds

We have seen that a convertible bond is equivalent to a package of a bond and an option to buy stock. This means that the option-valuation models that we described in Chapter 21 can also be used to value the option to convert. We don’t want to repeat that material here, but we should note three wrinkles that you need to look out for when valuing a convertible:

 1.  Dividends. If you hold the common stock, you may receive dividends. The investor who holds an option to convert into common stock misses out on these dividends. In fact the convertible holder loses out every time a cash dividend is paid because the dividend reduces the stock price and thus reduces the value of the conversion option. If the dividends are high enough, it may even pay to convert before maturity to capture the extra income. We showed how dividend payments affect option value in Section 21-5.

 2.  Dilution. The second complication arises because conversion increases the number of outstanding shares. Therefore, exercise means that each shareholder is entitled to a smaller proportion of the firm’s assets and profits.³⁸ This problem of dilution never arises with traded options. If you buy an option through an option exchange and subsequently exercise it, you have no effect on the number of shares outstanding.

 3.  Changing bond value. When investors convert to shares, they give up their bond. The exercise price of the option is therefore the value of the bond that they are relinquishing. But this bond value is not constant. If the bond value at issue is less than the face value (and it usually is less), it is likely to change as maturity approaches. Also the bond value varies as interest rates change and as the company’s credit standing changes. If there is some possibility of default, investors cannot even be certain of what the bond will be worth at maturity. In Chapter 21 we did not get into the complication of uncertain exercise prices.

A Variation on Convertible Bonds: The Bond–Warrant Package

Instead of issuing a convertible bond, companies sometimes sell a package of straight bonds and warrants. Warrants are simply long-term call options that give the investor the right to buy the firm’s common stock. For example, each warrant might allow the holder to buy a share of stock for $50 at any time during the next five years. Obviously, the warrant holders hope that the company’s stock will zoom up, so that they can exercise their warrants at a profit. But, if the company’s stock price remains below $50, holders will choose not to exercise, and the warrants will expire worthless.

Convertible bonds consist of a package of a straight bond and an option. An issue of bonds and warrants also contains a straight bond and an option. But there are some differences:

 1.  Warrants are usually issued privately. Packages of bonds with warrants tend to be more common in private placements. By contrast, most convertible bonds are issued publicly.

 2.  Warrants can be detached. When you buy a convertible, the bond and the option are bundled together. You cannot sell them separately. This may be inconvenient. If your tax position or attitude to risk inclines you to bonds, you may not want to hold options as well. Warrants are sometimes also “nondetachable,” but usually you can keep the bond and sell the warrant.

 3.  Warrants are exercised for cash. When you convert a bond, you simply exchange your bond for common stock. When you exercise warrants, you generally put up extra cash, though occasionally you have to surrender the bond or can choose to do so. This means that the bond–warrant package and the convertible bond have different effects on the company’s cash flow and on its capital structure.

 4.  A package of bonds and warrants may be taxed differently. There are some tax differences between warrants and convertibles. Suppose that you are wondering whether to issue a convertible bond at 100. You can think of this convertible as a package of a straight bond worth, say, 90 and an option worth 10. If you issue the bond and option separately, the IRS will note that the bond is issued at a discount and that its price will rise by 10 points over its life. The IRS will allow you, the issuer, to spread this prospective price appreciation over the life of the bond and deduct it from your taxable profits. The IRS will also allocate the prospective price appreciation to the taxable income of the bondholder. Thus, by issuing a package of bonds and warrants rather than a convertible, you may reduce the tax paid by the issuing company and increase the tax paid by the investor.

 5.  Warrants may be issued on their own. Warrants do not have to be issued in conjunction with other securities. Often they are used to compensate investment bankers for underwriting services. Many companies also give their executives long-term options to buy stock. These executive stock options are not usually called warrants, but that is exactly what they are. Companies can also sell warrants on their own directly to investors, though they rarely do so.

Innovation in the Bond Market

Domestic bonds and eurobonds, fixed- and floating-rate bonds, coupon bonds and zeros, callable and puttable bonds, straight bonds and convertible bonds—you might think that this would give you as much choice as you need. Yet almost every day some new type of bond seems to be issued. Table 24.3 lists some of the more interesting bonds that have been invented in recent years.³⁹ Earlier in the chapter we cited the “Bowie bonds” as an example of asset-backed securities, and in Chapter 26 we discuss catastrophe bonds whose payoffs are linked to the occurrence of natural disasters.

   TABLE 24.3 Some examples of innovation in bond design.

Some financial innovations appear to serve little or no economic purpose; they may flower briefly but then wither. For example, toward the end of the 1990s in the United States there was a bout of new issues of floating-price convertibles, or, as they were more commonly called, death-spiral, or toxic, convertibles. When death-spiral convertibles are issued, the conversion price is set below the current stock price. Moreover, each bond is convertible not into a fixed number of shares but into shares with a fixed value. Therefore, the more the share price falls, the more shares that the convertible bondholder is entitled to. With a normal convertible, the value of the conversion option falls whenever the value of the firm’s assets falls; so the convertible holder shares some of the pain with the stockholders. With a death-spiral convertible, the holder is entitled to shares with a fixed value, so the entire effect of the decrease in the asset price falls on the common stockholders. Death-spiral convertibles were issued largely by companies that were already in desperate straits, and, when the issuers failed to recover, the toxic chicken came home to roost. After the initial flurry of issues in the United States, death-spiral convertibles seem now to have been consigned to the garbage heap of unsuccessful innovations.

Many other innovations seem to have a more obvious purpose. Here are some important motives for creating new securities:

 1.  Investor choice. Sometimes new financial instruments are created to widen investor choice. Economists refer to such securities as helping to “complete the market.” This was the idea behind the 2006 issue of nearly €350 million of mortality bonds by the French insurance company Axa. One of the big risks for a life insurance company is a pandemic or other disaster that results in a sharp increase in the death rate. Axa’s bond, therefore, offers investors a higher interest rate for taking on some of that risk. Holders of the bond will lose their entire investment if death rates for two consecutive years are 10% or more above expectations.

Pension funds are in the opposite position to insurance companies. Their worry is that the scheme’s members will continue to draw their pensions into a ripe old age. Investment bankers have therefore been working to design longevity bonds that pay a higher rate of interest if an unusually high proportion of the population survives to a particular age. A pension fund that held these bonds would be protected against an unexpected increase in longevity.⁴⁰

Both mortality and longevity bonds widen investor choice. They allow insurance companies and pension funds to protect themselves against adverse changes in mortality and they spread the risk widely around the market.

 2.  Government regulation and tax. Merton Miller has described new government regulations and taxes as the sand in the oyster that stimulates the design of new types of security. For example, we have already seen how the eurobond market was a response to the U.S. government’s imposition of a tax on purchases of foreign securities.

Asset-backed securities provide another instance of a market that was encouraged by regulation. To reduce the likelihood of failure, banks are obliged to finance part of their loan portfolio with equity capital. Many banks were able to reduce the amount of capital that they needed to hold by packaging up their loans or credit card receivables and selling them off as bonds. Bank regulators have worried about this. They think that banks may be tempted to sell off their riskiest loans and to keep their safest ones. They have therefore introduced new regulations that will link the capital requirement to the riskiness of the loans.

 3.  Reducing agency costs. At the turn of the century investors were worried by the huge spending plans of telecom companies. So when Deutsche Telecom, the German telecom giant, decided to sell $15 billion of bonds in 2000, it offered a provision to reassure investors. Under this arrangement, Deutsche Telecom was required to increase the coupon rate on the bonds by 50 basis points if ever its bonds were downgraded to below investment grade by Moody’s or Standard & Poor’s. Deutsche Telecom’s credit-sensitive bonds protected investors against possible future attempts by the company to exploit existing bondholders by loading on more debt.

Here is another example where bond design can help to solve agency problems. Bankers love to borrow rather than issue equity. The problem is that when banks encounter heavy weather, the shareholders may refuse to come to the rescue with more capital. One suggested remedy is for the banks to issue contingent convertible bonds (or cocos). These are bonds that convert automatically into equity if the bank hits trouble. For example, in 2011 Credit Suisse issued CHF6 billion of Swiss franc cocos. If Credit Suisse’s capital falls below a specified level, the cocos reduce the bank’s leverage by changing into equity.

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Contingent convertibles

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Dreaming up these new financial instruments is only half the battle. The other problem is to produce them efficiently. Think, for example, of the problems of packaging together several hundred million dollars’ worth of credit card receivables and allocating the cash flows to a diverse group of investors. That requires good computer systems. The deal also needs to be structured so that, if the issuer goes bankrupt, the receivables will not be part of the bankruptcy estate. That depends on the development of legal structures that will stand up in the event of a dispute.

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Longevity swaps

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 24-3   Bank Loans

Bonds are generally long-term loans and more often than not are sold publicly by the borrowing company. It is now time to look at shorter-term debt. This is not usually issued publicly and is largely supplied by banks. Whereas the typical bond issue has a maturity of 10 years, the bank loan is generally repaid in about 3 years.⁴¹ Of course, there is plenty of variation around these figures.

In the United States, bank loans are a less important source of finance than the bond market, but for many smaller firms, they are the only source of borrowing. Bank loans come in a variety of flavors. Here are a few of the ways that they differ.

Commitment

Companies sometimes wait until they need the money before they apply for a bank loan, but about 90% of commercial loans by U.S. banks are made under commitment. In this case the company establishes a line of credit that allows it to borrow up to an established limit from the bank. This line of credit may be an evergreen credit with no fixed maturity, but more commonly it is a revolving credit (revolver) with a fixed maturity. One other common arrangement is a 364-day facility that allows the company, over the next year, to borrow, repay, and re-borrow as its need for cash varies.⁴²

Credit lines are relatively expensive; in addition to paying interest on any borrowings, the company must pay a commitment fee of around .25% on the unused amount. In exchange for this extra cost, the firm receives a valuable option: it has guaranteed access to the bank’s money at a fixed spread over the general level of interest rates.

The growth in the use of credit lines has changed the role of banks. They are no longer simply lenders; they are also in the business of providing companies with liquidity insurance.

Maturity

Many bank loans are for only a few months. For example, a company may need a short-term bridge loan to finance the purchase of new equipment or the acquisition of another firm. In this case the loan serves as interim financing until the purchase is completed and long-term financing arranged. Often a short-term loan is needed to finance a temporary increase in inventory. Such a loan is described as self-liquidating; in other words, the sale of goods provides the cash to repay the loan.

Banks also provide longer-maturity loans, known as term loans. A term loan typically has a maturity of four to five years. Usually the loan is repaid in level amounts over this period, though there is sometimes a large final balloon payment or just a single bullet payment at maturity. Banks can accommodate the precise repayment pattern to the anticipated cash flows of the borrower. For example, the first repayment might be delayed a year until the new factory is completed. Term loans are often renegotiated before maturity. Banks are willing to do this if the borrower is an established customer, remains creditworthy, and has a sound business reason for making the change.⁴³

Rate of Interest

Most short-term bank loans are made at a fixed rate of interest, which is often quoted as a discount. For example, if the interest rate on a one-year loan is stated as a discount of 5%, the borrower receives $100 – $5 = $95 and undertakes to pay $100 at the end of the year. The return on such a loan is not 5%, but 5/95 = .0526, or 5.26%.

FINANCE IN PRACTICE

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LIBOR

Each day at around 11 a.m. in London, some 19 major banks provide estimates of the interest rate at which they could borrow funds from another bank in reasonable market size. They produce these estimates for 15 maturities that range from overnight to one year. In each case the top and bottom quarter of the estimates are dropped, and the remainder are averaged to provide the set of rates known as LIBOR. The rates most commonly quoted as LIBOR are for borrowing U.S. dollars, but similar sets of LIBOR are also produced for nine other currencies—the euro; the Japanese yen; the pound sterling; the Swiss franc; the Danish kroner; the Swedish krona; and the Canadian, Australian, and New Zealand dollars. The British Bankers’ Association, which publishes these rates, estimates that the payments on about $360 trillion of loans and swaps are tied to LIBOR.⁴⁵

Figure 24.5 plots the difference between the interest rate on three-month Treasury bills and LIBOR. This spread is known as the TED spread. For many years the TED spread was typically less than 50 basis points (.5%), but in 2008 it widened dramatically, at one point reaching 360 basis points (3.6%). Suddenly the choice of benchmark for bank loans began to be very important.

   FIGURE 24.5 Month-end values for the spread between the interest rate on three-month Treasury bills and LIBOR (the TED spread), August 2004–October 2011.

Source: British Bankers’ Association and the Federal Reserve Board.

For longer-term bank loans the interest rate is usually linked to the general level of interest rates. The most common benchmarks are LIBOR, the federal funds rate,⁴⁴ or the bank’s prime rate. Thus, if the rate is set at “1% over LIBOR,” the borrower may pay 5% in the first three months when LIBOR is 4%, 6% in the next three months when LIBOR is 5%, and so on. The nearby box describes how LIBOR is set and its relationship to the Treasury bill rate.

BEYOND THE PAGE

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The LIBOR scandal

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Syndicated Loans

Some bank loans and credit lines are too large for a single lender. In these cases the borrower may pay an arrangement fee to one or more lead banks, which then parcel out the loan or credit line among a syndicate of banks.⁴⁶ For example, in 2011 Chrysler needed to borrow $4.3 billion to finance some maturing debt. It did so by means of a package of a $3.0 billion term loan and a $1.3 billion revolving credit facility. The package was arranged by BankAmerica Merrill, Citibank, Goldman Sachs, and Morgan Stanley. The loans had a maturity of five to six years and were priced at 4.75% above LIBOR. In addition, Chrysler was required to pay a commitment fee of .75% on any unused portion of the revolving credit.

The syndicate arranger serves as underwriter to the loan. It prices the loan, markets it to other banks, and may also guarantee to take on any unsold portion. The arranger’s first step is to prepare an information memo that provides potential lenders with information on the loan. The syndicate desk will then try to sound out the level of interest in the deal before the loan is finally priced and marketed to interested buyers. If the borrower has good credit or if the arranging bank has a particularly good reputation, the majority of the loan is likely to be syndicated. In other cases the arranging bank may need to demonstrate its faith in the deal by keeping a high proportion of the loan on its own books.⁴⁷

Bank loans used to be illiquid; once the bank had made a loan, it was stuck with it. This is no longer the case, so that banks with an excess demand for loans may solve the problem by selling a portion of their existing loans to other institutions. For example, about 20% of syndicated loans are subsequently resold, and these sales are reported weekly in The Wall Street Journal.⁴⁸

Security

If a bank is concerned about a firm’s credit risk, it will ask the firm to provide security for the loan. This is most common for longer-term bank loans, over half of which are secured.⁴⁹ The collateral usually consists of liquid assets such as receivables, inventories, or securities. Sometimes the bank will take a floating charge. This gives it a general claim if the firm defaults. However, it does not specify the assets in detail, and it sets few restrictions on what the company can do with the assets.

More commonly, banks require specific collateral. For example, suppose that there is a significant delay between the time that you ship your goods and when your customers pay you. If you need the money up front, you can borrow by using these receivables as collateral. First, you must send the bank a copy of each invoice and provide it with a claim against the money that you receive from your customers. The bank will then lend up to 80% of the value of the receivables.

Each day, as you make more sales, your collateral increases and you can borrow more money. Each day also some customers pay their bills. This money is placed in a special collateral account under the bank’s control and is periodically used to reduce the size of the loan. Therefore, as the firm’s business fluctuates, so does the amount of the collateral and the size of the loan.

You can also use inventories as security for a loan. For example, if your goods are stored in a warehouse, you need to arrange for an independent warehouse company to provide the bank with a receipt showing that the goods are held on the bank’s behalf. The bank will generally be prepared to lend up to 50% of the value of the inventories. When the loan is repaid, the bank returns the warehouse receipt and you are free to remove the goods.⁵⁰

Banks are naturally choosey about the security that they will accept. They want to make sure that they can identify and sell the collateral if you default. They may be happy to lend against a warehouse full of a standard nonperishable commodity, but they would turn up their nose at a warehouse of ripe Camembert.

Banks also need to ensure that the collateral is safe and that the borrower doesn’t sell the assets and run off with the money. This is what happened in the great salad oil swindle. Fifty-one banks and companies made loans of nearly $200 million to the Allied Crude Vegetable Oil Refining Corporation. In return the company agreed to provide security in the form of storage tanks full of valuable salad oil. Unfortunately, cursory inspections failed to notice that the tanks contained seawater and sludge. When the fraud was discovered, the president of Allied went to jail and the 51 lenders were left out in the cold, looking for their $200 million.

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Hazards of secure bank lending

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Debt Covenants

We saw earlier that bond issues may contain covenants that restrict companies from taking actions that would increase the risk of their debt. For publicly issued bonds these restrictions are often mild. In the case of privately placed debt, the covenants are generally more severe. Since privately placed debt keeps the borrower on a fairly short leash, it is quite common for a covenant to be breached. This is not as calamitous as it may sound. As long as the borrower is in good financial health, the lender may simply adjust the terms of the covenant. Only if covenants continue to be violated will the lender choose to take more drastic action.

Covenants on bank loans and privately placed bonds are principally of three kinds.⁵¹ The first and most common covenant sets a maximum fraction of net income that can be paid out as dividends. A second set of covenants, called sweeps, state that all or part of the loan must be repaid if the borrower makes a large sale of assets or a substantial issue of debt. The third group places conditions on key financial ratios, such as the borrower’s debt ratio, interest coverage ratio, or current ratio.

 24-4   Commercial Paper and Medium-Term Notes

Commercial Paper

Banks borrow money from one group of firms or individuals and relend the money to another group. They make their profit by charging the borrowers a higher rate of interest than they offer the lender.

Sometimes it is convenient to have a bank in the middle. It saves the lenders the trouble of looking for borrowers and assessing their creditworthiness, and it saves the borrowers the trouble of looking for lenders. Depositors do not care to whom the bank lends: They need only satisfy themselves that the bank as a whole is safe.

There are also occasions on which it is not worth paying an intermediary to perform these functions. Large well-known companies can bypass the banking system by issuing their own short-term unsecured notes. These notes are known as commercial paper (CP). Financial institutions, such as bank holding companies and finance companies,⁵² also issue commercial paper, sometimes in very large quantities. For example, in 2010 GE Capital Corporation had $42 billion of commercial paper in issue. The major issuers of commercial paper have set up their own marketing departments and sell their paper directly to investors, often using the Web to do so. Smaller companies sell through dealers who receive a fee for marketing the issue.

Commercial paper in the United States has a maximum maturity of nine months, though most paper is for fewer than 60 days. Buyers generally hold it to maturity, but the company or dealer that sells the paper is usually prepared to repurchase it earlier.

Commercial paper is not risk-free. When California was mired in the energy crisis of 2001, Southern California Edison and Pacific Gas and Electric defaulted on $1.4 billion of commercial paper. And in 2008 Lehman Brothers filed for bankruptcy with $3 billion of paper outstanding. But such defaults are rare. The majority of commercial paper is issued by high-grade, nationally known companies,⁵³ and the issuers generally support their borrowing by arranging a backup line of credit with a bank, which guarantees that they can find the money to repay the paper.⁵⁴

Because investors are reluctant to buy commercial paper that does not have the highest credit rating, companies cannot rely on the commercial paper market to provide them always with the short-term capital that they need. For example, when the rating services downgraded the commercial paper of Ford and General Motors, both companies were forced to sharply reduce their sales of paper. Ford Credit had $45 billion of unsecured commercial paper outstanding at the end of 2000; by 2011 it had effectively none.

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Commercial paper and the financial crisis

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When Lehman Brothers filed for bankruptcy in September 2008, the commercial paper market nosedived. The spread between the interest rates on commercial paper and Treasury bills doubled, while the market closed entirely for low-grade issuers. Many firms that found themselves shut out of the commercial paper market rushed to borrow on their bank lines of credit. For example, the CFO of the hotel giant Marriott reported that the company drew on its $900 million revolver because it “decided it was prudent” to supplement the significantly reduced liquidity in commercial paper. Firms that had no such alternative source of borrowing were forced to cut back on their investment plans.⁵⁵ Only after the Fed announced plans to buy large quantities of high-grade paper did the market begin to return to normal.

In addition to unsecured commercial paper, there is also a market for asset-backed commercial paper. In this case the company sells its assets to a special-purpose vehicle that then issues the paper. For example, as the auto companies reduced their sales of unsecured commercial paper, they increasingly relied on asset-backed paper secured by the firm’s receivables. As the customers paid their bills, the cash was passed through to the holders of this paper.

By 2007 asset-backed paper accounted for almost half the commercial paper market, but weaknesses surfaced after a number of banks set up structured investment vehicles (SIVs) that invested in mortgage-backed securities financed by asset-backed paper. Because the buyers of the commercial paper bore the credit risk, the banks had less incentive to worry about the quality of the underlying mortgages. Once it became clear that this quality was very low, many of the SIVs found it impossible to refinance the maturing paper and went into default.

Medium-Term Notes

New issues of securities do not need to be registered with the SEC as long as they mature within 270 days. So by limiting the maturity of commercial paper issues, companies can avoid the delays and expense of registration. However, large blue-chip companies also make regular issues of unsecured medium-term notes (MTNs).

You can think of MTNs as a hybrid between corporate bonds and commercial paper. Like bonds they are relatively long-term instruments; their maturity is never less than 270 days, though it is typically less than 10 years.⁵⁶ On the other hand, like commercial paper, MTNs are not underwritten but are sold on a regular basis either through dealers or, occasionally, directly to investors. Dealers support a secondary market in these MTNs and are prepared to buy the notes back before maturity.

Borrowers such as finance companies, which always need cash, welcome the flexibility of MTNs. For example, a company may tell its dealers the amount of money that it needs to raise that week, the range of maturities that it can offer, and the maximum interest that it is prepared to pay. It is then up to the dealers to find the buyers. Investors may also suggest their own terms to one of the dealers, and, if these terms are acceptable, the deal is done.

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SUMMARY

You should now have a fair idea of what you are letting yourself in for when you make an issue of bonds. The detailed bond agreement is set out in the indenture between your company and a trustee, but the main provisions are summarized in the prospectus to the issue. The indenture states whether the bonds are senior or subordinated, and whether they are secured or unsecured. Most bonds are unsecured debentures or notes. This means that they are general claims on the corporation. The principal exceptions are utility mortgage bonds, collateral trust bonds, and equipment trust certificates. In the event of default, the trustee to these issues can repossess the company’s assets to pay off the debt. Sometimes firms raise money using asset-backed securities, which involve bundling assets together and selling the cash flows from them.

Some long-term bond issues have a sinking fund. This means that the company must set aside enough money each year to retire a specified number of bonds. A sinking fund reduces the average life of the bond, and it provides a yearly test of the company’s ability to service its debt. It therefore helps to protect the bondholders against the risk of default.

Long-dated bonds may be callable before maturity. The option to call the bond may be very valuable. If interest rates decline and bond value rises, you may be able to call a bond that would be worth substantially more than the call price. Of course, if investors know that you may call the bond, the call price will act as a ceiling on the market price. Your best strategy, therefore, is to call the bond as soon as the market price hits the call price. You are unlikely to do better than that.

Lenders usually seek to prevent the borrower from taking actions that would damage the value of their loans. Here are some examples of debt covenants:

 1.  The loan agreement may limit the amount of additional borrowing by the company.

 2.  Unsecured loans may incorporate a negative pledge clause, which prohibits the company from securing additional debt without giving equal treatment to the existing unsecured bonds.

 3.  Lenders may place a limit on the company’s dividend payments or repurchases of stock.

Bonds can be issued in the public markets in the U.S., in which case they must be registered with the SEC. Alternatively if they are issued to a limited number of buyers, they can be privately placed. They can also be issued in a foreign bond market or in the Eurobond market. Eurobonds are marketed simultaneously in a number of foreign countries by the London branches of international banks and security dealers.

Most bonds start and finish their lives as bonds, but convertible bonds give their owner the option to exchange the bond for common stock. The conversion ratio measures the number of shares into which each bond can be exchanged. You can think of a convertible bond as equivalent to a straight bond plus a call option on the stock. Sometimes, instead of issuing a convertible, companies may decide to issue a package of bonds and options (or warrants) to buy the stock. If the stock price rises above the exercise price, the investor may then keep the bond and exercise the warrants for cash.

There is an enormous variety of bond issues and new forms of bonds are spawned almost daily. By a process of natural selection, some of these new instruments become popular and may even replace existing species. Others are ephemeral curiosities. Some innovations succeed because they widen investor choice or reduce agency costs. Others owe their origin to tax rules and government regulation.

Many corporations, particularly smaller ones, obtain finance from banks. Bank loans usually have shorter maturities than bonds. Most bank loans come in the form of commitments. Firms pay a commitment fee to keep a credit line open that they can draw upon when they need the cash. Many bank loans are short term at a fixed rate of interest. The interest rate on longer-term bank loans is usually linked to LIBOR or some other index of interest rates. Often bank loans are provided by a syndicate of banks if the amount needed is too large to be provided by a single bank. Loans are frequently secured by collateral such as receivables, inventories, or securities. Covenants are usually more restrictive than with bonds.

Commercial paper and medium-term notes are a cheaper alternative to bank loans for many large firms. They can be sold directly to lenders or through dealers. Commercial paper can be unsecured or asset-backed. Medium-term notes are a hybrid between bonds and commercial paper. They are longer term than commercial paper but are sold in a similar way.

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FURTHER READING

A useful general work on debt securities is:

F. J. Fabozzi (ed.), The Handbook of Fixed Income Securities, 8th ed. (New York: McGraw-Hill, 2011).

For nontechnical discussions of the pricing of convertible bonds and the reasons for their use, see:

M. J. Brennan and E. S. Schwartz, “The Case for Convertibles,” Journal of Applied Corporate Finance 1 (Summer 1988), pp. 55–64.

C. M. Lewis, R. J. Rogalski, and J. K. Seward, “Understanding the Design of Convertible Debt,” Journal of Applied Corporate Finance 11 (Spring 1998), pp. 45–53.

Discussions of project finance include:

B. C. Esty, Modern Project Finance: A Casebook (NewYork: John Wiley, 2003).

B. C. Esty, “Returns on Project-Financed Investments: Evolution and Managerial Implications,” Journal of Applied Corporate Finance 15 (Spring 2002), pp. 71–86.

R. A. Brealey, I. A. Cooper, and M. Habib, “Using Project Finance to Fund Infrastructure Investments,” Journal of Applied Corporate Finance 9 (Fall 1996), pp. 25–38.

The readings listed at the end of Chapter 17 include several articles on financial innovation.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Debt types Select the most appropriate term from within the parentheses:

 a. (High-grade utility bonds/Low-grade industrial bonds) generally have only light sinking-fund requirements.

 b. Collateral trust bonds are often issued by (utilities/industrial holding companies).

 c. (Utility bonds/Industrial bonds) are usually unsecured.

 d. Equipment trust certificates are usually issued by (railroads/financial companies).

 e. Mortgage pass-through certificates are an example of (an asset-backed security/project finance).

2.  Sinking funds For each of the following sinking funds, state whether the fund increases or decreases the value of the bond at the time of issue (or whether it is impossible to say):

 a. An optional sinking fund operating by drawings at par.

 b. A mandatory sinking fund operating by drawings at par or by purchases in the market.

 c. A mandatory sinking fund operating by drawings at par.

3.  Seniority

 a. As a senior bondholder, would you like the company to issue more junior debt to finance its investment program, would you prefer it not to do so, or would you not care?

 b. You hold debt secured on the company’s existing property. Would you like the company to issue more unsecured debt to finance its investments, would you prefer it not to do so, or would you not care?

4.  Bond contracts Use Table 24.1 (but not the text) to answer the following questions:

 a. Who are the principal underwriters for the J.C. Penney bond issue?

 b. Who is the trustee for the issue?

 c. How many dollars does the company receive for each debenture after deduction of the underwriters’ spread?

 d. Is the debenture “bearer” or “registered”?

 e. At what price was the issue callable in 2005?

5.  Bond contracts Look at Table 24.1:

 a. Suppose the debenture was issued on September 1, 1992, at 99.489%. How much would you have to pay to buy one bond delivered on September 15? Don’t forget to include accrued interest.

 b. When is the first interest payment on the bond, and what is the amount of the payment?

 c. On what date do the bonds finally mature, and what is the principal amount of the bonds that is due to be repaid on that date?

 d. Suppose that the market price of the bonds rises to 102 and thereafter does not change. When should the company call the issue?

6.  Private placements Explain the three principal ways in which the terms of private placement bonds commonly differ from those of public issues.

7.  Debt characteristics True or false? Briefly explain in each case.

 a. It is better to hold unsecured bonds than secured bonds in the event of default.

 b. Many new and exotic debt securities are triggered by government policies or regulations.

 c. Call provisions give a valuable option to debt investors.

 d. Restrictive covenants have been shown to protect debt investors when takeovers are financed with large amounts of debt.

 e. Privately placed debt issues often include stricter covenants than public debt. However, public debt covenants are more difficult and expensive to renegotiate.

8.  Convertible bonds Maple Aircraft has issued a 4 ¾% convertible subordinated debenture due 2014. The conversion price is $47.00 and the debenture is callable at 102.75% of face value. The market price of the convertible is 91% of face value, and the price of the common is $41.50. Assume that the value of the bond in the absence of a conversion feature is about 65% of face value.

 a. What is the conversion ratio of the debenture?

 b. If the conversion ratio were 50, what would be the conversion price?

 c. What is the conversion value?

 d. At what stock price is the conversion value equal to the bond value?

 e. Can the market price be less than the conversion value?

 f. How much is the convertible holder paying for the option to buy one share of common stock?

 g. By how much does the common have to rise by 2014 to justify conversion?

 h. When should Maple call the debenture?

9.  Convertible bonds True or false?

 a. Convertible bonds are usually senior claims on the firm.

 b. The higher the conversion ratio, the more valuable the convertible.

 c. The higher the conversion price, the more valuable the convertible.

 d. Convertible bonds do not share fully in the price of the common stock, but they provide some protection against a decline.

INTERMEDIATE

10.  Bond pricing Suppose that the J.C. Penney bond was issued at face value and that investors continue to demand a yield of 8.25%. Sketch what you think would happen to the bond price as the first interest payment date approaches and then passes. What about the price of the bond plus accrued interest?

11.  Bond terms Find the terms and conditions of a recent bond issue and compare them with those of the J.C. Penney issue.

12.  Bond pricing Bond prices can fall either because of a change in the general level of interest rates or because of an increased risk of default. To what extent do floating-rate bonds and puttable bonds protect the investor against each of these risks?

13.  Claim priority Proctor Power has fixed assets worth $200 million and net working capital worth $100 million. It is financed partly by equity and partly by three issues of debt. These consist of $250 million of First Mortgage Bonds secured only on the company’s fixed assets, $100 million of senior debentures, and $120 million of subordinated debentures. If the debt were due today, how much would each debtholder be entitled to receive?

14.  Claim priority Elixir Corporation has just filed for bankruptcy. Elixir is a holding company whose assets consist of real estate worth $80 million and 100% of the equity of its two operating subsidiaries. It is financed partly by equity and partly by an issue of $400 million of senior collateral trust bonds that are just about to mature. Subsidiary A has issued directly $320 million of debentures and $15 million of preferred stock. Subsidiary B has issued $180 million of senior debentures and $60 million of subordinated debentures. A’s assets have a market value of $500 million and B’s have a value of $220 million. How much will each security holder receive if the assets are sold and distributed strictly according to precedence?

15.  Mortgages

 a. Residential mortgages may stipulate either a fixed rate or a variable rate. As a borrower, what considerations might cause you to prefer one rather than the other?

 b. Why might holders of mortgage pass-through certificates wish the mortgages to have a floating rate?

16.  Call provisions After a sharp change in interest rates, newly issued bonds generally sell at yields different from those of outstanding bonds of the same quality. One suggested explanation is that there is a difference in the value of the call provisions. Explain how this could arise.

17.  Call provisions Suppose that a company simultaneously issues a zero-coupon bond and a coupon bond with identical maturities. Both are callable at any time at their face values. Other things equal, which is likely to offer the higher yield? Why?

18.  Call provisions

 a. If interest rates rise, will callable or noncallable bonds fall more in price?

 b. Sometimes you encounter bonds that can be repaid after a fixed interval at the option of either the issuer or the bondholder. If the exercise price of each option is the same and both the issuer and bondholder act rationally, what will happen when the options can be exercised? (Ignore refinements such as transactions or issue costs.)

19.  Put provisions A puttable bond is a bond that may be repaid before maturity at the investor’s option. Sketch a diagram similar to Figure 24.3 showing the relationship between the value of a straight bond and that of a puttable bond.

20.  Covenants Alpha Corp. is prohibited from issuing more senior debt unless net tangible assets exceed 200% of senior debt. Currently the company has outstanding $100 million of senior debt and has net tangible assets of $250 million. How much more senior debt can Alpha Corp. issue?

21.  Covenants Explain carefully why bond indentures may place limitations on the following actions:

 a. Sale of the company’s assets.

 b. Payment of dividends to shareholders.

 c. Issue of additional senior debt.

22.  Convertible bonds The Surplus Value Company had $10 million (face value) of convertible bonds outstanding in 2010. Each bond has the following features.

 a. What is the bond’s conversion value?

 b. Can you explain why the bond is selling above conversion value?

 c. Should Surplus call? What will happen if it does so?

23.  Convertible bonds Oyasuminasai Kabushiki Gaisha has issued a zero-coupon 10-year bond with a face value of ¥100,000 that can be converted into 10 Oyasuminasai shares. Comparable straight bonds are yielding 8%. Oyasuminasai stock is priced at ¥5,000 a share.

 a. Suppose that you had to make a now-or-never decision on whether to convert or to stay with the bond. Which would you do?

 b. If the convertible bond is priced at ¥55,000, how much are investors paying for the option to buy Oyasuminasai shares?

 c. If after one year the value of the conversion option is unchanged, what is the value of the convertible bond?

24.  Convertible bonds Iota Microsystems’ 10% convertible is about to mature. The conversion ratio is 27.

 a. What is the conversion price?

 b. The stock price is $47. What is the conversion value?

 c. Should you convert?

25.  Convertible bonds In 1996 Marriott International made an issue of unusual bonds called liquid yield option notes, or LYONS. The bond matured in 2011, had a zero coupon, and was issued at $532.15. It could have been converted into 8.76 shares. Beginning in 1999 the bonds could have been called by Marriott. The call price was $603.71 in 1999 and increased by 4.3% a year thereafter. Holders had an option to put the bond back to Marriott in 1999 at $603.71 and in 2006 at $810.36. At the time of issue the price of the common stock was about $50.50.

 a. What was the yield to maturity on the bond?

 b. Assuming that comparable nonconvertible bonds yielded 10%, how much were investors paying for the conversion option?

 c. What was the conversion value of the bonds at the time of issue?

 d. What was the initial conversion price of the bonds?

 e. What was the conversion price in 2005? Why did it change?

 f. If the price of the bond in 2006 was less than $810.36, would you have put the bond back to Marriott?

 g. At what price could Marriott have called the bonds in 2006? If the price of the bond in 2006 was more than this, should Marriott have called them?

26.  Convertible bonds In September 2009, the Belgian pharmaceutical company UCB issued €500 million of 4.5% senior unsecured six-year convertible bonds. The bonds were issued at face value. The conversion price was €38.746 per share, a premium of 35% to the recent stock price.

 a. What is the conversion ratio of the convertible? If the price of UCB stock in 2015 is €45, will bondholders convert? If they do convert, how many additional shares will UCB need to issue?

 b. Suppose that the yield on straight (non-convertible) UCB bonds is 5.5%. What does this suggest that UCB investors are paying for the option to convert?

 c. UCB could have issued a bond-warrant package. Design such a package that raises about €500 million and shares the main features of the UCB convertible. What are the advantages and disadvantages of the bond-warrant package?

CHALLENGE

27.  Tax benefits Dorlcote Milling has outstanding a $1 million 3% mortgage bond maturing in 10 years. The coupon on any new debt issued by the company is 10%. The finance director, Mr. Tulliver, cannot decide whether there is a tax benefit to repurchasing the existing bonds in the marketplace and replacing them with new 10% bonds. What do you think? Does it matter whether bond investors are taxed?

28.  Convertible bonds This question illustrates that when there is scope for the firm to vary its risk, lenders may be more prepared to lend if they are offered a piece of the action through the issue of a convertible bond. Ms. Blavatsky is proposing to form a new start-up firm with initial assets of $10 million. She can invest this money in one of two projects. Each has the same expected payoff, but one has more risk than the other. The relatively safe project offers a 40% chance of a $12.5 million payoff and a 60% chance of an $8 million payoff. The risky project offers a 40% chance of a $20 million payoff and a 60% chance of a $5 million payoff.

Ms. Blavatsky initially proposes to finance the firm by an issue of straight debt with a promised payoff of $7 million. Ms. Blavatsky will receive any remaining payoff. Show the possible payoffs to the lender and to Ms. Blavatsky if (a) she chooses the safe project and (b) she chooses the risky project. Which project is Ms. Blavatsky likely to choose? Which will the lender want her to choose?

Suppose now that Ms. Blavatsky offers to make the debt convertible into 50% of the value of the firm. Show that in this case the lender receives the same expected payoff from the two projects.

29.   Convertible bonds Occasionally it is said that issuing convertible bonds is better than issuing stock when the firm’s shares are undervalued. Suppose that the financial manager of the Butternut Furniture Company does have inside information indicating that the Butternut stock price is too low. Butternut’s future earnings will in fact be higher than investors expect. Suppose further that the inside information cannot be released without giving away a valuable competitive secret. Clearly, selling shares at the present low price would harm Butternut’s existing shareholders. Will they also lose if convertible bonds are issued? If they do lose in this case, is the loss more or less than it would be if common stock were issued?

Now suppose that investors forecast earnings accurately, but still undervalue the stock because they overestimate Butternut’s actual business risk. Does this change your answers to the questions posed in the preceding paragraph? Explain.

MINI-CASE ● ● ● ● ●

The Shocking Demise of Mr. Thorndike

It was one of Morse’s most puzzling cases. That morning Rupert Thorndike, the autocratic CEO of Thorndike Oil, was found dead in a pool of blood on his bedroom floor. He had been shot through the head, but the door and windows were bolted on the inside and there was no sign of the murder weapon.

Morse looked in vain for clues in Thorndike’s bedroom and office. He had to take another tack. He decided to investigate the financial circumstances surrounding Thorndike’s demise. The company’s capital structure was as follows:

•  5% debentures: £250 million face value. The bonds mature in 10 years and offer a yield of 12%.

•  Stock: 30 million shares, which closed at £9 a share the day before the murder.

•  10% subordinated convertible notes: The notes mature in one year and are convertible at any time at a conversion ratio of 110. The day before the murder these notes were priced at 5% more than their conversion value.

Yesterday Thorndike had flatly rejected an offer by T. Spoone Dickens to buy all of the common stock for £10 a share. With Thorndike out of the way, it appeared that Dickens’s offer would be accepted, much to the profit of Thorndike Oil’s other shareholders.⁵⁷

Thorndike’s two nieces, Doris and Patsy, and his nephew John all had substantial investments in Thorndike Oil and had bitterly disagreed with Thorndike’s dismissal of Dickens’s offer. Their stakes are shown in the following table:

All debt issued by Thorndike Oil would be paid off at face value if Dickens’s offer went through. Holders of the convertible notes could choose to convert and tender their shares to Dickens.

Morse kept coming back to the problem of motive. Which niece or nephew, he wondered, stood to gain most by eliminating Thorndike and allowing Dickens’s offer to succeed?

QUESTION

1.  Help Morse solve the case. Which of Thorndike’s relatives stood to gain most from his death?

APPENDIX ● ● ● ● ●

Project Finance

Project finance loans are loans that are tied as closely as possible to the fortunes of a particular project and that minimizes the exposure of the parent. These loans are usually referred to simply as project finance and are a specialty of large international banks.

Project finance means debt supported by the project, not by the project’s sponsoring companies. Debt ratios are nevertheless very high for most project financings. They can be high because the debt is supported not just by the project’s assets but also by a variety of contracts and guarantees provided by customers, suppliers, and local governments as well as by the project’s owners.

EXAMPLE 24A.1 • Project Finance for a Power Station

Here is how project finance was used to construct a $1.8 billion oil-fired power plant in Pakistan. First, a separate firm, the Hub Power Company (Hubco) was established to own the power station. Hubco then engaged a consortium of companies, headed by the Japanese company Mitsui & Co., to build the power station, while the British company International Power became responsible for managing and running it for an initial period of 12 years. Hubco agreed to buy the fuel from the Pakistan State Oil Company and to sell the power station’s output to another government body, the Water and Power Development Authority (WAPDA).

Hubco’s lawyers drew up a complex series of contracts to make certain that each of these parties came up to scratch. For example, the contractors agreed to deliver the plant on time and to ensure that it would operate to specifications. International Power, the plant manager, agreed to maintain the plant and operate it efficiently. Pakistan State Oil Company entered into a long-term contract to supply oil to Hubco, and WAPDA agreed to buy Hubco’s output for the next 30 years.⁵⁸ Since WAPDA would pay for the electricity with rupees, Hubco was concerned about the possibility of a fall in the value of the rupee. The State Bank of Pakistan therefore arranged to provide Hubco with foreign exchange for debt service at guaranteed exchange rates. The Pakistan government guaranteed that WAPDA, Pakistan State Oil, and the State Bank would honor their agreements.

The effect of these contracts was to ensure that each risk was borne by the party that was best able to measure and control it. For example, the contractors were best placed to ensure that the plant was completed on time, so it made sense to ask them to bear the risk of construction delays. Similarly, the plant operator was best placed to operate the plant efficiently and would be penalized if it failed to do so. The contractors and the plant manager were prepared to take on these risks because the project involved an established technology and there was relatively little chance of unpleasant surprises.

While these contracts sought to be as precise as possible about each party’s responsibilities, they could not cover every eventuality; inevitably the contracts were incomplete. Therefore, to buttress the formal legal agreements, the contractors and the plant manager became major shareholders in Hubco. This meant that if they cut corners in building and running the plant, they would share in the losses.

The equity in Hubco was highly levered. Over 75% of the $1.8 billion investment in the project was financed by debt. Just under $600 million was junior debt provided by a fund that was set up by the World Bank and the export credit agencies of France, Italy, and Japan. The remainder was senior debt provided in seven different currencies by 58 local and international banks.⁵⁹ The banks were encouraged to invest because they knew that the World Bank and several governments were in the front line and would take a hit if the project were to fail. But they were still concerned that the government of Pakistan might prevent Hubco from paying out foreign currency or it might impose a special tax or prevent the company from bringing in the specialist staff it needed. Therefore, to protect Hubco against these political risks, the government promised to pay compensation if it interfered in such ways with the operation of the project. Of course, the government could not be prevented from tearing up that agreement, but, if it did, Hubco could call on a $360 million guarantee by the World Bank and the Japan Bank for International Cooperation. This was supposed to keep the Pakistan government honest once the plant was built and operating. Governments can be surprisingly relaxed when faced with the wrath of a private corporation but are usually reluctant to break an agreement that lands the World Bank with a large bill.

The arrangements for the Hubco project were complex, costly, and time-consuming. Over 200 person-years were spent in setting up the project. Not everything was plain sailing. The project was suspended for over a year by a Pakistani court ruling that the interest on the loans contravened Islamic law. Ten years after the start of the discussions the final agreement on financing the project was signed and within a short time Hubco was producing a fifth of all Pakistan’s electricity.

That was not the end of the Hubco story. WAPDA was obliged by its contract to make regular payments to Hubco regardless of whether it took the electricity, and as a result found itself on the brink of collapse. After the fall of Benazir Bhutto’s government in Pakistan, the new government terminated the contract with Hubco and announced a 30% cut in electricity tariffs. After three years of painful dispute, which threatened Pakistan’s relationships with the World Bank, Hubco finally agreed to a new tariff. The feud with the government was finally over, and by 2006 Hubco had fully repaid its senior debts.

Some Common Features

No two project financings are alike, but they have some common features:

 •  The project is established as a separate company.

 •  Equity ownership is privately held by a small group of investors. These usually include the contractors and the plant manager, who therefore share in the risk of the project’s failure.

 •  The project company enters into a complex series of contracts that distribute risk among the contractors, the plant manager, the suppliers, and the customers.

 •  The government may guarantee that it will provide the necessary permits, allow the purchase of foreign exchange, and so on.

 •  The detailed contractual arrangements and the government guarantees typically allow about 70% of the capital for the project to be provided in the form of bank debt or other privately placed borrowing. This debt is supported by the project cash flows; if these flows are insufficient, the lenders do not have any recourse against the parent companies.

The Role of Project Finance

Project finance is widely used in developing countries to fund power, telecommunications, and transportation projects, but it is also used in the major industrialized countries. In the United States project finance has been most commonly used to fund power plants. For example, an electric utility company may get together with an industrial company to construct a cogeneration plant that provides electricity to the utility and waste heat to a nearby industrial plant. The utility stands behind the cogeneration project and guarantees its revenue stream. Banks are happy to lend a high proportion of the cost of the project because they know that once the project is up and running, the cash flow is insulated from most of the risks facing normal businesses.⁶⁰

Project financing is costly to arrange⁶¹ and the project debt usually carries a relatively high interest rate. So why don’t companies simply finance the projects by borrowing against their existing assets? Notice that most of the projects have limited lives and employ established technologies. They generate substantial free cash flow, and there are few options to make profitable follow-on investments. If such investments are funded with project finance, management has little discretion over how the cash flows are used. Instead, the debt-service requirements ensure that the cash must be returned to investors rather than frittered away on unprofitable future ventures.⁶²

Our example of the Hubco power station illustrates another important motivation for project finance. The success of the project depends on the performance of a number of different parties. For example, Hubco had only one source of fuel and one customer. To prevent any of the parties from changing the rules of the game after the project has begun, all of them need to enter into a complex set of contracts that are designed to ensure that risks are borne by those best able to control them. And because project viability is often dependent on the goodwill of the government, the government is also often a party to these contracts and the financing is structured to reduce the chance of punitive government action.

QUESTIONS

1.  Explain when it makes sense to use project finance rather than a direct debt issue by the parent company.

2.  Refer to the Hub Power project above. There were many other ways that the Hubco project could have been financed. For example, a government agency could have invested in the power plant and hired National Power to run it. Alternatively, National Power could have owned the power plant directly and funded its cost by a mixture of new borrowing and the sale of shares. What do you think were the advantages of setting up a separately financed company to undertake the project?

___________

¹The remark was made by the late Senator Everett Dirksen. However, he was talking billions.

²If a bond pays interest semiannually, investors usually calculate a semiannually compounded yield to maturity on the bond. In other words, the yield is quoted as twice the six-month yield. When bonds pay interest annually, it is conventional to quote their yields to maturity on an annually compounded basis. For more on this, see Section 3-1.

³There is one type of bond on which the borrower is obliged to pay interest only if it is covered by the year’s earnings. These so-called income bonds are rare and have largely been issued as part of railroad reorganizations.

⁴Any bond that is issued at a discount is known as an original issue discount bond. A zero-coupon bond is often called a “pure discount bond.” The capital appreciation on a discount bond is not taxed as income as long as it amounts to less than .25% a year (IRS Code Section 1272).

⁵The ultimate of ultimates was an issue of a perpetual zero-coupon bond on behalf of a charity.

⁶Instead of issuing a capped floating-rate loan, a company sometimes issues an uncapped loan and at the same time buys a cap from a bank. The bank pays the interest in excess of the specified level.

⁷In the U.S. corporate bond market, accrued interest is calculated on the assumption that a year is composed of twelve 30-day months; in some other markets (such as the U.S. Treasury bond market) calculations recognize the actual number of days in each calendar month.

⁸For example, the indenture for an earlier J.C. Penney bond stated: “In any case where several matters are required to be certified by, or covered by an opinion of, any specified Person, it is not necessary that all matters be certified by, or covered by the opinion of, only one such Person, or that they be certified or covered by only one document, but one such Person may certify or give an opinion with respect to some matters and one or more such other Persons as to other matters, and any such Person may certify or give an opinion as to such matters in one or several documents.” Try saying that three times fast.

⁹This is known as a negative pledge clause.

¹⁰If a mortgage is closed, no more bonds may be issued against the mortgage. However, usually there is no specific limit to the amount of bonds that may be secured (in which case the mortgage is said to be open). Many mortgages are secured not only by existing property but also by “after-acquired” property. However, if the company buys only property that is already mortgaged, the bondholder would have only a junior claim on the new property. Therefore, mortgage bonds with after-acquired property clauses also limit the extent to which the company can purchase additional mortgaged property.

¹¹If a bond does not specifically state that it is junior, you can assume that it is senior.

¹²Hence the bonds are often termed pass-through certificates.

¹³See J. Matthews, “David Bowie Reinvents Himself, This Time as a Bond Issue,” Washington Post, February 7, 1997.

¹⁴J. D. Coval, J. Jurek, and E. Stafford, “Economic Catastrophe Bonds,” American Economic Review 3 (June 2009), pp. 628–666.

¹⁵Data on issuance are available on www.sifma.org.

¹⁶CDO fees for the originating bank were in the region of 1.5% to 1.75%, more than three times the amount that the bank could earn from underwriting an investment-grade bond. However, many banks during the crisis seem to have persuaded themselves that the underlying mortgages were not junk and kept a large portion of the loans on their own books. See, for example, V. Acharya and M. Richardson (eds.), Restoring Financial Stability (Hoboken, NJ: Wiley, 2009).

¹⁷Every investor dreams of buying up the entire supply of a sinking-fund bond that is selling way below face value and then forcing the company to buy the bonds back at face value. Cornering the market in this way is fun to dream about but difficult to do.

¹⁸Of course, this assumes that the bond is correctly priced, that investors are behaving rationally, and that investors expect the firm to behave rationally. Also we ignore some complications. First, you may not wish to call a bond if you are prevented by a nonrefunding clause from issuing new debt. Second, the call premium is a tax-deductible expense for the company but is taxed as a capital gain to the bondholder. Third, both the company and the investor face other possible tax consequences from replacing a high-coupon bond with a lower-coupon bond. Fourth, calling and reissuing debt involves costs and delays.

¹⁹We described in Section 18-3 some of the games that managers can play at the expense of bondholders.

²⁰“Me too” is not acceptable legal jargon. Instead the bond agreement may state that the company “will not consent to any lien on its assets without securing the existing bonds equally and ratably.”

²¹A dividend restriction might typically prohibit the company from paying dividends if their cumulative amount would exceed the sum of (1) cumulative net income, (2) the proceeds from the sale of stock or conversion of debt, and (3) a dollar amount equal to one year’s dividend.

²²P. Asquith and T. Wizman, “Event Risk, Covenants, and Bondholder Returns in Leveraged Buyouts,” Journal of Financial Economics 27 (September 1990), pp. 195–213. Leveraged buyouts (LBOs) are company acquisitions that are financed by large issues of (usually unsecured) debt. We describe LBOs in Chapter 32.

²³D. J. Denis and V. T. Mihov estimated that the value of privately-placed bond issues is less than 20% that of total bond issues. See D. J. Denis and V. T. Mihov, “The Choice Among Bank Debt, Non-Bank Private Debt and Public Debt: Evidence from New Corporate Borrowings,” Journal of Financial Economics 70 (2003), pp. 3–28.

²⁴Of course debt with the same terms could be offered publicly, but then 200 separate investigations would be required—a much more expensive proposition.

²⁵See D. J. Denis and V. T. Mihov, “The Choice Among Bank Debt, Non-Bank Private Debt, and Public Debt: Evidence from New Corporate Borrowings,” Journal of Financial Economics 70 (2003), pp. 3–28.

²⁶We described Rule 144A in Section 15-5.

²⁷You should not, however, get the impression that the eurobond market is some lawless wilderness. Eurobond contracts typically state that the issue is subject to either British or New York law.

²⁸To make matters more confusing, the term “eurobond” has also been used to refer to bonds that in the future might be issued jointly by eurozone governments.

²⁹You may recognize this as the position diagram for a default-free bond minus a put option on the assets with an exercise price equal to the face value of the bonds. See Section 23-2.

³⁰Nokia can call its bonds if the stock price is 150% of the conversion price.

³¹The financial manager might delay calling if interest payments on the convertible are less than the extra dividends that would be paid after conversion. This delay would reduce cash payments to bondholders. Nothing is lost if the financial manager calls on the way down. Note that investors may convert voluntarily if they would thereby increase their income.

³²She might even point out to you that several Japanese companies have issued convertible bonds at a negative yield. Investors actually paid the companies to hold their debt.

³³That is much the same as already having the stock together with the right to sell it for the convertible’s bond value. In other words, instead of thinking of a convertible as a bond plus a call option, you could think of it as the stock plus a put option. Now you can see why it is wrong to think of a convertible as equivalent to the sale of stock; it is equivalent to the sale of both stock and a put option. If there is any possibility that investors will want to hold on to their bond, this put option has value.

³⁴See J. R. Graham and C. R. Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187–243.

³⁵In the survey referred to above, a further 44% of the respondents reported that an important factor in their decision was the fact that convertibles were attractive to investors who were unsure about the riskiness of the company.

³⁶Changes in risk are more likely when the firm is small and its debt is low-grade. Therefore, we should find that convertible bonds of such firms offer their holders a larger potential ownership share. This is indeed the case. See C. M. Lewis, R. J. Rogalski, and J. K. Seward, “Understanding the Design of Convertible Debt,” Journal of Applied Corporate Finance 11 (Spring 1998), pp. 45–53.

³⁷Of course, the firm could also make an equity issue rather than an issue of straight debt or convertibles. However, a convertible issue sends a better signal to investors than an issue of common stock. As we explained in Chapter 15, announcement of a stock issue prompts worries of overvaluation and usually depresses the stock price. Convertibles are hybrids of debt and equity and send a less negative signal. If the company is likely to need equity, its willingness to issue a convertible and take the chance that the stock price will rise enough to lead to conversion also signals management’s confidence in the future. See J. Stein, “Convertible Bonds as Backdoor Equity Financing,” Journal of Financial Economics 32 (1992), pp. 3–21.

³⁸In their financial statements companies recognize the possibility of dilution by showing how earnings would be affected by the issue of the extra shares.

³⁹For a more comprehensive list of innovations, see K. A. Carrow and J. J. McConnell, “A Survey of U.S. Corporate Financing Innovations: 1970–1997,” Journal of Applied Corporate Finance 12 (Spring 1999), pp. 55–69.

⁴⁰The French bank BNP Paribas attempted to launch a $1 billion issue of longevity bonds in 2004, but had difficulty attracting buyers. However, there is now an active market in longevity swaps, which insure the buyer against a general rise in longevity. (We discuss swaps in Chapter 26.)

⁴¹See D. J. Denis and V. T. Mihov, “The Choice Among Bank Debt, Non-Bank Private Debt, and Public Debt: Evidence from New Corporate Borrowings,” Journal of Financial Economics 70(2003), pp 3–28.

⁴²The 364-day facilities are popular with banks because they do not need to set aside capital for commitments of less than a year.

⁴³One study of private debt agreements found that over 90% are renegotiated before maturity. In most cases this is not because of financial distress. See M. R. Roberts and A. Sufi, “Renegotiation of Financial Contracts: Evidence from Private Credit Agreements,” Journal of Financial Economics, 93 (2009), pp.159–184.

⁴⁴The federal funds rate is the rate at which banks lend excess reserves to each other.

⁴⁵In the case of euro deposits, the European Banking Federation calculates an alternative measure, known as Euribor. You can find historical values for LIBOR on www.bbalibor.com and for Euribor on www.euribor.org.

⁴⁶For a standard loan to a blue-chip company the fee for arranging a syndicated loan may be as low as 10 basis points, while a complex deal with a highly leveraged firm may carry a fee of up to 250 basis points. For good reviews of the syndicated loan market see S. C. Miller, “A Guide to the Syndicated Loan Market,” Standard & Poor’s, September 2005 (www.standardandpoors.com); and B. Gadanecz, “The Syndicated Loan Market: Structure, Development and Implications,” BIS Quarterly Review, December 2004, pp. 75–89 (www.bis.org).

⁴⁷See A. Sufi, “Information Asymmetry and Financing Arrangements: Evidence from Syndicated Loans,” Journal of Finance 62 (April 2007), pp. 629–668.

⁴⁸Loan sales generally take one of two forms: assignments or participations. In the former case a portion of the loan is transferred with the agreement of the borrower. In the second case the lead bank maintains its relationship with the borrower but agrees to pay over to the buyer a portion of the cash flows that it receives.

⁴⁹The results of a survey of the terms of business lending by banks in the United States are published quarterly in the Federal Reserve Bulletin (see www.federalreserve.gov/releases/E2).

⁵⁰It is not always practicable to keep inventory in a warehouse. For example, automobile dealers need to display their cars in a showroom. One solution is to enter into a floor-planning arrangement in which the finance company buys the cars and the dealer holds them in trust. When the cars are sold, the proceeds are used to redeem the cars from the finance company. The interest or “flooring charge” depends on how long the cars have been in the showroom.

⁵¹For an analysis of loan covenants in privately placed debt see M. Bradley and M. R. Roberts, “The Structure and Pricing of Corporate Debt Covenants,” working paper, Wharton School, University of Pennsylvania, 2003.

⁵²A bank holding company is a firm that owns both a bank and nonbanking subsidiaries.

⁵³Moody’s, Standard and Poor’s, and Fitch publish quality ratings for commercial paper. For example, Moody’s provides three ratings, from P-1 (that is, Prime 1, the highest-grade paper) to P-3. Most investors are reluctant to buy low-rated paper. For example, money-market funds are largely limited to holding P-1 paper.

⁵⁴For top-tier issuers the credit line is generally 75% of the amount of paper; for lower-grade issuers it is 100%. The company may not be able to draw on this line of credit if it does not satisfy bank covenants. Therefore, lower-rated companies may need to back their paper with an irrevocable line of credit.

⁵⁵For an analysis of firm reaction to the collapse of the commercial paper market, see P. Gao and H. Yun, “Commercial Paper, Lines of Credit, and the Real Effects of the Financial Crisis of 2008: Firm-Level Evidence from the Manufacturing Industry,” working paper, University of Notre Dame, 2010.

⁵⁶Occasionally, an MTN registration may be used to issue much longer term bonds. For example, Disney has even used its MTN program to issue a 100-year bond.

⁵⁷Rupert Thorndike’s shares would go to a charitable foundation formed to advance the study of financial engineering and its crucial role in world peace and progress. The managers of the foundation’s endowment were not expected to oppose the takeover.

⁵⁸WAPDA entered into a take-or-pay agreement with Hubco; if it did not take the electricity, it still had to pay for it. In the case of pipeline projects the contract with the customer is often in the form of a throughput agreement, whereby the customer agrees to make a minimum use of the pipeline. Another arrangement for transferring revenue risk to a customer is the tolling contract, whereby the customer agrees to deliver to the project company materials that the company is to process and return to the customer. One purpose of transferring revenue risk to customers is to encourage them to estimate their demand for the project’s output thoroughly.

⁵⁹Notice that, although most of Hubco’s debt had a maturity of about 12 years, the project was not financed by a public bond issue. The concentrated ownership of bank debt induces the lenders to evaluate the project carefully and to monitor its subsequent progress. It also facilitates the renegotiation of the debt if the project company runs into difficulties.

⁶⁰There are some interesting regulatory implications to this arrangement. When a utility builds a power plant, it is entitled to a fair return on its investment: Regulators are supposed to set customer charges that will allow the utility to earn its cost of capital. Unfortunately, the cost of capital is not easily measured and is a natural focus for argument in regulatory hearings. But when a utility buys electric power, the cost of capital is rolled into the contract price and treated as an operating cost. In this case the pass-through to the customer may be less controversial.

⁶¹Total transaction costs for infrastructure projects average 3% to 5% of the amount invested. See M. Klein, J. So, and B. Shin, “Transaction Costs in Private Infrastructure Projects—Are They Too High?” The World Bank Group, October 1996.

⁶²Because the project is an independent company, it cannot drag down the parent company if something does go badly wrong with the project.

Part 7 Debt Financing

Leasing

Most of us occasionally rent a car, bicycle, or boat. Usually such personal rentals are short-lived; we may rent a car for a day or week. But in corporate finance longer-term rentals are common. A rental agreement that extends for a year or more and involves a series of fixed payments is called a lease.

Firms lease as an alternative to buying capital equipment. In Europe and the U.S., about 30% of new capital equipment is leased. Trucks and farm machinery are often leased; so are railroad cars, aircraft, and ships. Just about every kind of asset can be leased. For example, the two pandas in Washington’s National Zoo are leased from the Chinese government at a cost of $500,000 per year.

Every lease involves two parties. The user of the asset is called the lessee. The lessee makes periodic payments to the owner of the asset, who is called the lessor. For example, if you sign an agreement to rent an apartment for a year, you are the lessee and the owner is the lessor.

You often see references to the leasing industry. This refers to lessors. (Almost all firms are lessees to at least a minor extent.) Who are the lessors?

Some of the largest lessors are equipment manufacturers. For example, IBM is a large lessor of computers, and Deere is a major lessor of agricultural and construction equipment. Volkswagen is one of the largest equipment lessors in Europe.

The other two major groups of lessors are banks and independent leasing companies. Leasing companies play an enormous role in the airline business. For example, in 2012 GE Capital Aviation Services, a subsidiary of GE Capital, owned and leased out over 1,700 commercial aircraft. The world’s airlines rely largely on leasing to finance their fleets.

Leasing companies offer a variety of services. Some act as lease brokers (arranging lease deals) as well as being lessors. Others specialize in leasing automobiles, trucks, and standardized industrial equipment; they succeed because they can buy equipment in quantity, service it efficiently, and if necessary resell it at a good price.

We begin this chapter by cataloging the different kinds of leases and some of the reasons for their use. Then we show how short-term, or cancelable, lease payments can be interpreted as equivalent annual costs. The remainder of the chapter analyzes long-term leases used as alternatives to debt financing.

 25-1   What Is a Lease?

Leases come in many forms, but in all cases the lessee (user) promises to make a series of payments to the lessor (owner). The lease contract specifies the monthly or semiannual payments, with the first payment usually due as soon as the contract is signed. The payments are usually level, but their time pattern can be tailored to the user’s needs. For example, suppose that a manufacturer leases a machine to produce a complex new product. There will be a year’s “shakedown” period before volume production starts. In this case, it might be possible to arrange for lower payments during the first year of the lease.

When a lease is terminated, the leased equipment reverts to the lessor. However, the lease agreement often gives the user the option to purchase the equipment or take out a new lease.

Some leases are short-term or cancelable during the contract period at the option of the lessee. These are generally known as operating leases. Others extend over most of the estimated economic life of the asset and cannot be canceled or can be canceled only if the lessor is reimbursed for any losses. These are called capital, financial, or full-payout leases.

Financial leases are a source of financing. Signing a financial lease contract is like borrowing money. There is an immediate cash inflow because the lessee is relieved of having to pay for the asset. But the lessee also assumes a binding obligation to make the payments specified in the lease contract. The user could have borrowed the full purchase price of the asset by accepting a binding obligation to make interest and principal payments to the lender. Thus the cash-flow consequences of leasing and borrowing are similar. In either case, the firm raises cash now and pays it back later. Later in this chapter we compare leasing and borrowing as financing alternatives.

Leases also differ in the services provided by the lessor. Under a full-service, or rental, lease, the lessor promises to maintain and insure the equipment and to pay any property taxes due on it. In a net lease, the lessee agrees to maintain the asset, insure it, and pay any property taxes. Financial leases are usually net leases.

Most financial leases are arranged for brand new assets. The lessee identifies the equipment, arranges for the leasing company to buy it from the manufacturer, and signs a contract with the leasing company. This is called a direct lease. In other cases, the firm sells an asset it already owns and leases it back from the buyer. These sale and lease-back arrangements are common in real estate. For example, firm X may wish to raise cash by selling an office or factory but still retain use of the building. It could do this by selling the building for cash to a leasing company and simultaneously signing a long-term lease contract. For example, in 2009 HSBC sold its head office building in London for £772.5 million, or about $1.3 billion. HSBC then leased the building back at an annual rent of £46 million.¹ Thus legal ownership of the building passed to the new owner, but the right to use it remained with HSBC.

You may also encounter leveraged leases. These are financial leases in which the lessor borrows part of the purchase price of the leased asset, using the lease contract as security for the loan. This does not change the lessee’s obligations, but it can complicate the lessor’s analysis considerably.

 25-2   Why Lease?

You hear many suggestions about why companies should lease equipment rather than buy it. Let us look at some sensible reasons and then at four more dubious ones.

Sensible Reasons for Leasing

Short-Term Leases Are Convenient Suppose you want the use of a car for a week. You could buy one and sell it seven days later, but that would be silly. Quite apart from the fact that registering ownership is a nuisance, you would spend some time selecting a car, negotiating purchase, and arranging insurance. Then at the end of the week you would negotiate resale and cancel the registration and insurance. When you need a car only for a short time, it clearly makes sense to rent it. You save the trouble of registering ownership, and you know the effective cost. In the same way, it pays a company to lease equipment that it needs for only a year or two. Of course, this kind of lease is always an operating lease.²

Sometimes the cost of short-term rentals may seem prohibitively high, or you may find it difficult to rent at any price. This can happen for equipment that is easily damaged by careless use. The owner knows that short-term users are unlikely to take the same care they would with their own equipment. When the danger of abuse becomes too high, short-term rental markets do not survive. Thus, it is easy enough to buy a Lamborghini Gallardo, provided your pockets are deep enough, but nearly impossible to rent one.

Cancellation Options Are Valuable Some leases that appear expensive really are fairly priced once the option to cancel is recognized. We return to this point in the next section.

Maintenance Is Provided Under a full-service lease, the user receives maintenance and other services. Many lessors are well equipped to provide efficient maintenance. However, bear in mind that these benefits will be reflected in higher lease payments.

Standardization Leads to Low Administrative and Transaction Costs Suppose that you operate a leasing company that specializes in financial leases for trucks. You are effectively lending money to a large number of firms (the lessees) that may differ considerably in size and risk. But, because the underlying asset is in each case the same salable item (a truck), you can safely “lend” the money (lease the truck) without conducting a detailed analysis of each firm’s business. You can also use a simple, standard lease contract. This standardization makes it possible to “lend” small sums of money without incurring large investigative, administrative, or legal costs.

For these reasons leasing is often a relatively cheap source of cash for the small company with few tangible assets to support a debt issue.³ It offers secure financing on a flexible, piecemeal basis, with lower transaction costs than in a bond or stock issue.

Tax Shields Can Be Used The lessor owns the leased asset and deducts its depreciation from taxable income. If the lessor can make better use of depreciation tax shields than an asset’s user can, it may make sense for the leasing company to own the equipment and pass on some of the tax benefits to the lessee in the form of low lease payments.

Leasing and Financial Distress Lessors in financial leases are in many ways similar to secured lenders, but lessors may fare better in bankruptcy. If a lessee defaults on a lease payment, you might think that the lessor could pick up the leased asset and take it home. But if the bankruptcy court decides that the asset is “essential” to the lessee’s business, it affirms the lease. Then the bankrupt firm can continue to use the asset. It must continue to make the lease payments, however. This can be good news for the lessor, who is paid while other creditors cool their heels. Even secured creditors are not paid until the bankruptcy process works itself out.

If the lease is not affirmed but rejected, the lessor can recover the leased asset. If it is worth less than the present value of the remaining lease payments, the lessor can try to recoup this loss. But in this case the lender must get in line with unsecured creditors.

Unfortunately for lessors, there is a third possibility. A lessee in financial distress may be able to renegotiate the lease, forcing the lessor to accept lower lease payments. For example, in 2001 American Airlines (AA) acquired most of the assets of Trans World Airlines (TWA). TWA was bankrupt, and AA’s purchase contract was structured so that AA could decide whether to affirm or reject TWA’s aircraft leases. AA contacted the lessors and threatened to reject. The lessors realized that rejection would put about 100 leased aircraft back in their laps to sell or re-lease, probably at fire-sale prices. (The market for used aircraft was not strong at the time.) The lessors ended up accepting renegotiated lease rates that were about half what TWA had been paying.⁴

Avoiding the Alternative Minimum Tax Red-blooded financial managers want to earn lots of money for their shareholders but report low profits to the tax authorities. Tax law in the United States allows this. A firm may use straight-line depreciation in its annual report but choose accelerated depreciation (and the shortest possible asset life) for its tax books. By this and other perfectly legal and ethical devices, profitable companies have occasionally managed to escape tax entirely. Almost all companies pay less tax than their public income statements suggest.⁵

But there is a trap for U.S. companies that shield too much income: the alternative minimum tax (AMT). Corporations must pay the AMT whenever it is higher than their tax computed in the regular way.

Here is how the AMT works: It requires a second calculation of taxable income, in which part of the benefit of accelerated depreciation and other tax-reducing items⁶ is added back. The AMT is 20% of the result.

Suppose Yuppytech Services would have $10 million in taxable income but for the AMT, which forces it to add back $9 million of tax privileges:

Yuppytech must pay $3.8 million, not $3.5.⁷

How can this painful payment be avoided? How about leasing? Lease payments are not on the list of items added back in calculating the AMT. If you lease rather than buy, tax depreciation is less and the AMT is less. There is a net gain if the lessor is not subject to the AMT and can pass back depreciation tax shields in the form of lower lease payments.

Some Dubious Reasons for Leasing

Leasing Avoids Capital Expenditure Controls In many companies lease proposals are scrutinized as carefully as capital expenditure proposals, but in others leasing may enable an operating manager to avoid the approval procedures needed to buy an asset. Although this is a dubious reason for leasing, it may be influential, particularly in the public sector. For example, city hospitals have sometimes found it politically more convenient to lease their medical equipment than to ask the city government to provide funds for purchase.

Leasing Preserves Capital Leasing companies provide “100% financing”; they advance the full cost of the leased asset. Consequently, they often claim that leasing preserves capital, allowing the firm to save its cash for other things.

But the firm can also “preserve capital” by borrowing money. If Greymare Bus Lines leases a $100,000 bus rather than buying it, it does conserve $100,000 cash. It could also (1) buy the bus for cash and (2) borrow $100,000, using the bus as security. Its bank balance ends up the same whether it leases or buys and borrows. It has the bus in either case, and it incurs a $100,000 liability in either case. What’s so special about leasing?

Leases May Be Off-Balance-Sheet Financing In some countries financial leases are off-balance-sheet financing; that is, a firm can acquire an asset, finance it through a financial lease, and show neither the asset nor the lease contract on its balance sheet.

In the United States, the Financial Accounting Standards Board (FASB) requires that all capital (i.e., financial) leases be capitalized. This means that the present value of the lease payments must be calculated and shown alongside debt on the right-hand side of the balance sheet. The same amount must be shown as an asset on the left-hand side and written off over the life of the lease.

The FASB defines capital leases as leases that meet any one of the following requirements:

 1.  The lease agreement transfers ownership to the lessee before the lease expires.

 2.  The lessee can purchase the asset for a bargain price when the lease expires.

 3.  The lease lasts for at least 75% of the asset’s estimated economic life.

 4.  The present value of the lease payments is at least 90% of the asset’s value.

All other leases are operating leases as far as the accountants are concerned.⁸

Many financial managers have tried to take advantage of this arbitrary boundary between operating and financial leases. Suppose that you want to finance a computer-controlled machine tool costing $1 million. The machine tool’s life is expected to be 12 years. You could sign a lease contract for 8 years 11 months (just missing requirement 3), with lease payments having a present value of $899,000 (just missing requirement 4). You could also make sure the lease contract avoids requirements 1 and 2. Result? You have off-balance-sheet financing. This lease would not have to be capitalized, although it is clearly a long-term, fixed obligation.

Now we come to the $64,000 question: Why should anyone care whether financing is off balance sheet or on balance sheet? Shouldn’t the financial manager worry about substance rather than appearance?

When a firm obtains off-balance-sheet financing, the conventional measures of financial leverage, such as the debt–equity ratio, understate the true degree of financial leverage. Some believe that financial analysts do not always notice off-balance-sheet lease obligations (which are still referred to in footnotes) or the greater volatility of earnings that results from the fixed lease payments. They may be right if off-balance-sheet lease obligations are moderate and “lost in the noise” of all the firm’s other activities. But we would not expect investors, security analysts, and debt-rating agencies to miss large hidden obligations unless they were systematically misled by management.

Leasing Affects Book Income Leasing can make the firm’s balance sheet and income statement look better by increasing book income or decreasing book asset value, or both.

A lease that qualifies as off-balance-sheet financing affects book income in only one way: The lease payments are an expense. If the firm buys the asset instead and borrows to finance it, both depreciation and interest expense are deducted. Leases are usually set up so that payments in the early years are less than depreciation plus interest under the buy-and-borrow alternative. Consequently, leasing increases book income in the early years of an asset’s life. The book rate of return can increase even more dramatically, because the book value of assets (the denominator in the book-rate-of-return calculation) is understated if the leased asset never appears on the firm’s balance sheet.

Leasing’s impact on book income should in itself have no effect on firm value. In efficient capital markets investors will look through the firm’s accounting results to the true value of the asset and the liability incurred to finance it.

 25-3    Operating Leases

Remember our discussion of equivalent annual costs in Chapter 6? We defined the equivalent annual cost of, say, a machine as the annual rental payment sufficient to cover the present value of all the costs of owning and operating it.

In Chapter 6’s examples, the rental payments were hypothetical—just a way of converting a present value to an annual cost. But in the leasing business the payments are real. Suppose you decide to lease a machine tool for one year. What will the rental payment be in a competitive leasing industry? The lessor’s equivalent annual cost, of course.

Example of an Operating Lease

The boyfriend of the daughter of the CEO of Establishment Industries takes her to the senior prom in a pearly white stretch limo. The CEO is impressed. He decides Establishment Industries ought to have one for VIP transportation. Establishment’s CFO prudently suggests a one-year operating lease instead and approaches Acme Limolease for a quote.

Table 25.1 shows Acme’s analysis. Suppose it buys a new limo for $75,000 that it plans to lease out for seven years (years 0 through 6). The table gives Acme’s forecasts of operating, maintenance, and administrative costs, the latter including the costs of negotiating the lease, keeping track of payments and paperwork, and finding a replacement lessee when Establishment’s year is up. For simplicity we assume zero inflation and use a 7% real cost of capital. We also assume that the limo will have zero salvage value at the end of year 6. The present value of all costs, partially offset by the value of depreciation tax shields,⁹ is $98,150. Now, how much does Acme have to charge to break even?

Acme can afford to buy and lease out the limo only if the rental payments forecasted over six years have a present value of at least $98,150. The problem, then, is to calculate a six-year annuity with a present value of $98,150. We follow common leasing practice and assume rental payments in advance.¹⁰

As Table 25.1 shows, the required annuity is $26,190, that is, about $26,000.¹¹ This annuity’s present value (after taxes) exactly equals the present value of the after-tax costs of owning and operating the limo. The annuity provides Acme with a competitive expected rate of return (7%) on its investment. Acme could try to charge Establishment Industries more than $26,000, but if the CFO is smart enough to ask for bids from Acme’s competitors, the winning lessor will end up receiving this amount.

   TABLE 25.1 Calculating the zero-NPV rental rate (or equivalent annual cost) for Establishment Industries’ pearly white stretch limo (figures in $ thousands). The break-even rent is set so that the PV of after-tax lease payments equals 98.15, the PV of the after-tax cost of buying and operating the limo.

Note: We assume no inflation and a 7% real cost of capital. The tax rate is 35%.

a Depreciation tax shields are calculated using the five-year schedule from Table 6.4.

b Note that the first payment of these annuities comes immediately. The standard annuity factor must be multiplied by 1 + r = 1.07.

Remember that Establishment Industries is not compelled to use the limo for more than one year. Acme may have to find several new lessees over the limo’s economic life. Even if Establishment continues, it can renegotiate a new lease at whatever rates prevail in the future. Thus Acme does not know what it can charge in year 1 or afterward. If pearly white falls out of favor with teenagers and CEOs, Acme is probably out of luck.

In real life Acme would have several further things to worry about. For example, how long will the limo stand idle when it is returned at year 1? If idle time is likely before a new lessee is found, then lease rates have to be higher to compensate.¹²

In an operating lease, the lessor absorbs these risks, not the lessee. The discount rate used by the lessor must include a premium sufficient to compensate its shareholders for the risks of buying and holding the leased asset. In other words, Acme’s 7% real discount rate must cover the risks of investing in stretch limos. (As we see in the next section, risk bearing in financial leases is fundamentally different.)

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Lease or Buy?

If you need a car or limo for only a day or a week you will surely rent it; if you need one for five years you will probably buy it. In between there is a gray region in which the choice of lease or buy is not obvious. The decision rule should be clear in concept, however: If you need an asset for your business, buy it if the equivalent annual cost of ownership and operation is less than the best lease rate you can get from an outsider. In other words, buy if you can “rent to yourself” cheaper than you can rent from others. (Again we stress that this rule applies to operating leases.)

If you plan to use the asset for an extended period, your equivalent annual cost of owning the asset will usually be less than the operating lease rate. The lessor has to mark up the lease rate to cover the costs of negotiating and administering the lease, the foregone revenues when the asset is off-lease and idle, and so on. These costs are avoided when the company buys and rents to itself.

There are two cases in which operating leases may make sense even when the company plans to use an asset for an extended period. First, the lessor may be able to buy and manage the asset at less expense than the lessee. For example, the major truck leasing companies buy thousands of new vehicles every year. That puts them in an excellent bargaining position with truck manufacturers. These companies also run very efficient service operations, and they know how to extract the most salvage value when trucks wear out and it is time to sell them. A small business, or a small division of a larger one, cannot achieve these economies and often finds it cheaper to lease trucks than to buy them.

Second, operating leases often contain useful options. Suppose Acme offers Establishment Industries the following two leases:

 1.  A one-year lease for $26,000.

 2.  A six-year lease for $28,000, with the option to cancel the lease at any time from year 1 on.¹³

The second lease has obvious attractions. Suppose Establishment’s CEO becomes fond of the limo and wants to use it for a second year. If rates increase, lease 2 allows Establishment to continue at the old rate. If rates decrease, Establishment can cancel lease 2 and negotiate a lower rate with Acme or one of its competitors.

Of course, lease 2 is a more costly proposition for Acme: In effect it gives Establishment an insurance policy protecting it from increases in future lease rates. The difference between the costs of leases 1 and 2 is the annual insurance premium. But lessees may happily pay for insurance if they have no special knowledge of future asset values or lease rates. A leasing company acquires such knowledge in the course of its business and can generally sell such insurance at a profit.

Airlines face fluctuating demand for their services and the mix of planes that they need is constantly changing. Most airlines, therefore, lease a proportion of their fleet on a short-term, cancelable basis and are willing to pay a premium to lessors for bearing the cancelation risk. Specialist aircraft lessors are prepared to bear this risk, for they are well-placed to find new customers for any aircraft that are returned to them. Aircraft owned by specialist lessors spend less time parked and more time flying than aircraft owned by airlines.¹⁴

Be sure to check out the options before you sign (or reject) an operating lease.¹⁵

 25-4    Valuing Financial Leases

For operating leases the decision centers on “lease versus buy.” For financial leases the decision amounts to “lease versus borrow.” Financial leases extend over most of the economic life of the leased equipment. They are not cancelable. The lease payments are fixed obligations equivalent to debt service.

Financial leases make sense when the company is prepared to take on the business risks of owning and operating the leased asset. If Establishment Industries signs a financial lease for the stretch limo, it is stuck with that asset. The financial lease is just another way of borrowing money to pay for the limo.

Financial leases do offer special advantages to some firms in some circumstances. However, there is no point in further discussion of these advantages until you know how to value financial lease contracts.

Example of a Financial Lease

Imagine yourself in the position of Thomas Pierce III, president of Greymare Bus Lines. Your firm was established by your grandfather, who was quick to capitalize on the growing demand for transportation between Widdicombe and nearby townships. The company has owned all its vehicles from the time the company was formed; you are now reconsidering that policy. Your operating manager wants to buy a new bus costing $100,000. The bus will last only eight years before going to the scrap yard. You are convinced that investment in the additional equipment is worthwhile. However, the representative of the bus manufacturer has pointed out that her firm would also be willing to lease the bus to you for eight annual payments of $16,900 each. Greymare would remain responsible for all maintenance, insurance, and operating expenses.

Table 25.2 shows the direct cash-flow consequences of signing the lease contract. (An important indirect effect is considered later.) The consequences are as follows:

 1.  Greymare does not have to pay for the bus. This is equivalent to a cash inflow of $100,000.

 2.  Greymare no longer owns the bus and so cannot depreciate it. Therefore it gives up a valuable depreciation tax shield. In Table 25.2, we have assumed depreciation would be calculated using the five-year MACRS depreciation schedule. (See Table 6.4.)

 3.  Greymare must pay $16,900 per year for eight years to the lessor. The first payment is due immediately.

 4.  However, these lease payments are fully tax-deductible. At a 35% marginal tax rate, the lease payments generate tax shields of $5,920 per year. You could say that the after-tax cost of the lease payment is $16,900 – $5,920 = $10,980.

We must emphasize that Table 25.2 assumes that Greymare will pay taxes at the full 35% marginal rate. If the firm were sure to lose money, and therefore pay no taxes, lines 2 and 4 would be left blank. The depreciation tax shields are worth nothing to a firm that pays no taxes, for example.

Table 25.2 also assumes the bus will be worthless when it goes to the scrap yard at the end of year 7. Otherwise there would be an entry for salvage value lost.

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Who Really Owns the Leased Asset?

To a lawyer or a tax accountant, that would be a silly question: The lessor is clearly the legal owner of the leased asset. That is why the lessor is allowed to deduct depreciation from taxable income.

   TABLE 25.2 Cash-flow consequences of the lease contract offered to Greymare Bus Lines (figures in $ thousands; some columns do not add due to rounding).

From an economic point of view, you might say that the user is the real owner, because in a financial lease, the user faces the risks and receives the rewards of ownership. Greymare cannot cancel a financial lease. If the new bus turns out to be hopelessly costly and unsuited for Greymare’s routes, that is Greymare’s problem, not the lessor’s. If it turns out to be a great success, the profit goes to Greymare, not the lessor. The success or failure of the firm’s business operations does not depend on whether the buses are financed by leasing or some other financial instrument.

In many respects, a financial lease is equivalent to a secured loan. The lessee must make a series of fixed payments; if the lessee fails to do so, the lessor can repossess the asset. Thus we can think of a balance sheet like this:

as being economically equivalent to a balance sheet like this:

Having said this, we must immediately qualify. Legal ownership can make a big difference when a financial lease expires because the lessor gets the asset. Once a secured loan is paid off, the user owns the asset free and clear.

Leasing and the Internal Revenue Service

We have already noted that the lessee loses the tax depreciation of the leased asset but can deduct the lease payment in full. The lessor, as legal owner, uses the depreciation tax shield but must report the lease payments as taxable rental income.

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However, the Internal Revenue Service is suspicious by nature and will not allow the lessee to deduct the entire lease payment unless it is satisfied that the arrangement is a genuine lease and not a disguised installment purchase or secured loan agreement.¹⁶

Some leases are designed not to qualify as a true lease for tax purposes. Suppose a manufacturer finds it convenient to lease a new computer but wants to keep the depreciation tax shields. This is easily accomplished by giving the manufacturer the option to purchase the computer for $1 at the end of the lease.¹⁷ Then the Internal Revenue Service treats the lease as an installment sale, and the manufacturer can deduct depreciation and the interest component of the lease payment for tax purposes. But the lease is still a lease for all other purposes.

A First Pass at Valuing a Lease Contract

When we left Thomas Pierce III, president of Greymare Bus Lines, he had just set down in Table 25.2 the cash flows of the financial lease proposed by the bus manufacturer.

These cash flows are typically assumed to be about as safe as the interest and principal payments on a secured loan issued by the lessee. This assumption is reasonable for the lease payments because the lessor is effectively lending money to the lessee. But the various tax shields might carry enough risk to deserve a higher discount rate. For example, Greymare might be confident that it could make the lease payments but not confident that it could earn enough taxable income to use these tax shields. In that case the cash flows generated by the tax shields would probably deserve a higher discount rate than the borrowing rate used for the lease payments.

A lessee might, in principle, end up using a separate discount rate for each line of Table 25.2, each rate chosen to fit the risk of that line’s cash flow. But established, profitable firms usually find it reasonable to simplify by discounting the types of flows shown in Table 25.2 at a single rate based on the rate of interest the firm would pay if it borrowed rather than leased. We assume Greymare’s borrowing rate is 10%.

At this point we must go back to our discussion in the Appendix to Chapter 19 of debt-equivalent flows. When a company lends money, it pays tax on the interest it receives. Its net return is the after-tax interest rate. When a company borrows money, it can deduct interest payments from its taxable income. The net cost of borrowing is the after-tax interest rate. Thus the after-tax interest rate is the effective rate at which a company can transfer debt-equivalent flows from one time period to another. Therefore, to value the incremental cash flows stemming from the lease, we need to discount them at the after-tax interest rate.

Since Greymare can borrow at 10%, we should discount the lease cash flows at rD (1 – Tc) = .10(1 – .35) = .065, or 6.5%. This gives

Since the lease has a negative NPV, Greymare is better off buying the bus.

A positive or negative NPV is not an abstract concept; in this case Greymare’s shareholders really are $700 poorer if the company leases. Let us now check how this situation comes about.

Look once more at Table 25.2. The lease cash flows are

The lease payments are contractual obligations like the principal and interest payments on secured debt. Thus you can think of the incremental lease cash flows in years 1 through 7 as the “debt service” of the lease. Table 25.3 shows a loan with exactly the same debt service as the lease. The initial amount of the loan is $89.72 thousand. If Greymare borrowed this sum, it would need to pay interest in the first year of .10 × 89.72 = 8.97 and would receive a tax shield on this interest of .35 × 8.97 = 3.14. Greymare could then repay 12.15 of the loan, leaving a net cash outflow of 17.99 (exactly the same as for the lease) in year 1 and an outstanding debt at the start of year 2 of 77.56.

As you walk through the calculations in Table 25.3, you see that it costs exactly the same to service a loan that brings an immediate inflow of 89.72 as it does to service the lease, which brings in only 89.02. That is why we say that the lease has a net present value of 89.02 – 89.72 = –.7, or –$700. If Greymare leases the bus rather than raising an equivalent loan,¹⁸ there will be $700 less in Greymare’s bank account.

   TABLE 25.3 Details of the equivalent loan to the lease offered to Greymare Bus Lines (figures in $ thousands; cash outflows shown with negative sign).

Our example illustrates two general points about leases and equivalent loans. First, if you can devise a borrowing plan that gives the same cash flow as the lease in every future period but a higher immediate cash flow, then you should not lease. If, however, the equivalent loan provides the same future cash outflows as the lease but a lower immediate inflow, then leasing is the better choice.

Second, our example suggests two ways to value a lease:

 1.  Hard way. Construct a table like Table 25.3 showing the equivalent loan.

 2.  Easy way. Discount the lease cash flows at the after-tax interest rate that the firm would pay on an equivalent loan. Both methods give the same answer—in our case an NPV of –$700.

The Story So Far

We concluded that the lease contract offered to Greymare Bus Lines was not attractive because the lease provided $700 less financing than the equivalent loan. The underlying principle is as follows: A financial lease is superior to buying and borrowing if the financing provided by the lease exceeds the financing generated by the equivalent loan.

The principle implies this formula:

where N is the length of the lease. Initial financing provided equals the cost of the leased asset minus any immediate lease payment or other cash outflow attributable to the lease.¹⁹

Notice that the value of the lease is its incremental value relative to borrowing via an equivalent loan. A positive lease value means that if you acquire the asset, lease financing is advantageous. It does not prove you should acquire the asset.

However, sometimes favorable lease terms rescue a capital investment project. Suppose that Greymare had decided against buying a new bus because the NPV of the $100,000 investment was –$5,000 assuming normal financing. The bus manufacturer could rescue the deal by offering a lease with a value of, say, +$8,000. By offering such a lease, the manufacturer would in effect cut the price of the bus to $92,000, giving the bus-lease package a positive value to Greymare. We could express this more formally by treating the lease’s NPV as a favorable financing side effect that adds to project adjusted present value (APV):²⁰

Notice also that our formula applies to net financial leases. Any insurance, maintenance, and other operating costs picked up by the lessor have to be evaluated separately and added to the value of the lease. If the asset has salvage value at the end of the lease, that value should be taken into account also.

Suppose, for example, that the bus manufacturer offers to provide routine maintenance that would otherwise cost $2,000 per year after tax. However, Mr. Pierce reconsiders and decides that the bus will probably be worth $10,000 after eight years. (Previously he assumed the bus would be worthless at the end of the lease.) Then the value of the lease increases by the present value of the maintenance savings and decreases by the present value of the lost salvage value.

Maintenance and salvage value are harder to predict than the cash flows shown in Table 25.2, and normally deserve a higher discount rate. Suppose that Mr. Pierce uses 12%. Then the maintenance savings are worth

The lost salvage value is worth $10,000/(1.12)8 = $4,000.²¹ Remember that we previously calculated the value of the lease as –$700. The revised value is therefore –700 +11,100 – 4,000 = $6,400. Now the lease looks like a good deal.

 25-5    When Do Financial Leases Pay?

We have examined the value of a lease from the viewpoint of the lessee. However, the lessor’s criterion is simply the reverse. As long as lessor and lessee are in the same tax bracket, every cash outflow to the lessee is an inflow to the lessor, and vice versa. In our numerical example, the bus manufacturer would project cash flows in a table like Table 25.2, but with the signs reversed. The value of the lease to the bus manufacturer would be

In this case, the values to lessee and lessor exactly offset (–$700 + $700 = 0). The lessor can win only at the lessee’s expense.

But both lessee and lessor can win if their tax rates differ. Suppose that Greymare paid no tax (Tc = 0). Then the only cash flows of the bus lease would be

These flows would be discounted at 10%, because rD(1 – Tc) = rD when Tc = 0. The value of the lease is

In this case there is a net gain of $700 to the lessor (who has the 35% tax rate) and a net gain of $820 to the lessee (who pays zero tax). This mutual gain is at the expense of the government. On the one hand, the government gains from the lease contract because it can tax the lease payments. On the other hand, the contract allows the lessor to take advantage of depreciation and interest tax shields that are of no use to the lessee. However, because the depreciation is accelerated and the interest rate is positive, the government suffers a net loss in the present value of its tax receipts as a result of the lease.

Now you should begin to understand the circumstances in which the government incurs a loss on the lease and the other two parties gain. Other things being equal, the combined gains to lessor and lessee are highest when

 •  The lessor’s tax rate is substantially higher than the lessee’s.

 •  The depreciation tax shield is received early in the lease period.

 •  The lease period is long and the lease payments are concentrated toward the end of the period.

 •  The interest rate rD is high—if it were zero, there would be no advantage in present value terms to postponing tax.

Leasing around the World

In most developed economies, leasing is widely used to finance investment in plant and equipment.²² But there are important differences in the treatment of long-term financial leases for tax and accounting purposes. For example, some countries allow the lessor to use depreciation tax shields, just as in the U.S. In other countries the lessee claims depreciation deductions. Accounting usually follows suit.

A number of big-ticket leases are cross-border deals. Cross-border leasing can be attractive when the lessor is located in a country that offers generous depreciation allowances. The ultimate cross-border transaction occurs when both the lessor and the lessee can claim depreciation deductions. Ingenious leasing companies look for such opportunities to double-dip. Tax authorities look for ways to stop them.²³

 25-6    Leveraged Leases

Big-ticket leases are usually leveraged leases. The structure of a leveraged lease is summarized in Figure 25.1. In this example, the leasing company (or a syndicate of several leasing companies) sets up a special-purpose entity (SPE) to buy and lease a commercial aircraft. The SPE raises up to 80% of the cost of the aircraft by borrowing, usually from insurance companies or other financial institutions. The leasing company puts up the remaining 20% as the equity investment in the lease.

Once the lease is up and running, lease payments begin and depreciation and interest tax shields are generated. All (or almost all) of the lease payments go to debt service. The leasing company gets no cash inflows until the debt is paid off, but does get all depreciation and interest deductions, which generate tax losses that can be used to shield other income.

By the end of the lease, the debt is paid off and the tax shields exhausted. At this point the lessee has the option to purchase the aircraft. The leasing company gets the purchase price if the lessee’s purchase option is exercised, and takes back the aircraft otherwise. (In some cases the lessee also has an early buyout option partway through the term of the lease.)

The debt in a leveraged lease is nonrecourse. The lenders have first claim on the lease payments and on the aircraft if the lessee can’t make scheduled payments, but no claim on the leasing company. Thus the lenders must depend solely on the airline lessee’s credit and on the airplane as collateral.

So the leasing company puts up only 20% of the money, gets 100% of the tax shields, but is not on the hook if the lease transaction falls apart. Does this sound like a great deal? Don’t jump to that conclusion, because the lenders will demand a higher interest rate in exchange for giving up recourse. In efficient debt markets, paying extra interest to avoid recourse should be a zero-NPV transaction—otherwise one side of the deal would get a free ride at the expense of the other. Nevertheless, nonrecourse debt, as part of the overall structure shown in Figure 25.1, is a customary and convenient financing method.²⁴

   FIGURE 25.1 Structure of a leveraged lease for commercial aircraft.

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SUMMARY

A lease is just an extended rental agreement. The owner of the equipment (the lessor) allows the user (the lessee) to operate the equipment in exchange for regular lease payments.

There is a wide variety of possible arrangements. Short-term, cancelable leases are known as operating leases. In these leases the lessor bears the risks of ownership. Long-term, noncancelable leases are called full-payout, financial, or capital leases. In these leases the lessee bears the risks. Financial leases are sources of financing for assets the firm wishes to acquire and use for an extended period.

The key to understanding operating leases is equivalent annual cost. In a competitive leasing market, the annual operating lease payment will be forced down to the lessor’s equivalent annual cost. Operating leases are attractive to equipment users if the lease payment is less than the user’s equivalent annual cost of buying the equipment. Operating leases make sense when the user needs the equipment only for a short time, when the lessor is better able to bear the risks of obsolescence, or when the lessor can offer a good deal on maintenance. Remember too that operating leases often have valuable options attached.

A financial lease extends over most of the economic life of the leased asset and cannot be canceled by the lessee. Signing a financial lease is like signing a secured loan to finance purchase of the leased asset. With financial leases, the choice is not “lease versus buy” but “lease versus borrow.”

Many companies have sound reasons for financing via leases. For example, companies that are not paying taxes can usually strike a favorable deal with a tax-paying lessor. Also, it may be less costly and time-consuming to sign a standardized lease contract than to negotiate a long-term secured loan.

When a firm borrows money, it pays the after-tax rate of interest on its debt. Therefore, the opportunity cost of lease financing is the after-tax rate of interest on the firm’s bonds. To value a financial lease, we need to discount the incremental cash flows from leasing by the after-tax interest rate.

An equivalent loan is one that commits the firm to exactly the same future cash flows as a financial lease. When we calculate the net present value of the lease, we are measuring the difference between the amount of financing provided by the lease and the financing provided by the equivalent loan:

Value of lease = financing provided by lease – value of equivalent loan

We can also analyze leases from the lessor’s side of the transaction, using the same approaches we developed for the lessee. If lessee and lessor are in the same tax bracket, they will receive exactly the same cash flows but with signs reversed. Thus, the lessee can gain only at the lessor’s expense, and vice versa. However, if the lessee’s tax rate is lower than the lessor’s, then both can gain at the federal government’s expense. This is a tax timing advantage, because the lessor gets interest and depreciation tax shields early in the lease.

Leveraged leases are three-way transactions that include lenders as well as the lessor and lessee. Lenders advance up to 80% of the cost of the leased equipment and lessors put in the rest as an equity investment. The lenders get first claim on the lease payments and on the asset but have no recourse to the equity lessors if the lessee can’t pay. The lessor’s return comes mostly from interest and depreciation tax shields early in the lease and the value of the leased asset at the end of the lease. Leveraged leases are common in big-ticket, cross-border lease-financing transactions.

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FURTHER READING

Two useful general references on leasing are:

J. S. Schallheim, Lease or Buy? Principles for Sound Decision Making (Boston: Harvard Business School Press, 1994).

P. K. Nevitt and F. J. Fabozzi, Equipment Leasing, 4th ed. (Hoboken, NJ: John Wiley & Sons, 2002).

Smith and Wakeman discuss the economic motives for leasing:

C. W. Smith, Jr., and L. M. Wakeman, “Determinants of Corporate Leasing Policy,” Journal of Finance 40 (July 1985), pp. 895–908.

The options embedded in many operating leases are discussed in:

J. J. McConnell and J. S. Schallheim, “Valuation of Asset Leasing Contracts,” Journal of Financial Economics 12 (August 1983), pp. 237–261.

S. R. Grenadier, “Valuing Lease Contracts: A Real Options Approach,” Journal of Financial Economics 38 (July 1995), pp. 297–331.

S. R. Grenadier, “An Equilibrium Analysis of Real Estate Leases,” Journal of Business 78 (2005), pp. 1173–1214.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

 1.  Types of lease The following terms are often used to describe leases:

 a. Direct

 b. Full-service

 c. Operating

 d. Financial

 e. Rental

 f. Net

 g. Leveraged

 h. Sale and lease-back

 i. Full-payout

Match one or more of these terms with each of the following statements:

 A. The initial lease period is shorter than the economic life of the asset.

 B. The initial lease period is long enough for the lessor to recover the cost of the asset.

 C. The lessor provides maintenance and insurance.

 D. The lessee provides maintenance and insurance.

 E. The lessor buys the equipment from the manufacturer.

 F. The lessor buys the equipment from the prospective lessee.

 G. The lessor finances the lease contract by issuing debt and equity claims against it.

 2.  Reasons for leasing Some of the following reasons for leasing are rational. Others are irrational or assume imperfect or inefficient capital markets. Which of the following reasons are the rational ones?

 a. The lessee’s need for the leased asset is only temporary.

 b. Specialized lessors are better able to bear the risk of obsolescence.

 c. Leasing provides 100% financing and thus preserves capital.

 d. Leasing allows firms with low marginal tax rates to “sell” depreciation tax shields.

 e. Leasing increases earnings per share.

 f. Leasing reduces the transaction cost of obtaining external financing.

 g. Leasing avoids restrictions on capital expenditures.

 h. Leasing can reduce the alternative minimum tax.

 3.  Operating leases Explain why the following statements are true:

 a. In a competitive leasing market, the annual operating lease payment equals the lessor’s equivalent annual cost.

 b. Operating leases are attractive to equipment users if the lease payment is less than the user’s equivalent annual cost.

 4.  Lease characteristics True or false?

 a. Lease payments are usually made at the start of each period. Thus the first payment is usually made as soon as the lease contract is signed.

 b. Some financial leases can provide off-balance-sheet financing.

 c. The cost of capital for a financial lease is the interest rate the company would pay on a bank loan.

 d. An equivalent loan’s principal plus after-tax interest payments exactly match the after-tax cash flows of the lease.

 e. A financial lease should not be undertaken unless it provides more financing than the equivalent loan.

 f. It makes sense for firms that pay no taxes to lease from firms that do.

 g. Other things equal, the net tax advantage of leasing increases as nominal interest rates increase.

 5.  Lease treatment in bankruptcy What happens if a bankrupt lessee affirms the lease? What happens if the lease is rejected?

 6.  Lease characteristics How does a leveraged lease differ from an ordinary, long-term financial lease? List the key differences.

 7.  Nonrecourse debt Lenders to leveraged leases hold nonrecourse debt. What does “nonrecourse” mean? What are the benefits and costs of nonrecourse debt to the equity investors in the lease?

INTERMEDIATE

 8.  Operating leases Acme has branched out to rentals of office furniture to start-up companies. Consider a $3,000 desk. Desks last for six years and can be depreciated on a five-year MACRS schedule (see Table 6.4). What is the break-even operating lease rate for a new desk? Assume that lease rates for old and new desks are the same and that Acme’s pretax administrative costs are $400 per desk per year. The cost of capital is 9% and the tax rate is 35%. Lease payments are made in advance, that is, at the start of each year. The inflation rate is zero.

 9.  Financial leases Refer again to Problem 8. Suppose a blue-chip company requests a six-year financial lease for a $3,000 desk. The company has just issued five-year notes at an interest rate of 6% per year. What is the break-even rate in this case? Assume administrative costs drop to $200 per year. Explain why your answers to Problem 8 and this question differ.

 10.  Inflation and leasing In Problem 8 we assumed identical lease rates for old and new desks.

 a. How does the initial break-even lease rate change if the expected inflation rate is 5% per year? Assume that the real cost of capital does not change. (Hint: Look at the discussion of equivalent annual costs in Chapter 6.)

 b. How does your answer to part (a) change if wear and tear force Acme to cut lease rates by 10% in real terms for every year of a desk’s age?

 11.  Technological change and leasing Look at Table 25.1. How would the initial break-even operating lease rate change if rapid technological change in limo manufacturing reduces the costs of new limos by 5% per year? (Hint: We discussed technological change and equivalent annual costs in Chapter 6.)

 12.  Financial leases Suppose that National Waferonics has before it a proposal for a four-year financial lease. The firm constructs a table like Table 25.2. The bottom line of its table shows the lease cash flows:

These flows reflect the cost of the machine, depreciation tax shields, and the after-tax lease payments. Ignore salvage value. Assume the firm could borrow at 10% and faces a 35% marginal tax rate.

 a. What is the value of the equivalent loan?

 b. What is the value of the lease?

 c. Suppose the machine’s NPV under normal financing is –$5,000. Should National Waferonics invest? Should it sign the lease?

The following questions all apply to financial leases. To answer Problems 13 to 17 you may find it helpful to use the live Excel spreadsheets at www.mcgraw-hill.co.uk/textbooks/brealey.

Visit us at www.mcgraw-hill.co.uk/textbooks/brealey

 13.  Taxes and leasing Look again at the bus lease described in Table 25.2.

 a. What is the value of the lease if Greymare’s marginal tax rate is Tc = .20?

 b. What would the lease value be if Greymare had to use five-year straight-line depreciation for tax purposes?

 14.  Taxes and leasing In Section 25-4 we showed that the lease offered to Greymare Bus Lines had a positive NPV of $820 if Greymare paid no tax and a +$700 NPV to a lessor paying 35% tax. What is the minimum lease payment the lessor could accept under these assumptions? What is the maximum amount that Greymare could pay?

 15.  Valuing leases In Section 25-5 we listed four circumstances in which there are potential gains from leasing. Check them out by conducting a sensitivity analysis on the Greymare Bus Lines lease, assuming that Greymare does not pay tax. Try, in turn, (a) a lessor tax rate of 50% (rather than 35%), (b) immediate 100% depreciation in year 0 (rather than five-year MACRS), (c) a three-year lease with four annual rentals (rather than an eight-year lease), and (d) an interest rate of 20% (rather than 10%). In each case, find the minimum rental that would satisfy the lessor and calculate the NPV to the lessee.

 16.  Valuing leases In Section 25-5 we stated that if the interest rate were zero, there would be no advantage in postponing tax and therefore no advantage in leasing. Value the Greymare Bus Lines lease with an interest rate of zero. Assume that Greymare does not pay tax. Can you devise any lease terms that would make both a lessee and a lessor happy? (If you can, we would like to hear from you.)

 17.  Valuing leases A lease with a varying rental schedule is known as a structured lease. Try structuring the Greymare Bus Lines lease to increase value to the lessee while preserving the value to the lessor. Assume that Greymare does not pay tax. (Note: In practice the tax authorities will allow some structuring of rental payments but might be unhappy with some of the schemes you devise.)

 18.  Valuing leases Nodhead College needs a new computer. It can either buy it for $250,000 or lease it from Compulease. The lease terms require Nodhead to make six annual payments (prepaid) of $62,000. Nodhead pays no tax. Compulease pays tax at 35%. Compulease can depreciate the computer for tax purposes over five years. The computer will have no residual value at the end of year 5. The interest rate is 8%.

 a. What is the NPV of the lease for Nodhead College?

 b. What is the NPV for Compulease?

 c. What is the overall gain from leasing?

 19.  Valuing leases The Safety Razor Company has a large tax-loss carryforward and does not expect to pay taxes for another 10 years. The company is therefore proposing to lease $100,000 of new machinery. The lease terms consist of eight equal lease payments prepaid annually. The lessor can write the machinery off over seven years using the tax depreciation schedules given in Table 6.4. There is no salvage value at the end of the machinery’s economic life. The tax rate is 35%, and the rate of interest is 10%. Wilbur Occam, the president of Safety Razor, wants to know the maximum lease payment that his company should be willing to make and the minimum payment that the lessor is likely to accept. Can you help him?

 20.  Lease treatment in bankruptcy How does the position of an equipment lessor differ from the position of a secured lender when a firm falls into bankruptcy? Assume that the secured loan would have the leased equipment as collateral. Which is better protected, the lease or the loan? Does your answer depend on the value of the leased equipment if it were sold or re-leased?

 21.  Valuing leases How would the lessee in Figure 25.1 evaluate the NPV of the lease? Sketch the correct valuation procedure. Then suppose that the equity lessor wants to evaluate the lease. Again sketch the correct procedure. (Hint: APV. How would you calculate the combined value of the lease to lessee and lessor?)

CHALLENGE

 22.  Valuing leases Magna Charter has been asked to operate a Beaver bush plane for a mining company exploring north and west of Fort Liard. Magna will have a firm one-year contract with the mining company and expects that the contract will be renewed for the five-year duration of the exploration program. If the mining company renews at year 1, it will commit to use the plane for four more years.

Magna Charter has the following choices:

 •  Buy the plane for $500,000.

 •  Take a one-year operating lease for the plane. The lease rate is $118,000, paid in advance.

 •  Arrange a five-year, noncancelable financial lease at a rate of $75,000 per year, paid in advance.

These are net leases; all operating costs are absorbed by Magna Charter.

How would you advise Agnes Magna, the charter company’s CEO? For simplicity assume five-year, straight-line depreciation for tax purposes. The company’s tax rate is 35%. The weighted-average cost of capital for the bush-plane business is 14%, but Magna can borrow at 9%. The expected inflation rate is 4%.

Ms. Magna thinks the plane will be worth $300,000 after five years. But if the contract with the mining company is not renewed (there is a 20% probability of this outcome at year 1), the plane will have to be sold on short notice for $400,000.

If Magna Charter takes the five-year financial lease and the mining company cancels at year 1, Magna can sublet the plane, that is, rent it out to another user.

Make additional assumptions as necessary.

 23.  Leasing and IRRs Reconstruct Table 25.2 as a leveraged lease, assuming that the lessor borrows $80,000, 80% of the cost of the bus, nonrecourse at an interest rate of 11%. All lease payments are devoted to debt service (interest and principal) until the loan is paid off. Assume that the bus is worth $10,000 at the end of the lease. Calculate after-tax cash flows on the lessor’s equity investment of $20,000. What is the IRR of the equity cash flows? Is there more than one IRR? How would you value the lessor’s equity investment?

 24.  Valuing leases Suppose that the Greymare lease gives the company the option to purchase the bus at the end of the lease period for $1. How would this affect the tax treatment of the lease? Recalculate its value to Greymare and the manufacturer. Could the lease payments be adjusted to provide a positive NPV to both parties?

___________

¹This was not the first time that HSBC had leased its head office. In 2007 it sold the building for £1.09 billion and leased it back. It repurchased the building one year later for £838 million.

²The market for used cars suffers from a “lemons” problem, since the seller typically knows more about the quality of the car than the would-be buyer. Because off-lease used cars are generally of above-average quality, leasing can help to alleviate this problem. Igal Hendel and Alessandro Lizzeri argue that this may help to explain the prevalence of car leasing. See I. Hendel and A. Lizzeri, “The Role of Leasing under Adverse Selection,” Journal of Political Economy 110 (February 2002), pp. 113–143. Thomas Gilligan uses a similar argument to analyze the market for aircraft leasing. See T. W. Gilligan, “Lemons and Leases in the Used Business Aircraft Market,” Journal of Political Economy 112 (2004), pp. 1157–1180.

³For evidence that leasing is relatively more common in such firms, see J. R. Graham and M. T. Leary, “A Review of Empirical Capital Structure Research and Directions for the Future,” Annual Review of Financial Economics 3 (2011), pp. 309–345.

⁴If the leases had been rejected, the lessors would have had a claim only on TWA’s assets and cash flows, not AA’s. The renegotiation of the TWA leases is described in E. Benmelech and N. K. Bergman, “Liquidation Values and the Credibility of Financial Contract Renegotiation: Evidence from U.S. Airlines,” Quarterly Journal of Economics 123 (2008), pp. 1635–1677.

⁵Year-by-year differences between reported tax expense and taxes actually paid are explained in footnotes to the financial statements. The cumulative difference is shown on the balance sheet as a deferred tax liability. (Note that accelerated depreciation postpones taxes; it does not eliminate taxes.)

⁶Other items include some interest receipts from tax-exempt municipal securities and taxes deferred by use of completed contract accounting. (The completed contract method allows a manufacturer to postpone reporting taxable profits until a production contract is completed. Since contracts may span several years, this deferral can have a substantial positive NPV.)

⁷But Yuppytech can carry forward the $.3 million difference. If later years’ AMTs are lower than regular taxes, the difference can be used as a tax credit. Suppose the AMT next year is $4 million and the regular tax is $5 million. Then Yuppytech pays only 5 – .3 = $4.7 million.

⁸In 2010 the FASB and the International Accounting Standards Board issued proposals for new accounting rules that would no longer distinguish between capital leases and operating leases of longer than a year. If the rules are implemented, the present values of both types of lease would be shown on the balance sheet.

⁹The depreciation tax shields are safe cash flows if the tax rate does not change and Acme is sure to pay taxes. If 7% is the right discount rate for the other flows in Table 25.1, the depreciation tax shields deserve a lower rate. A more refined analysis would discount safe depreciation tax shields at an after-tax borrowing or lending rate. See the Appendix to Chapter 19 or the next section of this chapter.

¹⁰In Section 6-3 the hypothetical rentals were paid in arrears.

¹¹This is a level annuity because we are assuming that (1) there is no inflation and (2) the services of a six-year-old limo are no different from a brand-new limo’s. If users of aging limos see them as obsolete or unfashionable, or if purchase costs of new limos are declining, then lease rates have to decline as limos age. This means that rents follow a declining annuity. Early users have to pay more to make up for declining rents later.

¹²If, say, limos were off-lease and idle 20% of the time, lease rates would have to be 25% above those shown in Table 25.1.

¹³Acme might also offer a one-year lease for $28,000 but give the lessee an option to extend the lease on the same terms for up to five additional years. This is, of course, identical to lease 2. It doesn’t matter whether the lessee has the (put) option to cancel or the (call) option to continue.

¹⁴A. Gavazza, “Asset Liquidity and Financial Contracts: Evidence from Aircraft Leases,” Journal of Financial Economics 95 (January 2010), pp. 62–84.

¹⁵McConnell and Schallheim calculate the value of options in operating leases under various assumptions about asset risk, depreciation rates, etc. See J. J. McConnell and J. S. Schallheim, “Valuation of Asset Leasing Contracts,” Journal of Financial Economics 12 (August 1983), pp. 237–261.

¹⁶For example, the IRS will disallow the lease if the lessee has an option to acquire the asset for a nominal sum. The lessee will almost certainly exercise such a bargain-purchase option, leaving the lessor with no chance of future ownership. Special-purpose assets that can only be used by the lessee will also be disqualified, because the lessee will end up owning them.

¹⁷Such leases are known as $1 out leases.

¹⁸When we compare the lease to its equivalent loan, we do not mean to imply that the bus alone could support all of that loan. Some part of the loan would be supported by Greymare’s other assets. Some part of the lease obligation would likewise be supported by the other assets.

¹⁹The principles behind lease valuation were originally set out in S. C. Myers, D. A. Dill, and A. J. Bautista, “Valuation of Financial Lease Contracts,” Journal of Finance 31 (June 1976), pp. 799–819; and J. R. Franks and S. D. Hodges, “Valuation of Financial Lease Contracts: A Note,” Journal of Finance 33 (May 1978), pp. 647–669.

²⁰See Chapter 19 for the general definition and description of APV.

²¹For simplicity, we have assumed that maintenance expenses are paid at the start of the year and that salvage value is measured at the end of year 8.

²²For example, in 2009 leasing accounted for 19% of all European investments in industrial equipment (www.leaseurope.org).

²³Currently in the U.S. the tax authorities seem to be winning. The American Jobs Creation Act (JOBS) of 2004 eliminated much of the profit from cross-border leases.

²⁴Leveraged leases have special tax and accounting requirements, which we won’t go into here. Also, the equity investment in leveraged leases can be tricky to value, because the stream of after-tax cash flows changes sign more than once. That is no problem if you use the NPV rule, but it causes difficulties if you wish to calculate the internal rate of return (IRR). This requires use of modified internal rates of return, if you insist on using IRRs. We discussed multiple IRRs and modified IRRs in Section 5-3. Also take a look at Problem 23 at the end of this chapter.

Part 8 Risk Management

Managing Risk

Most of the time we take risk as God-given. A project has its beta, and that’s that. Its cash flow is exposed to changes in demand, raw material costs, technology, and a seemingly endless list of other uncertainties. There’s nothing the manager can do about it.

That’s not wholly true. The manager can avoid some risks. We have already come across one way to do so: firms use real options to provide flexibility. For example, a petrochemical plant that is designed to use either oil or natural gas as a feedstock reduces the risk of an unfavorable shift in the price of raw materials. As another example, think of a company that employs standard machine tools rather than custom machinery and thereby lowers the cost of bailing out if its products do not sell. In other words, the standard machinery provides the firm with a valuable abandonment option.

We covered real options in Chapter 22. This chapter explains how companies also use financial contracts to protect against various hazards. We discuss the pros and cons of corporate insurance policies that protect against specific risks, such as fire, floods, or environmental damage. We describe forward and futures contracts, which can be used to lock in the future price of commodities such as oil, copper, or soybeans. Financial forward and futures contracts allow the firm to lock in the prices of financial assets such as interest rates or foreign exchange rates. We also describe swaps, which are packages of forward contracts.

Most of this chapter describes how financial contracts may be used to reduce business risks. But why bother? Why should shareholders care whether the company’s future profits are linked to future changes in interest rates, exchange rates, or commodity prices? We start the chapter with that question.

 26-1   Why Manage Risk?

Financial transactions undertaken solely to reduce risk do not add value in perfect and efficient markets. Why not? There are two basic reasons.

 •  Reason 1: Hedging is a zero-sum game. A corporation that insures or hedges a risk does not eliminate it. It simply passes the risk to someone else. For example, suppose that a heating-oil distributor contracts with a refiner to buy all of next winter’s heating-oil deliveries at a fixed price. This contract is a zero-sum game, because the refiner loses what the distributor gains, and vice versa.¹ If next winter’s price of heating oil turns out to be unusually high, the distributor wins from having locked in a below-market price, but the refiner is forced to sell below the market. Conversely, if the price of heating oil is unusually low, the refiner wins, because the distributor is forced to buy at the high fixed price. Of course, neither party knows next winter’s price at the time that the deal is struck, but they consider the range of possible prices, and in an efficient market they negotiate terms that are fair (zero-NPV) on both sides of the bargain.

 •  Reason 2: Investors’ do-it-yourself alternative. Corporations cannot increase the value of their shares by undertaking transactions that investors can easily do on their own. When the shareholders in the heating-oil distributor made their investment, they were presumably aware of the risks of the business. If they did not want to be exposed to the ups and downs of energy prices, they could have protected themselves in several ways. Perhaps they bought shares in both the distributor and refiner, and do not care whether one wins next winter at the other’s expense.

Of course, shareholders can adjust their exposure only when companies keep investors fully informed of the transactions that they have made. For example, when a group of European central banks announced in 1999 that they would limit their sales of gold, the gold price immediately shot up. Investors in gold-mining shares rubbed their hands at the prospect of rising profits. But when they discovered that some mining companies had protected themselves against price fluctuations and would not benefit from the price rise, the hand-rubbing by investors turned to hand-wringing.²

Some stockholders of these gold-mining companies wanted to make a bet on rising gold prices; others didn’t. But all of them gave the same message to management. The first group said, “Don’t hedge! I’m happy to bear the risk of fluctuating gold prices, because I think gold prices will increase.” The second group said, “Don’t hedge! I’d rather do it myself.” We have seen this do-it-yourself principle before. Think of other ways that the firm could reduce risk. It could do so by diversifying, for example, by acquiring another firm in an unrelated industry. But we know that investors can diversify on their own, and so diversification by corporations is redundant.³

Corporations can also lessen risk by borrowing less. But we showed in Chapter 17 that just reducing financial leverage does not make shareholders any better or worse off, because they can instead reduce financial risk by borrowing less (or lending more) in their personal accounts. Modigliani and Miller (MM) proved that a corporation’s debt policy is irrelevant in perfect financial markets. We could extend their proof to say that risk management is also irrelevant in perfect financial markets.

Of course, in Chapter 18 we decided that debt policy is relevant, not because MM were wrong, but because of other things, such as taxes, agency problems, and costs of financial distress. The same line of argument applies here. If risk management affects the value of the firm, it must be because of “other things,” not because risk shifting is inherently valuable.

Let’s review the reasons that risk-reducing transactions can make sense in practice.⁴

Reducing the Risk of Cash Shortfalls or Financial Distress

Transactions that reduce risk make financial planning simpler and reduce the odds of an embarrassing cash shortfall. This shortfall might mean only an unexpected trip to the bank, but a financial manager’s worst nightmare is landing in a financial pickle and having to pass up a valuable investment opportunity for lack of funds. In extreme cases an unhedged setback could trigger financial distress or even bankruptcy.

Banks and bondholders recognize these dangers. They try to keep track of the firm’s risks, and before lending they may require the firm to carry insurance or to implement hedging programs. Risk management and conservative financing are therefore substitutes, not complements. Thus a firm might hedge part of its risk in order to operate safely at a higher debt ratio.

Smart financial managers make sure that cash (or ready financing) will be available if investment opportunities expand. That happy match of cash and investment opportunities does not necessarily require hedging, however. Let’s contrast two examples.

Cirrus Oil produces from several oil fields and also invests to find and develop new fields. Should it lock in future revenues from its existing fields by hedging oil prices? Probably not, because its investment opportunities expand when oil prices rise and contract when they fall. Locking in oil prices could leave it with too much cash when oil prices fall and too little, relative to its investment opportunities, when prices rise.

Cumulus Pharmaceuticals sells worldwide and half of its revenues are received in foreign currencies. Most of its R&D is done domestically. Should it hedge at least some of its foreign exchange exposure? Probably yes, because pharmaceutical R&D programs are very expensive, long-term investments. Cumulus can’t turn its R&D program on or off depending on a particular year’s earnings, so it may wish to stabilize cash flows by hedging against fluctuations in exchange rates.

Agency Costs May Be Mitigated by Risk Management

In some cases hedging can make it easier to monitor and motivate managers. Suppose your confectionery division delivers a 60% profit increase in a year when cocoa prices fall by 12%. Does the division manager deserve a stern lecture or a pat on the back? How much of the profit increase is due to good management and how much to lower cocoa prices? If the cocoa prices were hedged, it’s probably good management. If they were not hedged, you will have to sort things out with hindsight, probably by asking, “What would profits have been if cocoa prices had been hedged?”

The fluctuations in cocoa prices are outside the manager’s control. But she will surely worry about cocoa prices if her bottom line and bonus depend on them. Hedging prices ties her bonus more closely to risks that she can control and allows her to spend worrying time on these risks.

Hedging external risks that would affect individual managers does not necessarily mean that the firm ends up hedging. Some large firms allow their operating divisions to hedge away risks in an internal “market.” The internal market operates with real (external) market prices, transferring risks from the division to the central treasurer’s office. The treasurer then decides whether to hedge the firm’s aggregate exposure.

This sort of internal market makes sense for two reasons. First, divisional risks may cancel out. For example, your refining division may benefit from an increase in heating-oil prices at the same time that your distribution division suffers. Second, because operating managers do not trade actual financial contracts, there is no danger that the managers will cause the firm to take speculative positions. For example, suppose that profits are down late in the year, and hope for end-year bonuses is fading. Could you be tempted to make up the shortfall with a quick score in the cocoa futures market? Well . . . not you, of course, but you can probably think of some acquaintances who would try just one speculative fling.

The dangers of permitting operating managers to make real speculative trades should be obvious. The manager of your confectionery division is an amateur in the cocoa futures market. If she were a skilled professional trader, she would probably not be running chocolate factories.⁵

Risk management requires some degree of centralization. These days many companies appoint a chief risk officer to develop a risk strategy for the company as a whole. The risk manager needs to come up with answers to the following questions:

 1.  What are the major risks that the company is facing and what are the possible consequences? Some risks are scarcely worth a thought, but there are others that might cause a serious setback or even bankrupt the company.

 2.  Is the company being paid for taking these risks? Managers are not paid to avoid all risks, but if they can reduce their exposure to risks for which there are no corresponding rewards, they can afford to place larger bets when the odds are stacked in their favor.

 3.  How should risks be controlled? Should the company reduce risk by building extra flexibility into its operations? Should it change its operating or financial leverage? Or should it insure or hedge against particular hazards?

The Evidence on Risk Management

Which firms use financial contracts to manage risk? Almost all do to some extent. For example, they may have contracts that fix prices of raw materials or output, at least for the near future. Most take out insurance policies against fire, accidents, and theft. In addition, as we shall see, managers employ a variety of specialized tools for hedging risk. These are known collectively as derivatives. A survey of the world’s 500 largest companies found that most of them use derivatives to manage their risk.⁶ Eighty-three percent of the companies employ derivatives to control interest rate risk. Eighty-eight percent use them to manage currency risk, and 49% to manage commodity price risk.

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Derivatives usage

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Risk policies differ. For example, some natural resource companies work hard to hedge their exposure to price fluctuations; others shrug their shoulders and let prices wander as they may. Explaining why some hedge and others don’t is not easy. Peter Tufano’s study of the gold-mining industry suggests that managers’ personal risk aversion may have something to do with it. Hedging of gold prices appears to be more common when top management has large personal shareholdings in the company. It is less common when top management holds lots of stock options. (Remember that the value of an option falls when the risk of the underlying security is reduced.) David Haushalter’s study of oil and gas producers found the firms that hedged the most had high debt ratios, no debt ratings, and low dividend payouts. It seems that for these firms hedging programs were designed to improve the firms’ access to debt finance and to reduce the likelihood of financial distress.⁷

 26-2    Insurance

Most businesses buy insurance against a variety of hazards—the risk that their plants will be damaged by fire; that their ships, planes, or vehicles will be involved in accidents; that the firm will be held liable for environmental damage; and so on.

When a firm takes out insurance, it is simply transferring the risk to the insurance company. Insurance companies have some advantages in bearing risk. First, they may have considerable experience in insuring similar risks, so they are well placed to estimate the probability of loss and price the risk accurately. Second, they may be skilled at providing advice on measures that the firm can take to reduce the risk, and they may offer lower premiums to firms that take this advice. Third, an insurance company can pool risks by holding a large, diversified portfolio of policies. The claims on any individual policy can be highly uncertain, yet the claims on a portfolio of policies may be very stable. Of course, insurance companies cannot diversify away market or macroeconomic risks; firms generally use insurance policies to reduce their diversifiable risk and they find other ways to avoid macro risks.

Insurance companies also suffer some disadvantages in bearing risk, and these are reflected in the prices they charge. Suppose your firm owns a $1 billion offshore oil platform. A meteorologist has advised you that there is a 1-in-10,000 chance that in any year the platform will be destroyed as a result of a storm. Thus the expected loss from storm damage is $1 billion/10,000 = $100,000.

The risk of storm damage is almost certainly not a macroeconomic risk and can potentially be diversified away. So you might expect that an insurance company would be prepared to insure the platform against such destruction as long as the premium was sufficient to cover the expected loss. In other words, a fair premium for insuring the platform should be $100,000 a year.⁸ Such a premium would make insurance a zero-NPV deal for your company. Unfortunately, no insurance company would offer a policy for only $100,000. Why not?

 •  Reason 1: Administrative costs. An insurance company, like any other business, incurs a variety of costs in arranging the insurance and handling any claims. For example, disputes about the liability for environmental damage can eat up millions of dollars in legal fees. Insurance companies need to recognize these costs when they set their premiums.

 •  Reason 2: Adverse selection. Suppose that an insurer offers life insurance policies with “no medical exam needed, no questions asked.” There are no prizes for guessing who will be most tempted to buy this insurance. Our example is an extreme case of the problem of adverse selection. Unless the insurance company can distinguish between good and bad risks, the latter will always be most eager to take out insurance. Insurers increase premiums to compensate or require the owners to share any losses.

 •  Reason 3: Moral hazard. Two farmers met on the road to town. “George,” said one, “I was sorry to hear about your barn burning down.” “Shh,” replied the other, “that’s tomorrow night.” The story is an example of another problem for insurers, known as moral hazard. Once a risk has been insured, the owner may be less careful to take proper precautions against damage. Insurance companies are aware of this and factor it into their pricing.

The extreme forms of adverse selection and moral hazard (like the fire in the farmer’s barn) are rarely encountered in professional corporate finance. But these problems arise in more subtle ways. That oil platform may not be a “bad risk,” but the oil company knows more about the platform’s weaknesses than the insurance company does. The oil company will not purposely scuttle the platform, but once insured it could be tempted to save on maintenance or structural reinforcements. Thus, the insurance company may end up paying for engineering studies or for a program to monitor maintenance. All these costs are rolled into the insurance premium.

When the costs of administration, adverse selection, and moral hazard are small, insurance may be close to a zero-NPV transaction. When they are large, insurance is a costly way to protect against risk.

Many insurance risks are jump risks; one day there is not a cloud on the horizon and the next day the hurricane hits. The risks can also be huge. For example, the attack on the World Trade Center on September 11, 2001, cost insurance companies about $36 billion, the Japanese tsunami involved payments of $35–$40 billion, and Hurricane Katrina cost insurers a record $66 billion.

If the losses from such disasters can be spread more widely, the cost of insuring them should decline. Therefore, insurance companies have been looking for ways to share catastrophic risks with investors. One solution is for the companies to issue catastrophe bonds (or Cat bonds). If a catastrophe occurs, the payment on a Cat bond is reduced or eliminated.⁹ For example, in 2012 Munich Re issued $75 million worth of Cat bonds. The bonds cover Munich Re for three years against any losses in excess of a specified level resulting from U.S. hurricanes or European windstorms. For taking on this risk, investors receive a tempting interest rate of 8.5% above the yield on money market funds.

 26-3    Reducing Risk with Options

Managers regularly buy options on currencies, interest rates, and commodities to limit downside risk. Consider, for example, the problem faced by the Mexican government. Forty percent of its revenue comes from Pemex, the state-owned oil company. So, if oil prices fall, the government may be compelled to reduce its planned spending. That is always an unwelcome outcome, but it was particularly so in 2008 when the country faced recession.

The Mexican government’s solution was to establish a floor on the price at which it could sell 330 million barrels of oil, equivalent to the country’s total expected net oil exports in 2009. To do this, the government bought put options that gave it the right to sell oil at an exercise price of $70 per barrel. If oil prices rose above this figure, Mexico would reap the benefit. But if oil prices fell below $70 a barrel, the payoff to the put options would exactly offset the revenue shortfall. Of course, you don’t get something for nothing. The price that the government paid for insurance against a fall in the price of oil was the estimated $1.5 billion cost of the put options.

   FIGURE 26.1 How put options protected Mexico against a fall in oil prices.

Figure 26.1 illustrates the nature of Mexico’s insurance strategy. Panel (a) shows the revenue derived from selling 330 million barrels of oil. If the price of oil falls, so do the government’s revenues. But, as panel (b) illustrates, the payoff on the option to sell 330 million barrels rises as oil prices fall below $70 a barrel. This payoff exactly offsets the decline in oil revenues. Panel (c) shows the government’s total revenues after buying the put options. For prices below $70 per barrel, revenues are fixed at 70 × 330 = $23,100 million. But for every dollar that oil prices rise above $70, revenues increase by $330 million. The profile in panel (c) should be familiar to you as the protective put strategy that we encountered in Section 20-2.

Crude oil prices for 2009 averaged less than $54 a barrel and Pemex’s insurance proved a very worthwhile investment.¹⁰

 26-4    Forward and Futures Contracts

Hedging involves taking on one risk to offset another. It potentially removes all uncertainty, eliminating the chance of both happy and unhappy surprises. We explain shortly how to set up a hedge, but first we give some examples and describe some tools that are specially designed for hedging. These are forwards, futures, and swaps. Together with options, they are known as derivative instruments or derivatives because their value depends on the value of another asset.

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Worldwide futures volume

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A Simple Forward Contract

We start with an example of a simple forward contract. Arctic Fuels, the heating-oil distributor, plans to deliver one million gallons of heating oil to its retail customers next January. Arctic worries about high heating-oil prices next winter and wants to lock in the cost of buying its supply. Northern Refineries is in the opposite position. It will produce heating oil next winter, but doesn’t know what the oil can be sold for. So the two firms strike a deal: Arctic Fuels agrees in September to buy one million gallons from Northern Refineries at $3.20 per gallon, to be paid on delivery in January. Northern agrees to sell and deliver one million gallons to Arctic in January at $3.20 per gallon.

Arctic and Northern are now the two counterparties in a forward contract. The forward price is $3.20 per gallon. This price is fixed today, in September in our example, but payment and delivery occur later. (The price for immediate delivery is called the spot price.) Arctic, which has agreed to buy in January, has the long position in the contract. Northern Refineries, which has agreed to sell in January, has the short position.

We can think of each counterparty’s long and short positions in balance-sheet format, with long positions on the right (asset) side and short positions on the left (liability) side.

Northern Refineries starts with a long position, because it will produce heating oil. Arctic Fuels starts with a short position, because it will have to buy to supply its customers. The forward contract creates an offsetting short position for Northern Refineries and an offsetting long position for Arctic Fuels. The offsets mean that each counterparty ends up locking in a price of $3.20, regardless of what happens to future spot prices.

Do not confuse this forward contract with an option. Arctic does not have the option to buy. It has committed to buy, even if spot prices in January turn out much lower than $3.20 per gallon. Northern does not have the option to sell. It cannot back away from the deal, even if spot prices for delivery in January turn out much higher than $3.20 per gallon. Note, however, that both the distributor and refiner have to worry about counterparty risk, that is, the risk that the other party will not perform as promised.

We confess that our heating oil example glossed over several complications. For example, we assumed that the risk of both companies is reduced by locking in the price of heating oil. But suppose that the retail price of heating oil moves up and down with the wholesale price. In that case the heating-oil distributor is naturally hedged because costs and revenues move together. Locking in costs with a futures contract could actually make the distributor’s profits more volatile. The nearby box illustrates that hedging decisions are not always straightforward.

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The Pros and Cons of Hedging Airline Fuel Costs

  Jet fuel is a major cost of running an airline. For example, in 2010 purchases of kerosene accounted for nearly 20% of the operating costs of the German airline, Lufthansa. Jet fuel costs are notoriously volatile. They touched $3.89 a gallon in July 2008 before falling to $1.26 in February 2009, and then rising to $3.09 at the start of 2012. Therefore, Lufthansa like many airlines uses a variety of market instruments, such as forward contracts and options, to hedge against unexpected fluctuations in fuel prices. For example, in early 2011 the company had hedged 72% of the year’s fuel requirements, plus 29% of the following year’s requirements.

Carter, Rogers, and Simkins, who conducted a study of hedging by U.S. airlines, concluded that investors placed a premium on airlines that hedged their fuel costs. The reason for this premium, they suggested, was that airlines may be led to cut back on profitable investments when fuel prices are high and operating cash flows are low. An airline that is protected against rising fuel prices is better placed to take advantage of investment opportunities.

Hedging has its advantages for airlines, but there are also dangers. One problem is that if fuel prices fall, those airlines that have entered into contracts to cover their future fuel needs will suffer losses on these contracts. If they bought the contracts on a futures exchange, they will need to put up collateral to cover these losses. This was the case for many airlines when fuel prices plunged in the second half of 2008. Writing in Aviation Week, Adrian Schofield noted that at the end of 2008 Delta and United Airlines each had about $1 billion in cash tied up as hedge collateral. These were large amounts of cash to find when the skies were far from friendly for U.S. airlines.

Schofield added an additional caution for would-be hedgers: “Competition among airlines paying lower jet-fuel prices should lead to lower fares. When that happens, lower fuel costs are offset by lower revenues, and losses on hedging contracts fall straight down to bottom-line income. Costs that are passed through to customers are naturally hedged.” Usually, only a portion of any increase in costs is passed through, so the natural hedge is partial. However, a firm needs to be careful when adding a financial hedge transaction to a natural hedge. It could overshoot and increase risk, not reduce it.

Sources: D. A. Carter, D. A. Rogers, and B. J. Simkins, “Hedging and Value in the U.S. Airline Industry,” Journal of Applied Corporate Finance 18 (Fall 2006), pp. 21–33; and A. Schofield, “High Anxiety,” Aviation Week & Space Technology, February 2, 2009, pp. 24–25.

Futures Exchanges

Our heating-oil distributor and refiner do not have to negotiate a one-off, bilateral contract. Each can go to an exchange where standardized forward contracts on heating oil are traded. The distributor would buy contracts and the refiner would sell.

Here we encounter some tricky vocabulary. When a standardized forward contract is traded on an exchange, it is called a futures contract—same contract, but a different label. The exchange is called a futures exchange. The distinction between “futures” and “forward” does not apply to the contract, but to how the contract is traded. We describe futures trading in a moment.

Table 26.1 lists a few of the most important commodity futures contracts and the exchanges on which they are traded.¹¹ Our refiner and distributor can trade heating oil futures on the New York Mercantile Exchange (NYMEX). A forest products company and a homebuilder can trade lumber futures on the Chicago Mercantile Exchange (CME). A mining company and a stainless steel producer can trade nickel futures on the London Metals Exchange.

   TABLE 26.1 Some important commodity futures and some of the exchanges on which they are traded.

Key to abbreviations:

CBOT

Chicago Board of Trade

CME

Chicago Mercantile Exchange

COMEX

Commodity Exchange Division of NYMEX

DCE

Dalian Commodity Exchange (China)

ICE

Intercontinental Exchange

LIFFE

NYSE Euronext LIFFE

LME

London Metal Exchange

MCX

Multi Commodity Exchange (India)

NYMEX

New York Mercantile Exchange

SHFE

Shanghai Futures Exchange

ZCE

Zhengzhou Commodity Exchange

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Financial futures by region

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For many firms the wide fluctuations in interest rates and exchange rates have become at least as important a source of risk as changes in commodity prices. Financial futures are similar to commodity futures, but instead of placing an order to buy or sell a commodity at a future date, you place an order to buy or sell a financial asset at a future date. Table 26.2 lists some important financial futures. Like Table 26.1 it is far from complete. For example, you can also trade futures on the Thai stock market index, the Hungarian forint, Finnish government bonds, and many other financial assets.

Almost every day some new futures contract seems to be invented. At first there may be just a few private deals between a bank and its customers, but if the idea proves popular, one of the futures exchanges will try to muscle in on the business. For example, in the last few years the Chicago Mercantile Exchange has offered futures contracts on the weather in 18 U.S. cities and on house prices in 10 cities.

The Mechanics of Futures Trading

When you buy or sell a futures contract, the price is fixed today but payment is not made until later. You will, however, be asked to put up margin in the form of either cash or Treasury bills to demonstrate that you have the money to honor your side of the bargain. As long as you earn interest on the margined securities, there is no cost to you.

   TABLE 26.2 Some important financial futures and some of the exchanges on which they are traded.

Key to abbreviations:

CBOT

Chicago Board of Trade

CME

Chicago Mercantile Exchange

Eurex

Eurex Exchange

LIFFE

NYSE Euronext LIFFE

OSE

Osaka Securities Exchange

SGX

Singapore Exchange

TFX

Tokyo Financial Futures Exchange

TSE

Tokyo Stock Exchange

In addition, futures contracts are marked to market. This means that each day any profits or losses on the contract are calculated; you pay the exchange any losses and receive any profits. For example, suppose that in September Arctic Fuels buys one million gallons of January heating-oil futures contracts at a futures price of $3.20 per gallon. The next day the price of the January contract increases to $3.24 per gallon. Arctic now has a profit of $.04 × 1,000,000 = $40,000. The exchange’s clearinghouse therefore pays $40,000 into Arctic’s margin account. If the price then drops back to $3.22, Arctic’s margin account pays $20,000 back to the clearing house.

Of course Northern Refineries is in the opposite position. Suppose it sells one million gallons of January heating-oil futures contracts at a futures price of $3.20 per gallon. If the price increases to $3.24 cents per gallon, it loses $.04 × 1,000,000 = $40,000 and must pay this amount into the clearinghouse. Notice that neither the distributor nor the refiner has to worry about whether the other party will honor the other side of the bargain. The futures exchange guarantees the contracts and protects itself by settling up profits or losses each day. Futures trading eliminates counterparty risk.

Now consider what happens over the life of the futures contract. We’re assuming that Arctic and Northern take offsetting long and short positions in the January contract (not directly with each other, but with the exchange). Suppose that a severe cold snap pushes the spot price of heating oil in January up to $3.40 per gallon. Then the futures price at the end of the contract will also be $3.40 per gallon.¹² So Arctic gets a cumulative profit of (3.40 – 3.20) × 1,000,000 = $200,000. It can take delivery of one million gallons, paying $3.40 per gallon, or $3,400,000. Its net cost, counting the profits on the futures contract, is $3,400,000 – 200,000 = $3,200,000, or $3.20 per gallon. Thus it has locked in the $3.20 per gallon price quoted in September when it first bought the futures contract. You can easily check that Arctic’s net cost always ends up at $3.20 per gallon, regardless of the spot price and ending futures price in January.

Northern Refineries suffers a cumulative loss of $200,000 if the January price is $3.40. That’s the bad news; the good news is that it can sell and deliver heating oil for $3.40 per gallon. Its net revenues are $3,400,000 – 200,000 = $3,200,000, or $3.20 per gallon, the futures price in September. Again, you can easily check that Northern’s net selling price always ends up at $3.20 per gallon.

Arctic does not have to take delivery directly from the futures exchange, and Northern Refineries does not have to deliver to the exchange. They will probably close out their futures positions just before the end of the contract, take their profits or losses, and buy or sell in the spot market.¹³

Taking delivery directly from an exchange can be costly and inconvenient. For example, the NYMEX heating-oil contract calls for delivery in New York Harbor. Arctic Fuels will be better off taking delivery from a local source such as Northern Refineries. Northern Refineries will likewise be better off delivering heating oil locally than shipping it to New York. Both parties can nevertheless use the NYMEX futures contract to hedge their risks.

The effectiveness of this hedge depends on the correlation between changes in heating-oil prices locally and in New York Harbor. Prices in both locations will be positively correlated because of a common dependence on world energy prices. But the correlation is not perfect. What if a local cold snap hits Arctic Fuels’s customers but not New York? A long position in NYMEX futures won’t hedge Arctic Fuels against the resulting increase in the local spot price. This is an example of basis risk. We return to the problems created by basis risk later in this chapter.

Trading and Pricing Financial Futures Contracts

Financial futures trade in the same way as commodity futures. Suppose your firm’s pension fund manager thinks that the German stock market will outperform other European markets over the next six months. She forecasts a 10% six-month return. How can she place a bet? She can buy German stocks, of course. But she could also buy futures contracts on the DAX index of German stocks, which are traded on the Eurex exchange. Suppose she buys 10 six-month futures contracts at 7,000. Each contract pays off 25 times the level of the index, so she has a long position of 10 × 25 × 7,000 = €1,750,000. This position is marked to market daily. If the DAX goes up, Eurex puts the profits into your fund’s margin account; if the DAX falls, the margin account falls too. If your pension manager is right about the German market, and the DAX ends up at 7,700 after six months, then your fund’s cumulative profit on the futures position is 10 × (7,700 – 7,000) × 25 = €175,000.

If you want to buy a security, you have a choice. You can buy for immediate delivery at the spot price or you can “buy forward” by placing an order for future delivery at the futures price. You end up with the same security either way, but there are two differences. First, if you buy forward, you don’t pay up front, and so you can earn interest on the purchase price. Second, you miss out on any interest or dividend that is paid in the meantime. This tells us the relationship between spot and futures prices:

where Ft is the futures price for a contract lasting t periods, S0 is today’s spot price, rf is the risk-free interest rate, and y is the dividend yield or interest rate.¹⁴ The following example shows how and why this formula works.

EXAMPLE 26.1 • Valuing Index Futures

Suppose the six-month DAX futures contract trades at 7,000 when the current (spot) DAX index is 6,965.17. The interest rate is 3% per year (about 1.5% over six months) and the dividend yield on the index is 2% (about 1% over six months). These numbers fit the formula perfectly because

But why are the numbers consistent?

Suppose you just buy the DAX index for 6,965.17 today. Then in six months you will own the index and also have dividends of .01 × 6,965.17 = 69.65. But you decide to buy a futures contract for 7,000 instead, and you put €6,965.17 in the bank. After six months, the bank account has earned interest at 1.5%, so you have 6,965.17 × 1.015 = €7,069.65, enough to buy the index for 7,000 with €69.65 left over—just enough to cover the dividend you missed by buying futures rather than spot. You get what you pay for.¹⁵

Spot and Futures Prices—Commodities

The difference between buying commodities today and buying commodity futures is more complicated. First, because payment is again delayed, the buyer of the future earns interest on her money. Second, she does not need to store the commodities and, therefore, saves warehouse costs, wastage, and so on. On the other hand, the futures contract gives no convenience yield, which is the value of being able to get your hands on the real thing. The manager of a supermarket can’t burn heating oil futures if there’s a sudden cold snap, and he can’t stock the shelves with orange juice futures if he runs out of inventory at 1 p.m. on a Saturday.

Let’s express storage costs and convenience yield as fractions of the spot price. For commodities, the futures price for t periods ahead is¹⁶

It’s interesting to compare this formula with the formula for a financial future. Convenience yield plays the same role as dividends or interest foregone (y) on securities. But financial assets cost nothing to store, and storage costs do not appear in the formula for financial futures.

Usually you can’t observe storage cost or convenience yield, but you can infer the difference between them by comparing spot and futures prices. This difference—that is, convenience yield less storage cost—is called net convenience yield (net convenience yield = convenience yield – storage costs).

EXAMPLE 26.2 • Calculating Net Convenience Yield

In January 2009, the spot price of crude oil was $41.65 a barrel and the one-year futures price was $56.38 per barrel. The interest rate was about 0.15%. Thus

So net convenience yield was negative, that is, net convenience yield = convenience yield – storage costs = –.352, or –35.2% over one year. Evidently the cost of holding of crude oil inventories was greater than the convenience yield provided by those inventories. Oil in 2009 was in ample supply and users had no worries that they would run short in the months ahead.

Figure 26.2 plots the annualized net convenience yield for crude oil since 1990.

Notice how much the spread between the spot and futures price can bounce around. When there are shortages or fears of an interruption of supply, traders may be prepared to pay a hefty premium for the convenience of having inventories of crude oil rather than the promise of future delivery.

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Gold convenience value

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There is one further complication that we should note. There are some commodities that cannot be stored at all. You can’t store electricity, for example. As a result, electricity supplied in, say, six-months’ time is a different commodity from electricity available now, and there is no simple link between today’s price and that of a futures contract to buy or sell at the end of six months. Of course, generators and electricity users will have their own views of what the spot price is likely to be, and the futures price will reveal these views to some extent.¹⁷

   FIGURE 26.2 Annualized percentage net convenience yield (convenience yield less storage costs) for crude oil.

Source: Wikiposit.

More about Forward Contracts

Each day billions of dollars of futures contracts are bought and sold. This liquidity is possible only because futures contracts are standardized and mature on a limited number of dates each year.

Fortunately there is usually more than one way to skin a financial cat. If the terms of futures contracts do not suit your particular needs, you may be able to buy or sell a tailor-made forward contract. The main forward market is in foreign currency. We discuss forward exchange rates in the next chapter.

It is also possible to enter into a forward interest rate contract. For example, suppose you know that at the end of three months you are going to need a six-month loan. If you are worried that interest rates will rise over the three-month period, you can lock in the interest rate on the loan by buying a forward rate agreement (FRA) from a bank.¹⁸ For example, the bank might sell you a 3-against-9 month (or 3 × 9) FRA at 7%. If at the end of three months the six-month interest rate is higher than 7%, then the bank will make up the difference;¹⁹ if it is lower, then you must pay the bank the difference.²⁰

Homemade Forward Rate Contracts

Suppose that you borrow $90.91 for one year at 10% and lend $90.91 for two years at 12%. These interest rates are for loans made today; therefore, they are spot interest rates.

The cash flows on your transactions are as follows:

Notice that you do not have any net cash outflow today but you have contracted to pay out money in year 1. The interest rate on this forward commitment is 14.04%. To calculate this forward interest rate, we simply worked out the extra return for lending for two years rather than one:

In our example you manufactured a forward loan by borrowing short term and lending long. But you can also run the process in reverse. If you wish to fix today the rate at which you borrow next year, you borrow long and lend the money until you need it next year.

 26-5    Swaps

Some company cash flows are fixed. Others vary with the level of interest rates, rates of exchange, prices of commodities, and so on. These characteristics may not always result in the desired risk profile. For example, a company that pays a fixed rate of interest on its debt might prefer to pay a floating rate, while another company that receives cash flows in euros might prefer to receive them in yen. Swaps allow them to change their risk in these ways.

The market for swaps is huge. In 2011 the total notional amount of interest rate and currency swaps outstanding was over $460 trillion. By far the major part of this figure consisted of interest rate swaps.²¹ We therefore show first how interest rate swaps work, and then describe a currency swap. We conclude with a brief look at total return swaps.

Interest Rate Swaps

Friendly Bancorp has made a five-year, $50 million loan to fund part of the construction cost of a large cogeneration project. The loan carries a fixed interest rate of 8%. Annual interest payments are therefore $4 million. Interest payments are made annually, and all the principal will be repaid at year 5.

Suppose that instead of receiving fixed interest payments of $4 million a year, the bank would prefer to receive floating-rate payments. It can do so by swapping the $4 million, five-year annuity (the fixed interest payments) into a five-year floating-rate annuity. We show first how Friendly Bancorp can make its own homemade swap. Then we describe a simpler procedure.

The bank (we assume) can borrow at a 6% fixed rate for five years.²² Therefore, the $4 million interest it receives can support a fixed-rate loan of 4/.06 = $66.67 million. The bank can now construct the homemade swap as follows: It borrows $66.67 million at a fixed interest rate of 6% for five years and simultaneously lends the same amount at LIBOR. We assume that LIBOR is initially 5%.²³ LIBOR is a short-term interest rate, so future interest receipts will fluctuate as the bank’s investment is rolled over.

The net cash flows to this strategy are shown in the top portion of Table 26.3. Notice that there is no net cash flow in year 0 and that in year 5 the principal amount of the short-term investment is used to pay off the $66.67 million loan. What’s left? A cash flow equal to the difference between the interest earned (LIBOR × 66.67) and the $4 million outlay on the fixed loan. The bank also has $4 million per year coming in from the project financing, so it has transformed that fixed payment into a floating payment keyed to LIBOR.

Of course, there’s an easier way to do this, shown in the bottom portion of Table 26.3. The bank can just enter into a five-year swap.²⁴ Naturally, Friendly Bancorp takes this easier route. Let’s see what happens.

   TABLE 26.3 The top panel shows the cash flows in millions of dollars to a homemade fixed-to-floating interest rate swap. The bottom panel shows the cash flows to a standard swap transaction.

Friendly Bancorp calls a swap dealer, which is typically a large commercial or investment bank, and agrees to swap the payments on a $66.67 million fixed-rate loan for the payments on an equivalent floating-rate loan. The swap is known as a fixed-to-floating interest rate swap and the $66.67 million is termed the notional principal amount of the swap. Friendly Bancorp and the dealer are the counterparties to the swap.

The dealer is quoting a rate for five-year swaps of 6% against LIBOR.²⁵ This figure is sometimes quoted as a spread over the yield on U.S. Treasuries. For example, if the yield on five-year Treasury notes is 5.25%, the swap spread is .75%.

The first payment on the swap occurs at the end of year 1 and is based on the starting LIBOR rate of 5%.²⁶ The dealer (who pays floating) owes the bank 5% of $66.67 million, while the bank (which pays fixed) owes the dealer $4 million (6% of $66.67 million). The bank therefore makes a net payment to the dealer of 4 – (.05 × 66.67) = $.67 million:

The second payment is based on LIBOR at year 1. Suppose it increases to 6%. Then the net payment is zero:

The third payment depends on LIBOR at year 2, and so on.

The notional value of this swap is $66.67 million. The fixed and floating interest rates are multiplied by the notional amount to calculate dollar amounts of fixed and floating interest. But the notional value vastly overstates the economic value of the swap. At creation the economic value of the swap is zero because the NPV of the cash flows to each counterparty is zero. The NPV drifts away from zero as time passes and interest rates change. But the economic value will always be far less than notional value. Careless references to notional values give the impression that swap markets are impossibly gigantic; in fact they are merely very large.

The economic value of a swap depends on the path of long-term interest rates. For example, suppose that after two years interest rates are unchanged, so a 6% note issued by the bank would continue to trade at its face value. In this case the swap still has zero value. (You can confirm this by checking that the NPV of a new three-year homemade swap is zero.) But if long rates increase over the two years to 7% (say), the value of a three-year note falls to

Now the fixed payments that the bank has agreed to make are less valuable and the swap is worth 66.67 – 64.92 = $1.75 million.

How do we know the swap is worth $1.75 million? Consider the following strategy:

 1.  The bank can enter a new three-year swap deal in which it agrees to pay LIBOR on the same notional principal of $66.67 million.

 2.  In return it receives fixed payments at the new 7% interest rate, that is, .07 × 66.67 = $4.67 per year.

The new swap cancels the cash flows of the old one, but it generates an extra $.67 million for three years. This extra cash flow is worth

Remember, ordinary interest rate swaps have no initial cost or value (NPV = 0), but their value drifts away from zero as time passes and long-term interest rates change. One counterparty wins as the other loses.

In our example, the swap dealer loses from the rise in interest rates. Dealers will try to hedge the risk of interest rate movements by engaging in a series of futures or forward contracts or by entering into an offsetting swap with a third party. As long as Friendly Bancorp and the other counterparty honor their promises, the dealer is fully protected against risk. The recurring nightmare for swap managers is that one party will default, leaving the dealer with a large unmatched position. This is another example of counterparty risk.

The market for interest rate swaps is large and liquid. Consequently, financial analysts often look at swap rates when they want to know how interest rates vary with maturity. For example, Figure 26.3 shows swap rates in March 2012 for the U.S. dollar, the euro, and the yen. You can see that in each country long-term interest rates are much higher than short-term rates, though the level of swap rates varies from one country to another.

Currency Swaps

We now look briefly at an example of a currency swap.

Suppose that the Possum Company needs 11 million euros to help finance its European operations. We assume that the euro interest rate is about 5%, whereas the dollar rate is about 6%. Since Possum is better known in the United States, the financial manager decides not to borrow euros directly. Instead, the company issues $10 million of five-year 6% notes in the United States. Then it arranges with a counterparty to swap this dollar loan into euros. Under this arrangement the counterparty agrees to pay Possum sufficient dollars to service its dollar loan, and in exchange Possum agrees to make a series of annual payments in euros to the counterparty.

   FIGURE 26.3 Swap curves for three currencies, March 2012.

Here are Possum’s cash flows (in millions):

Look first at the cash flows in year 0. Possum receives $10 million from its issue of dollar notes, which it then pays over to the swap counterparty. In return the counterparty sends Possum a check for €8 million. (We assume that at current rates of exchange $10 million is worth €8 million.)

Now move to years 1 through 4. Possum needs to pay interest of 6% on its debt issue, which works out at .06 × 10 = $.6 million. The swap counterparty agrees to provide Possum each year with sufficient cash to pay this interest and in return Possum makes an annual payment to the counterparty of 5% of €8 million, or €.4 million. Finally, in year 5 the swap counterparty pays Possum enough to make the final payment of interest and principal on its dollar notes ($10.6 million), while Possum pays the counterparty €8.4 million.

The combined effect of Possum’s two steps (line 3) is to convert a 6% dollar loan into a 5% euro loan. You can think of the cash flows for the swap (line 2) as a series of contracts to buy euros in years 1 through 5. In each of years 1 through 4 Possum agrees to purchase $.6 million at a cost of .4 million euros; in year 5 it agrees to buy $10.6 million at a cost of 8.4 million euros.²⁷

Total Return Swaps

While interest rate and currency swaps are the most popular type of contract, there is a wide variety of other possible swaps or related contracts. For example, in Chapter 23 we encountered credit default swaps that allow investors to insure themselves against the default on a corporate bond.

You can also enter into a total return swap where one party (party A) makes a series of agreed payments and the other (party B) pays the total return on a particular asset. This asset might be a common stock, a loan, a commodity, or a market index. For example, suppose that B owns $10 million of IBM stock. It now enters into a two-year swap agreement to pay A each quarter the total return on this stock. In exchange A agrees to pay B interest of LIBOR + 1%. B is known as the total return payer and A is the total return receiver. Suppose LIBOR is 5%. Then A must pay B 6% of $10 million, or about 1.5% a quarter. If IBM stock returns more than this, there will be a net payment from B to A; if the return is less than 1.5%, A must make a net payment to B. Although ownership of the IBM stock does not change hands, the effect of this total return swap is the same as if B had sold the asset to A and bought it back at an agreed future date.

 26-6    How to Set Up a Hedge

There can be many ways to hedge a risk exposure. Some hedges are zero-maintenance: Once established, the financial manager can walk away and worry about other matters. Other hedges are dynamic: They work only if adjusted at frequent intervals.

The forward contract between Northern Refineries and Arctic Fuels, which we described in Section 26-4, was zero-maintenance because each counterparty locked in the price of heating oil at $3.20 per gallon, regardless of the future path of heating-oil prices. Now we look at an example where the financial manager will probably implement a dynamic hedge.

Hedging Interest Rate Risk

Potterton Leasing has acquired a warehouse and leased it to a manufacturer for fixed payments of $2 million per year for 20 years. The lease cannot be cancelled by the manufacturer, so Potterton has a safe, debt-equivalent asset. The interest rate is 10%, and we ignore taxes for simplicity. The PV of Potterton’s rental income is $17 million:

The lease exposes Potterton to interest rate risk. If interest rates increase, the PV of the lease payments falls. If interest rates decrease, the PV increases. Potterton’s CFO decides to issue an offsetting debt liability:

Thus Potterton is long $17 million and also short $17 million. But it may not be hedged. Simply borrowing $17 million at some random maturity does not eliminate interest rate risk. Suppose the CFO took out a one-year, $17 million bank loan, with a plan to refinance the loan annually. Then she would be borrowing short and lending long (via the 20-year lease), which amounts to a $17 million bet that interest rates will fall. If instead they rise, her company will end up paying more interest in years 2 to 20, with no compensating increase in the lease cash flows.

To hedge interest-rate risk, the CFO has to design the debt issue so that any change in interest rates has the same (and thus offsetting) impact on the PV of the lease payments and the PV of the debt. There are two ways to accomplish this:

 1.  Zero-maintenance. Issue debt requiring interest and principal payments of exactly $2 million per year for 20 years. This debt would be similar to a real-estate mortgage with level payments. In this case, lease payments would exactly cover debt service in each year. The PVs of the lease payments and the offsetting debt would always be identical, regardless of the level of future interest rates.

 2.  Match duration. Issue debt with the same duration as the lease payments. Here debt service does not have to match the lease payments in each (or any) year. If durations are matched, then small changes in interest rates, say from 10% down to 9.5% or up to 10.5%, will have the same impact on the PVs of the lease payments and the debt.

The duration-matching strategy is usually more convenient, but it is not zero-maintenance because durations will drift out of line as interest rates change and time passes. Thus the CFO will have to revisit and reset the hedge. She will have to execute a dynamic strategy to make duration-matching work.

Let’s work out the duration-matching strategy. The duration of the lease payments is 7.5 years:

The duration of a “zero-maintenance” debt-issue, with debt service of exactly $2 million per year for 20 years, would of course also be 7.5 years.

Many other debt instruments have a duration of 7.5 years. For example, you can check that a 12-year bond with a 10% coupon has a 7.5-year duration. But suppose the CFO finds it more convenient to raise $17 million by issuing a zero-coupon note with a maturity of exactly 7.5 years.²⁸ The note has only one cash payment at 7.5 years and therefore a duration of 7.5 years. Is Potterton now hedged against interest rate risk?

Figure 26.4 plots the PVs of the lease payments (on the left) and the 7.5-year note (on the right) as a function of the interest rate. On the right we have also plotted the PV curve for the “zero-maintenance” debt package with debt service exactly matching the lease payments. All the PV curves are downward-sloping but convex; note how each curve comes down steeply at low interest rates but flattens out at higher interest rates.

Now compare the slope of the PV curve for the lease payments (and also the “zero-maintenance” debt package) to the slope of the 7.5-year zero. The slopes are identical at the current 10% interest rate because the duration is identical at this rate. As we pointed out in Chapter 4, (modified) duration measures the percentage change in bond price for a 1 percentage-point change in the interest rate.²⁹ If the interest rate falls to 9.5% or increases to 10.5%, the PVs of the lease cash flows and the zero-coupon debt change by the same amount. Potterton is therefore hedged, so long as the interest rate does not stray too far from the current level of 10%.

   FIGURE 26.4 Hedging Potterton’s interest rate risk by matching duration. The PV of lease cash inflows is plotted on the left, the PV of debt on the right. All durations are 7.5 years, so the slopes of the PV curves are identical at the current 10% interest rate. Therefore, Potterton’s net exposure to small changes in interest rates is zero.

The hedge is not zero-maintenance, however. You can see from Figure 26.4 that the PV curve for the 7.5-year zero has less curvature (less convexity) than the PV curve for the lease. The zero has lower duration (shallower slope) at low interest rates and higher duration (steeper slope) at high interest rates. Thus if interest rates move much higher or lower than 10%, Potterton’s CFO will have to reconsider and reset the hedge. Also she will have to reset the hedge later even if interest rates do not change because the duration of the 7.5-year zero will decrease faster than the duration of the 20-year lease. Think forward 7.5 years: The zero will mature, while the lease will still have 12.5 years to maturity.

You can see why duration is a useful tool for measuring and hedging interest rate risk.³⁰ The mini-case at the end of this chapter offers another opportunity to use this concept.

Hedge Ratios and Basis Risk

In our example of Potterton Leasing, the CFO matched lease cash flows worth $17 million against debt worth $17 million. In other words, the hedge ratio for Potterton was exactly 1.

Hedge ratios can be much higher or lower than 1. For example, suppose a farmer owns 100,000 bushels of wheat and wishes to hedge by selling wheat futures. In practice, the wheat that the farmer owns and the wheat that he sells in the futures markets are unlikely to be identical. If he sells wheat futures on the Kansas City exchange, he agrees to deliver hard, red winter wheat in Kansas City in September. But perhaps he is growing northern spring wheat many miles from Kansas City; in this case, the prices of the two wheats will not move exactly together.

Figure 26.5 shows how changes in the prices of the two types of wheat may have been related in the past. The slope of the fitted line shows that a 1% change in the price of Kansas wheat was, on average, associated with an .8% change in the price of the farmer’s wheat. Because the price of the farmer’s wheat is relatively insensitive to changes in Kansas prices, he needs to sell .8 × 100,000 bushels of wheat futures to minimize risk.

Let us generalize. Suppose that you already own an asset, A (e.g., wheat), and you wish to hedge against changes in the value of A by making an offsetting sale of another asset, B (e.g., wheat futures). Suppose also that percentage changes in the value of A are related in the following way to percentage changes in the value of B:

Delta (δ) measures the sensitivity of A to changes in the value of B. It is also equal to the hedge ratio—that is, the number of units of B that should be sold to hedge the purchase of A. You minimize risk if you offset your position in A by the sale of delta units of B.

The trick in setting up a hedge is to estimate the delta or hedge ratio. Our farmer could use past experience to do so, but often a strong dose of judgment is called for. For example, suppose that Antarctic Air would like to protect itself against a hike in oil prices. As the financial manager, you need to decide how much a rise in oil price would affect firm value.

Suppose the company spent $200 million on fuel last year. Other things equal, a 10% increase in the price of oil will cost the company an extra .1 × 200 = $20 million. But perhaps you can partially offset the higher costs by charging higher ticket prices, in which case earnings will fall by less than $20 million. Or perhaps an oil price rise will lead to a slowdown in business activity and therefore lower passenger numbers. In that case earnings will decline by more than $20 million. Working out the likely effect on firm value is even trickier because it depends on whether the rise is likely to be permanent. Perhaps the price rise will induce an increase in production or encourage consumers to economize on energy usage.

   FIGURE 26.5 Hypothetical plot of past changes in the price of the farmer’s wheat against changes in the price of Kansas City wheat futures. A 1% change in the futures price implies, on average, an .8% change in the price of the farmer’s wheat.

Whenever the two sides of the hedge do not move exactly together, there will be some basis risk. That is not a problem for the CFO of Potterton. As long as interest rates do not change sharply, any changes in the value of Potterton’s lease should be exactly offset by changes in the value of the debt. In this case there is no basis risk, and Potterton is perfectly hedged.

Our wheat farmer is less fortunate. The scatter of points in Figure 26.5 shows that it is not possible for the farmer to construct a perfect hedge using wheat futures. Since the underlying commodity (the farmer’s wheat) and the hedging instrument (Kansas City wheat futures) are imperfectly correlated, some basis risk remains.

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Jet fuel and basis risk

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WTI and Brent oil futures

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 26-7    Is “Derivative” A Four-Letter Word?

Our wheat farmer sold wheat futures to reduce business risk. But if you were to copy the farmer and sell futures without an offsetting holding of wheat, you would increase risk, not reduce it. You would be speculating.

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Major derivatives losses

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Speculators in search of large profits (and prepared to tolerate large losses) are attracted by the leverage that derivatives provide. By this we mean that it is not necessary to lay out much money up front and the profits or losses may be many times the initial outlay. “Speculation” has an ugly ring, but a successful derivatives market needs speculators who are prepared to take on risk and provide more cautious people such as farmers or millers with the protection they need. For example, if an excess of farmers wishes to sell wheat futures, the price of futures will be forced down until enough speculators are tempted to buy in the hope of a profit. If there is a surplus of millers wishing to buy wheat futures, the reverse will happen. The price of wheat futures will be forced up until speculators are drawn in to sell.

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LTCM

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Speculation may be necessary to a thriving derivatives market, but it can get companies into serious trouble. The nearby Finance in Practice box describes how the French bank Société Générale took a $7.2 billion bath from unauthorized trading by one of its staff. The bank has plenty of company. In 2011 the Swiss bank UBS reported that a rogue trader had notched up losses of $2.3 billion. And in 1995 Baring Brothers, a blue-chip British merchant bank with a 200-year history, became insolvent. The reason: Nick Leeson, a trader in Baring’s Singapore office, had placed very large bets on the Japanese stock market index that resulted in losses of $1.4 billion.

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Metallgesellschaft

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These tales of woe have some cautionary messages for all corporations. During the 1970s and 1980s many firms turned their treasury operations into profit centers and proudly announced their profits from trading in financial instruments. But it is not possible to make large profits in financial markets without also taking large risks, so these profits should have served as a warning rather than a matter for congratulation.

FINANCE IN PRACTICE

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The World’s Poorest Man

  In October 2010 Jérôme Kerviel became the world’s poorest man when a French court sentenced him to five years in prison and fined him €4.9 billion. Until his arrest two years earlier, he had been a trader in the French bank Société Générale. But then it was discovered that he had engaged in unauthorized trading, resulting in record losses for the bank of €4.9 billion ($7.2 billion).

Kerviel joined the back office of SocGen in 2000. Five years later he realized his dream when he was promoted to be a trader on the Delta One desk, which mainly trades equities, futures, and exchange-traded funds.* In most banks the Delta One desk focuses on arbitrage opportunities, and Kerviel’s job was to exploit small price differences between equity futures contracts, rather than to bet on the markets’ direction.

Soon after taking up his new position, Kerviel took an unauthorized bet on a downturn for the market. The trade proved successful and resulted in a profit of €500,000. Although it was not hedged and exceeded Kerviel’s credit limit, the bank took no action. Spurred on by this success, Kerviel continued to take unhedged bets on the outlook for the market. To hide the fact that his trades were unhedged, he created a series of fictitious offsetting trades.

For a while fortune smiled on Kerviel and by 2007 he had made a profit of €1.4 billion. But in January 2008 everything started to unravel. As stock prices collapsed, Kerviel took larger and larger bets that the markets would recover. Every time he lost, Kerviel doubled up on his bets. By mid-January, he had about €50 billion—more than the bank’s total market capitalization—riding on a market turnaround.

During early January, SocGen received several queries from the Eurex derivatives exchange about unusual trading patterns and the bank began to investigate Kerviel’s activities. By January 21, it had learned the full extent of his positions and frantically moved to close them out. The resulting loss of €4.9 billion amounted to more than 10% of the value of the bank’s equity.

Société Générale’s failure to spot the unauthorized trading was the subject of much criticism. Some commented that a trader who had worked in the back office would be particularly well informed about ways to hide his activities. Banks took comfort in the fact that such a breakdown in controls could never happen again—that is until 2011, when the Swiss Bank, UBS, revealed that a trader who had been promoted from the back office to the Delta One desk had lost $2 billion in unauthorized trading.

*Delta One desks are so called because they trade equity derivatives that have a hedge ratio, or delta, of 1.0 with the underlying securities. Delta One desks, therefore, do not trade options.

A Boeing 747 weighs 400 tons, flies at nearly 600 miles per hour, and is inherently very dangerous. But we don’t ground 747s; we just take precautions to ensure that they are flown with care. Similarly, it is foolish to suggest that firms should ban the use of derivatives, but it makes obvious sense to take precautions against their misuse. Here are two bits of horse sense:

 •  Precaution 1: Don’t be taken by surprise. By this we mean that senior management needs to monitor regularly the value of the firm’s derivatives positions and to know what bets the firm has placed. At its simplest, this might involve asking what would happen if interest rates or exchange rates were to change by 1%. But large banks and consultants have also developed sophisticated models for measuring the risk of derivatives positions.

 •  Precaution 2: Place bets only when you have some comparative advantage that ensures the odds are in your favor. If a bank were to announce that it was drilling for oil or launching a new soap powder, you would rightly be suspicious about whether it had what it takes to succeed. You should be equally suspicious if an oil producer or consumer products company announced that it was placing a bet on interest rates or currencies.

Imprudent speculation in derivatives is undoubtedly an issue of concern for the company’s shareholders, but is it a matter for more general concern? Some people believe, like Warren Buffett, that derivatives are “financial weapons of mass destruction.” They point to the huge volume of trading in derivatives and argue that speculative losses could lead to major defaults that might threaten the whole financial system. These worries have led to calls for increased regulation of derivatives markets.

Now, this is not the place for a discussion of regulation, but we should warn you about careless measures of the size of the derivatives markets and the possible losses. In December 2011 the notional value of outstanding derivative contracts was $671 trillion.³¹ This is a very large sum, but it tells you nothing about the money that was being put at risk. For example, suppose that a bank enters into a $10 million interest rate swap and the other party goes bankrupt the next day. How much has the bank lost? Nothing. It hasn’t paid anything up front; the two parties simply promised to pay sums to each other in the future. Now the deal is off.

Suppose that the other party does not go bankrupt until a year after the bank entered into the swap. In the meantime interest rates have moved in the bank’s favor, so it should be receiving more money from the swap than it is paying out. When the other side defaults on the deal, the bank loses the difference between the interest that it is due to receive and the interest that it should pay. But it doesn’t lose $10 million.³²

The only meaningful measure of the potential loss from default is the amount that it would cost firms showing a profit to replace their swap positions. This figure is only about 1% of the principal amount of swaps outstanding.

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SUMMARY

As a manager, you are paid to take risks, but you are not paid to take just any risks. Some risks are simply bad bets, and others could jeopardize the value of the firm. Hedging risks, when it is practical to do so, can make sense if it reduces the chance of cash shortfalls or financial distress. In some cases, hedging can also make it easier to monitor and motivate operating managers. Relieving managers of risk outside their control helps them concentrate on what can be controlled.

Most businesses insure against possible losses. Insurance companies specialize in assessing risks and can pool risks by holding a diversified portfolio of policies. Insurance works less well when policies are taken up by companies that are most at risk (adverse selection) or when the insured company is tempted to skip on maintenance or safety procedures (moral hazard).

Firms can also hedge with options and with forward and futures contracts. A forward contract is an advance order to buy or sell an asset. The forward price is fixed today, but payment is not made until the delivery date at the end of the contract. Forward contracts traded on organized futures exchanges are called futures contracts. Futures contracts are standardized and traded in huge volumes. The futures markets allow firms to lock in future prices for dozens of different commodities, securities, and currencies.

Instead of buying or selling a standardized futures contract, you may be able to arrange a tailor-made forward contract with a bank. Firms can protect against changes in foreign exchange rates by buying or selling forward currency contracts. Forward rate agreements (FRAs) provide protection against changes in interest rates. You can also construct homemade forward contracts. For example, if you borrow for two years and at the same time lend for one year, you have effectively taken out a forward loan.

Firms also hedge with swap contracts. For example, a firm can make a deal to pay interest to a bank at a fixed long-term rate and receive interest from the bank at a floating short-term rate. The firm swaps a fixed for a floating rate. Such a swap could make sense if the firm has relatively easy access to short-term borrowing but dislikes the exposure to fluctuating short-term interest rates.

The theory of hedging is straightforward. You find two closely related assets. You then buy one and sell the other in proportions that minimize the risk of your net position. If the assets are perfectly correlated, you can make the net position risk-free. If they are less than perfectly correlated, you will have to absorb some basis risk.

The trick is to find the hedge ratio or delta—that is, the number of units of one asset that is needed to offset changes in the value of the other asset. Sometimes the best solution is to look at how the prices of the two assets have moved together in the past. For example, suppose you observe that a 1% change in the value of B has been accompanied on average by a 2% change in the value of A. Then delta equals 2.0; to hedge each dollar invested in A, you need to sell two dollars of B.

On other occasions theory can help to set up the hedge. For example, the effect of a change in interest rates on an asset’s value depends on the asset’s duration. If two assets have the same duration, they will be equally affected by fluctuations in interest rates.

Many of the hedges described in this chapter are static. Once you have set up the hedge, you can take a long vacation, confident that the firm is well protected. However, some hedges, such as those that match durations, are dynamic. As time passes and prices change, you need to rebalance your position to maintain the hedge.

Hedging and risk reduction sound as wholesome as mom’s apple pie. But remember that hedging solely to reduce risk, with no other business purpose, cannot add value. It is a zero-sum game: risks aren’t eliminated, just shifted to some counterparty. And remember that your shareholders can also hedge by adjusting the composition of their portfolios or by trading in futures or other derivatives. Investors won’t reward the firm for doing something that they can do perfectly well for themselves.

Some companies have decided that speculation is much more fun than hedging. This view can lead to serious trouble. We do not believe that speculation makes sense for an industrial company, but we caution against the view that derivatives are a threat to the financial system.

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FURTHER READING

Three general articles on corporate risk management are:

K. A. Froot, D. Scharfstein, and J. C. Stein, “A Framework for Risk Management,” Harvard Business Review 72 (November–December 1994), pp. 59–71.

B. W. Nocco and R. M. Stulz, “Enterprise Risk Management: Theory and Practice,” Journal of Applied Corporate Finance 18 (Fall 2006), pp. 8–20.

C. H. Smithson and B. Simkins, “Does Risk Management Add Value? A Survey of the Evidence,” Journal of Applied Corporate Finance 17 (Summer 2005), pp. 8–17.

The Summer 2005 and Fall 2006 issues of the Journal of Applied Corporate Finance are devoted to risk management, and current news and developments are discussed in Risk magazine. You may also wish to refer to the following texts:

J. C. Hull, Options, Futures, and other Derivatives, 8th ed. (Englewood Cliffs, NJ: Prentice Hall, 2011).

C. H. Smithson, Managing Financial Risk, 3rd ed. (New York: McGraw-Hill, 1998).

R. M. Stulz, Risk Management and Derivatives (Cincinnati, OH: Thomson-Southwestern Publishing, 2003).

Schaefer’s paper is a useful review of how duration measures are used to immunize fixed liabilities:

S. M. Schaefer, “Immunisation and Duration: A Review of Theory, Performance and Applications,” Midland Corporate Finance Journal 3 (Autumn 1984), pp. 41–58.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

 1.  Vocabulary check Define the following terms:

 a. Spot price

 b. Forward vs. futures contract

 c. Long vs. short position

 d. Basis risk

 e. Mark to market

 f. Net convenience yield

 2.  Futures contracts True or false?

 a. Hedging transactions in an active futures market have zero or slightly negative NPVs.

 b. When you buy a futures contract, you pay now for delivery at a future date.

 c. The holder of a financial futures contract misses out on any dividend or interest payments made on the underlying security.

 d. The holder of a commodities futures contract does not have to pay for storage costs, but foregoes convenience yield.

 3.  Mark to market Yesterday you sold six-month futures on the German DAX stock market index at a price of 7,120. Today the DAX closed at 7,100 and DAX futures closed at 7,140. You get a call from your broker, who reminds you that your futures position is marked to market each day. Is she asking you to pay money, or is she about to offer to pay you?

 4.  Futures prices Calculate the value of a six-month futures contract on a Treasury bond. You have the following information:

   • Six-month interest rate: 10% per year, or 4.9% for six months.

   • Spot price of bond: 95.

   • The bond pays an 8% coupon, 4% every six months.

 5.  Hedging “Northern Refineries does not avoid risk by selling oil futures. If prices stay above $3.20 a gallon, then it will actually have lost by selling oil futures at that price.” Is this a fair comment?

 6.  Convenience yield Calculate convenience yield for magnoosium scrap from the following information:

 • Spot price: $2,550 per ton.

 • Futures price: $2,408 for a one-year contract.

 • Interest rate: 12%.

 • Storage costs: $100 per year.

 7.  Convenience yield Residents of the northeastern United States suffered record-setting low temperatures throughout November and December 2021. Spot prices of heating oil rose 25%, to over $7 a gallon.

 a. What effect did this have on the net convenience yield and on the relationship between futures and spot prices?

 b. In late 2022 refiners and distributors were surprised by record-setting high temperatures. What was the effect on net convenience yield and spot and futures prices for heating oil?

 8.  Convenience yield After a record harvest, grain silos are full to the brim. Are storage costs likely to be high or low? What does this imply for the net convenience yield?

 9.  Interest rate swaps A year ago a bank entered into a $50 million five-year interest rate swap. It agreed to pay company A each year a fixed rate of 6% and to receive in return LIBOR. When the bank entered into this swap, LIBOR was 5%, but now interest rates have risen, so on a four-year interest rate swap the bank could expect to pay 6½% and receive LIBOR.

 a. Is the swap showing a profit or loss to the bank?

 b. Suppose that at this point company A approaches the bank and asks to terminate the swap. If there are four annual payments still remaining, how much should the bank charge A to terminate?

 10.  Basis risk What is basis risk? In which of the following cases would you expect basis risk to be most serious?

 a. A broker owning a large block of Disney common stock hedges by selling index futures.

 b. An lowa corn farmer hedges the selling price of her crop by selling Chicago corn futures.

 c. An importer must pay 900 million euros in six months. He hedges by buying euros forward.

 11.  Hedging You own a $1 million portfolio of aerospace stocks with a beta of 1.2. You are very enthusiastic about aerospace but uncertain about the prospects for the overall stock market. Explain how you could hedge out your market exposure by selling the market short. How much would you sell? How in practice would you go about “selling the market”?

 12.  Futures hedging

 a. Marshall Arts has just invested $1 million in long-term Treasury bonds. Marshall is concerned about increasing volatility in interest rates. He decides to hedge using bond futures contracts. Should he buy or sell such contracts?

 b. The treasurer of Zeta Corporation plans to issue bonds in three months. She is also concerned about interest rate volatility and wants to lock in the price at which her company could sell 5% coupon bonds. How would she use bond futures contracts to hedge?

INTERMEDIATE

 13.  Insurance Large businesses spend millions of dollars annually on insurance. Why? Should they insure against all risks or does insurance make more sense for some risks than others?

 14.  Catastrophe bonds On some catastrophe bonds, payments are reduced if the claims against the issuer exceed a specified sum. In other cases payments are reduced only if claims against the entire industry exceed some sum. What are the advantages and disadvantages of the two structures? Which involves more basis risk? Which may create a problem of moral hazard?

 15.  Futures contracts List some of the commodity futures contracts that are traded on exchanges. Who do you think could usefully reduce risk by buying each of these contracts? Who do you think might wish to sell each contract?

 16.  Futures hedging Phoenix Motors wants to lock in the cost of 10,000 ounces of platinum to be used in next quarter’s production of catalytic converters. It buys three-month futures contracts for 10,000 ounces at a price of $1,650 per ounce.

 a. Suppose the spot price of platinum falls to $1,500 in three months’ time. Does Phoenix have a profit or loss on the futures contract? Has it locked in the cost of purchasing the platinum it needs?

 b. How do your answers change if the spot price of platinum increases to $1,800 after three months?

 17.  Futures prices In March 2012, 12 month futures on the Australian S&P/ASX 200 Index traded at 4,244. Spot was 4,276. The interest rate was 3.90%, and the dividend yield was about 5%. Were the futures fairly priced?

 18.  Futures prices If you buy a nine-month T-bill future, you undertake to buy a three-month bill in nine months’ time. Suppose that Treasury bills and notes currently offer the following yields:

What is the value of a nine-month bill future?

   TABLE 26.4 Spot and six-month futures prices for selected commodities and securities. See Problem 19.

 19.  Futures prices Table 26.4 contains spot and six-month futures prices for several commodities and financial instruments. There may be some money-making opportunities. See if you can find them, and explain how you would trade to take advantage of them. The interest rate is 14.5%, or 7% over the six-month life of the contracts.

 20.  Futures prices The following table shows 2012 gold futures prices for varying contract lengths. Gold is predominantly an investment good, not an industrial commodity. Investors hold gold because it diversifies their portfolios and because they hope its price will rise. They do not hold it for its convenience yield.

Calculate the interest rate faced by traders in gold futures, assuming a zero net convenience yield, for each of the contract lengths shown below. The spot price is $1,657 per ounce.

 21.  Swap values In September 2017 swap dealers were quoting a rate for five-year euro interest-rate swaps of 4.5% against Euribor (the short-term interest rate for euro loans). Euribor at the time was 4.1%. Suppose that A arranges with a dealer to swap a €10 million five-year fixed-rate loan for an equivalent floating-rate loan in euros.

 a. What is the value of this swap at the time that it is entered into?

 b. Suppose that immediately after A has entered into the swap, the long-term interest rate rises by 1%. Who gains and who loses?

 c. What is now the value of the swap?

 22.  Duration hedging Securities A, B, and C have the following cash flows:

 a. Calculate their durations if the interest rate is 8%.

 b. Suppose that you have an investment of €10 million in A. What combination of B and C would hedge this investment against interest rate changes?

 c. Now suppose that you have a €10 million investment in B. How would you hedge?

 23.  Hedge ratios What is meant by “delta” (δ) in the context of hedging? Give examples of how delta can be estimated or calculated.

 24.  Risk management A gold-mining firm is concerned about short-term volatility in its revenues. Gold currently sells for $1,600 an ounce, but the price is extremely volatile and could fall as low as $1,520 or rise as high as $1,680 in the next month. The company will bring 1,000 ounces to the market next month.

 a. What will be total revenues if the firm remains unhedged for gold prices of $1,520, $1,600, and $1,680 an ounce?

 b. The futures price of gold for delivery one month ahead is $1,610. What will be the firm’s total revenues at each gold price if the firm enters into a one-month futures contract to deliver 1,000 ounces of gold?

 c. What will total revenues be if the firm buys a one-month put option to sell gold for $1,600 an ounce? The put option costs $110 per ounce.

 25.  Futures hedging Legs Diamond owns shares in a Vanguard Index 500 mutual fund worth $1 million on July 15. (This is an index fund that tracks the Standard and Poor’s 500 Index.) He wants to cash in now, but his accountant advises him to wait six months so as to defer a large capital gains tax. Explain to Legs how he can use stock index futures to hedge out his exposure to market movements over the next six months. Could Legs “cash in” without actually selling his shares?

 26.  Hedge ratios Price changes of two gold-mining stocks have shown strong positive correlation. Their historical relationship is

Changes in B explain 60% of the variation of the changes in A (R² = .6).

 a. Suppose you own $100,000 of A. How much of B should you sell to minimize the risk of your net position?

 b. What is the hedge ratio?

 c. Here is the historical relationship between stock A and gold prices:

If R² = .5, can you lower the risk of your net position by hedging with gold (or gold futures) rather than with stock B? Explain.

 27.  Risk management Petrochemical Parfum (PP) is concerned about a possible increase in the price of heavy fuel oil, which is one of its major inputs. Show how PP can use either options or futures contracts to protect itself against a rise in the price of crude oil. Show how the payoffs in each case would vary if the oil price were $70, $80, or $90 a barrel. What are the advantages and disadvantages for PP of using futures rather than options to reduce risk?

   TABLE 26.5 Spot prices for selected commodities and financial assets. See Problem 28.

 28.  Futures prices Consider the commodities and financial assets listed in Table 26.5. The risk-free interest rate is 6% a year, and the term structure is flat.

 a. Calculate the six-month futures price for each case.

 b. Explain how a magnoosium producer would use a futures market to lock in the selling price of a planned shipment of 1,000 tons of magnoosium six months from now.

 c. Suppose the producer takes the actions recommended in your answer to (b), but after one month magnoosium prices have fallen to $2,200. What happens? Will the producer have to undertake additional futures market trades to restore its hedged position?

 d. Does the biotech index futures price provide useful information about the expected future performance of biotech stocks?

 e. Suppose Allen Wrench stock falls suddenly by $10 per share. Investors are confident that the cash dividend will not be reduced. What happens to the futures price?

 f. Suppose interest rates suddenly fall to 4%. The term structure remains flat. What happens to the six-month futures price on the five-year Treasury note? What happens to a trader who shorted 100 notes at the futures price calculated in part (a)?

 g. An importer must make a payment of one million ruples three months from now. Explain two strategies the importer could use to hedge against unfavorable shifts in the ruple–dollar exchange rate.

 29.  Swaps Is a total return swap on a bond the same as a credit default swap (see Section 23-1)? Why or why not?

 30.  Hedging “Speculators want futures contracts to be incorrectly priced; hedgers want them to be correctly priced.” Why?

 31.  Hedge ratios Your investment bank has an investment of €100 million in the stock of the Swiss Roll Corporation and a short position in the stock of the Frankfurter Sausage Company. Here is the recent price history of the two stocks:

On the evidence of these six months, how large would your short position in Frankfurter Sausage need to be to hedge you as far as possible against movements in the price of Swiss Roll?

CHALLENGE

 32.  Interest rate swaps Phillip’s Screwdriver Company has borrowed $20 million from a bank at a floating interest rate of 2 percentage points above three-month Treasury bills, which now yield 5%. Assume that interest payments are made quarterly and that the entire principal of the loan is repaid after five years.

Phillip’s wants to convert the bank loan to fixed-rate debt. It could have issued a fixed-rate five-year note at a yield to maturity of 9%. Such a note would now trade at par. The five-year Treasury note’s yield to maturity is 7%.

 a. Is Phillip’s stupid to want long-term debt at an interest rate of 9%? It is borrowing from the bank at 7%.

 b. Explain how the conversion could be carried out by an interest rate swap. What will be the initial terms of the swap? (Ignore transaction costs and the swap dealer’s profit.)

One year from now short- and medium-term Treasury yields decrease to 6%, so the term structure then is flat. (The changes actually occur in month 5.) Phillip’s credit standing is unchanged; it can still borrow at 2 percentage points over Treasury rates.

 c. What net swap payment will Phillip’s make or receive?

 d. Suppose that Phillip’s now wants to cancel the swap. How much would it need to pay the swap dealer? Or would the dealer pay Phillip’s? Explain.

 33.  Hedging strategy Many companies that face significant exposure to commodity-price risks decide not to hedge. For example, the 2011 Annual Report for Rio Tinto, a UK and Australian mining company, states: “The Group’s normal policy is to sell its products at prevailing market prices and not to enter into price hedging arrangements.” Rio Tinto also avoids hedging of foreign exchange rates. Check out Rio Tinto’s website and financial reports. Do the company’s hedging policies make sense to you?

● ● ● ● ●

FINANCE ON THE WEB

 1.   The websites of the major commodities exchanges provide futures prices. Calculate and plot (as in Figure 26.2) the annualized net convenience yield for a commodity of your choice. (Note: You may need to use the futures price of a contract that is about to mature as your estimate of the current spot price.)

 2.   You can find swap rates for the U.S. dollar and the euro on www.ft.com. Plot the current swap curves as in Figure 26.3.

 3.   You can find spot and futures prices for a variety of equity indexes on www.wsj.com. Pick one and check whether it is fairly priced. You will need to do some detective work to find the dividend yield on the index and the interest rate.

MINI-CASE ● ● ● ● ●

Rensselaer Advisers

You are a vice president of Rensselaer Advisers (RA), a London-based asset manager, managing portfolios for institutional investors (primarily corporate pension plans) and wealthy individuals. In mid-2014 RA had about £1.1 billion under management, invested in a wide range of common-stock and fixed-income portfolios. Its management fees average 55 basis points (.55%), so RA’s total revenue for 2014 will be about .0055 × £1.1 billion = £6.05 million.

You are attempting to land a new client, Tintagel Mills, a conservative, long-established manufacturer of papermaking felt. Tintagel has established a defined-benefit pension plan for its employees. RA would manage the pension assets that Tintagel has set aside to cover defined-benefit obligations for retired employees.

Defined benefit means that an employer is committed to pay retirement income according to a formula. For example, annual retirement income could equal 40% of the employee’s average salary in the five years prior to retirement. In a defined-benefit plan, retirement income does not depend on the performance of the pension assets. If the assets in the fund are not sufficient to cover pension benefits, the company is required to contribute enough additional cash to cover the shortfall. Thus the PV of promised retirement benefits is a debt-equivalent obligation of the company.³³

Table 26.6 shows Tintagel’s obligations to its already retired employees from 2015 to 2033. Each of these employees receives a fixed dollar amount each month. Total payments decline as the employees die off. The PV of the obligations in Table 26.6 is about £89 million at the current (2014) 5% long-term interest rate. Table 26.6 also calculates the duration of the obligations at 7.87 years.

   TABLE 26.6 Tintagel Mills Pension Fund, projected benefits for retired employees.

Tintagel has set aside £90 million in pension assets to cover the obligations in Table 26.6, so this part of its pension plan is fully funded.³⁴ The pension assets are now invested in a diversified portfolio of common stocks, corporate bonds, and notes.

After reviewing Tintagel’s existing portfolio, you schedule a meeting with Hendrik van Wie, Tintagel’s CFO. Mr. van Wie stresses Tintagel’s conservative management philosophy and warns against “speculation.” He complains about the performance of the previous manager of the pension assets. He suggests that you propose a plan of investing in safe assets in a way that minimizes exposure to equity markets and changing interest rates. You promise to prepare an illustration of how this goal could be achieved.

Later you discover that RA has competition for Tintagel’s investment management business. SPX Associates is proposing a strategy of investing 70% of the portfolio (£63 million) in index funds tracking the UK stock market and 30% of the portfolio (£27 million) in UK government securities. SPX argues that their strategy is “safe in the long run,” because the UK stock market has delivered an average risk premium of about 7% per year. In addition, SPX argues that the growth in its stock market portfolio will far outstrip Tintagel’s pension obligations. SPX also claims that the £27 million invested in government bonds will provide ample protection against short-term stock market volatility. Finally, SPX proposes to charge an investment management fee of only 20 basis points (.20%). RA had planned to charge 30 basis points (.30%).

QUESTIONS

 1.  Prepare a memo for Mr. van Wie explaining how RA would invest to minimize both risk and exposure to changing interest rates. Give an example of a portfolio that would accomplish this objective. Explain how the portfolio would be managed as time passes and interest rates change. Also explain why SPX’s proposal is not advisable for a conservative company like Tintagel.

RA manages several fixed-income portfolios. For simplicity, you decide to propose a mix of the following three portfolios:

 •  A portfolio of long-term government bonds with an average duration of 14 years.

 •  A portfolio of medium-term governments with an average duration of 7 years.

 •  A portfolio of short-term bonds with an average duration of 1 year.

The term structure is flat, and the yield on all three portfolios is 5%.

 2.  Sorry, you lost. SPX won and implemented its proposed strategy. Now the recession of 2015 has knocked down UK stock prices by 20%. The value of the Tintagel portfolio, after paying benefits for 2015, has fallen from £90 million to £78 million. At the same time interest rates have dropped from 5% to 4% as the Bank of England relaxes monetary policy to combat the recession.

Mr. van Wie calls again, chastened by the SPX experience, and he invites a new proposal to invest the pension assets in a way that minimizes exposure to the stock market and changing interest rates. Update your memo with a new example of how to accomplish Mr. van Wie’s objectives. You can use the same portfolios and portfolio durations as in Question 1. You will have to recalculate the PV and duration of the pension benefits from 2016 onward. Assume a flat term structure with all interest rates at 4%. (Hint: Tintagel’s pension obligations are now underfunded. Nevertheless you can hedge interest rate risk if you increase the duration of the pension assets.)

___________

¹In game theory, “zero-sum” means that the payoffs to all players add up to zero, so that one player can win only at the others’ expense.

²The news was worst for the shareholders of Ashanti Goldfields, the huge Ghanaian mining company. Ashanti had gone to the opposite extreme and placed a bet that gold prices would fall. The 1999 price rise nearly drove Ashanti into bankruptcy.

³See Section 7-5 and also our discussion of diversifying mergers in Chapter 31. Note that diversification reduces overall risk, but not necessarily market risk.

⁴There may be other, special reasons not covered here. For example, governments are quick to tax profits, but may be slow to rebate taxes when there are losses. In the United States, losses can only be set against tax payments in the last two years. Any losses that cannot be offset in this way can be carried forward and used to shield future profits. Thus a firm with volatile income and more frequent losses has a higher effective tax rate. A firm can reduce the fluctuations in its income by hedging. For most firms this motive for risk reduction is not a big deal. See J. R. Graham and C. W. Smith, Jr., “Tax Incentives to Hedge,” Journal of Finance 54 (December 1999), pp. 2241–2262.

⁵Amateur speculation is doubly dangerous when the manager’s initial trades are losers. At that point the manager is already in deep trouble and has nothing more to lose by going for broke.

⁶International Swap Dealers Association (ISDA), “2009 Derivatives Usage Survey,” www.isda.org.

⁷See P. Tufano, “The Determinants of Stock Price Exposure: Financial Engineering and the Gold Mining Industry,” Journal of Finance 53 (June 1998), pp. 1014–1052; and G. D. Haushalter, “Financing Policy, Basis Risk and Corporate Hedging,” Journal of Finance 55 (February 2000), pp. 107–152.

⁸If the premium is paid at the beginning of the year and the claim is not settled until the end, then the zero-NPV premium equals the discounted value of the expected claim or $100,000/(1 + r).

⁹For a discussion of Cat bonds and other techniques to spread insurance risk, see N. A. Doherty, “Financial Innovation in the Management of Catastrophe Risk,” Journal of Applied Corporate Finance 10 (Fall 1997), pp. 84–95; and K. Froot, “The Market for Catastrophe Risk: A Clinical Examination,” Journal of Financial Economics 60 (2001), pp. 529–571.

¹⁰In the following three years, Mexico continued to hedge prices for a large portion of its output.

¹¹By the time you read this, the list of futures contracts will almost certainly be out of date, as thinly traded contracts are terminated and new contracts are introduced. The list of futures exchanges may also be out of date. There have been plenty of mergers in recent years. In July 2007 the CME and CBOT merged to form the CME Group. Also in 2007 the Intercontinental Exchange acquired the New York Board of Trade and, NYSE merged with Euronext, which owned the futures exchange, LIFFE. In August 2008 the CME Group acquired NYMEX Holdings, which operates the NYMEX and COMEX exchanges.

¹²Recall that the spot price is the price for immediate delivery. The futures contract also calls for immediate delivery when the contract ends in January. Therefore, the ending price of a futures or forward contract must converge to the spot price at the end of the contract.

¹³Some financial futures contracts prohibit delivery. All positions are closed out at the spot price at contract maturity.

¹⁴This formula is strictly true only for forward contracts that are not marked to market. Otherwise the value of the future depends on the path of interest rates over the life of the contract. In practice this qualification is usually not important, and the formula works for futures as well as forward contracts.

¹⁵We can derive our formula as follows. Let S6 be the value of the index after six months. Today S6 is unknown. You can invest S0 in the index today and get S6 + yS0 after six months. You can also buy the futures contract, put S0 in the bank, and use your bank balance to pay the futures price F6 in six months. In the latter strategy you get S6 – F6 + S0(1 + rf) after six months. Since the investment is the same, and you get S6 with either strategy, the payoffs must be the same:

Here we assume that rf and y are six-month rates. If they are monthly rates, the general formula is Ft = S0(1 + rf – y)t, where t is the number of months. If they are annual rates, the formula is Ft = S0(1 + rf – y)t/12.

¹⁶This formula could overstate the futures price if no one is willing to hold the commodity, that is, if inventories fall to zero or some absolute minimum.

¹⁷Critics and proponents of futures markets sometimes argue about whether the markets provide “price discovery.” That is, they argue about whether futures prices reveal traders’ forecasts of spot prices when the futures contract matures. If one of these fractious personalities comes your way, we suggest that you respond with a different question: Do futures prices reveal information about spot prices that is not already in today’s spot price? Our formulas reveal the answer to this question. There is useful information in futures prices, but it is information about convenience yields and storage costs, or about dividend or interest payments in the case of financial futures. Futures prices reveal information about spot prices only when a commodity is not stored or cannot be stored. Then the link between spot and futures prices is broken, and futures prices can assist with price discovery.

¹⁸Note that the party that profits from a rise in rates is described as the “buyer.” In our example you would be said to “buy three against nine months” money, meaning that the forward rate agreement is for a six-month loan in three months’ time.

¹⁹The interest rate is usually measured by LIBOR. LIBOR (London interbank offered rate) is the interest rate at which major international banks in London borrow dollars (or euros, yen, etc.) from each other.

²⁰These payments would be made when the loan matures nine months from now.

²¹Data on swaps are provided by the International Swaps and Derivatives Association (www.isda.org) and the Bank for International Settlements (www.bis.org).

²²The spread between the bank’s 6% borrowing rate and the 8% lending rate is the bank’s profit on the project financing.

²³Maybe the short-term interest rate is below the five-year interest rate because investors expect interest rates to rise.

²⁴Both strategies are equivalent to a series of forward contracts on LIBOR. The forward prices are $4 million each for LIBOR1 × $66.67, LIBOR2 × $66.67, and so on. Separately negotiated forward prices would not be $4 million for any one year, but the PVs of the “annuities” of forward prices would be identical.

²⁵Notice that the swap rate always refers to the interest rate on the fixed leg of the swap. Rates are generally quoted against LIBOR, though dealers will also be prepared to quote rates against other short-term debt.

²⁶More commonly, interest rate swaps are based on three-month LIBOR and involve quarterly cash payments.

²⁷Usually in a currency swap the two parties make an initial payment to each other (i.e., Possum pays the bank $10 million and receives €8 million). However, this is not necessary and Possum might prefer to buy the €8 million from another bank.

²⁸The principal of the zero-coupon note is $34.75 million. The PV of this promised payment is 34.75/(1.10)7.5 = $17 million.

²⁹The slope equals (minus) modified duration, defined as –D/(1 + y), where D = duration and y = the current interest rate. If durations are equal, modified durations must also be equal.

³⁰Duration is not a complete measure of interest rate risk. It measures only exposure to the level of interest rates, not to changes in the shape of the term structure. Duration in effect assumes that the term structure is “flat.” Duration is widely used, however, because it is a good first approximation to interest rate risk exposure.

³¹Bank of International Settlements, Derivatives Statistics (www.bis.org/statistics/derstats.htm).

³²This does not mean that firms don’t worry about the possibility of default, and there are a variety of ways that they try to protect themselves. In the case of swaps, firms are reluctant to deal with banks that do not have the highest credit rating.

³³In defined contribution plans, the corporation contributes to the pension fund on behalf of its employees. Each employee has a claim on part of the fund, just as if the employee held shares in a mutual fund. Employees’ retirement benefits depend on their balances in the fund at retirement. If the benefits fall short of an employee’s plans or expectations, he or she has no recourse to the company.

³⁴Tintagel must also set pension assets aside for current employees. For this mini-case, we concentrate only on retired employees’ benefits.

Part 8 Risk Management

Managing International Risks

The last chapter grappled with risks from changing interest rates and volatile commodity prices. Corporations that operate internationally face still more hazards from currency fluctuations and political risks.

To understand currency risk, you first have to understand how the foreign exchange market works and how currency exchange rates are determined. We cover those topics first, with special emphasis on the linkages between exchange rates and cross-country differences in interest rates and inflation. Then we describe how corporations assess and hedge their currency exposures.

We also review international capital investment decisions. Cash flows for an investment project in Germany, say, must be forecasted in euros, with attention to German inflation rates and taxes. But euro cash flows require a euro discount rate. How should that rate be estimated? Should it depend on whether the investing company is located in the U.S., Germany, or another country? Should the discount rate be adjusted for the risk that the euro may fall relative to other currencies? (The answer to the last question is no. The answers to the preceding questions are not so clear-cut.)

We conclude the chapter with a discussion of political risk. Political risk means possible adverse acts by a hostile foreign government, for example, discriminatory taxes or limits on the profits that can be taken out of the country. Sometimes governments expropriate businesses with minimal compensation. We explain how companies structure their operations and financing to reduce their exposure to political risks.

 27-1   The Foreign Exchange Market

A Mexican company that imports goods from France may need to buy euros to pay for the purchase. A Mexican company exporting to France may receive euros, which it sells in exchange for pesos. Both firms make use of the foreign exchange market.

The foreign exchange market has no central marketplace. Business is conducted electronically. The principal dealers are the larger commercial banks and investment banks. A corporation that wants to buy or sell currency usually does so through a commercial bank. Turnover in the foreign exchange market is huge. In London in 2010 $1,854 billion of currency changed hands each day. That is equivalent to an annual turnover of about $460 trillion ($460,000,000,000,000). New York and Tokyo together accounted for a further $1,216 billion of turnover per day.¹

   TABLE 27.1 Spot and forward exchange rates, January 27, 2012.

aRates show the number of units of foreign currency per U.S. dollar, except for the euro and the UK pound, which show the number of U.S. dollars per unit of foreign currency.

Table 27.1 shows a sample of exchange rates in January 2012. Exchange rates are generally expressed in terms of the number of units of the foreign currency needed to buy one U.S. dollar (USD). This is termed an indirect quote. In the first column of Table 27.1, the indirect quote for the Brazilian real shows that you could buy 1.7456 reals for $1. This is often written as BRL1.7456/USD1.

A direct exchange rate quote states how many dollars you can buy for one unit of foreign currency. The euro and the British pound sterling are usually shown as direct quotes.² For example, Table 27.1 shows that GBP1 is equivalent to USD1.5667 or, more concisely, USD1.5667/GBP1. If £1 buys $1.5667, then $1 must buy 1/1.5667 = GBP.6383. Thus the indirect quote for the pound is GBP.6383/USD1.³

The exchange rates in the second column of Table 27.1 are the prices of currency for immediate delivery. These are known as spot rates of exchange. The spot rate for the real is BRL1.7456/USD1, and the spot rate for the pound is USD1.5667/GBP1.

In addition to the spot exchange market, there is a forward market. In the forward market you buy and sell currency for future delivery. If you know that you are going to pay out or receive foreign currency at some future date, you can insure yourself against loss by buying or selling forward. Thus, if you need one million reals in three months, you can enter into a three-month forward contract. The forward exchange rate on this contract is the price you agree to pay in three months when the one million reals are delivered. If you look again at Table 27.1, you will see that the three-month forward rate for the real is quoted at BRL1.7781/USD1. If you buy reals for three months’ delivery, you get more reals for your dollar than if you buy them spot. In this case the real is said to trade at a forward discount relative to the dollar, because forward reals are cheaper than spot ones. Expressed as an annual rate, the forward discount is⁴

You could also say that the dollar was selling at a forward premium.

A forward purchase or sale is a made-to-measure transaction between you and the bank. It can be for any currency, any amount, and any delivery day. You could buy, say, 99,999 Vietnamese dong or Haitian gourdes for a year and a day forward as long as you can find a bank ready to deal. Most forward transactions are for six months or less, but the long-term currency swaps that we described in Chapter 26 are equivalent to a bundle of forward transactions. When firms want to enter into long-term forward contracts, they usually do so through a currency swap.⁵

There is also an organized market for currency for future delivery known as the currency futures market. Futures contracts are highly standardized; they are for specified amounts and for a limited choice of delivery dates.⁶

When you buy a forward or futures contract, you are committed to taking delivery of the currency. As an alternative, you can take out an option to buy or sell currency in the future at a price that is fixed today. Made-to-measure currency options can be bought from the major banks, and standardized options are traded on the options exchanges.

 27-2   Some Basic Relationships

You can’t develop a consistent international financial policy until you understand the reasons for the differences in exchange rates and interest rates. We consider the following four problems:

•  Problem 1. Why is the dollar rate of interest different from, say, the rate on Ruritanian pesos (RUPs)?

•  Problem 2. Why is the forward rate of exchange for the peso different from the spot rate?

•  Problem 3. What determines next year’s expected spot rate of exchange between dollars and pesos?

•  Problem 4. What is the relationship between the inflation rate in the United States and the inflation rate in Ruritania?

Suppose that individuals were not worried about risk and that there were no barriers or costs to international trade on capital flows. In that case the spot exchange rates, forward exchange rates, interest rates, and inflation rates would stand in the following simple relationship to one another:

Why should this be so?

Interest Rates and Exchange Rates

Suppose that you have $1,000 to invest for one year. U.S. dollar deposits are offering an interest rate of 5%; Ruritanian peso deposits are offering (an attractive?) 15.5%. Where should you put your money? Does the answer sound obvious? Let’s check:

 •  Dollar loan. The rate of interest on one-year dollar deposits is 5%. Therefore at the end of the year you get 1,000 × 1.05 = USD1,050.

 •  Peso loan. The current exchange rate is RUP50/USD1. Therefore, for $1,000, you can buy 1,000 × 50 = RUP50,000. The rate of interest on a one-year peso deposit is 15.5%. Therefore at the end of the year you get 50,000 × 1.155 = RUP57,750. Of course, you don’t know what the exchange rate is going to be in one year’s time. But that doesn’t matter. You can fix today the price at which you sell your pesos. The one-year forward rate is RUP55/USD1. Therefore, by selling forward, you can make sure that you will receive 57,750/55 = $1,050 at the end of the year.

Thus, the two investments offer almost exactly the same rate of return. They have to—they are both risk-free. If the domestic interest rate were different from the covered foreign rate, you would have a money machine.

When you make the peso loan, you receive a higher interest rate. But you get an offsetting loss because you sell pesos forward at a lower price than you pay for them today. The interest rate differential is

And the differential between the forward and spot exchange rates is

Interest rate parity theory says that the difference in interest rates must equal the difference between the forward and spot exchange rates:

In our example,

The Forward Premium and Changes in Spot Rates

Now let’s consider how the forward premium is related to changes in spot rates of exchange. If people didn’t care about risk, the forward rate of exchange would depend solely on what people expected the spot rate to be. For example, if the one-year forward rate on pesos is RUP55/USD1, that could only be because traders expect the spot rate in one year’s time to be RUP55/USD1. If they expected it to be, say, RUP60/USD1, nobody would be willing to buy pesos forward. They could get more pesos for their dollar by waiting and buying spot.

Therefore the expectations theory of exchange rates tells us that the percentage difference between the forward rate and today’s spot rate is equal to the expected change in the spot rate:

Of course, this assumes that traders don’t care about risk. If they do care, the forward rate can be either higher or lower than the expected spot rate. For example, suppose that you have contracted to receive one million pesos in three months. You can wait until you receive the money before you change it into dollars, but this leaves you open to the risk that the price of the peso may fall over the next three months. Your alternative is to sell the peso forward. In this case, you are fixing today the price at which you will sell your pesos. Since you avoid risk by selling forward, you may be willing to do so even if the forward price of pesos is a little lower than the expected spot price.

Other companies may be in the opposite position. They may have contracted to pay out pesos in three months. They can wait until the end of the three months and then buy pesos, but this leaves them open to the risk that the price of the peso may rise. It is safer for these companies to fix the price today by buying pesos forward. These companies may, therefore, be willing to buy forward even if the forward price of the peso is a little higher than the expected spot price.

Thus some companies find it safer to sell the peso forward, while others find it safer to buy the peso forward. When the first group predominates, the forward price of pesos is likely to be less than the expected spot price. When the second group predominates, the forward price is likely to be greater than the expected spot price. On average you would expect the forward price to underestimate the expected spot price just about as often as it overestimates it.

Changes in the Exchange Rate and Inflation Rates

Now we come to the third side of our quadrilateral—the relationship between changes in the spot exchange rate and inflation rates. Suppose that you notice that silver can be bought in Ruritania for 1,000 pesos a troy ounce and sold in the United States for $30.00. You think you may be on to a good thing. You take $20,000 and exchange it for $20,000 × RUP50/USD1 = 1,000,000 pesos. That’s enough to buy 1,000 ounces of silver. You put this silver on the first plane to the United States, where you sell it for $30,000. You have made a gross profit of $10,000. Of course, you have to pay transportation and insurance costs out of this, but there should still be something left over for you.

Money machines don’t exist—not for long, anyway. As others notice the disparity between the price of silver in Ruritania and the price in the United States, the price will be forced up in Ruritania and down in the United States until the profit opportunity disappears. Arbitrage ensures that the dollar price of silver is about the same in the two countries. Of course, silver is a standard and easily transportable commodity, but the same forces should act to equalize the domestic and foreign prices of other goods. Those goods that can be bought more cheaply abroad will be imported, and that will force down the price of domestic products. Similarly, those goods that can be bought more cheaply in the United States will be exported, and that will force down the price of the foreign products.

This is often called purchasing power parity.⁷ Just as the price of goods in Walmart stores must be roughly the same as the price of goods in Target, so the price of goods in Ruritania when converted into dollars must be roughly the same as the price in the United States:

Purchasing power parity implies that any differences in the rates of inflation will be offset by a change in the exchange rate. For example, if prices are rising by 1.0% in the United States and by 11.1% in Ruritania, the number of pesos that you can buy for $1 must rise by 1.111/1.01 – 1, or 10%. Therefore purchasing power parity says that to estimate changes in the spot rate of exchange, you need to estimate differences in inflation rates:⁸

In our example,

Interest Rates and Inflation Rates

Now for the fourth leg! Just as water always flows downhill, so capital tends to flow where returns are greatest. But investors are not interested in nominal returns; they care about what their money will buy. So, if investors notice that real interest rates are higher in Ruritania than in the United States, they will shift their savings into Ruritania until the expected real returns are the same in the two countries. If the expected real interest rates are equal, then the difference in nominal interest rates must be equal to the difference in the expected inflation rates:⁹

In Ruritania the real one-year interest rate is 4%:

In the United States it is also 4%:

Is Life Really That Simple?

We have described above four theories that link interest rates, forward rates, spot exchange rates, and inflation rates. Of course, such simple economic theories are not going to provide an exact description of reality. We need to know how well they predict actual behavior. Let’s check.

1. Interest Rate Parity Theory Interest rate parity theory says that the peso rate of interest covered for exchange risk should be the same as the dollar rate. As long as money can be moved easily between deposits in different currencies, interest rate parity almost always holds. In fact, dealers set the forward price of pesos by looking at the difference between the interest rates on deposits of dollars and pesos.

2. The Expectations Theory of Forward Rates How well does the expectations theory explain the level of forward rates? Scholars who have studied exchange rates have found that forward rates typically exaggerate the likely change in the spot rate. When the forward rate appears to predict a sharp rise in the spot rate (a forward premium), the forward rate tends to overestimate the rise in the spot rate. Conversely, when the forward rate appears to predict a fall in the currency (a forward discount), it tends to overestimate this fall.¹⁰

   FIGURE 27.1 Percentage error from using the one-year forward rate for UK pounds to forecast next year’s spot rate. Note that the forward rate overestimates and underestimates the spot rate with about equal frequency.

This finding is not consistent with the expectations theory. Instead it looks as if sometimes companies are prepared to give up return to buy forward currency and other times they are prepared to give up return to sell forward currency. In other words, forward rates seem to contain a risk premium, but the sign of this premium swings backward and forward.¹¹ You can see this from Figure 27.1. Almost half the time the forward rate for the UK pound overstates the likely future spot rate and half the time it understates the likely spot rate. On average the forward rate and future spot rate are almost identical. This is important news for the financial manager; it means that a company that always uses the forward market to protect against exchange rate movements does not pay any extra for this insurance.

That’s the good news. The bad news is that the forward rate is a fairly awful forecaster of the spot rate. For example, the large error in 1985 reflects the total failure of the forward rate to anticipate the 34% rise in the value of sterling.

3. Purchasing Power Parity Theory What about the third side of our quadrilateral—purchasing power parity theory? No one who has compared prices in foreign stores with prices at home really believes that prices are the same throughout the world. Look, for example, at Table 27.2, which shows the price of a Big Mac in different countries. Notice that at current rates of exchange a Big Mac costs $8.31 in Norway but only $4.07 in the United States. To equalize prices in the two countries, the number of Norwegian krone that you could buy for your dollar would need to increase by 8.31/4.07–1 = 1.04, or 104%.

This suggests a possible way to make a quick buck. Why don’t you buy a hamburger to-go in (say) India for the equivalent of $1.89 and take it for resale in Norway, where the price in dollars is $8.31? The answer, of course, is that the gain would not cover the costs. The same good can be sold for different prices in different countries because transportation is costly and inconvenient.¹²

On the other hand, there is clearly some relationship between inflation and changes in exchange rates. For example, in the five years leading up to 2011 prices in Ukraine rose by 86%. Or, to put it another way, you could say that the purchasing power of money in Ukraine declined by almost half. If exchange rates had not adjusted, Ukrainian exporters would have found it impossible to sell their goods. But, of course, exchange rates did adjust. In fact, the value of the Ukrainian hryvnia fell by a third relative to the U.S. dollar.

   TABLE 27.2 Price of Big Mac hamburgers in different countries.

Source: “Currency Comparisons, To Go” © The Economist Newspaper Limited, London (July 28, 2011). Used with permission via Copyright Clearance Center.

In Figure 27.2 we have plotted the relative change in purchasing power for a sample of countries against the change in the exchange rate. Ukraine is tucked in the bottom left-hand corner; Japan is at the top right. You can see that although the relationship is far from exact, large differences in inflation rates are generally accompanied by an offsetting change in the exchange rate.¹³

Strictly speaking, purchasing power parity theory implies that the differential inflation rate is always identical to the change in the spot rate. But we don’t need to go as far as that. We should be content if the expected difference in the inflation rates equals the expected change in the spot rate. That’s all we wrote on the third side of our quadrilateral. Look, for example, at Figure 27.3. The blue line in the first plot shows that in 2011 £1 sterling bought only 32% of the dollars that it did at the start of the twentieth century. But this decline in the value of sterling was largely matched by the higher inflation rate in the UK. The red line shows that the inflation-adjusted, or real, exchange rate ended the century at roughly the same level as it began.¹⁴ The second and third plots show the experiences of France and Italy, respectively. The fall in nominal exchange rates for both countries is much greater. Adjusting for changes in currency units, the equivalent of one French franc in 2011 bought about 1% of the dollars that it did at the start of 1900. The equivalent of one Italian lira bought about .4% of the number of dollars. In both cases the real exchange rates in 2011 are not much different from those at the beginning of the twentieth century. Of course, real exchange rates do change, sometimes quite sharply. For example, the real value of sterling fell by nearly 30% in 2008. However, if you were a financial manager called on to make a long-term forecast of the exchange rate, you could not have done much better than to assume that changes in the value of the currency would offset the difference in inflation rates.

   FIGURE 27.2 A decline in the exchange rate and a decline in a currency’s purchasing power tend to go hand in hand. In this diagram each of the 66 points represents the experience of a different country in the five years to 2011. The vertical axis shows the change in the value of the foreign currency relative to the average. The horizontal axis shows the change in the purchasing power relative to the average. The point in the lower left is Ukraine; the point at the top right is Japan.

   FIGURE 27.3 Nominal versus real exchange rates in the UK, France, and Italy. December 1899 = 1. (Values are shown on log scale.)

Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimist: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002). Reprinted by permission of Princeton University Press, with updates provided by the authors.

4. Equal Real Interest Rates Finally we come to the relationship between interest rates in different countries. Do we have a single world capital market with the same real rate of interest in all countries? Does the difference in money interest rates equal the difference in the expected inflation rates?

This is not an easy question to answer since we cannot observe expected inflation. However, in Figure 27.4 we have plotted the average interest rate in each of 59 countries against the inflation that subsequently occurred. Japan is tucked into the bottom-left corner of the chart, while Ukraine is represented by the dot in the top-right corner. You can see that, in general, the countries with the highest interest rates also had the highest inflation rates. There were much smaller differences between the real rates of interest than between the nominal (or money) rates.

   FIGURE 27.4 Countries with the highest interest rates generally have the highest inflation. In this diagram each of the 59 points represents the experience of a different country.

Source: Global Insight, WRDS (Wharton Research Data Services), http://wrds.wharton.upenn.edu

 27-3    Hedging Currency Risk

Sharp exchange rate movements can make a large dent in corporate profits. To illustrate how companies cope with this problem, we look at a typical company in the United States, Outland Steel, and walk through its foreign exchange operations.

EXAMPLE 27.1 • Outland Steel

Outland Steel has a small but profitable export business. Contracts involve substantial delays in payment, but since the company has a policy of always invoicing in dollars, it is fully protected against changes in exchange rates. Recently the export department has become unhappy with this practice and believes that it is causing the company to lose valuable export orders to firms that are willing to quote in the customer’s own currency.

You sympathize with these arguments, but you are worried about how the firm should price long-term export contracts when payment is to be made in foreign currency. If the value of that currency declines before payment is made, the company may suffer a large loss. You want to take the currency risk into account, but you also want to give the sales force as much freedom of action as possible.

Notice that Outland can insure against its currency risk by selling the foreign currency forward. This means that it can separate the problem of negotiating sales contracts from that of managing the company’s foreign exchange exposure. The sales force can allow for currency risk by pricing on the basis of the forward exchange rate. And you, as financial manager, can decide whether the company ought to hedge.

What is the cost of hedging? You sometimes hear managers say that it is equal to the difference between the forward rate and today’s spot rate. That is wrong. If Outland does not hedge, it will receive the spot rate at the time that the customer pays for the steel. Therefore, the cost of insurance is the difference between the forward rate and the expected spot rate when payment is received.

Insure or speculate? We generally vote for insurance. First, it makes life simpler for the firm and allows it to concentrate on its main business. Second, it does not cost much. (In fact, the cost is zero on average if the forward rate equals the expected spot rate, as the expectations theory of forward rates implies.) Third, the foreign currency market seems reasonably efficient, at least for the major currencies. Speculation should be a zero-NPV game, unless financial managers have information that is not available to the pros who make the market.

Is there any other way that Outland can protect itself against exchange loss? Of course. It can borrow foreign currency against its foreign receivables, sell the currency spot, and invest the proceeds in the United States. Interest rate parity theory tells us that in free markets the difference between selling forward and selling spot should be equal to the difference between the interest that you have to pay overseas and the interest that you can earn at home.

Our discussion of Outland’s export business illustrates four practical implications of our simple theories about forward exchange rates. First, you can use forward rates to adjust for exchange risk in contract pricing. Second, the expectations theory suggests that protection against exchange risk is usually worth having. Third, interest rate parity theory reminds us that you can hedge either by selling forward or by borrowing foreign currency and selling spot. Fourth, the cost of forward cover is not the difference between the forward rate and today’s spot rate; it is the difference between the forward rate and the expected spot rate when the forward contract matures.

Perhaps we should add a fifth implication. You don’t make money simply by buying currencies that go up in value and selling those that go down. For example, suppose that you buy Narnian leos and sell them after a year for 2% more than you paid for them. Should you give yourself a pat on the back? That depends on the interest that you have earned on your leos. If the interest rate on leos is 2 percentage points less than the interest rate on dollars, the profit on the currency is exactly canceled out by the reduction in interest income. Thus you make money from currency speculation only if you can predict whether the exchange rate will change by more or less than the interest rate differential. In other words, you must be able to predict whether the exchange rate will change by more or less than the forward premium or discount.

Transaction Exposure and Economic Exposure

The exchange risk from Outland Steel’s export business is due to delays in foreign currency payments and is therefore referred to as transaction exposure. Transaction exposure can be easily identified and hedged. Since a 1% fall in the value of the foreign currency results in a 1% fall in Outland’s dollar receipts, for every euro or yen that Outland is owed by its customers, it needs to sell forward one euro or one yen.¹⁵

BEYOND THE PAGE

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Operational hedging by auto producers

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However, Outland may still be affected by currency fluctuations even if its customers do not owe it a cent. For example, Outland may be in competition with Swedish steel producers. If the value of the Swedish krona falls, Outland will need to cut its prices in order to compete.¹⁶ Outland can protect itself against such an eventuality by selling the krona forward. In this case the loss on Outland’s steel business will be offset by the profit on its forward sale.

Notice that Outland’s exposure to the krona is not limited to specific transactions that have already been entered into. Financial managers often refer to this broader type of exposure as economic exposure.¹⁷ Economic exposure is less easy to measure than transaction exposure. For example, it is clear that the value of Outland Steel is positively related to the value of the krona, so to hedge its position it needs to sell kronor forward. But in practice it may be hard to say exactly how many kronor Outland needs to sell.

Large Swiss companies, such as Nestlé or the Swatch Group, sell their products around the world. Therefore, like Outland Steel, they need to manage their economic exposure. One solution is to undertake operational hedging by balancing production closely with sales. Look, for example, at Table 27.3, which summarizes the overseas sales and costs for a sample of well-known Swiss companies. Notice that Nestlé’s sales and costs are almost perfectly matched. It is, therefore, relatively immune to fluctuations in the exchange rate. By contrast, in the case of Swatch and Roche a substantial proportion of production costs arise in Switzerland, and therefore both companies are exposed to an appreciation of the Swiss franc.

   TABLE 27.3 The proportion of sales and costs for major Swiss companies that derive from particular currency areas.

Source: Hottinger Capital Corporation.

In addition to operational hedging, companies can also control exchange rate risk by using financial hedges. They do this by borrowing in foreign currencies, selling currency forward, or using foreign currency derivatives such as swaps and options. For example, in 2011 Swatch used forwards primarily to reduce its exposure to the euro and dollar. At the end of the year these forward contracts totalled 555 million Swiss francs.

 27-4    Exchange Risk and International Investment Decisions

Suppose that the Swiss pharmaceutical company, Roche, is evaluating a proposal to build a new plant in the United States. To calculate the project’s net present value, Roche forecasts the following dollar cash flows from the project:

These cash flows are stated in dollars. So to calculate their net present value Roche discounts them at the dollar cost of capital. (Remember dollars need to be discounted at a dollar rate, not the Swiss franc rate.) Suppose this cost of capital is 12%. Then

To convert this net present value to Swiss francs, the manager can simply multiply the dollar NPV by the spot rate of exchange. For example, if the spot rate is SFr1.2/$, then the NPV in Swiss francs is

Notice one very important feature of this calculation. Roche does not need to forecast whether the dollar is likely to strengthen or weaken against the Swiss franc. No currency forecast is needed, because the company can hedge its foreign exchange exposure. In that case, the decision to accept or reject the pharmaceutical project in the United States is totally separate from the decision to bet on the outlook for the dollar. For example, it would be foolish for Roche to accept a poor project in the United States just because management is optimistic about the outlook for the dollar; if Roche wishes to speculate in this way it can simply buy dollars forward. Equally, it would be foolish for Roche to reject a good project just because management is pessimistic about the dollar. The company would do much better to go ahead with the project and sell dollars forward. In that way, it would get the best of both worlds.¹⁸

When Roche ignores currency risk and discounts the dollar cash flows at a dollar cost of capital, it is implicitly assuming that the currency risk is hedged. Let us check this by calculating the number of Swiss francs that Roche would receive if it hedged the currency risk by selling forward each future dollar cash flow.

We need first to calculate the forward rate of exchange between dollars and francs. This depends on the interest rates in the United States and Switzerland. For example, suppose that the dollar interest rate is 6% and the Swiss franc interest rate is 4%. Then interest rate parity theory tells us that the one-year forward exchange rate is

Similarly, the two-year forward rate is

So, if Roche hedges its cash flows against exchange rate risk, the number of Swiss francs it will receive in each year is equal to the dollar cash flow times the forward rate of exchange:

These cash flows are in Swiss francs and therefore they need to be discounted at the risk-adjusted Swiss franc discount rate. Since the Swiss rate of interest is lower than the dollar rate, the risk-adjusted discount rate must also be correspondingly lower. The formula for converting from the required dollar return to the required Swiss franc return is¹⁹

In our example,

Thus the risk-adjusted discount rate in dollars is 12%, but the discount rate in Swiss francs is only 9.9%.

All that remains is to discount the Swiss franc cash flows at the 9.9% risk-adjusted discount rate:

Everything checks. We obtain exactly the same net present value by (a) ignoring currency risk and discounting Roche’s dollar cash flows at the dollar cost of capital and (b) calculating the cash flows in francs on the assumption that Roche hedges the currency risk and then discounting these Swiss franc cash flows at the franc cost of capital.

To repeat: When deciding whether to invest overseas, separate out the investment decision from the decision to take on currency risk. This means that your views about future exchange rates should NOT enter into the investment decision. The simplest way to calculate the NPV of an overseas investment is to forecast the cash flows in the foreign currency and discount them at the foreign currency cost of capital. The alternative is to calculate the cash flows that you would receive if you hedged the foreign currency risk. In this case you need to translate the foreign currency cash flows into your own currency using the forward exchange rate and then discount these domestic currency cash flows at the domestic cost of capital. If the two methods don’t give the same answer, you have made a mistake.

When Roche analyzes the proposal to build a plant in the United States, it is able to ignore the outlook for the dollar only because it is free to hedge the currency risk. Because investment in a pharmaceutical plant does not come packaged with an investment in the dollar, the opportunity for firms to hedge allows for better investment decisions.

The Cost of Capital for International Investments

Roche should discount dollar cash flows at a dollar cost of capital. But how should a Swiss company like Roche calculate a cost of capital in dollars for an investment in the U.S.? There is no simple, consensus procedure for answering this question, but we suggest the following procedure as a start.

First you need to decide on the risk of a U.S. pharmaceutical investment to a Swiss investor. You could look at the betas of a sample of U.S. pharmaceutical companies relative to the Swiss market index.

Why measure betas relative to the Swiss index, while a U.S. counterpart such as Merck would measure betas relative to the U.S. index? The answer lies in Section 7-4, where we explained that risk cannot be considered in isolation; it depends on the other securities in the investor’s portfolio. Beta measures risk relative to the investor’s portfolio. If U.S. investors already hold the U.S. market, an additional dollar invested at home is just more of the same. But if Swiss investors hold the Swiss market, an investment in the U.S. can reduce their risk because the Swiss and U.S. markets are not perfectly correlated. That explains why an investment in the U.S. can be lower risk for Roche’s shareholders than for Merck’s shareholders. It also explains why Roche’s shareholders may be willing to accept a relatively low expected return from a U.S. investment.²⁰

Suppose that you decide that the investment’s beta relative to the Swiss market is .8 and that the market risk premium in Switzerland is 7.4%. Then the required return on the project can be estimated as

This is the project’s cost of capital measured in Swiss francs. We used it above to discount the expected Swiss franc cash flows if Roche hedged the project against currency risk. We cannot use it to discount the dollar cash flows from the project.

To discount the expected dollar cash flows, we need to convert the Swiss franc cost of capital to a dollar cost of capital. This means running our earlier calculation in reverse:

In our example,

We used this 12% dollar cost of capital to discount the forecasted dollar cash flows from the project.

When a company measures risk relative to its domestic market as in our example, its managers are implicitly assuming that shareholders hold simply domestic stocks. That is not a bad approximation, particularly in the U.S. Although U.S. investors can reduce their risk by holding an internationally diversified portfolio of shares, they generally invest only a small proportion of their money overseas. Why they are so shy is a puzzle. It looks as if they are worried about the costs of investing overseas, such as the extra costs involved in identifying which stocks to buy, or the possibility of unfair treatment by foreign companies or governments.

The world is getting smaller and “flatter,” however, and investors everywhere are increasing their holdings of foreign securities. Pension funds and other institutional investors have diversified internationally, and dozens of mutual funds have been set up for people who want to invest abroad. If investors throughout the world held the world portfolio, then costs of capital would converge. The cost of capital would still depend on the risk of the investment, but not on the domicile of the investing company. There is some evidence that for large U.S. firms it does not make much difference whether a U.S. or global beta is used. For smaller countries the evidence is not so clear-cut and sometimes a global beta may be more appropriate.²¹

Do Some Countries Have a Lower Cost of Capital?

Some countries enjoy much lower interest rates than others. For example, in early 2012 short-term interest rates were less than 1% in Switzerland, Japan, and the United States. In Australia they were 3.7% and in Brazil they were 12.5%. People often conclude from this kind of comparison that the low-interest-rate countries enjoy a lower cost of capital.

This view is one part confusion and one part probable truth. The confusion arises because the interest rate is measured in different currencies. You would not say that a 10-inch-high rabbit is taller than a 9-foot elephant. In the same way it makes no sense to compare an interest payment in yen, say, with an interest payment in Australian dollars.

   FIGURE 27.5 Real interest rates on 10-year indexed bonds issued by governments with good credit ratings, April 2012.

But suppose that you measure the interest rate in real terms. Then you are comparing like with like, and it does make sense to ask whether the real cost of capital differs. In Chapter 3 we saw that some governments have issued indexed bonds that promise a fixed real rate of interest. Figure 27.5 shows the real yields to maturity on 10-year indexed bonds in seven countries. We have picked countries that all have credit ratings of AA or better. You can see that real interest rates do seem to diverge, though not as sharply as nominal rates.²² When real rates differ, investors may see a profit opportunity. For example, in 2012, many financial institutions made so-called carry trades; they borrowed heavily in Japan and the United States, and then used the cash to buy bonds in Australia and other high-interest-rate countries.

 27-5    Political Risk

So far we have focused on the management of exchange rate risk, but managers also worry about political risk. By this they mean the threat that a government will change the rules of the game—that is, break a promise or understanding—after the investment is made. Of course political risks are not confined to overseas investments. Businesses in every country are exposed to the risk of unanticipated actions by governments or the courts. But in some parts of the world foreign companies are particularly vulnerable.

A number of consultancy services offer analyses of political and economic risks and draw up country rankings.²³ For example, Table 27.4 is an extract from the 2011 political risk rankings provided by the PRS Group. You can see that each country is scored on 12 separate dimensions. Finland comes top of the class overall, while Somalia languishes at the bottom.

Some managers dismiss political risk as an act of God, like a hurricane or earthquake. But the most successful multinational companies structure their business to reduce political risk. Foreign governments are not likely to expropriate a local business if it cannot operate without the support of its parent. For example, the foreign subsidiaries of American computer manufacturers or pharmaceutical companies would have relatively little value if they were cut off from the know-how of their parents. Such operations are much less likely to be expropriated than, say, a mining operation that can be operated as a stand-alone venture.

We are not recommending that you turn your silver mine into a pharmaceutical company, but you may be able to plan your overseas manufacturing operations to improve your bargaining position with foreign governments. For example, Ford has integrated its overseas operations so that the manufacture of components, subassemblies, and complete automobiles is spread across plants in a number of countries. None of these plants would have much value on its own, and Ford can switch production between plants if the political climate in one country deteriorates.

   TABLE 27.4 Political risk scores for a sample of countries, January 2011.

Key:

A Government stability

B Socioeconomic conditions

C Investment profile

D Internal conflict

E External conflict

F Corruption

G Military in politics

H Religious tensions

I Law and order

J Ethnic tensions

K Democratic accountability

L Bureaucracy quality

Source: International Country Risk Guide, a publication of The PRS Group, Inc. (www.prsgroup.com), 2012.

Multinational corporations have also devised financing arrangements to help keep foreign governments honest. For example, suppose your firm is contemplating an investment of $500 million to reopen the San Tomé silver mine in Costaguana with modern machinery, smelting equipment, and shipping facilities.²⁴ The Costaguanan government agrees to invest in roads and other infrastructure and to take 20% of the silver produced by the mine in lieu of taxes. The agreement is to run for 25 years.

The project’s NPV on these assumptions is quite attractive. But what happens if a new government comes into power five years from now and imposes a 50% tax on “any precious metals exported from the Republic of Costaguana”? Or changes the government’s share of output from 20% to 50%? Or simply takes over the mine “with fair compensation to be determined in due course by the Minister of Natural Resources of the Republic of Costaguana”?

No contract can absolutely restrain sovereign power. But you can arrange project financing to make these acts as painful as possible for the foreign government. For example, you might set up the mine as a subsidiary corporation, which then borrows a large fraction of the required investment from a consortium of major international banks. If your firm guarantees the loan, make sure the guarantee stands only if the Costaguanan government honors its contract. The government will be reluctant to break the contract if that causes a default on the loans and undercuts the country’s credit standing with the international banking system.

If possible, you should arrange for the World Bank (or one of its affiliates) to finance part of the project or to guarantee your loans against political risk.²⁵ Few governments have the guts to take on the World Bank. Here is another variation on the same theme. Arrange to borrow, say, $450 million through the Costaguanan Development Agency. In other words, the development agency borrows in international capital markets and relends to the San Tomé mine. Your firm agrees to stand behind the loan as long as the government keeps its promises. If it does keep them, the loan is your liability. If not, the loan is its liability.

Political risk is not confined to the risk of expropriation. Multinational companies are always exposed to the criticism that they siphon funds out of countries in which they do business, and, therefore, governments are tempted to limit their freedom to repatriate profits. This is most likely to happen when there is considerable uncertainty about the rate of exchange, which is usually when you would most like to get your money out. Here again a little forethought can help. For example, there are often more onerous restrictions on the payment of dividends to the parent than on the payment of interest or principal on debt. Royalty payments and management fees are less sensitive than dividends, particularly if they are levied equally on all foreign operations. A company can also, within limits, alter the price of goods that are bought or sold within the group, and it can require more or less prompt payment for such goods.

Calculating NPVs for investment projects becomes exceptionally difficult when political risks are significant. You have to estimate cash flows and project life with extra caution. You may want to take a peek at the discounted payback period (see Chapter 5), on the theory that quick-payback projects are less exposed to political risks. But do not try to compensate for political risks by adding casual fudge factors to discount rates. Fudge factors spawn bias and confusion, as we explained in Chapter 9.

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SUMMARY

The international financial manager has to cope with different currencies, interest rates, and inflation rates. To produce order out of chaos, the manager needs some model of how they are related. We described four very simple but useful theories.

Interest rate parity theory states that the interest differential between two countries must be equal to the difference between the forward and spot exchange rates. In the international markets, arbitrage ensures that parity almost always holds. There are two ways to hedge against exchange risk: One is to take out forward cover; the other is to borrow or lend abroad. Interest rate parity tells us that the costs of the two methods should be the same.

The expectations theory of exchange rates tells us that the forward rate equals the expected spot rate. In practice forward rates seem to incorporate a risk premium, but this premium is about equally likely to be negative as positive.

In its strict form, purchasing power parity states that $1 must have the same purchasing power in every country. That doesn’t square well with the facts, for differences in inflation rates are not perfectly related to changes in exchange rates. This means that there may be some genuine exchange risks in doing business overseas. On the other hand, the difference in inflation rates is just as likely to be above as below the change in the exchange rate.

Finally, we saw that in an integrated world capital market real rates of interest would have to be the same. In practice, government regulation and taxes can cause differences in real interest rates. But do not simply borrow where interest rates are lowest. Those countries are also likely to have the lowest inflation rates and the strongest currencies.

With these precepts in mind we showed how you can use forward markets or the loan markets to hedge transactions exposure, which arises from delays in foreign currency payments and receipts. But the company’s financing choices also need to reflect the impact of a change in the exchange rate on the value of the entire business. This is known as economic exposure. Companies protect themselves against economic exposure either by hedging in the financial markets or by building plants overseas.

Because companies can hedge their currency risk, the decision to invest overseas does not involve currency forecasts. There are two ways for a company to calculate the NPV of an overseas project. The first is to forecast the foreign currency cash flows and to discount them at the foreign currency cost of capital. The second is to translate the foreign currency cash flows into domestic currency assuming that they are hedged against exchange rate risk. These domestic currency flows can then be discounted at the domestic cost of capital. The answers should be identical.

In addition to currency risk, overseas operations may be exposed to extra political risk. However, firms may be able to structure the financing to reduce the chances that government will change the rules of the game.

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FURTHER READING

There are a number of useful textbooks in international finance. Here is a small selection:

P. Sercu, International Finance: Theory into Practice (Princeton: Princeton University Press, 2009).

D. K. Eiteman, A. I. Stonehill, and M. H. Moffett, Multinational Business Finance, 12th ed. (Reading, MA: Pearson Addison Wesley, 2009).

A. C. Shapiro, Multinational Financial Management, 9th ed. (New York: John Wiley & Sons, 2009).

Here are some general discussions of international investment decisions and associated exchange risks:

G. Allayannis, J. Ihrig, and J. P. Weston, “Exchange-Rate Hedging: Financial versus Operational Strategies,” American Economic Review 91 (May 2001), pp. 391–395.

D. R. Lessard, “Global Competition and Corporate Finance in the 1990s,” Journal of Applied Corporate Finance 3 (Winter 1991), pp. 59–72.

M. D. Levi and P. Sercu, “Erroneous and Valid Reasons for Hedging Foreign Exchange Exposure,” Journal of Multinational Financial Management 1 (1991), pp. 25–37.

Listed below are a few of the articles on the relationship between interest rates, exchange rates, and inflation:

Forward and spot exchange rates

M. D. Evans and K. K. Lewis, “Do Long-Term Swings in the Dollar Affect Estimates of the Risk Premia?” Review of Financial Studies 8 (1995), pp. 709–742.

Interest rate parity

K. Clinton, “Transaction Costs and Covered Interest Arbitrage: Theory and Evidence,” Journal of Political Economy 96 (April 1988), pp. 358–370.

Purchasing power parity

K. Froot and K. Rogoff, “Perspectives on PPP and Long-run Real Exchange Rates,” in G. Grossman and K. Rogoff (eds.), Handbook of International Economics (Amsterdam: North-Holland Publishing Company, 1995).

K. Rogoff, “The Purchasing Power Parity Puzzle,” Review of Economic Literature 34 (June 1996), pp. 667–668.

A. M. Taylor and M. P. Taylor, “The Purchasing Power Parity Debate,” Journal of Economic Perspectives 18 (Autumn 2004), pp. 135–158.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

  1.  Exchange rates Look at Table 27.1.

 a. How many Japanese yen do you get for your dollar?

 b. What is the one-month forward rate for yen?

 c. Is the yen at a forward discount or premium on the dollar?

 d. Use the one-year forward rate to calculate the annual percentage discount or premium on yen.

 e. If the one-year interest rate on dollars is 1.5% annually compounded, what do you think is the one-year interest rate on yen?

 f. According to the expectations theory, what is the expected spot rate for yen in three months’ time?

 g. According to purchasing power parity theory, what then is the expected difference in the three-month rate of price inflation in the United States and Japan?

  2.  Terminology Define each of the following theories in a sentence or simple equation:

 a. Interest rate parity.

 b. Expectations theory of forward rates.

 c. Purchasing power parity.

 d. International capital market equilibrium (relationship of real and nominal interest rates in different countries).

  3.  Purchasing power parity In March 1997 the exchange rate for the Indonesian rupiah was R2,419 = $1. Inflation in the year to March 1998 was about 30% in Indonesia and 2% in the United States.

 a. If purchasing power parity held, what should have been the nominal exchange rate in March 1998?

 b. The actual exchange rate in March 1998 (in the middle of the Asian currency crisis) was R8,325 = $1. What was the change in the real exchange rate?

 4.  Interest rate parity The following table shows interest rates and exchange rates for the U.S. dollar and the Lilliputian nano. The spot exchange rate is 15 nanos = $1. Complete the missing entries:

  5.  Currency hedging An importer in the United States is due to take delivery of clothing from Mexico in six months. The price is fixed in Mexican pesos. Which of the following transactions could eliminate the importer’s exchange risk?

 a. Sell six-month call options on pesos.

 b. Buy pesos forward.

 c. Sell pesos forward.

 d. Sell pesos in the currency futures market.

 e. Borrow pesos; buy dollars at the spot exchange rate.

 f. Sell pesos at the spot exchange rate; lend dollars.

  6.  Currency hedging A U.S. company has committed to pay 10 million kronor to a Swedish company in one year. What is the cost (in present value) of covering this liability by buying kronor forward? The Swedish interest rate is .6%, and exchange rates are shown in Table 27.1. Briefly explain.

  7.  Currency hedging A firm in the United States is due to receive payment of €1 million in eight years’ time. It would like to protect itself against a decline in the value of the euro, but finds it difficult to get forward cover for such a long period. Is there any other way in which it can protect itself?

  8.  Currency risk Suppose that in 2020 two-year interest rates are 5.2% in the United States and 1.0% in Japan. The spot exchange rate is ¥120.22/$. Suppose that one year later interest rates are 3% in both countries, while the value of the yen has appreciated to ¥115.00/$.

 a. Benjamin Pinkerton from New York invested in a U.S. two-year zero-coupon bond at the start of the period and sold it after one year. What was his return?

 b. Madame Butterfly from Osaka bought some dollars. She also invested in the two-year U.S. zero-coupon bond and sold it after one year. What was her return in yen?

 c. Suppose that Ms. Butterfly had correctly forecasted the price at which she sold her bond and that she hedged her investment against currency risk. How could she have done so? What would have been her return in yen?

  9.  Investment decisions It is the year 2018 and Pork Barrels Inc. is considering construction of a new barrel plant in Spain. The forecasted cash flows in millions of euros are as follows:

The spot exchange rate is $1.2 = €1. The interest rate in the United States is 8% and the euro interest rate is 6%. You can assume that pork barrel production is effectively risk-free.

 a. Calculate the NPV of the euro cash flows from the project. What is the NPV in dollars?

 b. What are the dollar cash flows from the project if the company hedges against exchange rate changes?

 c. Suppose that the company expects the euro to depreciate by 5% a year. How does this affect the value of the project?

INTERMEDIATE

  10.  Exchange rates Table 27.1 shows the 90-day forward rate on the South African rand.

 a. Is the dollar at a forward discount or premium on the rand?

 b. What is the annual percentage discount or premium?

 c. If you have no other information about the two currencies, what is your best guess about the spot rate on the rand three months hence?

 d. Suppose that you expect to receive 100,000 rand in three months. How many dollars is this likely to be worth?

11.  Interest rate parity Look at Table 27.1. If the three-month interest rate on dollars is 0.2%, what do you think is the three-month interest rate on the Brazilian real? Explain what would happen if the rate were substantially above your figure.

12.  Interest rates and exchange rates Penny Farthing, the treasurer of International Bicycles, Inc., has noticed that the interest rate in Japan is below the rates in most other countries. She is, therefore, suggesting that the company should make an issue of Japanese yen bonds. Does this make sense?

13.  Currency hedging Suppose you are the treasurer of Lufthansa, the German international airline. How is company value likely to be affected by exchange rate changes? What policies would you adopt to reduce exchange rate risk?

14.  Currency risk Companies may be affected by changes in the nominal exchange rate or in the real exchange rate. Explain how this can occur. Which changes are easiest to hedge against?

15.  Economic exposure A Ford dealer in the United States may be exposed to a devaluation of the yen if this leads to a cut in the price of Japanese cars. Suppose that the dealer estimates that a 1% decline in the value of the yen would result in a permanent decline of 5% in the dealer’s profits. How should she hedge against this risk, and how should she calculate the size of the hedge position? (Hint: You may find it helpful to refer back to Section 26-6.)

16.  Currency risk You have bid for a possible export order that would provide a cash inflow of €1 million in six months. The spot exchange rate is $1.3549 = €1 and the six-month forward rate is $1.3620 = €1. There are two sources of uncertainty: (1) the euro could appreciate or depreciate and (2) you may or may not receive the export order. Illustrate in each case the final payoffs if (a) you sell one million euros forward, and (b) you buy a six-month option to sell euros with an exercise price of $1.3620/€.

17.  Currency risk In January 2012, an American investor buys 1,000 shares in a Mexican company at a price of 500 pesos each. The share does not pay any dividend. A year later she sells the shares for 550 pesos each. The exchange rates when she buys the stock are shown in Table 27.1. Suppose that the exchange rate at the time of sale is 15.7 pesos = $1.

 a. How many dollars does she invest?

 b. What is her total return in pesos? In dollars?

 c. Do you think that she has made an exchange rate profit or loss? Explain.

18.  Interest rate parity Table 27.5 shows the annual interest rate (annually compounded) and exchange rates against the dollar for different currencies. Are there any arbitrage opportunities? If so, how would you secure a positive cash flow today, while zeroing out all future cash flows?

   TABLE 27.5 Interest rates and exchange rates.

aNumber of units of foreign currency that can be exchanged for $1.

  19.  Currency hedging “Last year we had a substantial income in sterling, which we hedged by selling sterling forward. In the event sterling appreciated. So our decision to sell forward cost us a lot of money. I think that in the future we should either stop hedging our currency exposure or just hedge when we think sterling is overvalued.” As financial manager, how would you respond to your chief executive’s comment?

20.  Investment decisions Carpet Baggers, Inc., is proposing to construct a new bagging plant in a country in Europe. The two prime candidates are Germany and Switzerland. The forecasted cash flows from the proposed plants are as follows:

     The spot exchange rate for euros is $1.3/€, while the rate for Swiss francs is SFr 1.5/$. The interest rate is 5% in the United States, 4% in Switzerland, and 6% in the euro countries. The financial manager has suggested that, if the cash flows were stated in dollars, a return in excess of 10% would be acceptable.

          Should the company go ahead with either project? If it must choose between them, which should it take?

CHALLENGE

21.  Currency hedging Alpha and Omega are U.S. corporations. Alpha has a plant in Hamburg that imports components from the United States, assembles them, and then sells the finished product in Germany. Omega is at the opposite extreme. It also has a plant in Hamburg, but it buys its raw material in Germany and exports its output back to the United States. How is each firm likely to be affected by a fall in the value of the euro? How could each firm hedge itself against exchange risk?

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FINANCE ON THE WEB

Find the foreign exchange rate tables in the online versions of The Wall Street Journal (www.wsj.com) or the Financial Times (www.ft.com).

1.  a. How many U.S. dollars are worth one Canadian dollar today?

 b. How many Canadian dollars are worth one U.S. dollar today?

 c. Suppose that you arrange today to buy Canadian dollars in 90 days. How many Canadian dollars could you buy for each U.S. dollar?

 d. If forward rates simply reflect market expectations, what is the likely spot exchange rate for the Canadian dollar in 90 days’ time?

 e. Look at the table of money rates in the same issue. What is the three-month interest rate on dollars?

 f. Can you deduce the likely three-month interest rate for the Canadian dollar?

 g. You can also buy currency for future delivery in the financial futures market. Look at the table of futures prices. What is the rate of exchange for Canadian dollars to be delivered in approximately six months’ time?

2.  a. How many Swiss francs can you buy for $1?

 b. How many Hong Kong dollars can you buy?

 c. What rate do you think a Swiss bank would quote for buying or selling Hong Kong dollars? Explain what would happen if it quoted a rate that was substantially above your figure.

MINI-CASE ● ● ● ● ●

Exacta, s.a.

Exacta, s.a., is a major French producer, based in Lyons, of precision machine tools. About two-thirds of its output is exported. The majority of these sales is within the European Union. However, the company also has a thriving business in the United States, despite strong competition from several U.S. firms. Exacta usually receives payment for exported goods within two months of the invoice date, so that at any point in time only about one-sixth of annual exports to the United States is exposed to currency risk.

The company believes that its North American business is now large enough to justify a local manufacturing operation, and it has recently decided to establish a plant in South Carolina. Most of the output from this plant will be sold in the United States, but the company believes that there should also be opportunities for future sales in Canada and Mexico.

The South Carolina plant will involve a total investment of $380 million and is expected to be in operation by the year 2015. Annual revenues from the plant are expected to be about $420 million and the company forecasts net profits of $52 million a year. Once the plant is up and running, it should be able to operate for several years without substantial additional investment.

Although there is widespread enthusiasm for the project, several members of the management team have expressed anxiety about possible currency risk. M. Pangloss, the finance director, reassured them that the company was not a stranger to currency risk; after all, the company was already exporting about $320 million of machine tools each year to the United States and has managed to exchange its dollar revenue for euros without any major losses. But not everybody was convinced by this argument. For example, the CEO, M. B. Bardot, pointed out that the $380 million to be invested would substantially increase the amount of money at risk if the dollar fell relative to the euro. M. Bardot was notoriously risk-averse on financial matters and would push for complete hedging if practical.

M. Pangloss attempted to reassure the CEO. At the same time, he secretly shared some of the anxieties about exchange rate risk. Nearly all the revenues from the South Carolina plant would be in U.S. dollars and the bulk of the $380 million investment would likewise be incurred in the United States. About two-thirds of the operating costs would be in dollars, but the remaining one-third would represent payment for components brought in from Lyons plus the charge by the head office for management services and use of patents. The company has yet to decide whether to invoice its U.S. operation in dollars or euros for these purchases from the parent company.

M. Pangloss is optimistic that the company can hedge itself against currency risk. His favored solution is for Exacta to finance the plant by a $380 million issue of dollar bonds. That way the dollar investment would be offset by a matching dollar liability. An alternative is for the company to sell forward at the beginning of each year the expected revenues from the U.S. plant. But he realizes from experience that these simple solutions might carry hidden dangers. He decides to slow down and think more systematically about the additional exchange risk from the U.S. operation.

QUESTIONS

  1.  What would Exacta’s true exposure be from its new U.S. operations, and how would it change from the company’s current exposure?

  2.  Given that exposure, what would be the most effective and inexpensive approach to hedging?

___________

¹The results of the triennial survey of foreign exchange business are published on www.bis.org/forum/research.htm.

²The euro is the common currency of the European Monetary Union. The 17 members of the Union are Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Malta, Netherlands, Portugal, Slovenia, Slovakia, and Spain.

³Foreign exchange dealers usually refer to the exchange rate between pounds and dollars as cable. In Table 27.1 cable is 1.5667.

⁴Here is an occasional point of confusion. Since the quote for the real is indirect, we calculate the premium by taking the ratio of the spot rate to the forward rate. If we use direct quotes, then we need to calculate the ratio of the forward rate to the spot rate. In the case of the real, the forward discount with direct quotes is 4 × [(1/1.7781)/(1/1.7456) – 1] = –.073, or -7.3%.

⁵Notice that spot and short-term forward trades are sometimes undertaken together. For example, a company might need the use of Brazilian reals for one month. In this case it would buy reals spot and simultaneously sell them forward. Dealers refer to this as a swap trade. But do not confuse it with the longer term currency swaps that we described in Chapter 26.

⁶See Chapter 26 for a further discussion of the difference between forward and futures contracts.

⁷Economists use the term purchasing power parity to refer to the notion that the level of prices of goods in general must be the same in the two countries. They tend to use the phrase law of one price when they are talking about the price of a single good.

⁸In other words, the expected difference in inflation rates equals the expected change in the exchange rate. Strictly interpreted, purchasing power parity also implies that the actual difference in the inflation rates always equals the actual change in the exchange rate.

⁹In Section 3-5 we discussed Irving Fisher’s theory that over time money interest rates change to reflect changes in anticipated inflation. Here we argue that international differences in money interest rates also reflect differences in anticipated inflation. This theory is sometimes known as the international Fisher effect.

¹⁰Many researchers have even found that, when the forward rate predicts a rise, the spot rate is more likely to fall, and vice versa. For a readable discussion of this puzzling finding, see K. A. Froot and R. H. Thaler, “Anomalies: Foreign Exchange,” Journal of Economic Perspectives 4 (1990), pp. 179–192.

¹¹For evidence that forward exchange rates contain risk premiums that are sometimes positive and sometimes negative, see, for example, E. F. Fama, “Forward and Spot Exchange Rates,” Journal of Monetary Economics 14 (1984), pp. 319–338.

¹²Of course, even within a currency area there may be considerable price variations. The price of a Big Mac, for example, differs substantially from one part of the United States to another.

¹³Note that some of the countries represented in Figure 27.2 have highly controlled economies, so that their exchange rates are not those that would exist in an unrestricted market. The interest rates shown in Figure 27.4 are subject to a similar caveat.

¹⁴The real exchange rate is equal to the nominal exchange rate multiplied by the inflation differential. For example, suppose that the value of sterling falls from $1.65 = £1 to $1.50 = £1 at the same time that the price of goods rises 10% faster in the United Kingdom than in the United States. The inflation-adjusted, or real, exchange rate is unchanged at

¹⁵To put it another way, the hedge ratio is 1.0.

¹⁶Of course, if purchasing power parity always held, the fall in the value of the krona would be matched by higher inflation in Sweden. The risk for Outland is that the real value of the krona may decline, so that when measured in dollars Swedish costs are lower than previously. Unfortunately, it is much easier to hedge against a change in the nominal exchange rate than against a change in the real rate.

¹⁷Financial managers also refer to translation exposure, which measures the effect of an exchange rate change on the company’s financial statements.

¹⁸There is a general point here that is not confined to currency hedging. Whenever you face an investment that appears to have a positive NPV, decide what it is that you are betting on and then think whether there is a more direct way to place the bet. For example, if a copper mine looks profitable only because you are unusually optimistic about the price of copper, then maybe you would do better to buy copper futures or the shares of other copper producers rather than opening a copper mine.

¹⁹The following example should give you a feel for the idea behind this formula. Suppose the spot rate for Swiss francs is SFr 1.2 = $1. Interest rate parity tells us that the forward rate must be 1.2 × 1.04/1.06 = SFr 1.177/$. Now suppose that a share costs $100 and will pay an expected $112 at the end of the year. The cost to Swiss investors of buying the share is 100 × 1.2 = SFr 120. If the Swiss investors sell forward the expected payoff, they will receive an expected 112 × 1.177 = SFr 131.9. The expected return in Swiss francs is 131.9/120 – 1 = .099, or 9.9%. More simply, the Swiss franc return is 1.12 × 1.04/1.06 – 1 = .099.

²⁰When an investor holds an efficient portfolio, the expected reward for risk on each stock in the portfolio is proportional to its beta relative to the portfolio. So if the Swiss market index is an efficient portfolio for Swiss investors, then these investors will want Roche to invest in the U.S. if the expected rate of return more than compensates for the investment’s beta relative to the Swiss index.

²¹See R. M. Stulz, “The Cost of Capital in Internationally Integrated Markets: The Case of Nestlé,” European Financial Management 1, no. 1 (1995), pp. 11–22; R. S. Harris, F. C. Marston, D. R. Mishra, and T. J. O’Brien, “Ex Ante Cost of Capital Estimates of S&P 500 Firms: The Choice Between Global and Domestic CAPM,” Financial Management (Autumn 2003), pp. 51–66; and Standard & Poor’s, “Domestic vs. Global CAPM,” Global Cost of Capital Report, 4th Quarter 2003.

²²Why do we say “seem to diverge”? Because the terms of the bonds are not quite identical, and the governments may calculate the rate of inflation in different ways.

²³For a discussion of these services see C. Erb, C. R. Harvey, and T. Viskanta, “Political Risk, Financial Risk, and Economic Risk,” Financial Analysts Journal 52 (1996), pp. 28–46. Also, Campbell Harvey’s webpage (www.duke.edu/~charvey) is a useful source of information on political risk.

²⁴The early history of the San Tomé mine is described in Joseph Conrad’s Nostromo.

²⁵In the appendix to Chapter 24 we described how the World Bank provided the Hubco power project with a guarantee against political risk.

Part 9 Financial Planning and Working Capital Management

Financial Analysis

Good financial managers plan for the future. They check that they will have enough cash to pay the upcoming tax bill or dividend payment. They think about how much investment the firm will need to make and about how they might finance that investment. They reflect on whether they are well placed to ride out an unexpected downturn in demand or an increase in the cost of materials.

In Chapter 29 we will describe how financial managers develop both short- and long-term financial plans. But knowing where you stand today is a necessary prelude to contemplating where you might be in the future. Therefore, in this chapter we show how the firm’s financial statements help you to understand the firm’s overall performance and how some key financial ratios may alert senior management to potential problem areas.

You have probably heard stories of whizzes who can take a company’s accounts apart in minutes, calculate some financial ratios, and divine the company’s future. Such people are like abominable snowmen: often spoken of but never truly seen. Financial ratios are no substitute for a crystal ball. They are just a convenient way to summarize large quantities of financial data and to compare firms’ performance. The ratios help you to ask the right questions; they seldom answer them.

 28-1   Financial Ratios

Financial ratios are usually easy to calculate. That’s the good news. The bad news is that there are so many of them. To make it worse, the ratios are often presented in long lists that seem to require memorization rather than understanding.

We can mitigate the bad news by taking a moment to preview what the ratios are measuring and how they connect to the ultimate objective of value added for shareholders.

Shareholder value depends on good investment decisions. The financial manager evaluates investment decisions by asking several questions, including these: How profitable are the investments relative to the cost of capital? How should profitability be measured? What does profitability depend on? (We will see that it depends on efficient use of assets and on the bottom-line profits on each dollar of sales.)

Shareholder value also depends on good financing decisions. Again, there are obvious questions: Is the available financing sufficient? The firm cannot grow unless financing is available. Is the financing strategy prudent? The financial manager should not put the firm’s assets and operations at risk by operating at a dangerously high debt ratio. Does the firm have sufficient liquidity (a cushion of cash or assets that can be readily sold for cash)? The firm has to be able to pay its bills and respond to unexpected setbacks.

   FIGURE 28.1 An organization chart for financial ratios, showing how common financial ratios and other measures relate to shareholder value.

Figure 28.1 summarizes these questions in more detail. The boxes on the left are for investment, those on the right for financing. In each box we have posed a question and given examples of financial ratios or other measures that can help to answer it. For example, the bottom box on the far left asks about efficient use of assets. Three ratios that measure asset efficiency are turnover ratios for assets, inventory, and accounts receivable. The two bottom boxes on the right ask whether financial leverage is prudent and whether the firm has sufficient liquidity for the coming year. The ratios for tracking financial leverage include various debt ratios; the ratios for liquidity are the current, quick, and cash ratios.

BEYOND THE PAGE

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Try It! Financial ratios for U.S. companies

brealey.mhhe.com/c28

Figure 28.1 serves as a road map for this chapter. We will show how to calculate these and other common financial ratios and explain how they relate to the objective of shareholder value.

 28-2   Financial Statements

Public companies have a variety of stakeholders, such as shareholders, bondholders, bankers, suppliers, employees, and management. All these stakeholders need to monitor the firm and to ensure that their interests are being served. They rely on the company’s financial statements to provide the necessary information. Public companies report to their shareholders quarterly and annually. U.S. companies file their annual statements with the SEC on form 10-K and the quarterly statements are filed on form 10-Q. Therefore you often hear financial analysts refer loosely to the company’s “10-K” or its “10-Q.”

When reviewing a company’s financial statements, it is important to remember that accountants still have a fair degree of leeway in reporting earnings and book values. For example, they have discretion in the choice of depreciation method and the speed at which the firm’s assets are written off.

FINANCE IN PRACTICE

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A Study in Harmony

In 1973 the accounting bodies of 9 countries got together to produce some ‘‘basic’’ accounting standards, which, it was hoped, would lead to a harmonization of accounting standards worldwide. That early meeting sowed the seeds for the development of a common set of International Financial Reporting Standards (IFRS) overseen by the London-based International Accounting Standards Board (IASB). IFRS have become the basis for reporting throughout the European Union, and some 100 other countries have now adopted them or plan to do so. The principal exception remains the United States. Although the SEC has been working to bring U.S. standards more in line with international rules, any move to oblige U.S. companies to adopt IFRS seems a long way off.

These developments have been widely welcomed. In an increasingly integrated global economy, common standards make it easier for investors to compare corporate profitability. The moves are also supported by multinational companies that need to provide accounting statements for overseas subsidiaries. However, some have cautioned that there is a danger that the IASB may become a bureaucratic UN-style body that deters innovation. Thus, Professor Ray Ball of the University of Chicago stresses the benefits of competition in standard-setting, “Competition breeds innovation, encourages adaptation, dispels complacency and penalizes bureaucracy … . Imposing worldwide standards therefore is a risky centralization process in any innovation sphere of economic activity.”*

*R.J. Ball, “International Financial Reporting Standards (IFRS) Pros and Cons for Investors,” Accounting and Business Research, International Accounting Policy Forum (2006), pp. 5–27.

Although accountants around the world are working toward common practices, there are still considerable variations in the accounting rules of different countries. In Anglo-Saxon countries such as the U.S. or the UK, which have large and active equity markets, the rules have been designed largely with the shareholder in mind. By contrast, in Germany the focus of accounting standards is to verify that the creditors are properly protected.

Another difference is the way that taxes are shown in the income statement. For example, in Germany taxes are paid on the published profits, and the depreciation method must therefore be approved by the revenue service. That is not the case in Anglo-Saxon countries, where the numbers shown in the published accounts are generally not the basis for calculating the company’s tax payments. For instance, the depreciation method used to calculate the published profits usually differs from the depreciation method used by the tax authorities.

For investors and multinational companies these variations in accounting rules can be irksome. Accounting bodies have therefore been getting together to see whether they can iron out some of the differences. It is not a simple task, as the nearby box illustrates.

 28-3   Home Depot’s Financial Statements

Your task is to assess the financial standing of Home Depot, the home improvement company. Perhaps you are a mutual fund manager trying to decide whether to allocate $25 million of new money to Home Depot stock. You could be an investment banker seeking business from the company or a bondholder concerned with its credit standing. You could be the financial manager of Home Depot or of one of its competitors.

In each case, your first step is to assess the company’s current condition. You have before you the latest balance sheet and income statement.

The Balance Sheet

Table 28.1 sets out a simplified balance sheet for Home Depot for fiscal years 2011 and 2010. It provides a snapshot of the company’s assets at the end of the year and the sources of the money that was used to buy those assets.

The assets are listed in declining order of liquidity. For example, the accountant lists first those assets that are most likely to be turned into cash in the near future. They include cash itself, marketable securities and receivables (that is, bills to be paid by the firm’s customers), and inventories of raw materials, work in process, and finished goods. These assets are all known as current assets.

   TABLE 28.1 Balance sheet of Home Depot, fiscal 2010 and 2011 (figures in $ millions).

The remaining assets on the balance sheet consist of long-term, usually illiquid, assets such as warehouses, stores, fixtures, and vehicles. The balance sheet does not show up-to-date market values of these long-term assets. Instead, the accountant records the amount that each asset originally cost and deducts a fixed annual amount for depreciation of buildings, plant, and equipment. The balance sheet does not include all the company’s assets. Some of the most valuable ones are intangible, such as reputation, skilled management, and a well-trained labor force. Accountants are generally reluctant to record these assets in the balance sheet unless they can be readily identified and valued.

Now look at the right-hand portion of Home Depot’s balance sheet, which shows where the money to buy the assets came from.¹ The accountant starts by looking at the liabilities, that is, the money owed by the company. First come those liabilities that need to be paid off in the near future. These current liabilities include debts that are due to be repaid within the next year and payables (that is, amounts owed by the company to its suppliers).

The difference between the current assets and current liabilities is known as the net current assets or net working capital. It roughly measures the company’s potential reservoir of cash. For Home Depot in 2011

The bottom portion of the balance sheet shows the sources of the cash that was used to acquire the net working capital and fixed assets. Some of the cash has come from the issue of bonds and leases that will not be repaid for many years. After all these long-term liabilities have been paid off, the remaining assets belong to the common stockholders. The company’s equity is simply the total value of the net working capital and fixed assets less the long-term liabilities. Part of this equity has come from the sale of shares to investors, and the remainder has come from earnings that the company has retained and invested on behalf of the shareholders.

The Income Statement

If Home Depot’s balance sheet resembles a snapshot of the firm at a particular point in time, its income statement is like a video. It shows how profitable the firm has been over the past year.

Look at the summary income statement in Table 28.2. You can see that during 2011 Home Depot sold goods worth $70,395 million. The total cost of purchasing and selling these goods was $46,133 + $16,015 = $62,148 million.² In addition to these out-of-pocket expenses, Home Depot also deducted depreciation of $1,573 million for the value of the fixed assets used up in producing the goods. Thus Home Depot’s earnings before interest and taxes (EBIT) were

Of this sum $606 million went to pay the interest on the short- and long-term debt (remember debt interest is paid out of pretax income) and a further $2,185 million went to the government in the form of taxes. The $3,883 million that was left over belonged to the shareholders. Home Depot paid out $1,632 million as dividends and reinvested the remainder in the business.

   TABLE 28.2 Income statement of Home Depot, fiscal 2011 (figures in $ millions).

 28-4   Measuring Home Depot’s Performance

You want to use Home Depot’s financial statements to assess its financial performance and current standing. Where do you start?

At the close of fiscal 2011 Home Depot’s common stock was priced at $44.60 per share.³ There were 1,537 million shares outstanding, so total market capitalization was 1,537 × $44.60 = $68,550 million. This is a big number, of course, but Home Depot is a sizable
company. Its shareholders have, over the years, invested billions in the company. Therefore, you decide to compare Home Depot’s market capitalization with the book value of its equity. The book value measures shareholders’ cumulative investment in the company.

At the end of fiscal 2011 the book value of Home Depot’s equity was $17,898 million. Therefore, the market value added, the difference between the market value of the firm’s shares and the amount of money that shareholders have invested in the firm, was $68,550 – $17,898 = $50,652 million. In other words, Home Depot’s shareholders have contributed about $18 billion and ended up with shares worth about $69 billion. They have accumulated about $50 billion in market value added.

The consultancy firm, EVA Dimensions, calculates market value added for a large sample of U.S. companies. Table 28.3 shows a few of the firms from EVA Dimensions’ list. Exxon is nearly top of the class. It has created $206 billion of wealth for its shareholders. Bank of America languishes at the bottom; the market value of its shares is $203 billion less than the amount that shareholders have invested in the firm.

These two firms are large. Their managers have lots of assets to work with. A small firm could not hope to create so much extra value as Exxon Mobil or to lose as much as Bank of America. Therefore, financial managers and analysts also like to calculate how much value has been added for each dollar that shareholders have invested. To do this, they compute the ratio of market value to book value. For example, Home Depot’s market-to-book ratio is⁴

   TABLE 28.3 Stock market measures of company performance, 2011 (dollar values in millions). Companies are ranked by market value added.

Source: We are grateful to EVA Dimensions for providing these statistics.

In other words, Home Depot has multiplied the value of its shareholders’ investment 3.8 times.

Table 28.3 also shows market-to-book ratios for our sample of U.S. companies. Notice that Microsoft has a much higher market-to-book ratio than Exxon Mobil. But Exxon Mobil’s market value added is higher because of its larger scale.

The market value performance measures in Table 28.3 have three drawbacks. First, the market value of the company’s shares reflects investors’ expectations about future performance. Investors pay attention to current profits and investment, of course, but market-value measures can nevertheless be noisy measures of current performance.

Second, market values fluctuate because of many events that are outside the manager’s control. Thus, market values are noisy measures of how well the corporation is performing.

Third, you can’t look up the market value of privately owned companies whose shares are not traded. Nor can you observe the market value of divisions or plants that are parts of larger companies. You may use market values to satisfy yourself that Home Depot as a whole has performed well, but you can’t use them to drill down to look at the performance of, say, its overseas stores or particular U.S. stores. To do this, you need accounting measures of profitability. We start with economic value added (EVA).

Economic Value Added (EVA)

When accountants draw up an income statement, they start with revenues and then deduct operating and other costs. But one important cost is not included: the cost of the capital that the company has raised from investors. Therefore, to see whether the firm has truly created value, we need to measure whether it has earned a profit after deducting all costs, including its cost of capital.

The cost of capital is the minimum acceptable rate of return on capital investment. It is an opportunity cost of capital, because it equals the expected rate of return on investment opportunities open to investors in financial markets. The firm creates value for investors only if it can earn more than its cost of capital, that is, more than its investors can earn by investing on their own.

The profit after deducting all costs, including the cost of capital, is called the company’s economic value added or EVA. We encountered EVA in Chapter 12, where we looked at how firms often link executive compensation to accounting measures of performance. Let’s calculate EVA for Home Depot.

Total long-term capital, sometimes called total capitalization, is the sum of long-term debt and shareholders’ equity. Home Depot entered 2011 with a total capitalization of $27,596 million, which was made up of $8,707 million of long-term debt and $18,889 million of shareholders’ equity. This was the cumulative amount that had been invested in the past by the debt- and equityholders. Home Depot’s weighted-average cost of capital was about 9.2%. Therefore, in 2011 investors who provided the $27,596 million required the company to earn at least .092 × 27,596 = $2,538 million for its debt- and equityholders.

In 2011 Home Depot’s after-tax interest and net income totaled (1 – .35) × 606  + 3,883 = $4,277 million (we assume a 35% tax rate). If you deduct the total cost of the company’s capital from this figure, you can see that it earned $4,277 – 2,538 = $1,738 million more than investors required. This was Home Depot’s residual income, or EVA:

Sometimes it is helpful to re-express EVA as follows:

The return on capital (or ROC) is equal to the total profits that the company has earned for its debt- and equityholders, divided by the amount of money that they have contributed. If the company earns a higher return on its capital than investors require, EVA is positive.

In the case of Home Depot, the return on capital was

Home Depot’s cost of capital was about 9.2%. So,

The first four columns of Table 28.4 show measures of EVA for our sample of large companies. Exxon Mobil again heads the list. In 2011 it earned $39.5 billion more than was needed to satisfy investors. By contrast, Bank of America was a laggard. Although it earned an accounting profit of nearly $8 billion, this figure was calculated before deducting the cost of the capital that was employed. After deducting the cost of the capital, Bank of America made an EVA loss of $10.7 billion.

Accounting Rates of Return

EVA measures how many dollars a business is earning after deducting the cost of capital. Other things equal, the more assets the manager has to work with, the greater the opportunity to generate a large EVA. The manager of a small division may be highly competent, but if that division has few assets, she is unlikely to rank high in the EVA stakes. Therefore, when comparing managers, it can also be helpful to measure the firm’s return per dollar of investment.

   TABLE 28.4 Accounting measures of company performance, 2011 (dollar values in millions). Companies are ranked by economic value added (EVA).

Note: EVAs do not compute exactly because of rounding in column 2.

Source: We are grateful to EVA Dimensions for providing these statistics.

Three common return measures are the return on capital (ROC), the return on equity (ROE), and the return on assets (ROA). All are based on accounting information and are therefore known as book rates of return.

Return on Capital (ROC)⁵ We have already calculated Home Depot’s return on capital in 2011:

The company’s cost of capital (WACC) was about 9.2%. So we can say that the company earned 6.3% more than shareholders demanded.

Notice that, when we calculated Home Depot’s return on capital, we summed the company’s after-tax interest and net income.⁶ The reason that we subtracted the tax shield on debt interest was that we wished to calculate the income that the company would have earned with all-equity financing. The tax advantages of debt financing are picked up when we compare the company’s return on capital with its weighted-average cost of capital (WACC).⁷ WACC already includes an adjustment for the interest tax shield.⁸ More often than not, financial analysts ignore this refinement and use the gross interest payment to calculate ROC. It is only approximately correct to compare this measure with the weighted-average cost of capital.

The last column in Table 28.4 shows the return on capital for our sample of well-known companies. Notice that Microsoft’s return on capital was 73%, 63 percentage points higher than its cost of capital. Although Microsoft had a higher return than Exxon Mobil, it had a lower EVA. This was partly because Microsoft was more risky than Exxon Mobil, and so had a higher cost of capital, but also because it had far fewer dollars invested than Exxon.

Return on Equity (ROE) We measure the return on equity (ROE) as the income to shareholders per dollar invested. Home Depot had net income of $3,883 million in 2011 and stockholders’ equity of $18,889 million at the start of the year. So its return on equity was

Has the company provided an adequate return for shareholders? To answer that question, we need to compare it with the company’s cost of equity. Home Depot’s cost of equity capital in 2011 was about 10%, so its return on equity was 10 percentage points higher than its cost of equity.

Return on Assets (ROA) Return on assets measures the income available to debt and equity investors per dollar of the firm’s total assets. Total assets (which equal total liabilities plus shareholders’ equity) are greater than total capital because total capital does not include current liabilities.⁹ For Home Depot, return on assets was

When we subtract the tax shield on Home Depot’s interest payments, we are asking how much the company would have earned if all-equity-financed. This adjustment is helpful when comparing the profitability of firms with very different capital structures. Again, this refinement is ignored more often than not, and ROA is calculated using the gross interest payment. Sometimes analysts take no account of interest payments and measure ROA as the income for equityholders divided by total assets. This measure ignores entirely the income that the assets have generated for debtholders.

We will see shortly how Home Depot’s return on assets is determined by the sales that these assets generate and the profit margin that the company earns on its sales.

Problems with EVA and Accounting Rates of Return

Rate of return and economic value added have some obvious attractions as measures of performance. Unlike market-value-based measures, they show current performance and are not affected by the expectations about future events that are reflected in today’s stock market prices. Rate of return and economic value added can also be calculated for an entire company or for a particular plant or division. However, remember that both measures are based on book (balance sheet) values for assets. Debt and equity are also book values. Accountants do not show every asset on the balance sheet, yet our calculations take accounting data at face value. For example, we ignored the fact that Home Depot has invested large sums in marketing to establish its brand name. This brand name is an important asset, but its value is not shown on the balance sheet. If it were shown, the book values of assets, capital, and equity would increase, and Home Depot would not appear to earn such high returns.

EVA Dimensions, which produced the data in Tables 28.3 and 28.4, does make a number of adjustments to the accounting data. However, it is impossible to include the value of all assets or to judge how rapidly they depreciate. For example, did Microsoft really earn a return of 73% and add $17 billion of economic value? It’s difficult to say, because its investment over the years in Windows and other software is not shown on the balance sheet and cannot be measured exactly.

Remember also that the balance sheet does not show the current market values of the firm’s assets. The assets in a company’s books are valued at their original cost less any depreciation. Older assets may be grossly undervalued in today’s market conditions and prices. So a high return on assets indicates that the business has performed well by making profitable investments in the past, but it does not necessarily mean that you could buy the same assets today at their reported book values. Conversely a low return suggests some poor decisions in the past, but it does not always mean that today the assets could be employed better elsewhere.

 28-5   Measuring Efficiency

We began our analysis of Home Depot by calculating how much value the company has added for its shareholders and how much profit it is earning after deducting the cost of the capital that it employs. We examined the company’s rates of return on capital, equity, and total assets and found that its return has been higher than the cost of capital. Our next task is to probe a little deeper to understand the reasons for the company’s success. What factors contribute to a firm’s overall profitability? One factor clearly must be the efficiency with which it uses its various assets.

Asset Turnover Ratio The asset turnover, or sales-to-assets, ratio shows how much sales volume is generated by each dollar of total assets, and therefore it measures how hard the firm’s assets are working. For Home Depot, each dollar of assets produced $1.75 of sales:

Technical note: Like a number of other financial ratios, the sales-to-assets ratio compares a flow measure (sales over the entire year) with a snapshot measure (assets at a point in time). But which point in time should you use? We calculated the ratio of Home Depot’s sales to assets at the start of the year, but frequently analysts use the average of the firm’s assets at the start and end of the year. The idea is that this better measures the average assets during the year. In the case of Home Depot the two ratios are effectively identical:¹⁰

There is no obvious best measure. If assets are turned over very slowly, it may be better to use the value at the start of the year; if they are turned over fast, as is often the case, it may be preferable to use the average measure. However, it’s probably not worth getting too steamed up over the matter. After all, both measures rest on the doubtful assumption that the asset levels at the close of each financial year are typical of the rest of the year. But, like many retailers, Home Depot ends its financial year in January just after the busy holiday season, when inventories and receivables are unusually low.

The asset turnover ratio measures how efficiently the business is using its entire asset base. But you also might be interested in how hard particular types of assets are being put to use. Below are a couple of examples.

Inventory Turnover Efficient firms don’t tie up more capital than they need in raw materials and finished goods. They hold only a relatively small level of inventories of raw materials and finished goods, and they turn over those inventories rapidly. The balance sheet shows the cost of inventories rather than the amount that the finished goods will eventually sell for. So it is usual to compare the level of inventories with the cost of goods sold rather than with sales. In Home Depot’s case,

Another way to express this measure is to look at how many days of output are represented by inventories. This is equal to the level of inventories divided by the daily cost of goods sold:

Receivables Turnover Receivables are sales for which the company has not yet been paid. The receivables turnover ratio measures the firm’s sales as a proportion of its receivables. For Home Depot,

If customers are quick to pay, unpaid bills will be a relatively small proportion of sales and the receivables turnover will be high. Therefore, a comparatively high ratio often indicates an efficient credit department that is quick to follow up on late payers. Sometimes, however, a high ratio indicates that the firm has an unduly restrictive credit policy and offers credit only to customers who can be relied on to pay promptly.¹¹

Another way to measure the efficiency of the credit operation is by calculating the average length of time for customers to pay their bills. The faster the firm turns over its receivables, the shorter the collection period. Home Depot’s customers pay their bills in about 5.6 days:

The receivables turnover ratio and the inventory turnover ratio may help to highlight particular areas of inefficiency, but they are not the only possible indicators. For example, Home Depot might compare its sales per square foot with those of its competitors, a steel producer might calculate the cost per ton of steel produced, an airline might look at revenues per passenger-mile, and a law firm might look at revenues per partner. A little thought and common sense should suggest which measures are likely to produce the most helpful insights into your company’s efficiency.

 28-6   Analyzing the Return on Assets: The Du Pont System

We have seen that every dollar of Home Depot’s assets generates $1.75 of sales. But a company’s success depends not only on the volume of its sales but also on how profitable those sales are. This is measured by the profit margin.

Profit Margin The profit margin measures the proportion of sales that finds its way into profits. It is sometimes defined as

This definition can be misleading. When companies are partly financed by debt, a portion of the profits from the sales must be paid as interest to the firm’s lenders. We would not want to say that a firm is less profitable than its rivals simply because it employs debt finance and pays out part of its profits as interest. Therefore, when we are calculating the profit margin, it is useful to add back the debt interest to net income. This gives an alternative measure of profit margin, which is called the operating profit margin:¹²

The Du Pont System

We calculated earlier that Home Depot has earned a return of 10.7% on its assets. The following equation shows that this return depends on two factors—the sales that the company generates from its assets (asset turnover) and the profit that it earns on each dollar of sales (operating profit margin):

This breakdown of ROA into the product of turnover and margin is often called the Du Pont formula, after the chemical company that popularized the formula. In Home Depot’s case the formula gives the following breakdown of ROA:

All firms would like to earn a higher return on their assets, but their ability to do so is limited by competition. The Du Pont formula helps to identify the constraints that firms face. Fast-food chains, which have high asset turnover, tend to operate on low margins. Classy hotels have relatively low turnover ratios but tend to compensate with higher margins.

Firms often seek to improve their profit margins by acquiring a supplier. The idea is to capture the supplier’s profit as well as their own. Unfortunately, unless they have some special skill in running the new business, they are likely to find that any gain in profit margin is offset by a decline in asset turnover.

   TABLE 28.5 Merging with suppliers or customers generally increases the profit margin, but this increase is offset by a reduction in asset turnover.

A few numbers may help to illustrate this point. Table 28.5 shows the sales, profits, and assets of Admiral Motors and its components supplier, Diana Corporation. Both earn a 10% return on assets, though Admiral has a lower operating profit margin (20% versus Diana’s 25%). Since all of Diana’s output goes to Admiral, Admiral’s management reasons that it would be better to merge the two companies. That way, the merged company would capture the profit margin on both the auto components and the assembled car.

The bottom row of Table 28.5 shows the effect of the merger. The merged firm does indeed earn the combined profits. Total sales remain at $20 million, however, because all the components produced by Diana are used within the company. With higher profits and unchanged sales, the profit margin increases. Unfortunately, the asset turnover is reduced by the merger since the merged firm has more assets. This exactly offsets the benefit of the higher profit margin. The return on assets is unchanged.

 28-7  Measuring Leverage

When a firm borrows money, it promises to make a series of interest payments and then to repay the amount that it has borrowed. If profits rise, the debtholders continue to receive only the fixed interest payment, so all the gains go to the shareholders. Of course, the reverse happens if profits fall. In this case shareholders bear the greater part of the pain. If times are sufficiently hard, a firm that has borrowed heavily may not be able to pay its debts. The firm is then bankrupt, and shareholders lose most or all of their investment.

Because debt increases the returns to shareholders in good times and reduces them in bad times, it is said to create financial leverage. Leverage ratios measure how much financial leverage the firm has taken on. CFOs keep an eye on leverage ratios to ensure that lenders are happy to continue to take on the firm’s debt.

Debt Ratio Financial leverage is usually measured by the ratio of long-term debt to total long-term capital. (Here “long-term debt” should include not just bonds or other borrowing but also financing from long-term leases.)¹³ For Home Depot,

This means that 38 cents of every dollar of long-term capital is in the form of debt.

Leverage is also measured by the debt–equity ratio. For Home Depot,

Home Depot’s long-term debt ratio is fairly typical of U.S. nonfinancial companies, but some companies deliberately operate at much higher debt levels. For example, in Chapter 32 we look at leveraged buyouts (LBOs). Firms that are acquired in a leveraged buyout usually issue large amounts of debt. When LBOs first became popular in the 1990s, these companies had average debt ratios of about 90%. Many of them flourished and paid back their debtholders in full; others were not so fortunate.

Notice that debt ratios make use of book (i.e., accounting) values rather than market values.¹⁴ The market value of the company finally determines whether the debtholders get their money back, so you might expect analysts to look at the face amount of the debt as a proportion of the total market value of debt and equity. On the other hand, the market value includes the value of intangible assets generated by research and development, advertising, staff training, and so on. These assets are not readily salable and, if the company falls on hard times, their value may disappear altogether. For some purposes, it may be just as good to follow the accountant and ignore these intangible assets. This is what lenders do when they insist that the borrower should not allow the book debt ratio to exceed a specified limit.

Notice also that these measures of leverage ignore short-term debt. That probably makes sense if the short-term debt is temporary or is matched by similar holdings of cash, but if the company is a regular short-term borrower, it may be preferable to widen the definition of debt to include all liabilities. In this case,

Therefore, Home Depot is financed 56% with long- and short-term debt and 44% with equity.¹⁵ We could also say that its ratio of total debt to equity is 22,620/17,898 = 1.24.

Managers sometimes refer loosely to a company’s debt ratio, but we have just seen that the debt ratio may be measured in several different ways. For example, Home Depot has a debt ratio of .38 (the long-term debt ratio) and also .56 (the total debt ratio). This is not the first time we have come across several ways to define a financial ratio. There is no law stating how a ratio should be defined. So be warned: do not use a ratio without understanding how it has been calculated.

Times-Interest-Earned Ratio Another measure of financial leverage is the extent to which interest obligations are covered by earnings. Banks prefer to lend to firms whose earnings cover interest payments with room to spare. Interest coverage is measured by the ratio of earnings before interest and taxes (EBIT) to interest payments. For Home Depot,¹⁶

The company enjoys a comfortable interest coverage or times-interest-earned ratio. Sometimes lenders are content with coverage ratios as low as 2 or 3.

The regular interest payment is a hurdle that companies must keep jumping if they are to avoid default. Times-interest-earned measures how much clear air there is between hurdle and hurdler. The ratio is only part of the story, however. For example, it doesn’t tell us whether Home Depot is generating enough cash to repay its debt as it comes due.

Cash Coverage Ratio In the previous chapter we pointed out that depreciation is deducted when calculating the firm’s earnings, even though no cash goes out the door. Suppose we add back depreciation to EBIT to calculate operating cash flow.¹⁷ We can then calculate a cash coverage ratio. For Home Depot,

Leverage and the Return on Equity

When the firm raises cash by borrowing, it must make interest payments to its lenders. This reduces net profits. On the other hand, if a firm borrows instead of issuing equity, it has fewer equityholders to share the remaining profits. Which effect dominates? An extended version of the Du Pont formula helps us answer this question. It breaks down the return on equity (ROE) into four parts:

Notice that the product of the two middle terms is the return on assets. It depends on the firm’s production and marketing skills and is unaffected by the firm’s financing mix. However, the first and fourth terms do depend on the debt–equity mix. The first term, assets/equity, which we call the leverage ratio, can be expressed as (equity + liabilities)/equity, which equals 1 + total-debt-to-equity ratio. The last term, which we call the “debt burden,” measures the proportion by which interest expense reduces net income.

Suppose that the firm is financed entirely by equity. In this case, both the leverage ratio and the debt burden are equal to 1, and the return on equity is identical to the return on assets. If the firm borrows, however, the leverage ratio is greater than 1 (assets are greater than equity) and the debt burden is less than 1 (part of the profits is absorbed by interest). Thus leverage can either increase or reduce return on equity. You will usually find, however, that leverage increases ROE when the firm is performing well and ROA exceeds the interest rate.

 28-8   Measuring Liquidity

If you are extending credit to a customer or making a short-term bank loan, you are interested in more than the company’s leverage. You want to know whether the company can lay its hands on the cash to repay you. That is why credit analysts and bankers look at several measures of liquidity. Liquid assets can be converted into cash quickly and cheaply.

Think, for example, what you would do to meet a large unexpected bill. You might have some money in the bank or some investments that are easily sold, but you would not find it so easy to turn your old sweaters into cash. Companies, likewise, own assets with different degrees of liquidity. For example, accounts receivable and inventories of finished goods are generally quite liquid. As inventories are sold off and customers pay their bills, money flows into the firm. At the other extreme, real estate may be very illiquid. It can be hard to find a buyer, negotiate a fair price, and close a deal on short notice.

Managers have another reason to focus on liquid assets: Their book (balance sheet) values are usually reliable. The book value of a catalytic cracker may be a poor guide to its true value, but at least you know what cash in the bank is worth. Liquidity ratios also have some less desirable characteristics. Because short-term assets and liabilities are easily changed, measures of liquidity can rapidly become outdated. You might not know what the catalytic cracker is worth, but you can be fairly sure that it won’t disappear overnight. Cash in the bank can disappear in seconds.

Also, assets that seem liquid sometimes have a nasty habit of becoming illiquid. This happened during the subprime mortgage crisis in 2007. Some financial institutions had set up funds known as structured investment vehicles (SIVs) that issued short-term debt backed by residential mortgages. As mortgage default rates began to climb, the market in this debt dried up and dealers became very reluctant to quote a price. Investors who were forced to sell found that the prices that they received were less than half the debt’s estimated value.

Bankers and other short-term lenders applaud firms that have plenty of liquid assets. They know that when they are due to be repaid, the firm will be able to get its hands on the cash. But more liquidity is not always a good thing. For example, efficient firms do not leave excess cash in their bank accounts. They don’t allow customers to postpone paying their bills, and they don’t leave stocks of raw materials and finished goods littering the warehouse floor. In other words, high levels of liquidity may indicate sloppy use of capital. Here, EVA can help, because it penalizes managers who keep more liquid assets than they really need.

Net-Working-Capital-to-Total-Assets Ratio Current assets include cash, marketable securities, inventories, and accounts receivable. Current assets are mostly liquid. The difference between current assets and current liabilities is known as net working capital. Since current assets usually exceed current liabilities, net working capital is generally positive. For Home Depot,

Net working capital was 12.8% of total assets:

Current Ratio The current ratio is just the ratio of current assets to current liabilities:

Home Depot has $1.55 in current assets for every dollar in current liabilities.

Changes in the current ratio can be misleading. For example, suppose that a company borrows a large sum from the bank and invests it in marketable securities. Current liabilities rise and so do current assets. If nothing else changes, net working capital is unaffected but the current ratio changes. For this reason it is sometimes preferable to net short-term investments against short-term debt when calculating the current ratio.

Quick (Acid-Test) Ratio Some current assets are closer to cash than others. If trouble comes, inventory may not sell at anything above fire-sale prices. (Trouble typically comes because the firm can’t sell its inventory of finished products for more than production cost.) Thus managers often exclude inventories and other less liquid components of current assets when comparing current assets to current liabilities. They focus instead on cash, marketable securities, and bills that customers have not yet paid. This results in the quick ratio:

Cash Ratio A company’s most liquid assets are its holdings of cash and marketable securities. That is why analysts also look at the cash ratio:

A low cash ratio may not matter if the firm can borrow on short notice. Who cares whether the firm has actually borrowed from the bank or whether it has a guaranteed line of credit so it can borrow whenever it chooses? None of the standard measures of liquidity takes the firm’s “reserve borrowing power” into account.

 28-9   Interpreting Financial Ratios

We have shown how to calculate some common summary measures of Home Depot’s performance and financial condition. These are summarized in Table 28.6. Now that you have calculated these measures, you need some way to judge whether they are high or low. In some cases there may be a natural benchmark. For example, if a firm has negative economic value added or a return on capital less than the cost of that capital, it has not created wealth for its shareholders.

But what about some of our other measures? There is no right level for, say, the asset turnover or profit margin, and if there were, it would almost certainly vary from industry to industry and company to company. For example, you would not expect a soft-drink manufacturer to have the same profit margin as a jeweler or the same leverage as a finance company.

The alternative is to confine your comparison to companies that are in a similar business. A good starting point is to prepare common-size financial statements for each of these firms. In this case all items in the balance sheet are expressed as a percentage of total assets and all items in the income statement are expressed as a percentage of revenues.

We have not calculated here common-size statements for Home Depot but Tables 28.7 and 28.8 provide summary common-size statements for a sample of U.S. industries. Notice the large variations. For example, food retailers have a major investment in inventory; software companies have almost none. High-tech businesses, such as semiconductors, hold huge amounts of cash; utilities hold very little.¹⁸ Oil companies and utilities invest principally in fixed assets; software companies and computer manufacturers have mainly current assets.

   TABLE 28.6 Summary of Home Depot’s financial ratios.

Table 28.9 lists some financial ratios for these companies. The variation between industries also shows up in many of the ratios. The differences arise partly from chance; sometimes the sun shines more kindly on some industries than on others. But the differences also reflect some fundamental industry factors. For example, notice the high debt ratios of utilities. By contrast, software companies scarcely borrow at all. We pointed out earlier that some businesses are able to generate a high level of sales from relatively few assets. For example, you can see that the sales-to-assets ratio for retailers is more than three times that for pharmaceutical companies. But competition ensures that retailers earn a correspondingly lower margin on their sales.

   TABLE 28.7 Common-size balance sheets for U.S. companies in Standard & Poor’s Composite Index, 2011. Entries for each company are expressed as a percentage of total assets and averaged by industry.

Note: Some columns do not add up because of rounding.

Source: Compustat.

   TABLE 28.8 Common-size income statements for U.S. companies in Standard & Poor’s Composite Index, 2011. Entries are expressed as a percentage of sales and averaged across each industry.

Note: Some columns do not add up because of rounding.

Source: Compustat.

   TABLE 28.9 Median financial ratios for U.S. companies in Standard & Poor’s Composite Index, 2011.

a Computed using year-end capital.

Source: Compustat.

When comparing Home Depot’s financial position, it makes sense to limit your comparison to the firm’s main competitors. Table 28.10 sets out some key performance measures for Home Depot and Lowe’s. By most measures Home Depot was turning in the better performance. It had, for example, a higher ratio of market value to book value and a better return on assets. Home Depot’s additional return on assets reflected both its success in generating more sales per dollar of assets and earned a higher profit margin on these sales. Home Depot was less conservatively financed than Lowe’s, but had more liquid assets.¹⁹

It may also be helpful to compare Home Depot’s financial ratios in 2011 with the equivalent figures in earlier years. Figure 28.2 does so. You can see that starting in 2007 Home Depot’s profitability was hit by the downturn in the housing market, but until then the company’s return on assets had increased steadily. What accounts for that improvement? We know that ROA = asset turnover × operating profit margin. The figure shows that the sales that the company generated per dollar of assets declined. The progress in ROA came from the sharp increase in profit margins brought about by the company’s aggressive cost-cutting campaign.

   TABLE 28.10 Selected financial ratios for Home Depot and Lowe’s, 2011.

a Both companies sell most of their receivables to a third party.

   FIGURE 28.2 Home Depot’s financial ratios, 1996–2011.

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SUMMARY

Managers use financial statements to monitor their own company’s performance, to help understand the policies of a competitor, and to check on the financial health of customers. But there is a danger of being overwhelmed by the sheer volume of data in the company’s Annual Report.²⁰ That is why managers use a few salient ratios to summarize the firm’s market valuation, profitability, efficiency, capital structure, and liquidity. We have described some of the more popular financial ratios.

We offer the following general advice to users of these ratios:

 1.  Financial ratios seldom provide answers, but they do help you to ask the right questions.

 2.  There is no international standard for financial ratios. A little thought and common sense are worth far more than blind application of formulas.

 3.  You need a benchmark for assessing a company’s financial position. It is generally useful to compare the company’s current financial ratios with the equivalent ratios in the past and with the ratios of other firms in the same business.

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FURTHER READING

There are some good general texts on financial statement analysis. See, for example:

K. G. Palepu, V. L. Bernard, and P. M. Healy, Business Analysis and Valuation, 4th ed. (Cincinnati, OH: South-Western Publishing, 2008).

L. Revsine, D. Collins, B. Johnson, and F. Mittelstaedt, Financial Reporting and Analysis, 5th ed. (New York: McGraw-Hill/Irwin, 2011).

S. Penman, Financial Statement Analysis and Security Valuation, 5th ed. (New York: McGraw-Hill/Irwin, 2012).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Balance sheets Construct a balance sheet for Galactic Enterprises given the following data:

What is shareholders’ equity?

2.  Financial ratios Table 28.11 on the following page gives abbreviated balance sheets and income statements for Estée Lauder Companies. Calculate the following ratios:

a.  Return on assets.

b.  Operating profit margin.

c.  Sales-to-assets ratio.

d.  Inventory turnover.

e.  Debt–equity ratio.

f.  Current ratio.

g.  Quick ratio

3.  Common-size financial statements Look again at Table 28.11. Calculate a common-size balance sheet and income statement for Estée Lauder.

4.  Performance measures Look again at Table 28.11. At the end of fiscal 2011 Estée Lauder had 197 million shares outstanding²¹ with a share price of $105. The company’s weighted-average cost of capital was about 10%. Calculate:

a.  Market value added.

b.  Market-to-book ratio.

c.  Economic value added.

d.  Return on capital.

5.  Financial ratios There are no universally accepted definitions of financial ratios, but five of the following ratios are clearly incorrect. Substitute the correct definitions.

a.  Debt–equity ratio = (long-term debt + value of leases)/(long-term debt + value of leases + equity)

b.  Return on equity = (EBIT – tax)/average equity

c.  Profit margin = net income/sales

d.  Days in inventory = sales/(inventory/365)

e.  Current ratio = current liabilities/current assets

f.  Sales-to-net-working-capital = average sales/average net working capital

g.  Quick ratio = (current assets – inventories)/current liabilities

h.  Times-interest-earned = interest earned × long-term debt

   TABLE 28.11 Balance sheets and income statement for Estée Lauder Companies, fiscal 2011 (figures in $ millions).

6. Financial ratios True or false?

a.  A company’s debt–equity ratio is always less than 1.

b.  The quick ratio is always less than the current ratio.

c.  The return on equity is always less than the return on assets.

7.  Book rates of return Keller Cosmetics maintains an operating profit margin of 8% and a sales-to-assets ratio of 3. It has assets of $500,000 and equity of $300,000. Interest payments are $30,000 and the tax rate is 35%.

a.  What is the return on assets?

b.  What is the return on equity?

8. Debt ratios A firm has a long-term debt–equity ratio of .4. Shareholders’ equity is $1 million. Current assets are $200,000, and total assets are $1.5 million. If the current ratio is 2.0, what is the ratio of debt to total long-term capital?

9. Financial ratios Magic Flutes has total receivables of $3,000, which represent 20 days’ sales. Total assets are $75,000. The firm’s operating profit margin is 5%. Find the firm’s sales-to-assets ratio and return on assets.

10. Financial ratios Consider this simplified balance sheet for Geomorph Trading:

a.  Calculate the ratio of debt to equity.

b.  What are Geomorph’s net working capital and total long-term capital? Calculate the ratio of debt to total long-term capital.

11. Leverage and liquidity Look again at the balance sheet for Geomorph in Problem 10. Suppose that at year-end Geomorph had $30 in cash and marketable securities. Immediately after the year-end it used a line of credit to borrow $20 for one year, which it invested in additional marketable securities. Would the company appear to be (a) more or less liquid, (b) more or less highly leveraged? Make any additional assumptions that you need.

12. Current assets Airlux Antarctica has current assets of $300 million, current liabilities of $200 million and a crash—sorry—cash ratio of .05. How much cash and marketable securities does it hold?

13. Receivables On average, it takes Microlimp’s customers 60 days to pay their bills. If Microlimp has annual sales of $500 million, what is the average value of unpaid bills?

INTERMEDIATE

14. Interpretation of ratios This question reviews some of the difficulties encountered in interpreting accounting numbers.

a.  Give four examples of important assets, liabilities, or transactions that may not be shown on the company’s books.

b.  How does investment in intangible assets, such as research and development, distort accounting ratios? Give at least two examples.

15. Performance measures Describe some alternative measures of a firm’s overall performance. What are their advantages and disadvantages? In each case discuss what benchmarks you might use to judge whether performance is satisfactory.

16. Leverage ratios Discuss alternative measures of financial leverage. Should the market value of equity be used or the book value? Is it better to use the market value of debt or the book value? How should you treat off-balance-sheet obligations such as pension liabilities? How would you treat preferred stock?

17. Leverage ratios Suppose that a firm has both fixed-rate and floating-rate debt outstanding. What effect will a decline in interest rates have on the firm’s times-interest-earned ratio? What about the ratio of the market value of debt to that of equity? Would you judge that leverage has increased or decreased?

18. Current ratio How would the following actions affect a firm’s current ratio?

a.  Inventory is sold.

b.  The firm takes out a bank loan to pay its suppliers.

c.  The firm arranges a line of credit with a bank that allows it to borrow at any time to pay its suppliers.

d. A customer pays its overdue bills.

e.  The firm uses cash to purchase additional inventories.

19.  Return on assets Sara Togas sells all its output to Federal Stores. The following table shows selected financial data, in millions, for the two firms:

Calculate the sales-to-assets ratio, the operating profit margin, and the return on assets for the two firms. Now assume that the two companies merge. If Federal continues to sell goods worth $100 million, how will the three ratios change?

20.  Financial ratios As you can see, someone has spilled ink over some of the entries in the balance sheet and income statement of Transylvania Railroad (Table 28.12). Can you use the following information to work out the missing entries? (Note: For this problem, use the following definitions: inventory turnover = COGS/average inventory; receivables collection period = average receivables/[sales/365].)

•  Long-term debt ratio: .4.

•  Times-interest-earned: 8.0.

•  Current ratio: 1.4.

•  Quick ratio: 1.0.

   TABLE 28.12 Balance sheet and income statement of Transylvania Railroad (figures in $ millions).

•  Cash ratio: .2.

•  Inventory turnover: 5.0.

•  Receivables collection period: 73 days.

•  Tax rate = .4.

21.  Industry ratios Here are some data for five companies in the same industry:

You have been asked to calculate a measure of times-interest-earned for the industry. Discuss the possible ways that you might calculate such a measure. Does changing the method of calculation make a significant difference to the end result?

22.  Inflation How would rapid inflation affect the accuracy and relevance of a manufacturing company’s balance sheet and income statement? Does your answer depend on how much debt the firm has issued?

23.  Book measures of risk Suppose that you wish to use financial ratios to estimate the risk of a company’s stock. Which of those that we have described in this chapter are likely to be helpful? Can you think of other accounting measures of risk?

24.  Measures of financial distress Look up some firms that have been in trouble. Plot the changes over the preceding years in the principal financial ratios. Are there any patterns?

CHALLENGE

25.  Calculating EVA We noted that, when calculating EVA, you should calculate income as the sum of the after-tax interest payment and net income. Why do you need to deduct the tax shield? Would an alternative be to use a different measure of the cost of capital? Or would you get the same result if you simply deducted the cost of equity from net income (as is often done)?

26.  Return on capital Sometimes analysts use the average of capital at the start and end of the year to calculate return on capital. Provide some examples to illustrate when this does and does not make sense. (Hint: Start by assuming that capital increases solely as a result of retained earnings.)

27.  Leverage ratios Take another look at Geomorph Trading’s balance sheet in Problem 10 and consider the following additional information:

The “R&R reserve” covers the future costs of removal of an oil pipeline and environmental restoration of the pipeline route.

There are many ways to calculate a debt ratio for Geomorph. Suppose you are evaluating the safety of Geomorph’s debt and want a debt ratio for comparison with the ratios of other companies in the same industry. Would you calculate the ratio in terms of total liabilities or total capitalization? What would you include in debt—the bank loan, the deferred tax account, the R&R reserve, the unfunded pension liability? Explain the pros and cons of these choices.

28.  Financial ratios – International differences Go to the website of the Brazilian oil company Petrobras. Go to “Interactive Balance Sheets” under “Investor Relations.” This feature presents quarterly balance sheets and income statements for the company. You can convert to English if that’s convenient. Calculate a few key financial ratios for the company, then compare the ratios for a U.S. or European company, for example the French company Total. Can you find significant, long-lasting differences in the ratios for the two companies? What do the ratios say about the profitability and financial strategies of the two companies?

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FINANCE ON THE WEB

Use data from Yahoo! Finance (finance.yahoo.com) to answer the following questions.

1.  Select two companies that are in a similar line of business and find their simplified balance sheets and income statements. Then draw up common-size statements for each company and compute the principal financial ratios. Compare and contrast the companies based on these data.

2.  Look up the latest financial statements for a company of your choice and calculate the following ratios for the latest year:

a.  Return on capital.

b.  Return on equity.

c.  Operating profit margin.

d.  Days in inventory.

e.  Debt ratio.

f.  Times-interest-earned.

g.  Current ratio.

h.  Quick ratio.

3.  Select five companies and, using their financial statements, compare the days in inventory and average collection period for receivables. Can you explain the differences between the companies?

___________

¹The British and Americans can never agree whether to keep to the left or the right. British accountants list liabilities on the left and assets on the right. (The right-hand side is actually plotted below in the table.)

²For simplicity we have deducted $13 million of other income from the selling, general, and administrative expenses.

³Home Depot’s 2011 fiscal year ended on January 29, 2012.

⁴The market-to-book ratio can also be calculated by dividing stock price by book value per share.

⁵The expression, return on capital, is commonly used when calculating the profitability of an entire firm. When measuring the profitability of an individual plant, the equivalent measure is generally called return on investment (or ROI).

⁶This figure is called the company’s Net Operating Profit After Tax or NOPAT:

In the case of Home Depot

⁷For the same reason we used the after-tax interest payment when we calculated Home Depot’s EVA.

⁸Remember WACC is a weighted average of the after-tax rate of interest and the cost of equity.

⁹Although it is sometimes done, it is not correct to compare return on assets with WACC. Current liabilities are ignored when calculating WACC.

¹⁰Sometimes it is convenient to use a snapshot figure at the end of the year, although this is not strictly appropriate.

¹¹Where possible, it makes sense to look only at credit sales. Otherwise a high ratio might simply indicate that a small proportion of sales is made on credit.

¹²If a firm pays out most of its profits as interest, it will pay less tax and have a higher operating profit margin than one that is financed solely by equity. To obtain a measure of the profit margin that is unaffected by the firm’s financial structure, we need to subtract the tax savings on the interest.

¹³A finance lease is a long-term rental agreement that commits the firm to make regular payments. This commitment is just like the obligation to make payments on an outstanding loan. See Chapter 25.

¹⁴In the case of leased assets, accountants estimate the value of the lease commitments. In the case of long-term debt, they simply show the face value, which can be very different from market value. For example, the present value of low-coupon debt may be only a fraction of its face value. The difference between the book value of equity and its market value can be even more dramatic.

¹⁵In this case, the debt consists of all liabilities, including current liabilities.

¹⁶The numerator of times-interest-earned can be defined in several ways. Sometimes depreciation is excluded. Sometimes it is just earnings plus interest, that is, earnings before interest but after tax. This last definition seems nutty to us, because the point of times-interest-earned is to assess the risk that the firm won’t have enough money to pay interest. If EBIT falls below interest obligations, the firm won’t have to worry about taxes. Interest is paid before the firm pays taxes.

¹⁷Earnings before interest, taxes, depreciation, and amortization are often termed EBITDA.

¹⁸We return to this difference in Chapter 30.

¹⁹One apparently puzzling discrepancy between the two firms is the dramatic difference in the receivables turnover and collection period. With an average collection period of just over a day, Lowe’s appears to be far more efficient at collecting its bills. This is an illusion. The notes to Lowe’s financial statements reveal that the company finances most of its receivables by selling them to GE at a discount. The lesson? Ratios can tip you off to differences in strategy as well as to emerging business strengths or problems, but you will generally need to probe further to understand fully the implication of the numbers.

²⁰HSBC’s 2007 Annual Report totaled 454 pages. The Financial Times reported that Britain’s postal service was obliged to limit the number that its postmen carried in order to prevent back injuries.

²¹The shares outstanding include some class B shares.

Part 9 Financial Planning and Working Capital Management

Financial Planning

This chapter is concerned with financial planning. We look first at short-term planning where the focus is on ensuring that the firm does not run out of cash. Short-term planning is, therefore, often termed cash budgeting. In the second half of the chapter we look at how firms also use financial planning models to develop a coherent long-term strategy.

The principal short-term assets are inventory, accounts receivable, cash, and marketable securities. Decisions on these assets cannot be made in isolation. For example, suppose that the marketing manager wishes to give customers more time to pay for their purchases. This reduces the firm’s future cash balances. Or perhaps the production manager adopts a just-in-time system for ordering from suppliers. That allows the firm to get by on smaller inventories and frees up cash.

Managers concerned with short-term financial decisions can avoid many of the difficult conceptual issues encountered elsewhere in this book. In that respect short-term decisions are easier than long-term decisions, but they are not less important. A firm can identify extremely valuable capital investment opportunities, find the precise optimal debt ratio, follow the perfect dividend policy, and yet founder because no one bothers to raise the cash to pay this year’s bills. Hence the need for short-term planning.

Short-term planning rarely looks further ahead than the next 12 months. It seeks to ensure that the firm has enough cash to pay its bills and makes sensible short-term borrowing and lending decisions. But the financial manager also needs to think about the investments that will be needed to meet the firm’s long-term goals and the financing that must be arranged. Long-term financial planning focuses on the implications of alternative financial strategies. It allows managers to avoid some surprises and consider how they should react to surprises that cannot be avoided. And it helps to establish goals for the firm and to provide standards for measuring performance.

 29-1   Links Between Short-Term and Long-Term Financing Decisions

Short-term financial decisions differ in two ways from long-term decisions such as the purchase of plant and equipment or the choice of capital structure. First, they generally involve short-lived assets and liabilities, and, second, they are usually easily reversed. Compare, for example, a 60-day bank loan with an issue of 20-year bonds. The bank loan is clearly a short-term decision. The firm can repay it two months later and be right back where it started. A firm might conceivably issue a 20-year bond in January and retire it in March, but it would be extremely inconvenient and expensive to do so. In practice, the bond issue is a long-term decision, not only because of the bond’s 20-year maturity but also because the decision to issue it cannot be reversed on short notice.

   FIGURE 29.1 The firm’s cumulative capital requirement (red line) is the cumulative investment in all the assets needed for the business. This figure shows that the requirement grows year by year, but there is some seasonal fluctuation within each year. The requirement for short-term financing is the difference between long-term financing (lines A, B, and C) and the cumulative capital requirement. If long-term financing follows line C, the firm always needs short-term financing. At line B, the need is seasonal. At line A, the firm never needs short-term financing. There is always extra cash to invest.

All businesses require capital—that is, money invested in plant, machinery, inventories, accounts receivable, and all the other assets it takes to run a business. These assets can be financed by either long-term or short-term sources of capital. Let us call the total investment the firm’s cumulative capital requirement. For most firms the cumulative capital requirement grows irregularly, like the wavy line in Figure 29.1. This line shows a clear upward trend as the firm’s business grows. But the figure also shows seasonal variation around the trend, with the capital requirement peaking late in each year. In addition, there would be unpredictable week-to-week and month-to-month fluctuations, but we have not attempted to show these in Figure 29.1.

When long-term financing does not cover the cumulative capital requirement, the firm must raise short-term capital to make up the difference. When long-term financing more than covers the cumulative capital requirement, the firm has surplus cash available. Thus the amount of long-term financing raised, given the capital requirement, determines whether the firm is a short-term borrower or lender.

Lines A, B, and C in Figure 29.1 illustrate this. Each depicts a different long-term financing strategy. Strategy A implies a permanent cash surplus, which can be invested in short-term securities. Strategy C implies a permanent need for short-term borrowing. Under B, which is probably the most common strategy, the firm is a short-term lender during part of the year and a borrower during the rest.

What is the best level of long-term financing relative to the cumulative capital requirement? It is hard to say. There is no convincing theoretical analysis of this question. We can make practical observations, however. First, most financial managers attempt to “match maturities” of assets and liabilities.¹ That is, they largely finance long-lived assets like plant and machinery with long-term borrowing and equity. Second, most firms make a permanent investment in net working capital (current assets less current liabilities). This investment is financed from long-term sources.

   FIGURE 29.2 Cash as a percent of assets for U.S. nonfinancial firms.

Source: T. W. Bates, K. M. Kahle, and R. M. Stulz, “Why Do U.S. Firms Hold So Much More Cash than They Used To?” Journal of Finance 64 (2009), pp. 1985–2021. Used with permission from John Wiley and Sons, via Copyright Clearance Center. Updated to 2010 by the authors.

Current assets can be converted into cash more easily than long-term assets. So firms with large holdings of current assets enjoy greater liquidity. Of course, some of these assets are more liquid than others. Inventories are converted into cash only when the goods are produced, sold, and paid for. Receivables are more liquid; they become cash as customers pay their outstanding bills. Short-term securities can generally be sold if the firm needs cash on short notice and are therefore more liquid still.

Whatever the motives for holding cash, they seem more powerful today than they used to be. You can see from Figure 29.2 that, on average, firms in the United States now hold a much higher proportion of their assets in cash and marketable securities.

Some firms choose to hold more liquidity than others. For example, many high-tech companies, such as Intel and Cisco, hold huge amounts of short-term securities. On the other hand, firms in old-line manufacturing industries—such as chemicals, paper, or steel—manage with a far smaller reserve of liquidity. Why is this? One reason is that companies with rapidly growing profits may generate cash faster than they can redeploy it in new positive-NPV investments. This produces a surplus of cash that can be invested in short-term securities. Of course, companies faced with a growing mountain of cash may eventually respond by adjusting their payout policies. In Chapter 16 we saw how Apple reduced its cash mountain by paying a special dividend and repurchasing its stock.

There are some advantages to holding a large reservoir of cash, particularly for smaller firms that face relatively high costs of raising funds on short notice. For example, biotech firms require large amounts of cash to develop new drugs. Therefore, these firms generally have substantial cash holdings to fund their R&D programs. If these precautionary reasons for holding liquid assets are important, we should find that small companies in relatively high-risk industries are more likely to hold large cash surpluses. A study by Tim Opler and others confirms that this is in fact the case.²

Financial managers of firms with a surplus of long-term financing and with cash in the bank don’t have to worry about finding the money to pay next month’s bills. The cash can help to protect the firm against a rainy day and give it the breathing space to make changes to operations. However, there are also drawbacks to surplus cash. Holdings of marketable securities are at best a zero-NPV investment for a taxpaying firm.³ Also managers of firms with large cash surpluses may be tempted to run a less tight ship and may simply allow the cash to seep away in a succession of operating losses. For example, at the end of 2007 General Motors held $27 billion in cash and short-term investments. But shareholders valued GM stock at less than $14 billion. It seemed that shareholders realized (correctly) that the cash would be used to support ongoing losses and to service GM’s huge debts.

Pinkowitz and Williamson looked at the value that investors place on a firm’s cash and found that on average shareholders valued a dollar of cash at $1.20.⁴ They placed a particularly high value on liquidity in the case of firms with plenty of growth opportunities. At the other extreme, they found that, when a firm was likely to face financial distress, a dollar of cash within the firm was often worth less than a dollar to the shareholders.⁵

 29-2   Tracing Changes in Cash

Table 29.1 shows the 2012 income statement for Dynamic Mattress Company, and Table 29.2 compares the firm’s 2011 and 2012 year-end balance sheets. You can see that in 2012 Dynamic’s cash balance increased from $20 million to $25 million.

What caused this increase? Did the extra cash come from Dynamic’s issue of long-term debt, from reinvested earnings, from cash released by reducing inventory, or from extra credit extended by Dynamic’s suppliers? (Note the increase in accounts payable.) The answer is provided in the company’s cash flow statement shown in Table 29.3.

   TABLE 29.1 Income statement for Dynamic Mattress Company, 2012 (figures in $ millions).

Cash flow statements classify cash flows into those from operating activities, investing activities, and financing activities. Sources of cash are shown as positive numbers; uses of cash are shown as negative numbers. Dynamic’s cash flow statement shows that Dynamic generated cash from the following sources:

BEYOND THE PAGE

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Try It! Dynamic Mattress’s spreadsheet

brealey.mhhe.com/c29

   TABLE 29.2 Year-end balance sheets for 2012 and 2011 for Dynamic Mattress Company (figures in $ millions).

   TABLE 29.3 Statement of cash flows for Dynamic Mattress Company, 2012 (figures in $ millions).

 1.  It earned $60 million of net income (operating activity).

 2.  It set aside $20 million as depreciation. Remember that depreciation is not a cash outlay. Thus, it must be added back to obtain Dynamic’s cash flow (operating activity).

 3.  It reduced inventory, releasing $5 million (operating activity).

 4.  It increased its accounts payable, in effect borrowing an additional $25 million from its suppliers (operating activity).

 5.  It issued $30 million of long-term debt (financing activity).

Dynamic’s cash flow statement shows that it used cash for the following purposes:

 1.  It allowed accounts receivable to expand by $25 million (operating activity). In effect, it lent this additional amount to its customers.

 2.  It invested $30 million (investing activity). This shows up as the increase in gross fixed assets in Table 29.2.

 3.  It paid a $30 million dividend (financing activity). (Note: The $30 million increase in Dynamic’s equity in Table 29.2 is due to retained earnings: $60 million of equity income, less the $30 million dividend.)

 4.  It purchased $25 million of marketable securities (financing activity).

 5.  It repaid $25 million of short-term bank debt (financing activity).⁶

Look again at Table 29.3. Notice that to calculate cash flows from operating activities, we start with net income and then make two adjustments. First, since depreciation is not a cash outlay, we must add it back to net income.⁷ Second, we need to recognize the fact that the income statement shows sales and expenditures when they are made, rather than when cash changes hands. For example, think of what happens when Dynamic sells goods on credit. The company records a profit at the time of sale, but there is no cash inflow until the bills are paid. Since there is no cash inflow, there is no change in the company’s cash balance, although there is an increase in working capital in the form of an increase in accounts receivable. No net addition to cash would be shown in a cash flow statement like Table 29.3. The increase in cash from operations would be offset by an increase in accounts receivable. Later, when the bills are paid, there is an increase in the cash balance. However, there is no further profit at this point and no increase in working capital. The increase in the cash balance is exactly matched by a decrease in accounts receivable.

Table 29.3 adjusts the cash flow from operating activities downward by $25 million to reflect the additional credit that Dynamic has extended to its customers. On the other hand, in 2012 Dynamic reduced its inventories and increased the amount that is owed to its suppliers. The cash flow from operating activities is adjusted upward to reflect these changes.

That brings up an interesting characteristic of working capital. Imagine a company that conducts a very simple business. It buys raw materials for cash, processes them into finished goods, and then sells these goods on credit. The whole cycle of operations looks like this:

If you draw up a balance sheet at the beginning of the process, you see cash. If you delay a little, you find the cash replaced by inventories of raw materials and, still later, by inventories of finished goods. When the goods are sold, the inventories give way to accounts receivable, and, finally, when the customers pay their bills, the firm draws out its profit and replenishes the cash balance.

There is only one constant in this process, namely, working capital. That is one reason why (net) working capital is a useful summary measure of current assets and liabilities. The strength of the working-capital measure is that it is unaffected by seasonal or other temporary movements between different current assets or liabilities. But the strength is also its weakness, for the working-capital figure hides a lot of interesting information. In our example cash was transformed into inventory, then into receivables, and back into cash again. But these assets have different degrees of risk and liquidity. You can’t pay bills with inventory or with receivables. You must pay with cash.

The Cash Cycle

In Chapter 28 we showed how to calculate the average time that materials remain in inventory and the average time that it takes for customers to pay their bills. In the case of Dynamic:

We can also calculate the average time that it takes Dynamic to pay its bills:⁸

Think what this implies for the financing that is needed to maintain regular operations. Suppose that Dynamic purchases materials on day 0. It pays for these materials on day 24 (average payment period = 24 days). By day 29 Dynamic has converted the raw materials into finished mattresses that are then sold (days in inventory = 29). Twenty-one days later on day 50 Dynamic’s customers pay for their purchases (collection period = 21). Thus, cash went out the door on day 24; it did not come back in again until day 50. This 26-day interval is called the cash cycle or cash conversion period:⁹

The cash cycle affects the amount of working capital that the firm needs. For example, major machinery manufacturers typically hold large inventories and offer long payment periods. Their cash cycle is nearly six months and they need to make a substantial investment in net working capital. By contrast, utilities with their low investment in inventory have a cash cycle of only about one and a half months. Utilities often have negative working capital.

 29-3    Cash Budgeting

The past is interesting for what one can learn from it. The financial manager’s problem is to forecast future sources and uses of cash. These forecasts serve two purposes. First, they provide a standard, or budget, against which subsequent performance can be judged. Second, they alert the manager to future cash-flow needs. Cash, as we all know, has a habit of disappearing fast.

Preparing the Cash Budget: Inflows

We illustrate the preparation of the capital budget by continuing the example of Dynamic Mattress.

Most of Dynamic’s cash inflow comes from the sale of mattresses. We therefore start with a sales forecast by quarter for 2013:¹⁰

But sales become accounts receivable before they become cash. Cash flow comes from collections on accounts receivable.

Most firms keep track of the average time it takes customers to pay their bills. From this they can forecast what proportion of a quarter’s sales is likely to be converted into cash in that quarter and what proportion is likely to be carried over to the next quarter as accounts receivable. Suppose that 70% of sales are “cashed in” in the immediate quarter and 30% are cashed in the following quarter. Table 29.4 shows forecasted collections under this assumption. For example, you can see that in the first quarter collections from current sales are 70% of $560, or $392 million. But the firm also collects 30% of the previous quarter’s sales, or .3($397) = $119 million. Therefore total collections are $392 + $119 = $511 million.

Dynamic started the first quarter with $150 million of accounts receivable. The quarter’s sales of $560 million were added to accounts receivable, but collections of $511 million were subtracted. Therefore, Table 29.4 shows that Dynamic ended the quarter with accounts receivable of $150 + 560 – 511 = $199 million. The general formula is

Ending accounts receivable = beginning accounts receivable + sales – collections

   TABLE 29.4 To forecast Dynamic Mattress’s collections on accounts receivable, you have to forecast sales and collection rates in 2013 (figures in $ millions).

aWe assume that sales in the last quarter of the previous year were $397 million.

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   TABLE 29.5 Dynamic Mattress’s cash budget for 2013 (figures in $ millions)

The top section of Table 29.5 shows forecasted sources of cash for Dynamic Mattress. Collection of receivables is the main source, but it is not the only one. Perhaps the firm plans to dispose of some land or expects a tax refund or payment of an insurance claim. All such items are included as “other” sources. It is also possible that you may raise additional capital by borrowing or selling stock, but we don’t want to prejudge that question. Therefore, for the moment we just assume that Dynamic will not raise further long-term finance.

Preparing the Cash Budget: Outflows

So much for the incoming cash. Now for the outgoing. There always seem to be many more uses for cash than there are sources. For simplicity, we have condensed the uses into five categories in Table 29.5.

 1.  Payments on accounts payable. The firm has to pay its bills for raw materials, parts, electricity, etc. The cash-flow forecast assumes all these bills are paid on time, although Dynamic could probably delay payment to some extent. Delaying payment is sometimes called stretching payables. Stretching is one source of short-term financing, but for most firms it is an expensive source, because by stretching they lose discounts given to firms that pay promptly.

 2.  Increase in inventories. The expected increase in sales in 2013 requires additional investment in inventories.

 3.  Labor, administrative, and other expenses. This category includes all other regular business expenses.

 4.  Capital expenditures. Note that Dynamic Mattress plans a major capital outlay in the first quarter.

 5.  Taxes, interest, and dividend payments. This includes interest on presently outstanding long-term debt but does not include interest on any additional borrowing to meet cash requirements in 2013. At this stage in the analysis, Dynamic does not know how much it will have to borrow, or whether it will have to borrow at all.

The forecasted net inflow of cash (sources minus uses) is shown by the shaded line in Table 29.5. Note the large negative figure for the first quarter: a $141 million forecasted outflow. There is a smaller forecasted outflow in the second quarter, and then substantial cash inflows in the third and fourth quarters.

The bottom part of Table 29.5 calculates how much financing Dynamic will have to raise if its cash-flow forecasts are right. It starts the year with $25 million in cash. There is a $141 million cash outflow in the first quarter, and so Dynamic will have to obtain at least $141 – 25 = $116 million of additional financing. This would leave the firm with a forecasted cash balance of exactly zero at the start of the second quarter.

Most financial managers regard a planned cash balance of zero as driving too close to the edge of the cliff. They establish a minimum operating cash balance to absorb unexpected cash inflows and outflows. We assume that Dynamic’s minimum operating cash balance is $25 million. This means it will have to raise the full $141 million in the first quarter and $72.6 million more in the second quarter. Thus its cumulative financing requirement is $213.6 million by the second quarter. Fortunately, this is the peak: the cumulative requirement declines in the third quarter by $120 million to $93.6 million. In the final quarter Dynamic is out of the woods: its cash balance is $101.7 million, well clear of its minimum operating balance.

The next step is to develop a short-term financing plan that covers the forecasted requirements in the most economical way. We move on to that topic after two general observations:

 1.  The large cash outflows in the first two quarters do not necessarily spell trouble for Dynamic Mattress. In part, they reflect the capital investment made in the first quarter: Dynamic is spending $70 million, but it should be acquiring an asset worth that much or more. In part, the cash outflows reflect low sales in the first half of the year; sales recover in the second half.¹¹ If this is a predictable seasonal pattern, the firm should have no trouble borrowing to tide it over the slow months.

 2.  Table 29.5 is only a best guess about future cash flows. It is a good idea to think about the uncertainty in your estimates. For example, you could undertake a sensitivity analysis, in which you inspect how Dynamic’s cash requirements would be affected by a shortfall in sales or by a delay in collections. The trouble with such sensitivity analyses is that you are changing only one item at a time, whereas in practice a downturn in the economy might affect, say, sales levels and collection rates. An alternative but more complicated solution is to build a model of the cash budget and then to simulate possible alternative cash requirements. If cash requirements are difficult to predict, you may wish to hold additional cash or marketable securities to cover a possible unexpected cash outflow.

 29-4    The Short-Term Financing Plan

Dynamic’s cash budget defines its problem: its financial manager must find short-term financing to cover the firm’s forecasted cash requirements. There are dozens of sources of short-term financing, but for simplicity we assume that Dynamic has just two options.

Options for Short-Term Financing

 1.  Bank loan. Dynamic has an existing arrangement with its bank allowing it to borrow up to $100 million at an interest cost of 10% a year or 2.5% per quarter. The firm can borrow and repay whenever it wants to do so, as long as it does not exceed its credit limit.

 2.  Stretching payables. Dynamic can also raise capital by putting off paying its bills. The financial manager believes that Dynamic can defer up to $100 million of payables each quarter. Thus, $100 million can be saved in the first quarter by not paying bills in that quarter. (Note that the cash-flow forecasts in Table 29.5 assumed that these bills will be paid in the first quarter.) If deferred, these payments must be made in the second quarter, but a further $100 million of the second quarter bills can be deferred to the third quarter, and so on.

Stretching payables is often costly, even if no ill will is incurred. The reason is that suppliers may offer discounts for prompt payment. Dynamic loses this discount if it pays late. In this example we assume the lost discount is 5% of the amount deferred. In other words, if a $100 payment is delayed, the firm must pay $105 in the next quarter.

Dynamic’s Financing Plan

With these two options, the short-term financing strategy is obvious. Use the bank loan first, if necessary up to the $100 million limit. If there is still a shortage of cash, stretch payables.

Table 29.6 shows the resulting plan. In the first quarter the plan calls for borrowing the full amount from the bank ($100 million) and stretching $16 million of payables (see lines 1 and 2 in the table). In addition the company sells the $25 million of marketable securities it held at the end of 2012 (line 8). Thus it raises 100 + 16 – 25 = $141 million of cash in the first quarter (line 10).

   TABLE 29.6 Dynamic Mattress’s financing plan (figures in $ millions).

In the second quarter, the plan calls for Dynamic to continue to borrow $100 million from the bank and to stretch $92.4 million of payables. This raises $76.4 million after paying off the $16 million of bills deferred from the first quarter.

Why raise $76.4 million when Dynamic needs only an additional $72.6 million to finance its operations? The answer is that the company must pay interest on the borrowings that it undertook in the first quarter and it forgoes interest on the marketable securities that were sold.¹²

In the third and fourth quarters the plan calls for Dynamic to pay off its debt and to make a purchase of marketable securities.

Evaluating the Plan

Does the plan shown in Table 29.6 solve Dynamic’s short-term financing problem? No: the plan is feasible, but Dynamic can probably do better. The most glaring weakness is its reliance on stretching payables, an extremely expensive financing device. Remember that it costs Dynamic 5% per quarter to delay paying bills—an effective interest rate of over 20% per year. The first plan would merely stimulate the financial manager to search for cheaper sources of short-term borrowing.

The financial manager would ask several other questions as well. For example:

 1.  Does the plan yield satisfactory current and quick ratios?¹³ Its bankers may be worried if these ratios deteriorate.¹⁴

 2.  Are there intangible costs of stretching payables? Will suppliers begin to doubt Dynamic’s creditworthiness?

 3.  Does the plan for 2013 leave Dynamic in good financial shape for 2014? (Here the answer is yes, since Dynamic will have paid off its short-term borrowing by the end of the year.)

 4.  Should Dynamic try to arrange long-term financing for the major capital expenditure in the first quarter? This seems sensible, following the rule of thumb that long-term assets deserve long-term financing. It would also reduce the need for short-term borrowing dramatically. A counterargument is that Dynamic is financing the capital investment only temporarily by short-term borrowing. By year-end, the investment is paid for by cash from operations. Thus Dynamic’s initial decision not to seek immediate long-term financing may reflect a preference for ultimately financing the investment with retained earnings.

 5.  Is it possible to adjust the firm’s operating and investment plans to make the short-term financing problem easier? Perhaps there is a way to defer the first quarter’s large cash outflow? For example, suppose that the large capital investment in the first quarter is for new mattress-stuffing machines to be delivered and installed in the first half of the year. The new machines are not scheduled to be ready for full-scale use until August. Perhaps the machine manufacturer could be persuaded to accept 60% of the purchase price on delivery and 40% when the machines are installed and operating satisfactorily.

 6.  Should Dynamic release cash by reducing the level of other current assets? For example, it could reduce receivables by getting tough with customers who are late paying their bills. (The cost is that in the future these customers may take their business elsewhere.) Or it may be able to get by with lower inventories of mattresses. (The cost is that it may lose business if there is a rush of orders that it cannot supply.)

Short-term financing plans are developed by trial and error. You lay out one plan, think about it, and then try again with different assumptions on financing and investment alternatives. You continue until you can think of no further improvements.

Trial and error is important because it helps you understand the real nature of the problem the firm faces. Here we can draw a useful analogy between the process of planning and Chapter 10, “Project Analysis.” In Chapter 10 we described sensitivity analysis and other tools used by firms to find out what makes capital investment projects tick and what can go wrong with them. Dynamic’s financial manager faces the same kind of task here: not just to choose a plan but to understand what can go wrong and what will be done if conditions change unexpectedly.¹⁵

A Note on Short-Term Financial Planning Models

Working out a consistent short-term plan requires burdensome calculations.¹⁶ Fortunately much of the arithmetic can be delegated to a computer. Many large firms have built short-term financial planning models to do this. Smaller companies do not face so much detail and complexity and find it easier to work with a spreadsheet program on a personal computer. In either case the financial manager specifies forecasted cash requirements or surpluses, interest rates, credit limits, etc., and the model grinds out a plan like the one shown in Table 29.6.

The computer also produces balance sheets, income statements, and whatever special reports the financial manager may require. Smaller firms that do not want custom-built models can rent general-purpose models offered by banks, accounting firms, management consultants, or specialized computer software firms.

Most of these models simply work out the consequences of the assumptions and policies specified by the financial manager. Optimization models for short-term financial planning are also available. These models are usually linear programming models. They search for the best plan from a range of alternative policies identified by the financial manager. Optimization helps when the firm faces complex problems where trial and error might never identify the best combination of alternatives.

Of course the best plan for one set of assumptions may prove disastrous if the assumptions are wrong. Thus the financial manager has to explore the implications of alternative assumptions about future cash flows, interest rates, and so on.

 29-5    Long-Term Financial Planning

It’s been said that a camel looks like a horse designed by a committee. If a firm made every decision piecemeal, it would end up with a financial camel. That is why smart financial managers also need to plan for the long term and to consider the financial actions that will be needed to support the company’s long-term growth. Here is where finance and strategy come together. A coherent long-term plan demands an understanding of how the firm can generate superior returns by its choice of industry and by the way that it positions itself within that industry.

Long-term planning involves capital budgeting on a grand scale. It focuses on the investment by each line of business and avoids getting bogged down in details. Of course, some individual projects may be large enough to have significant individual impact. For example, when mining giant, Rio Tinto, committed to invest $4.6 billion in the Oyu Tolgoi copper mine in Mongolia, you can bet that this project was explicitly analyzed as part of its long-range financial plan. Normally, however, planners do not work on a project-by-project basis. Instead, they are content with rules of thumb that relate average levels of fixed and short-term assets to annual sales, and do not worry so much about seasonal variations in these relationships. In such cases, the likelihood that accounts receivable may rise as sales peak in the holiday season would be a needless detail that would distract from more important strategic decisions.

Why Build Financial Plans?

Firms spend considerable time and resources in long-term planning. What do they get for this investment?

Contingency Planning Planning is not just forecasting. Forecasting concentrates on the most likely outcomes, but planners worry about unlikely events as well as likely ones. If you think ahead about what could go wrong, then you are less likely to ignore the danger signals and you can respond faster to trouble.

Companies have developed a number of ways of asking “what if” questions about both individual projects and the overall firm. For example, managers often work through the consequences of their decisions under different scenarios. One scenario might envisage high interest rates contributing to a slowdown in world economic growth and lower commodity prices. A second scenario might involve a buoyant domestic economy, high inflation, and a weak currency. The idea is to formulate responses to inevitable surprises. What will you do, for example, if sales in the first year turn out to be 10% below forecast? A good financial plan should help you adapt as events unfold.

Considering Options Planners need to think whether there are opportunities for the company to exploit its existing strengths by moving into a wholly new area. Often they may recommend entering a market for “strategic” reasons—that is, not because the immediate investment has a positive net present value but because it establishes the firm in a new market and creates options for possibly valuable follow-on investments.

For example, Verizon’s costly fiber-optic initiative gives the company the real option to offer additional services that may be highly valuable in the future, such as the rapid delivery of an array of home entertainment services. The justification for the huge investment lies in these potential growth options.

Forcing Consistency Financial plans draw out the connections between the firm’s plans for growth and the financing requirements. For example, a forecast of 25% growth might require the firm to issue securities to pay for necessary capital expenditures, while a 5% growth rate might enable the firm to finance these expenditures by using only reinvested profits.

Financial plans should help to ensure that the firm’s goals are mutually consistent. For example, the chief executive might say that she is shooting for a profit margin of 10% and sales growth of 20%, but financial planners need to think about whether the higher sales growth may require price cuts that will reduce profit margin.

Moreover, a goal that is stated in terms of accounting ratios is not operational unless it is translated back into what that means for business decisions. For example, a higher profit margin can result from higher prices, lower costs, or a move into new, high-margin products. Why then do managers define objectives in this way? In part, such goals may be a code to communicate real concerns. For example, a target profit margin may be a way of saying that in pursuing sales growth, the firm has allowed costs to get out of control. The danger is that everyone may forget the code and the accounting targets may be seen as goals in themselves. No one should be surprised when lower-level managers focus on the goals for which they are rewarded. For example, when Volkswagen set a goal of a 6.5% profit margin, some VW groups responded by developing and promoting expensive, high-margin cars. Less attention was paid to marketing cheaper models, which had lower profit margins but higher sales volume. As soon as this became apparent, Volkswagen announced that it would de-emphasize its profit margin goal and would instead focus on return on investment. It hoped that this would encourage managers to get the most profit out of every dollar of invested capital.

A Long-Term Financial Planning Model for Dynamic Mattress

Financial planners often use a financial planning model to help them explore the consequences of alternative strategies. We will drop in again on the financial manager of Dynamic Mattress to see how he uses a simple spreadsheet program to draw up the firm’s long-term plan.

Long-term planning is concerned with the big picture. Therefore, when constructing long-term planning models it is generally acceptable to collapse all current assets and liabilities into a single figure for net working capital. Table 29.7 replaces Dynamic’s latest balance sheets with condensed versions that report only net working capital rather than individual current assets or liabilities.

Suppose that Dynamic’s analysis of the industry leads it to forecast a 20% annual growth in the company’s sales and profits over the next five years. Can the company realistically expect to finance this out of retained earnings and borrowing, or should it plan for an issue of equity? Spreadsheet programs are tailor-made for such questions. Let’s investigate.

The basic sources and uses relationship tells us that

Thus there are three steps to finding how much extra capital Dynamic will need and the implications for its debt ratio.

Step 1 Project next year’s net income plus depreciation, assuming the planned 20% increase in revenues. The first column of Table 29.8 shows this figure for Dynamic in the latest year (2012) and is taken from Table 29.1. The remaining columns show the forecasted values for the following five years.

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   TABLE 29.7 Condensed year-end balance sheets for 2012 and 2011 for Dynamic Mattress Company (figures in $ millions).

a When only net working capital appears on a firm’s balance sheet, this figure (the sum of long-term liabilities and net worth) is often referred to as total capitalization.

Step 2 Project what additional investment in net working capital and fixed assets will be needed to support this increased activity and how much of the net income will be paid out as dividends. The sum of these expenditures gives you the total uses of capital. If the total uses of capital exceed the cash flow generated by operations, Dynamic will need to raise additional long-term capital. The first column of Table 29.9 shows that in 2012 Dynamic needed to raise $30 million of new capital. The remaining columns forecast its capital needs for the following five years. For example, you can see that Dynamic will need to issue $144.5 million of debt in 2013 if it is to expand at the planned rate and not sell more shares.

Step 3 Finally, construct a forecast, or pro forma, balance sheet that incorporates the additional assets and the new levels of debt and equity. For example, the first column in Table 29.10 shows the latest condensed balance sheet for Dynamic Mattress. The remaining columns show that the company’s equity grows by the additional retained earnings (net income less dividends), while long-term debt increases steadily to $691 million.

   TABLE 29.8 Actual (2012) and forecasted operating cash flows for Dynamic Mattress Company (figures in $ millions).

   TABLE 29.9 Actual (2012) and forecasted amounts of external capital required for Dynamic Mattress Company (figures in $ millions).

   TABLE 29.10 Actual (2012) and pro forma balance sheets for Dynamic Mattress Company (figures in $ millions).

Over the five-year period Dynamic Mattress is forecasted to borrow an additional $601 million, and by year 2017 its debt ratio will have risen from 20% to 54%. The interest payments would still be comfortably covered by earnings and most financial managers could just about live with this amount of debt. However, the company could not continue to borrow at that rate beyond five years, and the debt ratio might be close to the limit set by the company’s banks and bondholders.

An obvious alternative is for Dynamic to issue a mix of debt and equity, but there are other possibilities that the financial manager may want to explore. One option may be to hold back dividends during this period of rapid growth. An alternative might be to investigate whether the company could cut back on net working capital. For example, it may be able to economize on inventories or speed up the collection of receivables. The model makes it easy to examine these alternatives.

We stated earlier that financial planning is not just about exploring how to cope with the most likely outcomes. It also needs to ensure that the firm is prepared for unlikely or unexpected ones. For example, management would certainly wish to check that Dynamic Mattress could cope with a cyclical decline in sales and profit margins. Sensitivity analysis or scenario analysis can help to do this.

Pitfalls in Model Design

The Dynamic Mattress model that we have developed is too simple for practical application. You probably have already thought of several ways to improve it—by keeping track of the outstanding shares, for example, and printing out earnings and dividends per share. Or you might want to distinguish between short-term lending and borrowing opportunities, now buried in working capital.

The model that we developed for Dynamic Mattress is known as a percentage of sales model. Almost all the forecasts for the company are proportional to the forecasted level of sales. However, in reality many variables will not be proportional to sales. For example, important components of working capital such as inventory and cash balances will generally rise less rapidly than sales. In addition, fixed assets such as plant and equipment are not usually added in small increments as sales increase. The Dynamic Mattress plant may well be operating at less than full capacity, so that the company can initially increase output without any additions to capacity. Eventually, however, if sales continue to increase, the firm may need to make a large new investment in plant and equipment.

But beware of adding too much complexity: There is always the temptation to make a model bigger and more detailed. You may end up with an exhaustive model that is too cumbersome for routine use. The fascination of detail, if you give in to it, distracts attention from crucial decisions like stock issues and payout policy.

Choosing a Plan

Financial planning models help the manager to develop consistent forecasts of crucial financial variables. For example, if you wish to value Dynamic Mattress, you need forecasts of future free cash flows. These are easily derived up to the end of the planning period from our financial planning model.¹⁷ However, a planning model does not tell you whether the plan is optimal. It does not even tell you which alternatives are worth examining. For example, we saw that Dynamic Mattress is planning for a rapid growth in sales and earnings per share. But is that good news for the shareholders? Well, not necessarily; it depends on the opportunity cost of the capital that Dynamic Mattress needs to invest. If the new investment earns more than the cost of capital, it will have a positive NPV and add to shareholder wealth. If the investment earns less than the cost of capital, shareholders will be worse off, even though the company expects steady growth in earnings.

The capital that Dynamic Mattress needs to raise depends on its decision to pay out 60% of its earnings as a dividend. But the financial planning model does not tell us whether this dividend payment makes sense or what mixture of equity or debt the company should issue. In the end the management has to decide. We would like to tell you exactly how to make the choice, but we can’t. There is no model that encompasses all the complexities encountered in financial planning and decision making.

As a matter of fact, there never will be one. This bold statement is based on Brealey, Myers, and Allen’s Third Law:¹⁸

Axiom: The number of unsolved problems is infinite.

Axiom: The number of unsolved problems that humans can hold in their minds is at any time limited to 10.

Law: Therefore in any field there will always be 10 problems that can be addressed but that have no formal solution.

BMA’s Third Law implies that no model can find the best of all financial strategies.¹⁹

 29-6    Growth and External Financing

We started this chapter by noting that financial plans force managers to be consistent in their goals for growth, investment, and financing. Before leaving the topic of financial planning, we should look at some general relationships between a firm’s growth objectives and its financing needs.

Recall that Dynamic Mattress ended 2012 with fixed assets and net working capital of $440 million. In 2013 it plans to plow back retained earnings of $35.9 million, so net assets will increase by 35.9/440, or 8.16%. Thus Dynamic Mattress can grow by 8.16% without needing to raise additional capital. The maximum growth rate that a company can achieve without external funds is known as the internal growth rate. For Dynamic Mattress

We can gain more insight into what determines this growth rate by multiplying the top and bottom of the expression for internal growth rate by net income and equity as follows:

In 2013 Dynamic Mattress expects to plow back 40% of net income and to earn a return of 25.66% on the equity with which it began the year. At the start of the year equity finances 79.55% of Dynamic Mattress’s net assets. Therefore

Notice that if Dynamic Mattress wishes to grow faster than this without raising equity capital, it would need to (1) plow back a higher proportion of its earnings, (2) earn a higher return on equity (ROE), or (3) have a lower debt-to-equity ratio.²⁰

Instead of focusing on how rapidly the company can grow without any external financing, Dynamic Mattress’s financial manager may be interested in the growth rate that can be sustained without additional equity issues. Of course, if the firm is able to raise enough debt, virtually any growth rate can be financed. It makes more sense to assume that the firm has settled on an optimal capital structure that it will maintain as equity is increased by the retained earnings. Thus the firm issues only enough debt to keep the debt–equity ratio constant. The sustainable growth rate is the highest growth rate the firm can maintain without increasing its financial leverage. It turns out that the sustainable growth rate depends only on the plowback rate and the return on equity:

For Dynamic Mattress,

We first encountered this formula in Chapter 4, where we used it to value common stocks.

These simple formulas remind us that firms may grow rapidly in the short term by relying on debt finance, but such growth can rarely be maintained without incurring excessive debt levels.

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SUMMARY

Short-term financial planning is concerned with the management of the firm’s short-term, or current, assets and liabilities. The most important current assets are cash, marketable securities, accounts receivable, and inventory. The most important current liabilities are short-term loans and accounts payable. The difference between current assets and current liabilities is called net working capital.

The nature of the firm’s short-term financial planning problem is determined by the amount of long-term capital it raises. A firm that issues large amounts of long-term debt or common stock, or that retains a large part of its earnings, may find it has permanent excess cash. In such cases there is never any problem paying bills, and short-term financial planning consists of managing the firm’s portfolio of marketable securities. A firm holding a reserve of cash is able to buy itself time to react to a short-term crisis. This may be important for growth firms that find it difficult to raise cash on short notice. However, large cash holdings can lead to complacency. We suggest that firms with permanent cash surpluses ought to consider returning the excess cash to their stockholders.

Other firms raise relatively little long-term capital and end up as permanent short-term debtors. Most firms attempt to find a golden mean by financing all fixed assets and part of current assets with equity and long-term debt. Such firms may invest cash surpluses during part of the year and borrow during the rest of the year.

The starting point for short-term financial planning is an understanding of sources and uses of cash. Firms forecast their net cash requirements by estimating collections on accounts receivable, adding other cash inflows, and subtracting all cash outlays. If the forecasted cash balance is insufficient to cover day-to-day operations and to provide a buffer against contingencies, the company will need to find additional finance. The search for the best short-term financial plan inevitably proceeds by trial and error. The financial manager must explore the consequences of different assumptions about cash requirements, interest rates, sources of finance, and so on. Firms use computerized financial models to help in this process. These models range from simple spreadsheet programs that merely help with the arithmetic to linear programming models that search for the best financial plan.

Short-term financial planning focuses on the firm’s cash flow over the coming year. But the financial manager also needs to consider what financial actions will be needed to support the firm’s plans for growth over the next 5 or 10 years. Most firms, therefore, prepare a long-term financial plan that describes the firm’s strategy and projects its financial consequences. The plan establishes financial goals and is a benchmark for evaluating subsequent performance.

The process that produces this plan is valuable in its own right. First, planning forces the financial manager to consider the combined effects of all the firm’s investment and financing decisions. This is important because these decisions interact and should not be made independently. Second, planning requires the manager to consider events that could upset the firm’s progress and to devise strategies to be held in reserve for counterattack when unhappy surprises occur.

There is no theory or model that leads straight to the optimal financial strategy. As in the case of short-term planning, many different strategies may be projected under a range of assumptions about the future. The dozens of separate projections that may need to be made generate a heavy load of arithmetic. We showed how you can use a simple spreadsheet model to analyze Dynamic Mattress’s long-term strategy.

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FURTHER READING

The following text is concerned with liquidity management and short-term planning:

J. G. Kallberg and K. Parkinson, Corporate Liquidity Management and Measurement (Burr Ridge, IL: Irwin/McGraw-Hill, 1996).

Long-term financial models are discussed in:

J. R. Morris and J. P Daley, Introduction to Financial Models for Management and Planning (Boca Raton, FL: Chapman & Hall/CRC Finance Series, 2009).

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

 1.  Cash and working capital Listed below are six transactions that Dynamic Mattress might make. Indicate how each transaction would affect (a) cash and (b) working capital.

  The transactions are

 i.  Pay out an extra $10 million cash dividend.

 ii.  Receive $2,500 from a customer who pays a bill resulting from a previous sale.

 iii.  Pay $50,000 previously owed to one of its suppliers.

 iv.  Borrow $10 million long term and invest the proceeds in inventory.

 v.  Borrow $10 million short term and invest the proceeds in inventory.

 vi.  Sell $5 million of marketable securities for cash.

 2.  Sources and uses of cash State how each of the following events would affect the firm’s balance sheet. State whether each change is a source or use of cash.

 a. An automobile manufacturer increases production in response to a forecasted increase in demand. Unfortunately, the demand does not increase.

 b. Competition forces the firm to give customers more time to pay for their purchases.

 c. Rising commodity prices increase the value of raw material inventories by 20%.

 d. The firm sells a parcel of land for $100,000. The land was purchased five years earlier for $200,000.

 e. The firm repurchases its own common stock.

 f. The firm doubles its quarterly dividend.

 g. The firm issues $1 million of long-term debt and uses the proceeds to repay a short-term bank loan.

 3.  Collections on receivables Here is a forecast of sales by National Bromide for the first four months of 2013 (figures in $ thousands):

On the average 50% of credit sales are paid for in the current month, 30% are paid in the next month, and the remainder are paid in the month after that. What is the expected cash inflow from operations in months 3 and 4?

 4.  Forecasts of payables Dynamic Futon forecasts the following purchases from suppliers:

 a. Forty percent of goods are supplied cash-on-delivery. The remainder are paid with an average delay of one month. If Dynamic Futon starts the year with payables of $22 million, what is the forecasted level of payables for each month?

 b. Suppose that from the start of the year the company stretches payables by paying 40% after one month and 20% after two months. (The remainder continue to be paid cash on delivery.) Recalculate payables for each month assuming that there are no cash penalties for late payment.

 5.  Dynamic’s short-term plan Each of the following events affects one or more tables in Sections 29-2 to 29-3. Show the effects of each event by adjusting the tables listed in parentheses:

 a. Dynamic repays only $10 million of short-term debt in 2012. (Tables 29.2 and 29.3)

 b. Dynamic issues an additional $40 million of long-term debt in 2012 and invests $25 million in a new warehouse. (Tables 29.1–29.3)

 c. In 2012 Dynamic reduces the quantity of stuffing in each mattress. Customers don’t notice, but operating costs fall by 10%. (Tables 29.1–29.3)

 d. Starting in the third quarter of 2013, Dynamic employs new staff members who prove very effective in persuading customers to pay more promptly. As a result, 90% of sales are paid for immediately and 10% are paid in the following quarter. (Tables 29.4 and 29.5)

 e. Starting in the first quarter of 2013, Dynamic cuts wages by $20 million a quarter. (Table 29.5)

 f. In the second quarter of 2013 a disused warehouse catches fire mysteriously. Dynamic receives a $50 million check from the insurance company. (Table 29.5)

 g. Dynamic’s treasurer decides he can scrape by on a $10 million operating cash balance. (Table 29.5)

 6.  Financial planning True or false?

 a. Financial planning should attempt to minimize risk.

 b. The primary aim of financial planning is to obtain better forecasts of future cash flows and earnings.

 c. Financial planning is necessary because financing and investment decisions interact and should not be made independently.

 d. Firms’ planning horizons rarely exceed three years.

 e. Financial planning requires accurate forecasting.

 f. Financial planning models should include as much detail as possible.

 7.  Long-term plans Table 29.11 summarizes the 2014 income statement and end-year balance sheet of Drake’s Bowling Alleys. Drake’s financial manager forecasts a 10% increase in sales and costs in 2015. The ratio of sales to average assets is expected to remain at .40. Interest is forecasted at 5% of debt at the start of the year.

 a. What is the implied level of assets at the end of 2015?

 b. If the company pays out 50% of net income as dividends, how much cash will Drake need to raise in the capital markets in 2015?

 c. If Drake is unwilling to make an equity issue, what will be the debt ratio at the end of 2015?

 8.  Long-term plans Abbreviated financial statements for Archimedes Levers are shown in Table 29.12 on the next page. If sales increase by 10% in 2014 and all other items, including debt, increase correspondingly, what must be the balancing item? What will be its value?

 9.  Forecast growth rate What is the maximum possible growth rate for Archimedes (see Problem 8) if the payout ratio is set at 50% and (a) no external debt or equity is to be issued? (b) the firm maintains a fixed debt ratio but issues no equity?

   TABLE 29.11 Financial statements for Drake’s Bowling Alleys, 2014 (figures in thousands). See Problem 7.

a Assets at the end of 2013 were $2,400,000.

b Debt at the end of 2013 was $500,000.

   TABLE 29.12 Financial statements for Archimedes Levers, 2013. See Problems 8 and 9.

INTERMEDIATE

 10.  Cash budget Table 29.13 lists data from the budget of Tonga Transport. Half the company’s sales are for cash on the nail; the other half are paid for with a one-month delay. The company pays all its credit purchases with a one-month delay. Credit purchases in January were 30 crores, and total sales in January were 180 crores. Complete the cash budget in Table 29.14 on the next page.

 11.  Collections on receivables If a firm pays its bills with a 30-day delay, what fraction of its purchases will be paid in the current quarter? In the following quarter? What if the delay is 60 days?

 12.  Dynamic’s short-term plan Which items in Table 29.6 would be affected by the following events?

 a. Interest rates rise.

 b. Suppliers demand interest for late payment.

 c. Dynamic receives an unexpected bill in the third quarter from the Internal Revenue Service for underpayment of taxes in previous years.

 13.  Sources and uses of cash Table 29.15 on the next page shows Dynamic Mattress’s year-end 2010 balance sheet, and Table 29.16 shows its income statement for 2011. Work out the statement of cash flows for 2011. Group these items into sources of cash and uses of cash.

 14.  Dynamic’s short-term plan Work out a short-term financing plan for Dynamic Mattress Company, assuming the limit on the line of credit is raised from $100 to $120 million. Otherwise keep to the assumptions used in developing Table 29.6 (on page 758).

 15.  Dynamic’s short-term plan Dynamic Mattress decides to lease its new mattress-stuffing machines rather than buy them. As a result, capital expenditure in the first quarter is reduced by $50 million, but the company must make lease payments of $2.5 million for each of the four quarters. Assume that the lease has no effect on tax payments until after the fourth quarter. Construct two tables like Tables 29.5 and 29.6 showing Dynamic’s cumulative financing requirement and a new financing plan.

   TABLE 29.13 Selected budget data for Tonga Transport (figures in crores). See Problem 10.

   TABLE 29.14 Cash budget for Tonga Transport. See Problem 10.

   TABLE 29.15 Year-end balance sheet for Dynamic Mattress for 2010 (figures in $ millions). See Problem 13.

   TABLE 29.16 Income statement for Dynamic Mattress for 2011 (figures in $ millions). See Problem 13.

Notes: Dividend = $30.

Retained earnings = $10.

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 16.  Dynamic’s long-term plan Our long-term planning model of Dynamic Mattress is an example of a top-down planning model. Some firms use a bottom-up financial planning model, which incorporates forecasts of revenues and costs for particular products, advertising plans, major investment projects, and so on. What sort of firms would you expect to use each type, and what would they use them for?

 17.  Performance measurement Corporate financial plans are often used as a basis for judging subsequent performance. What do you think can be learned from such comparisons? What problems are likely to arise, and how might you cope with these problems?

 18.  Long-term planning models The balancing item in the Dynamic long-term planning model is borrowing. What is meant by balancing item? How would the model change if dividends were made the balancing item instead? In that case how would you suggest that planned borrowing be determined?

 19.  Dynamic’s long-term plan Construct a new model for Dynamic Mattress based on your answer to Problem 18. Does your model generate a feasible financial plan for 2013? (Hint: If it doesn’t, you may have to allow the firm to issue stock.)

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 20.  Dynamic’s long-term plan

 a. Use the Dynamic Mattress model (Tables 29.8–29.10) and the spreadsheets on the book’s website at www.mcgraw-hill.co.uk/textbooks/brealey to produce pro forma income statements, balance sheets, and statements of cash flows for 2013 and 2014. Assume business as usual except that now sales and costs are planned to expand by 30% per year, as are fixed assets and net working capital. The interest rate is forecasted to remain at 10% and stock issues are ruled out. Dynamic also sticks to its 60% dividend payout ratio.

 b. What are the firm’s debt ratio and interest coverage under this plan?

 c. Can the company continue to finance expansion by borrowing?

 21.  Long-term plans The financial statements of Aguia SA are shown in Table 29.17. For simplicity, “Costs” include interest. Assume that Aguia’s assets are proportional to its sales.

 a. Find Aguia’s required external funds if it maintains a dividend payout ratio of 60% and plans a growth rate of 15% in 2015.

 b. If Aguia chooses not to issue new shares of stock, what variable must be the balancing item? What will its value be?

 c. Now suppose that the firm plans instead to increase long-term debt only to $1,100 and does not wish to issue any new shares of stock. Why must the dividend payment now be the balancing item? What will its value be?

 22.  Forecast growth rate

 a. What is the internal growth rate of Aguia SA (see Problem 21) if the dividend payout ratio is fixed at 60% and the equity-to-asset ratio is fixed at two-thirds?

 b. What is the sustainable growth rate?

   TABLE 29.17 Financial statements for Aguia SA (figures in Brazilian real), 2014. See Problem 21.

 23.  Forecast growth rate Bio-Plasma Corp. is growing at 30% per year. It is all-equity-financed and has total assets of $1 million. Its return on equity is 20%. Its plowback ratio is 40%.

 a. What is the internal growth rate?

 b. What is the firm’s need for external financing this year?

 c. By how much would the firm increase its internal growth rate if it reduced its payout rate to zero?

 d. By how much would such a move reduce the need for external financing? What do you conclude about the relationship between dividend policy and requirements for external financing?

 24.  Short-term forecasting A Scottish hospital buys supplies from hundreds of sources. Amounts and payment terms for January 2014 are:

The hospital’s accounts payable total £3,900,000 at the start of January. Work out a forecast of accounts payable from January through June. Also forecast the amount of cash the hospital will need to pay out for supplies. Assume:

 a. Purchases constant at £4,100,000 per month.

 b. Purchases increase by 1.5 percent per month.

 c. Purchases increase to £4,500,000 in February and March, but then fall back to a steady £4,100,000 per month.

CHALLENGE

 25.  Long-term plans Table 29.18 shows the 2013 financial statements for the Executive Cheese Company. Annual depreciation is 10% of fixed assets at the beginning of the year, plus 10% of new investment. The company plans to invest a further $200,000 per year in fixed assets for the next five years and net working capital is expected to remain a constant proportion of fixed assets. The company forecasts that the ratio of revenues to total assets at the start of each year will remain at 1.75. Fixed costs are expected to remain at $53, and variable costs at 80% of revenue. The company’s policy is to pay out two-thirds of net income as dividends and to maintain a book debt ratio of 20%.

 a. Construct a model for Executive Cheese like the one in Tables 29.8–29.10.

 b. Use your model to produce a set of financial statements for 2014.

   TABLE 29.18 Financial statements for Executive Cheese Company, 2013 (figures in thousands).

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FINANCE ON THE WEB

Look up the financial statements for any company on finance.yahoo.com. Make some plausible forecasts for future growth and the asset base needed to support that growth. Then use a spreadsheet program to develop a five-year financial plan. What financing is needed to support the planned growth? How vulnerable is the company to an error in your forecasts?

___________

¹A survey by Graham and Harvey found that managers considered that the desire to match the maturity of the debt with that of the assets was the single most important factor in their choice between short- and long-term debt. See J. R. Graham and C. R. Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of Financial Economics 61 (May 2001), pp. 187–243. Stohs and Mauer confirm that firms with a preponderance of short-term assets do indeed tend to issue short-term debt. See M. H. Stohs and D. C. Mauer, “The Determinants of Corporate Debt Maturity Structure,” Journal of Business 69 (July 1996), pp. 279–312.

²T. Opler, L. Pinkowitz, R. Stulz, and R. Williamson, “The Determinants and Implications of Corporate Cash Holdings,” Journal of Financial Economics 52 (April 1999), pp. 3–46.

³If, as most people believe, there is a tax advantage to borrowing there must be a corresponding tax disadvantage to lending, since the firm must pay tax at the corporate rate on the interest that it receives from Treasury bills. In this case investment in Treasury bills has a negative NPV. See Section 18-1.

⁴L. Pinkowitz and R. Williamson. “The Market Value of Cash,” Journal of Applied Corporate Finance 19 (2007), pp. 74–81.

⁵The apparent implication is that the firm should distribute the cash to shareholders. However, debtholders may place restrictions on dividend payments to the shareholders.

⁶This is principal repayment, not interest. Sometimes interest payments are explicitly recognized as a use of funds. If so, cash flow from operations would be defined before interest, that is, as net income plus interest plus depreciation.

⁷There is a potential complication here, for the depreciation figure shown in the company’s report to shareholders is rarely the same as the depreciation figure used to calculate tax. The reason is that firms can minimize their current tax payments by using accelerated depreciation when computing their taxable income. As a result, the shareholder books (which generally use straight-line depreciation) overstate the firm’s current tax liability. Accelerated depreciation does not eliminate taxes; it only delays them. Since the ultimate liability has to be recognized, the additional taxes that will need to be paid are shown on the balance sheet as a deferred tax liability. In the statement of cash flows any increase in deferred taxes is treated as a source of funds. In the Dynamic Mattress example we ignore deferred taxes.

⁸Since the balance sheet shows the cost of materials rather than the amount that the finished goods will eventually sell for, it makes sense to compare the level of inventories and payables with the cost of goods sold rather than with sales.

⁹The total length of time from the purchase of raw materials until the final payment by the customer is termed the operating cycle.

¹⁰Most firms would forecast by month instead of by quarter. Sometimes weekly or even daily forecasts are made. But presenting a monthly forecast would triple the number of entries in Table 29.4 and subsequent tables. We wanted to keep the examples as simple as possible.

¹¹Maybe people buy more mattresses late in the year when the nights are longer.

¹²The bank loan calls for quarterly interest of .025 × 100 = $2.5 million; the lost discount on the payables amounts to .05 × 16 = $.8 million, and the interest lost on the marketable securities is .02 × 25 = $.5 million.

¹³These ratios were discussed in Chapter 28.

¹⁴We have not worked out these ratios explicitly, but you can infer from Table 29.6 that they would be fine at the end of the year but relatively low midyear, when Dynamic’s borrowing is high.

¹⁵This point is even more important in long-term financial planning.

¹⁶If you doubt that, look again at Table 29.6. Notice that the cash requirements in each quarter depend on borrowing in the previous quarter, because borrowing creates an obligation to pay interest. Moreover, the problem’s complexity would have been tripled had we not simplified by forecasting per quarter rather than by month.

¹⁷Look back at Table 19.1, where we set out the free cash flows for Rio Corporation. A financial planning model would be a natural tool for deriving these figures.

¹⁸The Second Law is presented in Section 10-1.

¹⁹It is possible to build linear programming models that help search for the best strategy subject to specified assumptions and conditions. These models can be more effective in screening alternative financial strategies.

²⁰Notice, however, that if assets grow by only 8.16%, either the sales-to-assets ratio or the profit margin must increase to maintain a 25.66% return on equity.

Part 9 Financial Planning and Working Capital Management

Working Capital Management

Most of this book is devoted to long-term financial decisions such as capital budgeting and the choice of capital structure. It is now time to look at the management of the firm’s short-term assets and liabilities. Short-term, or current, assets and liabilities are collectively known as working capital. Table 30.1 gives a breakdown of working capital for all manufacturing corporations in the United States in 2011. Note that current assets are larger than current liabilities. Net working capital (current assets less current liabilities) is positive.

Look also at Figure 30.1, which shows the relative importance of working capital in different industries. For example, current assets constitute about 60% of the total assets of telecom companies, while they account for less than 10% of the assets of railroads. For some companies “current assets” means principally inventory; in others it means accounts receivable or cash and securities. For example, you can see that inventory constitutes the majority of the current assets of retail firms, receivables are more important for oil companies, and cash and short-term securities make up the bulk of the current assets of software companies.

In this chapter we focus on the four principal types of current asset. We look first at the management of inventory. To do business, firms need reserves of raw materials, work in process, and finished goods. But these inventories can be expensive to store and they tie up capital. Therefore, inventory management involves a trade-off between the advantages of holding large inventories and the costs. In manufacturing companies, the production manager is best placed to make this judgment, and the financial manager is not usually directly involved in inventory management. So we spend less time on this topic than on the management of other current assets.

Our second task is to look at accounts receivable. Companies frequently sell goods on credit, so that it may be weeks or even months before the company is paid. These unpaid bills are shown in the accounts as receivables. We explain how the company’s credit manager sets the terms for payment, decides which customers should be offered credit, and ensures that they pay promptly. Table 30.1 shows that firms in the United States have about the same amount invested in accounts receivable as in inventories.

Our next topic is the firm’s cash balances. The cash manager faces two principal problems. The first is to decide how much cash the firm needs to retain and, therefore, how much can be invested in interest bearing securities. The second is to ensure that cash payments are handled efficiently. You don’t want to stuff incoming checks into your desk drawer until you can get around to going to the bank; you want to get the money into your bank account as quickly as possible. We describe some of the techniques that firms use to move money around efficiently.

Cash that is not required immediately is usually invested in a variety of short-term securities. Some of these literally pay off the next day; others may mature in a few months. In the final section we describe the different features of these securities and show how to compare their yields.

   TABLE 30.1 Current assets and liabilities for U.S. manufacturing corporations, 4th quarter, 2011 (figures in $ billions).

Source: U.S. Census Bureau, Quarterly Financial Report for U.S. Manufacturing, Mining, and Trade Corporations, www.census.gov/econ/qfr/index.html.

   FIGURE 30.1 Current assets as a percentage of total assets in different industries. Figures are the mean percentages for companies in the S&P Composite Index in 2011.

Source: Compustat.

 30-1   The Operating and Cash Conversion Cycles

Figure 30.2 reproduces a figure from Chapter 29. It depicts the operations of a simple business that buys raw materials, processes them into finished goods, and then sells these goods on credit. The delay between the initial investment in inventories and the final sale date is called the inventory period. The delay between the time that the goods are sold and when the customers finally pay their bills is termed the accounts receivable period. The total length of time from the purchase of raw materials until the final payment by the customer is termed the operating cycle:

The firm is not out of cash for the entire length of the operating cycle. Although it starts by purchasing raw materials, it does not generally pay for them immediately. This accounts payable period reduces the amount of time that the firm is out of cash. The interval between the firm’s payment for its raw materials and the collection of payment from the customer is known as the firm’s cash conversion cycle:

   FIGURE 30.2 Simple cycle of operations.

This is illustrated in Figure 30.3. The longer the production process, the more cash the firm must keep tied up in inventories. Similarly, the longer it takes customers to pay their bills, the higher the value of accounts receivable. On the other hand, if a firm can delay paying for its own materials, it may reduce the amount of cash it needs. In other words, accounts payable reduce net working capital and the firm’s cash requirements.

Table 30.2 provides the information necessary to estimate the average cash conversion cycle for manufacturing firms in the United States in 2010:¹

   FIGURE 30.3 Operating and cash conversion cycles.

   TABLE 30.2 Data used to calculate the cash conversion cycle for U.S. manufacturing firms in 2011 (figures in billions).

Note: Cost of goods sold includes selling, general, and administrative expenses. Balance sheet data are start-of-year values.

Source: U.S. Department of Commerce, Quarterly Financial Report for Manufacturing, Mining and Trade Corporations, March 2012, Tables 1.0 and 1.1.

The cash conversion cycle is therefore

In other words, it is taking U.S. manufacturing companies an average of about six weeks from the time they lay out money on inventories to collect payment from their customers.

Of course, the cash conversion cycle is much shorter in some businesses than in others. For example, look at Table 30.3, which shows the average length of the cycle for a sample of companies. At one extreme, it takes about 15 months for Tiffany to produce and sell its jewelry, and this is reflected in its long cash conversion cycle. It takes Costco only a month to turn over its inventory, and this is reflected in the short cash cycle. Some firms, such as Southwest Airlines and Amazon, even have negative cash conversion cycles. They receive money from their customers well before they pay their suppliers.

   TABLE 30.3 Cash conversion cycle for selected companies in 2011.

The cash conversion cycle is not cast in stone. To a large extent it is within management’s control. Working capital can be managed. For example, accounts receivable are affected by the terms of credit that the firm offers to its customers. You can cut the amount of money tied up in receivables by getting tough with customers who are slow in paying their bills. (You may find, however, that in the future they take their business elsewhere.) Similarly, the firm can reduce its investment in inventories of raw materials. (Here the risk is that it may one day run out of inventories and production will grind to a halt.) Management of working capital involves a trade-off between these costs and benefits. It is time to look more carefully at these trade-offs. We start with inventories.

 30-2   Inventories

Most firms keep inventories of raw materials, work in process, or finished goods awaiting sale and shipment.

But firms are not obliged to do so. For example, they could buy materials day by day, as needed. But then they would pay higher prices for ordering in small lots, and they would risk production delays if the materials were not delivered on time. They can avoid that risk by ordering more than the firm’s immediate needs. Similarly, firms could do away with inventories of finished goods by producing only what they expect to sell tomorrow. But this too could be a dangerous strategy. A small inventory of finished goods may mean shorter and more costly production runs, and it may not be sufficient to meet an unexpected increase in demand.

There are also costs to holding inventories that must be set against these benefits. Money tied up in inventories does not earn interest, storage and insurance must be paid for, and there may be risk of spillage or obsolescence. Therefore, firms need to strike a sensible balance between the benefits of holding inventory and the costs.

EXAMPLE 30.1 • The Inventory Trade-Off

The Chinese company, Hongxi Wire Products, uses 255,000 tons a year of wire rod. How much should it order at one time? Suppose that it orders Q tons from the manufacturer. Just before delivery, Hongxi has effectively no inventories. Just after delivery it has an inventory of Q tons. Thus Hongxi’s inventory of wire rod roughly follows the sawtooth pattern in Figure 30.4.

   FIGURE 30.4 A simple inventory rule. The company waits until inventories of materials are about to be exhausted and then reorders a constant quantity.

There are two costs to this inventory. First, each order that Hongxi places involves a handling and delivery cost. Second, there are carrying costs, such as the cost of storage and the opportunity cost of the capital that is invested in inventory. Hongxi can reduce the order costs by placing fewer and larger orders. On the other hand, a larger order size increases the average quantity held in inventory, so that the carrying costs rise. Good inventory management requires a trade-off between these two types of cost.

   FIGURE 30.5 As the inventory order size is increased, order costs fall and inventory carrying costs rise. Total costs are minimized when the saving in order costs is equal to the increase in carrying costs.

BEYOND THE PAGE

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Try It! Figure 30.5:
Hongxi inventory costs

brealey.mhhe.com/c30

This is illustrated in Figure 30.5. We assume here that each order that Hongxi places involves a fixed order cost of 4,500 yuan, while the annual carrying cost of the inventory works out at about 550 yuan a ton. You can see how a larger order size results in lower order costs but higher carrying costs. The sum of the two costs is minimized when the size of each order is Q = 2,043 tons. The optimal order size (2,043 tons in our example) is termed the economic order quantity, or EOQ.²

Our example was not wholly realistic. For instance, most firms do not use up their inventory of raw material at a constant rate, and they would not wait until stocks had completely run out before they were replenished. But this simple model does capture some essential features of inventory management:

•  Optimal inventory levels involve a trade-off between carrying costs and order costs.

•  Carrying costs include the cost of storing goods as well as the cost of capital tied up in inventory.

•  A firm can manage its inventories by waiting until they reach some minimum level and then replenish them by ordering a predetermined quantity.³

•  When carrying costs are high and order costs are low, it makes sense to place more frequent orders and maintain higher levels of inventory.

•  Inventory levels do not rise in direct proportion to sales. As sales increase, the optimal inventory level rises, but less than proportionately.

It seems that carrying costs have been declining, for corporations today get by with lower levels of inventory than they used to. Twenty years ago, inventories held by U.S. companies accounted for 12% of firm assets. Today the figure is about 8%. One way that companies have reduced inventory levels is by moving to a just-in-time approach. Just-in-time was pioneered by Toyota in Japan. Toyota keeps inventories of auto parts to a minimum by ordering supplies only as they are needed. Thus deliveries of components to its plants are made throughout the day at intervals as short as one hour. Toyota is able to operate successfully with such low inventories only because it has a set of plans to ensure that strikes, traffic snarl-ups, or other hazards don’t halt the flow of components and bring production to a standstill.

Firms are finding that they can also reduce their inventories of finished goods by producing their goods to order. For example, Dell Computer discovered that it did not need to keep a large stock of finished machines. Its customers are able to use the Internet to specify what features they want on their PCs. The computer is then assembled to order and shipped to the customer.⁴

 30-3   Credit Management

We continue our tour of current assets with the firm’s accounts receivable. When one company sells goods to another, it does not usually expect to be paid immediately. These unpaid bills, or trade credit, compose the bulk of accounts receivable. The remainder is made up of consumer credit, that is, bills that are awaiting payment by the final customer.

Management of trade credit requires answers to five sets of questions:

 1.  How long are you going to give customers to pay their bills? Are you prepared to offer a cash discount for prompt payment?

 2.  Do you require some formal IOU from the buyer or do you just ask him to sign a receipt?

 3.  How do you determine which customers are likely to pay their bills?

 4.  How much credit are you prepared to extend to each customer? Do you play it safe by turning down any doubtful prospects? Or do you accept the risk of a few bad debts as part of the cost of building a large regular clientele?

 5.  How do you collect the money when it becomes due? What do you do about reluctant payers or deadbeats?

We discuss each of these topics in turn.

Terms of Sale

Not all sales involve credit. For example, if you are supplying goods to a wide variety of irregular customers, you may demand cash on delivery (COD). And, if your product is custom-designed, it may be sensible to ask for cash before delivery (CBD) or to ask for progress payments as the work is carried out.

When we look at transactions that do involve credit, we find that each industry seems to have its own particular practices.⁵ These norms have a rough logic. For example, firms selling consumer durables may allow the buyer a month to pay, while those selling perishable goods, such as cheese or fresh fruit, typically demand payment in a week. Similarly, a seller may allow more extended payment if its customers are in a low-risk business, if their accounts are large, if they need time to check the quality of the goods, or if the goods are not quickly resold.

To encourage customers to pay before the final date, it is common to offer a cash discount for prompt settlement. For example, pharmaceutical companies commonly require payment within 30 days but may offer a 2% discount to customers who pay within 10 days. These terms are referred to as “2/10, net 30.”

If goods are bought on a recurrent basis, it may be inconvenient to require separate payment for each delivery. A common solution is to pretend that all sales during the month in fact occur at the end of the month (EOM). Thus goods may be sold on terms of 8/10 EOM, net 60. This arrangement allows the customer a cash discount of 8% if the bill is paid within 10 days of the end of the month; otherwise the full payment is due within 60 days of the invoice date.

Cash discounts are often very large. For example, a customer who buys on terms of 2/10, net 30 may decide to forgo the cash discount and pay on the thirtieth day. This means that the customer obtains an extra 20 days’ credit but pays about 2% more for the goods. This is equivalent to borrowing money at a rate of 44.6% per annum.⁶ Of course, any firm that delays payment beyond the due date gains a cheaper loan but damages its reputation.

The Promise to Pay

Repetitive sales to domestic customers are almost always made on open account. The only evidence of the customer’s debt is the record in the seller’s books and a receipt signed by the buyer.

If you want a clear commitment from the buyer before you deliver the goods, you can arrange a commercial draft.⁷ This works as follows: You draw a draft ordering payment by the customer and send this to the customer’s bank together with the shipping documents. If immediate payment is required, the draft is termed a sight draft; otherwise it is known as a time draft. Depending on whether it is a sight draft or a time draft, the customer either pays up or acknowledges the debt by signing it and adding the word accepted. The bank then hands the shipping documents to the customer and forwards the money or trade acceptance to you, the seller.

If your customer’s credit is shaky, you can ask the customer to arrange for a bank to accept the time draft and thereby guarantee the customer’s debt. These bankers’ acceptances are often used in overseas trade. The bank guarantee makes the debt easily marketable. If you don’t want to wait for your money, you can sell the acceptance to a bank or to another firm that has surplus cash to invest.

An alternative when you are selling goods overseas is to ask the customer to arrange for an irrevocable letter of credit. In this case the customer’s bank sends you a letter stating that it has established a credit in your favor at a bank in the United States. You then know that the money is available and already in the country. You therefore draw a draft on the customer’s bank and present it to your bank together with the letter of credit and the shipping documents. Your bank arranges for this draft to be either accepted or paid, and forwards the documents to the customer’s bank.

If you sell your goods to a customer who proves unable to pay, you cannot get your goods back. You simply become a general creditor of the company together with many other unfortunates. You may be able to avoid this situation by making a conditional sale, so that you remain the owner of the goods until payment has been made. The conditional sale is common practice in Europe. In the United States it is used only for goods that are bought on an installment basis. So, if you buy a new car and fail to make all the payments, the dealer can repossess the car.

Credit Analysis

There are a number of ways to find out whether customers are likely to pay their debts. For existing customers an obvious indication is whether they have paid promptly in the past. For new customers you can use the firm’s financial statements to make your own assessment, or you may be able to look at how highly investors value the firm.⁸ However, the simplest way to assess a customer’s credit standing is to seek the views of a specialist in credit assessment. For example, in Chapter 23 we described how bond rating agencies, such as Moody’s and Standard and Poor’s, provide a useful guide to the riskiness of the firm’s bonds.

Bond ratings are usually available only for relatively large firms. However, you can obtain information on many smaller companies from a credit agency. Dun and Bradstreet is by far the largest of these agencies and its database contains credit information on millions of businesses worldwide. Credit bureaus are another source of data on a customer’s credit standing. In addition to providing data on small businesses, they can also provide an overall credit score for individuals.⁹

Finally, firms can also ask their bank to undertake a credit check. It will contact the customer’s bank and ask for information on the customer’s average balance, access to bank credit, and general reputation.

Of course you don’t want to subject each order to the same credit analysis. It makes sense to concentrate your attention on the large and doubtful orders.

The Credit Decision

Let us suppose that you have taken the first three steps toward an effective credit operation. In other words, you have fixed your terms of sale; you have decided on the contract that customers must sign; and you have established a procedure for estimating the probability that they will pay up. Your next step is to work out which of your customers should be offered credit.

If there is no possibility of repeat orders, the decision is relatively simple. Figure 30.6 summarizes your choice. On one hand, you can refuse credit. In this case you make neither profit nor loss. The alternative is to offer credit. Suppose that the probability that the customer will pay up is p. If the customer does pay, you receive additional revenues (REV) and you incur additional costs; your net gain is the present value of REV – COST. Unfortunately, you can’t be certain that the customer will pay; there is a probability (1 – p) of default. Default means that you receive nothing and incur the additional costs. The expected profit from each course of action is therefore as follows:

You should grant credit if the expected gain from doing so is positive.

Consider, for example, the case of the Spanish company, Empresa Generalife. On each nondelinquent sale Generalife receives revenues with a present value of €1,200 and incurs costs with a value of €1,000. Therefore the company’s expected profit if it offers credit is

   FIGURE 30.6 If you refuse credit, you make neither profit nor loss. If you offer credit, there is a probability p that the customer will pay and you will make REV – COST; there is a probability (1 – p) that the customer will default and you will lose COST.

If the probability of collection is 5/6, Generalife can expect to break even:

Therefore the company’s policy should be to grant credit whenever the chances of collection are better than 5 out of 6.

So far we have ignored the possibility of repeat orders. But one of the reasons for offering credit today is that it may help to get yourself a good, regular customer. Figure 30.7 illustrates the problem. Generalife has been asked to extend credit to a new customer. You can find little information on the firm, and you believe that the probability of payment is no better than .8. If you grant credit, the expected profit on this customer’s order is

You decide to refuse credit.

   FIGURE 30.7 In this example there is only a .8 probability that your customer will pay in period 1; but if payment is made, there will be another order in period 2. The probability that the customer will pay for the second order is .95. The possibility of this good repeat order more than compensates for the expected loss in period 1.

This is the correct decision if there is no chance of a repeat order. But look again at the decision tree in Figure 30.7. If the customer does pay up, there will be a repeat order next year. Because the customer has paid once, you can be 95% sure that he or she will pay again. For this reason any repeat order is very profitable:

Now you can reexamine today’s credit decision. If you grant credit today, you receive the expected profit on the initial order plus the possible opportunity to extend credit next year:

At any reasonable discount rate, you ought to extend credit. Notice that you should do so even though you expect to take a loss on the initial order. The expected loss is more than outweighed by the possibility that you will secure a reliable and regular customer. Generalife is not committed to making further sales to the customer, but by extending credit today, it gains a valuable option to do so. It will exercise this option only if the customer demonstrates its creditworthiness by paying promptly.

Of course real-life situations are generally far more complex than our simple examples. Customers are not all good or all bad. Many of them pay consistently late; you get your money, but it costs more to collect and you lose a few months’ interest. Then there is the uncertainty about repeat sales. There may be a good chance that the customer will give you further business, but you can’t be sure of that and you don’t know for how long she will continue to buy.

Like almost all financial decisions, credit allocation involves a strong dose of judgment. Our examples are intended as reminders of the issues involved rather than as cookbook formulas. Here are the basic things to remember.

 1.  Maximize profit. As credit manager, you should not focus on minimizing the number of bad accounts; your job is to maximize expected profit. You must face up to the following facts: The best that can happen is that the customer pays promptly; the worst is default. In the best case, the firm receives the full additional revenues from the sale less the additional costs; in the worst, it receives nothing and loses the costs. You must weigh the chances of these alternative outcomes. If the margin of profit is high, you are justified in a more liberal credit policy; if it is low, you cannot afford many bad debts.¹⁰

 2.  Concentrate on the dangerous accounts. You should not expend the same effort on analyzing all credit applications. If an application is small or clear-cut, your decision should be largely routine; if it is large or doubtful, you may do better to move straight to a detailed credit appraisal. Most credit managers don’t make decisions on an order-by-order basis. Instead, they set a credit limit for each customer. The sales representative is required to refer the order for approval only if the customer exceeds this limit.

 3.  Look beyond the immediate order. The credit decision is a dynamic problem. You cannot look only at the present. Sometimes it may be worth accepting a relatively poor risk as long as there is a good chance that the customer will become a regular and reliable buyer. New businesses must, therefore, be prepared to incur more bad debts than established businesses. This is part of the cost of building a good customer list.

Collection Policy

The final step in credit management is to collect payment. When a customer is in arrears, the usual procedure is to send a statement of account and to follow this at intervals with increasingly insistent letters or telephone calls. If none of these has any effect, most companies turn the debt over to a collection agent or an attorney.

Large firms can reap economies of scale in record keeping, billing, and so on, but the small firm may not be able to support a fully fledged credit operation. However, the small firm may be able to obtain some scale economies by farming out part of the job to a factor. This arrangement is known as factoring.

Factoring typically works as follows. The factor and the client agree on a credit limit for each customer. The client then notifies the customer that the factor has purchased the debt. Thereafter, whenever the client makes a sale to an approved customer, it sends a copy of the invoice to the factor, and the customer makes payment directly to the factor. Most commonly the factor does not have any recourse to the client if the customer fails to pay, but sometimes the client assumes the risk of bad debts. There are, of course, costs to factoring, and the factor typically charges a fee of 1% or 2% for administration and a roughly similar sum for assuming the risk of nonpayment. In addition to taking over the task of debt collection, most factoring agreements also provide financing for receivables. In these cases the factor pays the client 70% to 80% of the value of the invoice in advance at an agreed interest rate. Of course, factoring is not the only way to finance receivables; firms can also raise money by borrowing against their receivables.

Factoring is fairly prevalent in Europe, but in the United States it accounts for only a small proportion of debt collection. It is most common in industries such as clothing and toys. These industries are characterized by many small producers and retailers that do not have long-term relationships with each other. Because a factor may be employed by a number of manufacturers, it sees a larger proportion of the transactions than any single firm, and therefore is better placed to judge the creditworthiness of each customer.¹¹

If you don’t want help with collection but do want protection against bad debts, you can obtain credit insurance. For example, most governments have established agencies to insure export business. In the United States this insurance is provided by the Export-Import Bank in association with a group of insurance companies known as the Foreign Credit Insurance Association (FCIA). Banks are much more willing to lend when exports have been insured.

There is always a potential conflict of interest between the collection operation and the sales department. Sales representatives commonly complain that they no sooner win new customers than the collection department frightens them off with threatening letters. The collection manager, on the other hand, bemoans the fact that the sales force is concerned only with winning orders and does not care whether the goods are subsequently paid for.

There are also many instances of cooperation between the sales force and the collection department. For example, the specialty chemical division of a major pharmaceutical company actually made a business loan to an important customer that had been suddenly cut off by its bank. The pharmaceutical company bet that it knew its customer better than the customer’s bank did. The bet paid off. The customer arranged alternative bank financing, paid back the pharmaceutical company, and became an even more loyal customer. It was a nice example of financial management supporting sales.

It is not common for suppliers to make business loans in this way, but they lend money indirectly whenever they allow a delay in payment. Trade credit can be an important source of funds for indigent customers that cannot obtain a bank loan. But that raises an important question: if the bank is unwilling to lend, does it make sense for you, the supplier, to continue to extend trade credit? Here are two possible reasons why it may make sense: First, as in the case of our pharmaceutical company, you may have more information than the bank about the customer’s business. Second, you need to look beyond the immediate transaction and recognize that your firm may stand to lose some profitable future sales if the customer goes out of business.¹²

 30-4    Cash

Short-term securities pay interest, cash doesn’t. So why do corporations and individuals hold billions of dollars in cash and demand deposits? Why, for example, don’t you take all your cash and invest it in interest-bearing securities? The answer of course is that cash gives you more liquidity than do securities. You can use it to buy things. It is hard enough to get New York cab drivers to give you change for a $20 bill, but try asking them to split a Treasury bill.

In equilibrium all assets in the same risk class are priced to give the same expected marginal benefit. The benefit from holding Treasury bills is the interest that you receive; the benefit from holding cash is that it gives you a convenient store of liquidity. In equilibrium the marginal value of this liquidity is equal to the marginal value of the interest on Treasury bills. This is just another way of saying that Treasury bills have zero net present value; they are fair value relative to cash.

Does this mean that it does not matter how much cash you hold? Of course not. The marginal value of liquidity declines as you hold increasing amounts of cash. When you have only a small proportion of your wealth in cash, a little extra can be extremely useful; when you have a substantial holding, any additional liquidity is not worth much. Therefore, as financial manager you want to hold cash balances up to the point where the marginal value of the liquidity is equal to the value of the interest foregone.

In choosing between cash and short-term securities, the financial manager faces a task like that of the production manager. After all, cash is just another raw material that you need to do business, and there are costs and benefits to holding large “inventories” of cash. If the cash were invested in securities, it would earn interest. On the other hand, you can’t use those securities to pay the firm’s bills. If you had to sell them every time you needed to pay a bill, you could incur heavy transactions costs. The financial manager must trade off the cost of keeping an inventory of cash (the lost interest) against the benefits (the saving on transactions costs).

For small firms this trade-off can be important. But for very large firms the transactions costs of buying and selling securities become trivial compared with the opportunity cost of holding idle cash balances. Suppose that the interest rate is 5% a year, or roughly 5/365 = .0137% per day. Then the daily interest earned by $1 million is .000137 × 1,000,000 = $137. Even at a cost of $50 per transaction, which is generously high, it pays to buy Treasury bills today and sell them tomorrow rather than to leave $1 million idle overnight. Consider Walmart, which has annual sales of about $450 billion and an average daily cash flow of $450,000,000,000/365, or $1.2 billion. Firms of this size generally end up buying or selling securities once a day every day.

Banks have developed ways to help firms to invest idle cash. For example, they may provide sweep programs, where the bank automatically “sweeps” surplus funds into an interest-bearing investment, such as a money-market mutual fund.

Why then do large firms hold any significant amounts of cash? There are basically two reasons. First, cash may be left in non-interest-bearing accounts to compensate banks for the services they provide. Second, large corporations may have literally hundreds of accounts with dozens of different banks. It is often better to leave idle cash in these accounts than to monitor each account daily and make daily transfers among them.

One major reason for this proliferation of bank accounts is decentralized management. You cannot give a subsidiary operating autonomy without giving its managers the right to spend and receive cash. Good cash management nevertheless implies some degree of centralization. It is impossible to maintain your desired cash inventory if all the subsidiaries in the group are responsible for their own private pools of cash. And you certainly want to avoid situations in which one subsidiary is investing its spare cash at 5% while another is borrowing at 8%. It is not surprising, therefore, that even in highly decentralized companies there is generally central control over cash balances and bank relations.

How Purchases Are Paid For

Most small, face-to-face purchases are made with dollar bills. But you probably would not want to use cash to buy a new car, and you can’t use cash to make a purchase over the Internet. There are a variety of ways that you can pay for larger purchases or send payments to another location. Some of the more important ways are set out in Table 30.4.

Look now at Figure 30.8. You can see that there are large differences in the ways that people around the world pay for their purchases. For example, checks are almost unknown in Germany, the Netherlands, and Sweden.¹³ Most payments in these countries are by debit card or credit transfer. By contrast, Americans love to write checks. Each year individuals and firms in the United States write about 28 billion checks.

   TABLE 30.4 Small, face-to-face purchases are commonly paid for with cash, but here are some of the other ways to pay your bills.

   FIGURE 30.8 How purchases are paid for. Percentage of total volume of cashless transactions, 2010. (Data exclude small usage of card-based e-money.)

Source: Bank for International Settlements, “Statistics on Payment, Clearing, and Settlement Systems in the CPSS Countries – Figures for 2010,” January 2012, www.bis.org/publ/cpss99.htm.

But throughout the world the use of checks is on the decline. For one-off purchases they are being replaced by credit or debit cards. In addition mobile phone technology and the Internet are encouraging the development of new infant payment systems. For example,

 •  Electronic bill presentment and payment (or EBPP) allows companies to bill customers and receive payments via the Internet. EBPP is forecasted to grow rapidly.

 •  Stored-value cards (or e-money) let you transfer cash value to a card that can be used to buy a variety of goods and services. For example, Hong Kong’s Octopus card system, which was developed to pay for travel fares, has become a widely used electronic cash system throughout the territory.

There are three main ways that firms send and receive money electronically. These are direct payments, direct deposits, and wire transfers.

Recurring expenditures, such as utility bills, mortgage payments, and insurance premiums, are increasingly settled by direct payment (also called automatic debit or direct debit). In this case the firm’s customers simply authorize it to debit their bank account for the amount due. The company provides its bank with a file showing details of each customer, the amount to be debited, and the date. In the United States the payment then travels electronically through the Automated Clearing House (ACH) system. The firm knows exactly when the cash is coming in and avoids the labor-intensive process of handling thousands of checks.

The ACH system also allows money to flow in the reverse direction. Thus while a direct payment transaction provides an automatic debit, a direct deposit constitutes an automatic credit. Direct deposits are used to make bulk payments such as wages or dividends. Again the company provides its bank with a file of instructions. The bank then debits the company’s account and transfers the cash via the ACH to the bank accounts of the firm’s employees or shareholders.

The volume of direct payments and deposits has increased rapidly. Over 50% of U.S. households now use direct payment for recurring expenditures and nearly three-quarters of employees are paid by direct deposit. You can see from Table 30.5 that the total value of ACH transactions is similar to that of checks.¹⁴

   TABLE 30.5 Use of Payment Systems in the United States, 2010.

Sources: www.federalreserve.gov, www.nacha.org, and www.chips.org.

Large-value payments between companies are usually made electronically through Fedwire or CHIPS. Fedwire is operated by the Federal Reserve system, and connects nearly 9,000 financial institutions to the Fed and thereby to each other.¹⁵ CHIPS is a bank-owned system serving more than 1,400 U.S. financial institutions and hundreds of international participants. It mainly handles eurodollar payments and foreign exchange transactions, and is used for over 95% of cross-border payments in dollars. Table 30.5 shows that the number of payments by Fedwire and CHIPS is relatively small, but the sums involved are huge.

Speeding Up Check Collections

Although checks are rarely used for large-value payments, they continue to be the most common method of payment for smaller nonrecurring transactions. About three-quarters of business-to-business (B2B) transactions in the United States are still made by check.

Check handling is a cumbersome and labor-intensive task. However, changes to legislation in the United States at the beginning of the century helped to reduce costs and speed up collections. The Check Clearing for the 21st Century Act, usually known as Check 21, allows banks to send digital images of checks to one another rather than sending the checks themselves. As the new technology becomes more widespread, there will be fewer cargo planes crisscrossing the country to take bundles of checks from one bank to another. The cost of processing checks is also being reduced by a technological innovation known as check conversion. In this case, when you write a check, the details of your bank account and the amount of the payment are automatically captured at the point of sale, your check is handed back to you, and your bank account is immediately debited.

Firms that receive a large volume of checks have devised a number of ways to ensure that the cash becomes available as quickly as possible. For example, a retail chain may arrange for each branch to deposit receipts in a collection account at a local bank. Surplus funds are then periodically transferred electronically to a concentration account at one of the company’s principal banks. There are two reasons that concentration banking allows the company to gain quicker use of its funds. First, because the store is nearer to the bank, transfer times are reduced. Second, because the customer’s check is likely to be drawn on a local bank, the time taken to clear the check is also reduced.

Concentration banking is often combined with a lockbox system. In this case the firm’s customers are instructed to send their payments to a regional post-office box. The local bank then takes on the administrative chore of emptying the box and depositing the checks in the company’s local deposit account.

International Cash Management

Cash management in domestic firms is child’s play compared with cash management in large multinational corporations operating in dozens of countries, each with its own currency, banking system, and legal structure.

A single centralized cash management system is an unattainable ideal for these companies, although they are edging toward it. For example, suppose that you are treasurer of a large multinational company with operations throughout Europe. You could allow the separate businesses to manage their own cash, but that would be costly and would almost certainly result in each one accumulating little hoards of cash. The solution is to set up a regional system. In this case the company establishes a local concentration account with a bank in each country. Any surplus cash is swept daily into a central multicurrency account in London or another European banking center. This cash is then invested in marketable securities or used to finance any subsidiaries that have a cash shortage.

Payments can also be made out of the regional center. For example, to pay wages in each European country, the company just needs to send its principal bank a computer file of the payments to be made. The bank then finds the least costly way to transfer the cash from the company’s central accounts and arranges for the funds to be credited on the correct day to the employees in each country.

Rather than physically moving funds between local bank accounts and a regional concentration account, the company may employ a multinational bank with branches in each country and then arrange for the bank to pool all the cash surpluses and shortages. In this case no money is transferred between accounts. Instead, the bank just adds together the credit and debit balances, and pays the firm interest at its lending rate on any surplus.

When a company’s international branches trade with each other, the number of cross-border transactions can multiply rapidly. Rather than having payments flowing in all directions, the company can set up a netting system. Each branch can then calculate its net position and undertake a single transaction with the netting center. Several industries have set up netting systems for their members. For example, over 200 airlines have come together to establish a netting system for the foreign currency payments that they must make to each other.

Paying for Bank Services

Much of the work of cash management—processing checks, transferring funds, running lockboxes, helping keep track of the company’s accounts—is done by banks. And banks provide many other services not so directly linked to cash management, such as handling payments and receipts in foreign currency, or acting as custodian for securities.

All these services need to be paid for. Usually payment is in the form of a monthly fee, but banks may agree to waive the fee as long as the firm maintains a minimum average balance in an interest-free deposit. Banks are prepared to do this, because, after setting aside a portion of the money in a reserve account with the Fed, they can relend the money to earn interest. Demand deposits earmarked to pay for bank services are termed compensating balances. They used to be a very common way to pay for bank services, but since U.S. banks have been permitted to pay interest on demand deposits there has been a steady trend away from using compensating balances and toward direct fees.

 30-5    Marketable Securities

In September 2011 Apple was sitting on an $81.6 billion mountain of cash and fixed income investments, amounting to 70% of the company’s total assets. Of this sum, $2.9 billion was kept as cash and the remainder was invested as follows:

Most companies do not have the luxury of such huge cash surpluses, but they also park any cash that is not immediately needed in short-term investments. The market for these investments is known as the money market. The money market has no physical marketplace. It consists of a loose collection of banks and dealers linked together by telephones or through the Web. But a huge volume of securities is regularly traded on the money market, and competition is vigorous.

Most large corporations manage their own money-market investments, but small companies sometimes find it more convenient to hire a professional investment management firm or to put their cash into a money-market fund. This is a mutual fund that invests only in low-risk, short-term securities.¹⁶ Despite its large cash surplus, Apple invested a small proportion of its money in money-market funds.

The relative safety of money-market funds has made them particularly popular at times of financial stress. During the credit crunch of 2008 fund assets mushroomed as investors fled from plunging stock markets. Then it was revealed that one fund, the Reserve Primary Fund, had incurred heavy losses on its holdings of Lehman Brothers’ commercial paper. The fund became only the second money-market fund in history to “break the buck,” by offering just 97 cents on the dollar to investors who cashed in their holdings. That week investors pulled nearly $200 billion out of money-market funds, prompting the government to offer emergency insurance to investors.

Calculating the Yield on Money-Market Investments

Many money-market investments are pure discount securities. This means that they don’t pay interest. The return consists of the difference between the amount you pay and the amount you receive at maturity. Unfortunately, it is no good trying to persuade the Internal Revenue Service that this difference represents capital gain. The IRS is wise to that one and will tax your return as ordinary income.

Interest rates on money-market investments are often quoted on a discount basis. For example, suppose that three-month bills are issued at a discount of 5%. This is a rather complicated way of saying that the price of a three-month bill is 100 – (3/12) × 5 = 98.75. Therefore, for every $98.75 that you invest today, you receive $100 at the end of three months. The return over three months is 1.25/98.75 = .0127, or 1.27%. This is equivalent to an annual yield of 5.18%. Note that the return is always higher than the discount. When you read that an investment is selling at a discount of 5%, it is very easy to slip into the mistake of thinking that this is its return.¹⁷

Yields on Money-Market Investments

When we value long-term debt, it is important to take account of default risk. Almost anything may happen in 30 years, and even today’s most respectable company may get into trouble eventually. Therefore, corporate bonds offer higher yields than Treasury bonds.

Short-term debt is not risk-free, but generally the danger of default is less for money-market securities issued by corporations than for corporate bonds. There are two reasons for this. First, the range of possible outcomes is smaller for short-term investments. Even though the distant future may be clouded, you can usually be confident that a particular company will survive for at least the next month. Second, for the most part only well-established companies can borrow in the money market. If you are going to lend money for just a few days, you can’t afford to spend too much time in evaluating the loan. Thus, you will consider only blue-chip borrowers.

Despite the high quality of money-market investments, there are often significant differences in yield between corporate and government securities. Why is this? One answer is the risk of default. Another is that the investments have different degrees of liquidity or “moneyness.” Investors like Treasury bills because they are easily turned into cash on short notice. Securities that cannot be converted so quickly and cheaply into cash need to offer relatively high yields. During times of market turmoil investors may place a particularly high value on having ready access to cash. On these occasions the yield on illiquid securities can increase dramatically.

The International Money Market

In Chapter 24 we pointed out that there are two main markets for dollar bonds. There is the domestic market in the United States and there is the eurobond market centered in London. Similarly, in addition to the domestic money market, there is also an international market for short-term dollar investments, which is known as the eurodollar market.

Eurodollars have nothing to do with the euro, the currency of the European Monetary Union (EMU). They are simply dollars deposited in a bank in Europe. For example, suppose that an American oil company buys crude oil from an Arab sheik and pays for it with a $1 million check drawn on JP Morgan Chase. The sheik then deposits the check with his account at Barclays Bank in London. As a result, Barclays has an asset in the form of a $1 million credit in its account with JP Morgan Chase. It also has an offsetting liability in the form of a dollar deposit. Since that dollar deposit is placed in Europe, it is called a eurodollar deposit.¹⁸

Just as there is both a domestic U.S. money market and a eurodollar market, so there is both a domestic Japanese money market and a market in London for euroyen. So, if a U.S. corporation wishes to make a short-term investment in yen, it can deposit the yen with a bank in Tokyo or it can make a euroyen deposit in London. Similarly, there is both a domestic money market in the euro area as well as a money market for euros in London.¹⁹ And so on.

Major international banks in London lend dollars to one another at the London interbank offered rate (LIBOR). Similarly, they lend yen to each other at the yen LIBOR interest rate, and they lend euros at the euro interbank offered rate, or Euribor. These interest rates are used as a benchmark for pricing many types of short-term loans in the United States and in other countries. For example, a corporation in the United States may issue a floating-rate note with interest payments tied to dollar LIBOR.

If we lived in a world without regulation and taxes, the interest rate on a eurodollar loan would have to be the same as the rate on an equivalent domestic dollar loan. However, the international debt markets thrive because governments attempt to regulate domestic bank lending. When the U.S. government limited the rate of interest that banks in the United States could pay on domestic deposits, companies could earn a higher rate of interest by keeping their dollars on deposit in Europe. As these restrictions have been removed, differences in interest rates have largely disappeared.

In the late 1970s the U.S. government was concerned that its regulations were driving business overseas to foreign banks and the overseas branches of American banks. To attract some of this business back to the States, the government in 1981 allowed U.S. and foreign banks to establish international banking facilities (IBFs). An IBF is the financial equivalent of a free-trade zone; it is physically located in the United States, but it is not required to maintain reserves with the Federal Reserve and depositors are not subject to any U.S. tax.²⁰ However, there are tight restrictions on what business an IBF can conduct. In particular, it cannot accept deposits from domestic U.S. corporations or make loans to them.

Money-Market Instruments

The principal money-market instruments in the United States are summarized in Table 30.6. We describe each in turn.

U.S. Treasury Bills The first item in Table 30.6 is U.S. Treasury bills. These are usually issued weekly and mature in four weeks, three months, six months, or one year.²¹ Sales are by a uniform-price auction. This means that all successful bidders are allotted bills at the same price.²² You don’t have to participate in the auction to invest in Treasury bills. There is also an excellent secondary market in which billions of dollars of bills are bought and sold every week.

Federal Agency Securities “Agency securities” is a general term used to describe issues by government agencies and government sponsored enterprises (GSEs). Although most of this debt is not guaranteed by the U.S. government,²³ investors have generally assumed that the government would step in to prevent a default. That view was reinforced in 2008, when the two giant mortgage companies, the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac) ran into trouble and were taken into government ownership.

Agencies and GSEs borrow both short and long term. The short-term debt consists of discount notes, which are similar to Treasury bills. They are very actively traded and often held by corporations. These notes have traditionally offered somewhat higher yields than U.S. Treasuries. One reason is that agency debt is not quite as marketable as Treasury issues. In addition, unless the debt has an explicit government guarantee, investors have demanded an extra return to compensate for the (small?) possibility that the government would allow the agency to default.

Short-Term Tax-Exempts Short-term notes are also issued by states, municipalities, and agencies such as state universities and school districts.²⁴ These have one particular attraction—the interest is not subject to federal tax.²⁵ Of course, this tax advantage of municipal debt is usually recognized in its price. For many years, triple-A municipal debt yielded 10% to 30% less than equivalent Treasury debt.

   TABLE 30.6 Money-market investments in the United States.

Most tax-exempt debt is relatively low risk, and is often backed by an insurance policy, which promises to pay out if the municipality is about to default.²⁶ However, in the turbulent markets of 2008 even the backing of an insurance company did little to reassure investors, who worried that the insurers themselves could be in trouble. The tax advantage of “munis” no longer seemed quite so important and their yields have climbed above those on Treasuries.

Variable-Rate Demand Notes There is no law preventing firms from making short-term investments in long-term securities. If a firm has $1 million set aside for an income tax payment, it could buy a long-term bond on January 1 and sell it on April 15, when the taxes must be paid. However, the danger with this strategy is obvious. What happens if bond prices fall by 10% between January and April? There you are with a $1 million liability to the Internal Revenue Service, bonds worth only $900,000, and a very red face. Of course, bond prices could also go up, but why take the chance? Corporate treasurers entrusted with excess funds for short-term investments are naturally averse to the price volatility of long-term bonds.

One solution is to buy municipal variable-rate demand notes (VRDNs). These are long-term securities, whose interest payments are linked to the level of short-term interest rates. Whenever the interest rate is reset, investors have the right to sell the notes back to the issuer for their face value.²⁷ This ensures that on these reset dates the price of the notes cannot be less than their face value. Therefore, although VRDNs are long-term loans, their prices are very stable. In addition, the interest on municipal debt has the advantage of being tax-exempt. So a municipal variable-rate demand note offers a relatively safe, tax-free, short-term haven for your $1 million of cash.

Bank Time Deposits and Certificates of Deposit If you make a time deposit with a bank, you are lending money to the bank for a fixed period. If you need the money before maturity, the bank usually allows you to withdraw it but exacts a penalty in the form of a reduced rate of interest.

In the 1960s banks introduced the negotiable certificate of deposit (CD) for time deposits of $1 million or more. In this case, when a bank borrows, it issues a certificate of deposit, which is simply evidence of a time deposit with that bank. If a lender needs the money before maturity, it can sell the CD to another investor. When the loan matures, the new owner of the CD presents it to the bank and receives payment.²⁸

Commercial Paper and Medium-Term Notes As discussed in detail in Chapter 24, these consist of unsecured, short- and medium-term debt issued by companies on a fairly regular basis.

Bankers’ Acceptances We saw earlier in the chapter how bankers’ acceptances (BAs) may be used to finance exports or imports. An acceptance begins life as a written demand for the bank to pay a given sum at a future date. Once the bank accepts this demand, it becomes a negotiable security that can be bought or sold through money-market dealers. Acceptances by the large U.S. banks generally mature in one to six months and involve very low credit risk.

Repurchase Agreements Repurchase agreements, or repos, are effectively secured loans that are typically made to a government security dealer. They work as follows: The investor buys part of the dealer’s holding of Treasury securities and simultaneously arranges to sell them back again at a later date at a specified higher price.²⁹ The borrower (the dealer) is said to have entered into a repo; the lender (who buys the securities) is said to have a reverse repo.

Repos sometimes run for several months, but more frequently they are just overnight (24-hour) agreements. No other domestic money-market investment offers such liquidity. Corporations can treat overnight repos almost as if they were interest-bearing demand deposits.

Suppose that you decide to invest cash in repos for several days or weeks. You don’t want to keep renegotiating agreements every day. One solution is to enter into an open repo with a security dealer. In this case there is no fixed maturity to the agreement; either side is free to withdraw at one day’s notice. Alternatively, you may arrange with your bank to transfer any excess cash automatically into repos.

Floating-Rate Preferred Stock Common stock and preferred stock have an interesting tax advantage for corporations, since firms pay tax on only 30% of the dividends that they receive. So, for each $1 of dividends received, the firm gets to keep 1 – (.30 × .35) = $.895. Thus the effective tax rate is only 10.5%. This is higher than the zero tax rate on the interest from municipal debt but much lower than the rate that the company pays on other debt interest.

Suppose that you consider investing your firm’s spare cash in some other corporation’s preferred stock. The 10.5% tax rate is very tempting. On the other hand, you worry that the price of the preferred shares may change if long-term interest rates change. You can reduce that worry by investing in preferred shares whose dividend payments are linked to the general level of interest rates.³⁰

Varying the dividend payment doesn’t quite do the trick, for the price of the preferred stock could still fall if the risk increases. So a number of companies added another wrinkle to floating-rate preferred. Instead of being tied rigidly to interest rates, the dividend can be reset periodically by means of an auction that is open to all investors. Investors can state the yield at which they are prepared to buy the stock. Existing shareholders who require a higher yield simply sell their stock to the new investors at its face value. The idea is similar to the variable-rate demand note. As long as auction-rate preferred stock can be resold at regular intervals for its face value, its price should not wander far in the interim.³¹

In 2007 disaster hit the auction-rate preferred market, when investors found that no-one turned up at the auction for their stock. Holders claimed that banks had fraudulently marketed the issues as equivalent to cash, and many of the banks that originally handled the issues agreed to buy them back. Auction-rate preferred stock no longer seemed such a safe haven for cash.

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SUMMARY

The difference between a firm’s current assets and its current liabilities is called net working capital. Net working capital arises largely from the lags between the time that the firm obtains the raw materials for its product and the time before it finally collects payment from its customers. The cash conversion cycle is the length of time between the firm’s payment for materials and the date when it gets paid by its customers. This period is partly within the control of management. For example, management can choose to have a lower level of inventories or to demand more rapid payment by its customers. There are both costs and benefits to such policies.

Successful firms effectively manage the four principal current assets—inventories, accounts receivable, cash, and short-term securities. Inventories consist of raw materials, work in process, and finished goods. Inventories have benefits. For example, a stock of raw materials reduces the risk that the firm will be forced to shut down production because of an unexpected shortage. But inventories also tie up capital and are expensive to store. The task of the production manager is to strike a sensible balance between these benefits and costs. In recent years many companies have decided that they can get by on lower inventories than before. For example, some have adopted just-in-time systems that allow the firm to keep inventories to a minimum by receiving a regular flow of components and raw materials throughout the day.

Credit management (the management of receivables) involves five steps:

 1.  Establish the length of the payment period and the size of any cash discounts for customers who pay promptly.

 2.  Decide the form of the contract with your customer. For example, if your customer’s credit is somewhat shaky, you can ask the customer to arrange for a banker’s acceptance. In this case payment is guaranteed by the customer’s bank.

 3.  Assess your customer’s creditworthiness. You can either do your own homework or rely on a credit agency or credit bureau that specializes in gathering information about the credit standing of firms or individuals.

 4.  Establish sensible credit limits. Remember your aim is not to minimize the number of bad debts, it is to maximize profits. Remember also not to be too shortsighted in reckoning the expected profit. It may be worth accepting marginal applicants if there is a chance that they may become regular and reliable customers.

 5.  Collect. You need to be resolute with the truly delinquent customers, but you do not want to offend the good ones by writing demanding letters just because their check has been delayed in the mail.

You can think of cash as just another raw material that the firm needs to do business. There are always advantages to holding large “inventories” of cash. They reduce the risk of a sudden shortage and having to raise more at short notice. On the other hand, there is a cost to holding idle cash balances rather than putting the money to work in marketable securities. In balancing these benefits and costs the cash manager faces a task similar to that of the production manager. This trade-off is more important for small firms, for whom the costs of continually buying and selling securities are relatively large compared with the opportunity cost of holding idle cash balances.

Good cash management involves moving cash around efficiently. For example, if the firm receives a large number of small checks, it needs to ensure that they are not left lying about. We described how concentration banking and lockbox systems are used to speed up collections. Most large payments are made electronically by wire transfer. This allows companies to economize on the use of cash by transferring funds rapidly from local bank accounts to the firm’s main concentration bank. Electronic funds transfer also speeds up payments and makes it possible to automate more of the cash management process.

If you have more cash than is currently needed, you can invest it in the money market. There is a wide choice of money-market investments, with different degrees of liquidity and risk. Remember that the interest rate on these investments is often quoted as a discount. The compound return is always higher than the rate of discount. The principal money-market investments in the United States are U.S. Treasury bills, federal agency notes, short-term tax exempts, time deposits and certificates of deposit, repurchase agreements, commercial paper, and bankers’ acceptances.

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FURTHER READING

Here are some general textbooks on working capital management:

G. W. Gallinger and B. P. Healey, Liquidity Analysis and Management, 3rd ed. (Reading, MA: Addison-Wesley, 1996).

N. C. Hill and W. L. Sartoris, Short-Term Financial Management: Text and Cases, 3rd ed. (Englewood Cliffs, NJ: Prentice-Hall, Inc., 1994).

K. V. Smith and G. W. Gallinger, Readings on Short-Term Financial Management, 3rd. ed. (New York: West, 1988).

F. C. Scherr, Modern Working Capital Management: Text and Cases (Englewood Cliffs, NJ: Prentice-Hall, Inc., 1989).

A standard text on the practice and institutional background of credit management is:

R. H. Cole and L. Mishler, Consumer and Business Credit Management, 11th ed. (New York: McGraw-Hill, 1998).

For a more analytical discussion of credit policy, see:

S. Mian and C. W. Smith, “Extending Trade Credit and Financing,” Journal of Applied Corporate Finance 7 (Spring 1994), pp. 75–84.

M. A. Petersen and R. G. Rajan, “Trade Credit: Theories and Evidence,” Review of Financial Studies 10 (Fall 1997), pp. 661–692.

Two useful books on cash management are:

M. Allman-Ward and J. Sagner, Essentials of Managing Corporate Cash (New York: Wiley, 2003).

R. Bort, Corporate Cash Management Handbook (New York: Warren Gorham and Lamont, 2004).

Two readable discussions of why some companies maintain more liquidity than others are:

A. Dittmar, “Corporate Cash Policy and How to Manage It with Stock Repurchases,” Journal of Applied Corporate Finance 20 (Summer 2008), pp. 22–34.

L. Pinkowitz and R. Williamson, “What Is the Market Value of a Dollar of Corporate Cash?” Journal of Applied Corporate Finance 19 (Summer 2007), pp. 74–81.

For descriptions of the money-market and short-term lending opportunities, see:

F. J. Fabozzi, The Handbook of Fixed Income Securities, 8th ed. (New York: McGraw-Hill, 2012).

F. J. Fabozzi, S. V. Mann, and M. Choudhry, The Global Money Markets (New York: John Wiley, 2002).

Chapter 4 of U.S. Monetary Policy and Financial Markets, available on the New York Federal Reserve website, www.ny.frb.org.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

 1.  Cash conversion cycle In fiscal 2010 and 2011 Caterpillar’s financial statements included the following items. What was Caterpillar’s cash conversion cycle?

 2.  Cash conversion cycle What effect will each of the following have on the cash conversion cycle?

 a. The inventory turnover falls from 80 to 60 days.

 b. Customers are given a larger discount for cash transactions.

 c. The firm adopts a policy of reducing accounts payable.

 d. The firm starts producing more goods in response to customers’ advance orders instead of producing ahead of demand.

 e. A temporary glut in the commodity market induces the firm to stock up on raw materials while prices are low.

 3.  Inventories What are the trade-offs involved in the decision of how much inventory the firm should carry? In what way does the cash manager face a similar trade-off?

 4.  Credit policy Company X sells on a 1/30, net 60 basis. Customer Y buys goods invoiced at $1,000.

 a. How much can Y deduct from the bill if Y pays on day 30?

 b. What is the effective annual rate of interest if Y pays on the due date rather than on day 30?

 c. How would you expect payment terms to change under the following conditions?

   i. The goods are perishable.

   ii. The goods are not rapidly resold.

   iii. The goods are sold to high-risk firms.

 5.  Credit policy The lag between the purchase date and the date on which payment is due is known as the terms lag. The lag between the due date and the date on which the buyer actually pays is the due lag, and the lag between the purchase and actual payment dates is the pay lag. Thus,

   State how you would expect the following events to affect each type of lag:

 a. The company imposes a service charge on late payers.

 b. A recession causes customers to be short of cash.

 c. The company changes its terms from net 10 to net 20.

 6.  Credit policy The Branding Iron Company sells its irons for $50 apiece wholesale. Production cost is $40 per iron. There is a 25% chance that wholesaler Q will go bankrupt within the next year. Q orders 1,000 irons and asks for six months’ credit. Should you accept the order? Assume that the discount rate is 10% per year, there is no chance of a repeat order, and Q will pay either in full or not at all.

 7.  Credit policy Look back at Section 30-3. Generalife’s costs have increased from €1,000 to €1,050. Assuming there is no possibility of repeat orders, answer the following:

 a. When should the company grant or refuse credit?

 b. If it costs €12 to determine whether a customer has been a prompt or slow payer in the past, when should Generalife undertake such a check?

 8.  Credit policy Look back at the discussion in Section 30-3 of credit decisions with repeat orders. If p1 = .8, what is the minimum level of p2 at which Generalife is justified in extending credit?

 9.  Credit management True or false?

 a. Exporters who require greater certainty of payment arrange for the customers to sign a bill of lading in exchange for a sight draft.

 b. It makes sense to monitor the credit manager’s performance by looking at the proportion of bad debts.

 c. If a customer refuses to pay despite repeated reminders, the company usually turns the debt over to a factor or an attorney.

10.  Credit policy How should your willingness to grant credit be affected by differences in (a) the profit margin, (b) the interest rate, (c) the probability of repeat orders? In each case illustrate your answer with a simple example.

11.  Cash management How would you expect a firm’s cash balance to respond to the following changes?

 a. Interest rates increase.

 b. The volatility of daily cash flow decreases.

 c. The transaction cost of buying or selling marketable securities goes up.

 12.  Cash management Complete the passage that follows by choosing the appropriate terms from the following list: lockbox banking, Fedwire, CHIPS, concentration banking.

Firms can increase their cash resources by speeding up collections. One way to do this is to arrange for payments to be made to regional offices that pay the checks into local banks. This is known as _______ . Surplus funds are then transferred from the local bank to one of the company’s main banks. Transfers can be made electronically by the _______ or _______ systems. Another technique is to arrange for a local bank to collect the checks directly from a post office box. This is known as _______ .

13.  Short-term securities Suppose that you can hold cash that pays no interest or invest in securities that pay interest at 8%. The securities are not easily sold on short notice; therefore, you must make up any cash deficiency by drawing on a bank line of credit that charges interest at 10%. Should you invest more or less in securities under each of the following circumstances?

 a. You are unusually uncertain about future cash flows.

 b. The interest rate on bank loans rises to 11%.

 c. The interest rates on securities and on bank loans both rise by the same proportion.

 d. You revise downward your forecast of future cash needs.

14.  Calculating yields In October 2008, six-month (182-day) Treasury bills were issued at a discount of 1.4%. What was the annual yield?

15.  Short-term securities For each item below, choose the investment that best fits the accompanying description:

 a. Maturity often overnight (repurchase agreements/bankers’ acceptances).

 b. Maturity never more than 270 days (tax-exempts/commercial paper).

 c. Often directly placed with investors (finance company commercial paper/dealer commercial paper).

 d. Issued by the U.S. Treasury (tax-exempts/three-month bills).

 e. Quoted on a discount basis (certificates of deposit/Treasury bills).

 f. Sold by auction (tax-exempts/Treasury bills).

16.  Short-term securities Consider three securities:

 a. A floating-rate bond.

 b. A preferred share paying a fixed dividend.

 c. A floating-rate preferred.

If you were responsible for short-term investment of your firm’s excess cash, which security would you probably prefer to hold? Why? Explain briefly.

17.  Cash conversion cycle A firm is considering several policy changes to increase sales. It plans to increase the variety of goods it keeps in inventory, but this will increase inventory by $100,000. It will offer more liberal sales terms, but this will result in receivables increasing by $650,000. These actions are forecasted to increase sales by $8 million a year. Cost of goods sold will remain at 80% of sales. Because of the firm’s increased purchases for its own production needs, payables will increase by $350,000. What effect will these changes have on the firm’s cash conversion cycle?

INTERMEDIATE

18.  Credit terms Listed below are some common terms of sale. Can you explain what each means?

 a. 2/30, net 60

 b. 2/5, EOM, net 30

 c. COD

19.  Cash discounts Some of the items in Problem 18 involve a cash discount. For each of these, calculate the rate of interest paid by customers who pay on the due date instead of taking the cash discount.

20.  Credit terms Phoenix Lambert currently sells its goods cash-on-delivery. However, the financial manager believes that by offering credit terms of 2/10 net 30 the company can increase sales by 4%, without significant additional costs. If the interest rate is 6% and the profit margin is 5%, would you recommend offering credit? Assume first that all customers take the cash discount. Then assume that they all pay on day 30.

21.  Credit policy As treasurer of the Universal Bed Corporation, Aristotle Procrustes is worried about his bad debt ratio, which is currently running at 6%. He believes that imposing a more stringent credit policy might reduce sales by 5% and reduce the bad debt ratio to 4%. If the cost of goods sold is 80% of the selling price, should Mr. Procrustes adopt the more stringent policy?

22.  Credit policy Jim Khana, the credit manager of Velcro Saddles, is reappraising the company’s credit policy. Velcro sells on terms of net 30. Cost of goods sold is 85% of sales, and fixed costs are a further 5% of sales. Velcro classifies customers on a scale of 1 to 4. During the past five years, the collection experience was as follows:

The average interest rate was 15%.

What conclusions (if any) can you draw about Velcro’s credit policy? What other factors should be taken into account before changing this policy?

23.  Credit policy Look again at Problem 22. Suppose (a) that it costs $95 to classify each new credit applicant and (b) that an almost equal proportion of new applicants falls into each of the four categories. In what circumstances should Mr. Khana not bother to undertake a credit check?

24.  Credit terms Until recently, Augean Cleaning Products sold its products on terms of net 60, with an average collection period of 75 days. In an attempt to induce customers to pay more promptly, it has changed its terms to 2/10, EOM, net 60. The initial effect of the changed terms is as follows:

Calculate the effect of the changed terms. Assume

 • Sales volume is unchanged.

 • The interest rate is 12%.

 • There are no defaults.

 • Cost of goods sold is 80% of sales.

25.  Credit terms Look back at Problem 24. Assume that the change in credit terms results in a 2% increase in sales. Recalculate the effect of the changed credit terms.

26.  Cash management Knob, Inc., is a nationwide distributor of furniture hardware. The company now uses a central billing system for credit sales of $180 million annually. First National, Knob’s principal bank, offers to establish a new concentration banking system for a flat fee of $100,000 per year. The bank estimates that mailing and collection time can be reduced by three days. By how much will Knob’s cash balances be increased under the new system? How much extra interest income will the new system generate if the extra funds are used to reduce borrowing under Knob’s line of credit with First National? Assume that the borrowing rate is 12%. Finally, should Knob accept First National’s offer if collection costs under the old system are $40,000 per year?

27.  Lockboxes Anne Teak, the financial manager of a furniture manufacturer, is considering operating a lockbox system. She forecasts that 300 payments a day will be made to lockboxes, with an average payment size of $1,500. The bank’s charge for operating the lockboxes is either $.40 a check or compensating balances of $800,000.

 a. If the interest rate is 9%, which method of payment is cheaper?

 b. What reduction in the time to collect and process each check is needed to justify use of the lockbox system?

28.  Payment systems A parent company settles the collection account balances of its subsidiaries once a week. (That is, each week it transfers any balances in the accounts to a central account.) The cost of a wire transfer is $10. A check costs $.80. Cash transferred by wire is available the same day, but the parent must wait three days for checks to clear. Cash can be invested at 12% per year. How much money must be in a collection account before it pays to use a wire transfer?

29.  Lockboxes The financial manager of JAC Cosmetics is considering opening a lockbox in Pittsburgh. Checks cleared through the lockbox will amount to $300,000 per month. The lockbox will make cash available to the company three days earlier than is currently the case.

 a. Suppose that the bank offers to run the lockbox for a $20,000 compensating balance. Is the lockbox worthwhile?

 b. Suppose that the bank offers to run the lockbox for a fee of $.10 per check cleared instead of a compensating balance. What must the average check size be for the fee alternative to be less costly? Assume an interest rate of 6% per year.

 c. Why did you need to know the interest rate to answer (b) but not to answer (a)?

30.  Money-market yields A three-month Treasury bill and a six-month bill both sell at a discount of 10%. Which offers the higher annual yield?

31.  Money-market yields In Section 30-5 we described a three-month bill that was issued on an annually compounded yield of 5.18%. Suppose that one month has passed and the investment still offers the same annually compounded return. What is the percentage discount? What was your return over the month?

32.  Money-market yields Look again at Problem 31. Suppose another month has passed, so the bill has only one month left to run. It is now selling at a discount of 3%. What is the yield? What was your realized return over the two months?

33.  Short-term securities Look up current interest rates offered by short-term investment alternatives. Suppose that your firm has $1 million excess cash to invest for the next two months. How would you invest this cash? How would your answer change if the excess cash were $5,000, $20,000, $100,000, or $100 million?

34.  Tax-exempts In 2006 agency bonds sold at a yield of 5.32%, while high-grade tax-exempts of comparable maturity offered 3.7% annually. If an investor receives the same after-tax return from corporates and tax-exempts, what is that investor’s marginal rate of tax? What other factors might affect an investor’s choice between the two types of securities?

35.  Tax-exempts The IRS prohibits companies from borrowing money to buy tax-exempts and deducting the interest payments on the borrowing from taxable income. Should the IRS prohibit such activity? If it didn’t, would you advise the company to borrow to buy tax-exempts?

36.  After-tax yields Suppose you are a wealthy individual paying 35% tax on income. What is the expected after-tax yield on each of the following investments?

 a. A municipal note yielding 7.0% pretax.

 b. A Treasury bill yielding 10% pretax.

 c. A floating-rate preferred stock yielding 7.5% pretax.

How would your answer change if the investor is a corporation paying tax at 35%? What other factors would you need to take into account when deciding where to invest the corporation’s spare cash?

CHALLENGE

37.  Credit policy Reliant Umbrellas has been approached by Plumpton Variety Stores of Nevada. Plumpton has expressed interest in an initial purchase of 5,000 umbrellas at $10 each on Reliant’s standard terms of 2/30, net 60. Plumpton estimates that if the umbrellas prove popular with customers, its purchases could be in the region of 30,000 umbrellas a year. After deductions for variable costs, this account would add $47,000 per year to Reliant’s profits.

Reliant has been anxious for some time to break into the lucrative Nevada market, but its credit manager has some doubts about Plumpton. In the past five years, Plumpton had embarked on an aggressive program of store openings. In 2010, however, it went into reverse. The recession, combined with aggressive price competition, caused a cash shortage. Plumpton laid off employees, closed one store, and deferred store openings. The company’s Dun and Bradstreet rating is only fair, and a check with Plumpton’s other suppliers reveals that, although Plumpton traditionally took cash discounts, it has recently been paying 30 days slow. A check through Reliant’s bank indicates that Plumpton has unused credit lines of $350,000 but has entered into discussions with the banks for a renewal of a $1,500,000 term loan due at the end of the year. Table 30.7 summarizes Plumpton’s latest financial statements.

As credit manager of Reliant, how do you feel about extending credit to Plumpton?

38.  Credit policy Galenic, Inc., is a wholesaler for a range of pharmaceutical products. Before deducting any losses from bad debts, Galenic operates on a profit margin of 5%. For a long time the firm has employed a numerical credit scoring system based on a small number of key ratios. This has resulted in a bad debt ratio of 1%.

Galenic has recently commissioned a detailed statistical study of the payment record of its customers over the past eight years and, after considerable experimentation, has identified five variables that could form the basis of a new credit scoring system. On the evidence of the past eight years, Galenic calculates that for every 10,000 accounts it would have experienced the following default rates:

   TABLE 30.7 Plumpton Variety Stores: Summary financial statements (figures in millions).

By refusing credit to firms with a low credit score (less than 80), Galenic calculates that it would reduce its bad debt ratio to 60/9,160, or just under .7%. While this may not seem like a big deal, Galenic’s credit manager reasons that this is equivalent to a decrease of one-third in the bad debt ratio and would result in a significant improvement in the profit margin.

 a. What is Galenic’s current profit margin, allowing for bad debts?

 b. Assuming that the firm’s estimates of default rates are right, how would the new credit scoring system affect profits?

 c. Why might you suspect that Galenic’s estimates of default rates will not be realized in practice? What are the likely consequences of overestimating the accuracy of such a credit scoring scheme?

 d. Suppose that one of the variables in the proposed scoring system is whether the customer has an existing account with Galenic (new customers are more likely to default). How would this affect your assessment of the proposal?

39. Money-market rates Look up short-term LIBOR (London Interbank Offer Rate) interest rates in the Financial Times. You should find LIBOR rates for U.S. dollars, euros, Swiss francs, U.K. pounds and Japanese yen. Suppose that a Swiss firm has a large sum of cash on hand, say SFr200 million, and can invest internationally at LIBOR rates. Is there any advantage from investing internationally? Where would you invest the SFr100 million? Hint: Remember covered interest rate parity? See Chapter 27.

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FINANCE ON THE WEB

 1.  The Dun and Bradstreet website (www.dnb.com) contains a sample comprehensive report on a small business. Would you extend credit to the firm? Why or why not?

 2.  The three main credit bureaus maintain useful websites with examples of their business and consumer reports. Log on to www.equifax.com and look at the sample report on a small business. What information do you think would be most useful if you were considering granting credit to the firm?

 3.  Log on to the Federal Reserve site at www.federalreserve.gov and look up current money-market interest rates. Suppose your business has $7 million set aside for an expenditure in three months. How would you choose to invest it in the meantime? Would your decision be different if there were some chance that you might need the money earlier?

___________

¹Because inventories are valued at cost, we divide inventory levels by cost of goods sold rather than sales revenue to obtain the inventory period. This way, both numerator and denominator are measured by cost. The same reasoning applies to the accounts payable period. On the other hand, because accounts receivable are valued at product price, we divide average receivables by daily sales revenue to find the receivables period.

²Where the firm uses up materials at a constant rate, as in our example, there is a simple formula for calculating the economic order quantity (or EOQ). Its optimal size = . In our example .

³This is known as a reorder point (or two-bin) system. Some firms use instead a periodic review system, where the firm reviews inventory levels periodically and tops the inventory up to the desired amount.

⁴These examples of just-in-time and build-to-order production are taken from T. Murphy, “JIT When ASAP Isn’t Good Enough,” Ward’s Auto World (May 1999), pp. 67–73; R. Schreffler, “Alive and Well,” Ward’s Auto World (May 1999), pp. 73–77; “A Long March: Mass Customization,” The Economist, July 14, 2001, pp. 63–65.

⁵Standard credit terms in different industries are reported in C. K. Ng, J. K. Smith, and R. L. Smith, “Evidence on the Determinants of Credit Terms Used in Interfirm Trade,” Journal of Finance 54 (June 1999), pp. 1109–1129.

⁶The cash discount allows you to pay $98 rather than $100. If you do not take the discount, you get a 20-day loan, but you pay 2/98 = 2.04% more for your goods. The number of 20-day periods in a year is 365/20 = 18.25. A dollar invested for 18.25 periods at 2.04% per period grows to (1.0204)18.25 = $1.446, a 44.6% return on the original investment. If a customer is happy to borrow at this rate, it’s a good bet that he or she is desperate for cash (or can’t work out compound interest). For a discussion of this issue, see J. K. Smith, “Trade Credit and Information Asymmetry,” Journal of Finance 42 (September 1987), pp. 863–872.

⁷Commercial drafts are sometimes known by the general term bills of exchange.

⁸We discussed how you can use these sources of information in Section 23-4.

⁹We discussed credit scoring models in Section 23-4. Credit bureau scores are often called “FICO scores” because most credit bureaus use a credit scoring model developed by Fair Isaac and Company. FICO scores are provided by the three major credit bureaus—Equifax, Experian, and TransUnion.

¹⁰Look back at our Generalife example, where we concluded that the company is justified in granting credit if the probability of collection is greater than 5/6. If the customer pays, Generalife will earn a profit margin of 200/1200 = 1/6. In other words, the company is justified in granting credit if the probability of payment exceeds 1 – profit margin.

¹¹This point is made in S. L. Mian and C. W. Smith, Jr., “Accounts Receivable Management Policy: Theory and Evidence,” Journal of Finance 47 (March 1992), pp. 169–200.

¹²Of course, banks also need to recognize the possibility of continuing business from the firm. The question therefore is whether suppliers have a greater stake in the firm’s continuing prosperity. For some evidence on the determinants of the supply and demand for trade credit, see M. A. Petersen and R. G. Rajan, “Trade Credit: Theories and Evidence,” Review of Financial Studies 10 (Fall 1997), pp. 661–692.

¹³For a discussion of the reasons for these international differences in payment methods, see “Retail Payments in Selected Countries: A Comparative Study,” Committee on Payment and Settlement Systems, Bank for International Settlements, Basel, Switzerland, September 1999.

¹⁴The Automated Clearing House also handles the growing number of check conversion transactions (see below) and nonrecurring transactions made by telephone or over the Internet.

¹⁵Fedwire is a real-time, gross settlement system, which means that each transaction over Fedwire is settled individually and immediately. With a net settlement system transactions are put into a pot and periodically netted off before being settled. CHIPS is an example of a net system that settles at frequent intervals.

¹⁶We discussed money-market funds in Section 17-3.

¹⁷To confuse things even more, dealers in the money market often quote rates as if there were only 360 days in a year. So a discount of 5% on a bill maturing in 91 days translates into a price of 100 – 5 × (91/360) = 98.74%.

¹⁸The sheik could equally well deposit the check with the London branch of a U.S. bank or a Japanese bank. He would still have made a eurodollar deposit.

¹⁹Occasionally (but only occasionally) referred to as “euroeuros.”

²⁰For these reasons dollars held on deposit in an IBF are classed as eurodollars.

²¹Three-month bills actually mature 91 days after issue, six-month bills mature in 182 days, and one-year bills mature in 364 days. For information on bill auctions, see www.publicdebt.treas.gov.

²²A small proportion of bills is sold to noncompetitive bidders. Noncompetitive bids are filled at the same price as the successful competitive bids.

²³Exceptions are the Government National Mortgage Association (Ginnie Mae), the Small Business Administration, the General Services Administration (GSA), the Financial Assistance Corporation, the Agency for International Development, and the Private Export Funding Corporation. Their debts are backed by the “full faith and credit” of the U.S. government.

²⁴Some of these notes are general obligations of the issuer; others are revenue securities, and in these cases payments are made from rent receipts or other user charges.

²⁵This advantage is partly offset by the fact that Treasury securities are free of state and local taxes.

²⁶Defaults on tax-exempts have been rare and for the most part have involved not-for-profit hospitals. However, there have been a number of major defaults of tax-exempt debt. In 1983 Washington Public Power Supply System (unfortunately known as WPPSS or “WOOPS”) defaulted on $2.25 billion of bonds. In 1994 Orange County in California also defaulted after losing $1.7 billion on its investment portfolio. In 2011 Jefferson Country, Alabama, declared bankruptcy. With $4.2 billion in municipal debt, it was the largest municipal bankruptcy in U.S. history. Shortly afterward, Harrisburg, the Pennsylvania state capital, defaulted on its bonds.

²⁷The tendered bonds are then resold to new investors.

²⁸Some CDs are not negotiable and are simply identical to time deposits. For example, banks may sell low-value nonnegotiable CDs to individuals.

²⁹To reduce the risk of repos, it is common to value the security at less than its market value. This difference is known as a haircut.

³⁰The company issuing preferred stock must pay dividends out of after-tax income. So most tax-paying firms would prefer to issue debt rather than floating-rate preferred. However, there are plenty of firms that are not paying taxes and cannot make use of the interest tax shield. Moreover, they have been able to issue floating-rate preferred at yields lower than they would have to pay on a debt issue. The corporations buying the preferreds are happy with these lower yields because 70% of the dividends they receive escape tax.

³¹Most auction-rate preferred stock was issued by closed-end mutual funds.

Part 10 Mergers, Corporate Control, and Governance

Mergers

The scale and pace of merger activity in the United States have been remarkable. Table 31.1 lists just a few recent mergers. Notice that many of these have involved firms in different countries. Look also at Figure 31.1, which shows the number of mergers involving U.S. companies for each year from 1962 to 2011. In 2006, a record year for mergers, companies were involved in deals totaling nearly $1.5 trillion in the USA and a further $0.5 trillion in Europe. Asian companies, always laggards in the urge to merge, accounted for just $59 billion of deals. During such periods of intense merger activity, management spends significant amounts of time either searching for firms to acquire or worrying about whether some other firm will acquire them.

A merger adds value only if the two companies are worth more together than apart. This chapter covers why two companies could be worth more together and how to get the merger deal done if they are. Many marriages between companies are amicable, but sometimes one party is dragged unwillingly to the altar. So we also look at what is involved in hostile takeovers.

We proceed as follows.

• Motives. Sources of value added.

• Dubious motives. Don’t be tempted.

• Benefits and costs. It’s important to estimate them consistently.

• Mechanics. Legal, tax, and accounting issues.

• Takeover battles and tactics. We look at merger tactics and show some of the economic forces driving merger activity.

• Mergers and the economy. How can we explain merger waves? Who gains and who loses as a result of mergers?

   TABLE 31.1 Some important recent mergers.

Source: Mergers and Acquisitions, various issues.

Mergers are partly about economies from combining two firms, but they are also about who gets to run the company. Pick a merger, and you’ll almost always find that one firm is the protagonist and the other is the target. The top management of the target firm usually departs after the merger.

Financial economists now view mergers as part of a broader market for corporate control. The activity in this market goes far beyond ordinary mergers. It includes leveraged buyouts (LBOs), spin-offs and divestitures, and also nationalizations and privatizations where the government acquires or sells a business. These are the subject of the next chapter.

   FIGURE 31.1 The number of mergers in the United States, 1962–2011.

Source: Mergerstat, www.mergerstat.com.

 31-1   Sensible Motives for Mergers

Mergers are often categorized as horizontal, vertical, or conglomerate. A horizontal merger is one that takes place between two firms in the same line of business. Most of the mergers listed in Table 31.1 are horizontal.

A vertical merger involves companies at different stages of production. The buyer expands back toward the source of raw materials or forward in the direction of the ultimate consumer. The merger between Comcast and NBC Universal was mainly a vertical merger. NBC was a major provider of programming content, while Comcast’s cable networks distributed that content. Google’s acquisition of Motorola Mobility in 2011 is another recent example. The acquisition gave Google control over a major user of its Android operating system for smartphones.

A conglomerate merger involves companies in unrelated lines of businesses. For example, the Indian Tata Group is a huge, widely diversified company. In recent years, its acquisitions have been as diverse as Eight O’Clock Coffee, Corus Steel, Jaguar Land Rover, the Ritz Carlton (Boston), and British Salt. No U.S. company is as diversified as Tata, but in the 1960s and 1970s it was common in the United States for unrelated businesses to merge. Much of the action in the 1980s and 1990s came from breaking up the conglomerates that had been formed 10 to 20 years earlier.

With these distinctions in mind, we are about to consider motives for mergers, that is, reasons why two firms may be worth more together than apart. We proceed with some trepidation. The motives, though they often lead the way to real benefits, are sometimes just mirages that tempt unwary or overconfident managers into takeover disasters. This was the case for AOL, which spent a record-breaking $156 billion to acquire Time Warner. The aim was to create a company that could offer consumers a comprehensive package of media and information products. It didn’t work. Even more embarrassing was the acquisition by Hewlett Packard of Autonomy, a British software company. The purchase was made in October 2011 for $11.1 billion. In November of the following year Hewlett Packard announced that it was writing off $8.8 billion of the purchase cost, alleging that it had been misled by “serious accounting improprieties” in Autonomy.¹

Many mergers that seem to make economic sense fail because managers cannot handle the complex task of integrating two firms with different production processes, accounting methods, and corporate cultures. The nearby box shows how these difficulties bedeviled the merger of three Japanese banks.

The value of most businesses depends on human assets—managers, skilled workers, scientists, and engineers. If these people are not happy in their new roles in the merged firm, the best of them will leave. Beware of paying too much for assets that go down in the elevator and out to the parking lot at the close of each business day. They may drive into the sunset and never return.

Consider the $38 billion merger between Daimler-Benz and Chrysler. Although it was hailed as a model for consolidation in the auto industry, the early years were rife with conflicts between two very different cultures:

German management-board members had executive assistants who prepared detailed position papers on any number of issues. The Americans didn’t have assigned aides and formulated their decisions by talking directly to engineers or other specialists. A German decision worked its way through the bureaucracy for final approval at the top. Then it was set in stone. The Americans allowed midlevel employees to proceed on their own initiative, sometimes without waiting for executive-level approval. . . .

Cultural integration also was proving to be a slippery commodity. The yawning gap in pay scales fueled an undercurrent of tension. The Americans earned two, three, and, in some cases, four times as much as their German counterparts. But the expenses of U.S. workers were tightly controlled compared with the German system. Daimler-side employees thought nothing of flying to Paris or New York for a half-day meeting, then capping the visit with a fancy dinner and a night in an expensive hotel. The Americans blanched at the extravagance.²

Nine years after acquiring Chrysler, Daimler threw in the towel and announced that it was offloading an 80% stake in Chrysler to a leveraged-buyout firm, Cerberus Capital Management. Daimler actually paid Cerberus $677 million to take Chrysler off its hands. Cerberus in return assumed about $18 billion in pension and employee health care liabilities and agreed to invest $6 billion in Chrysler and its finance subsidiary.

There are also occasions when the merger does achieve gains but the buyer nevertheless loses because it pays too much. For example, the buyer may overestimate the value of stale inventory or underestimate the costs of renovating old plant and equipment, or it may overlook the warranties on a defective product. Buyers need to be particularly careful about environmental liabilities. If there is pollution from the seller’s operations or toxic waste on its property, the costs of cleaning up will probably fall on the buyer.

Now we turn to the possible sources of merger synergies, that is, the possible sources of added value.

FINANCE IN PRACTICE

● ● ● ● ●

Those Elusive Synergies

  When three of Japan’s largest banks combined to form Mizuho Bank the result was a bank with assets of $1.5 trillion, more than twice those of the world leader Deutsche Bank. The name “Mizuho” means “rich rice harvest” and the bank’s management forecasted that the merger would yield a rich harvest of synergies. In a message to shareholders, the bank president claimed that the merger would create “a comprehensive financial services group that will surge forward in the 21st century.” He predicted that the bank would “lead the new era through cutting-edge comprehensive financial services . . . by exploiting to the fullest extent the Group’s enormous strengths, which are backed by a powerful customer base and state-of-the-art financial and information technologies.” The cost of putting the banks together was forecasted at ¥130 billion, but management predicted future benefits of ¥466 billion a year.

Within a few months of the announcement, reports began to emerge of squabbles among the three partners. One problem area was IT. Each of the three merging banks had a different supplier for its computer system. At first it was proposed to use just one of these three systems, but then the banks decided to connect the three different systems together using “relay” computers.

Three years after the initial announcement the new company opened for business on April 1, 2002. Five days later, computer glitches resulted in a spectacular foul-up. Some 7,000 of the bank’s cash machines did not work, 60,000 accounts were debited twice for the same transaction, and millions of bills went unpaid. The Economist reported that two weeks later Tokyo Gas, the biggest gas company, was still missing ¥2.2 billion in payments, and the top telephone company, NTT, which was looking for ¥12.7 billion, was forced to send its customers receipts marked with asterisks in place of figures, since it did not know which of about 760,000 bills had been paid.

One of the objectives behind the formation of Mizuho was to exploit economies in its IT systems. The launch fiasco illustrated dramatically that it is easier to predict such merger synergies than to realize them.

Sources: The creation of Mizuho Bank and its launch problems are described in “Undispensable: A Fine Merger Yields One Fine Mess,” The Economist, April 27, 2002, p. 72; “Big, Bold, but . . .”, Euromoney, December 2000, pp. 30–35; and “Godzilla Bank,” Forbes, March 20, 2000, pp. 132–133.

Economies of Scale

Many mergers are intended to reduce costs and achieve economies of scale. For example, when Duke Energy and Progress Energy announced plans to merge in 2011, the savings were estimated to be as high as $1.6 billion over five years. Management anticipated that the merger would allow the two companies to reduce fuel costs and improve dispatch of electricity. Savings would also come from a reduction in staff of nearly 2,000. (Some of these savings involved senior management. For example, there were two chief financial officers before the merger and only one afterward.)

Achieving these economies of scale is the natural goal of horizontal mergers. But such economies have been claimed in conglomerate mergers, too. The architects of these mergers have pointed to the economies that come from sharing central services such as office management and accounting, financial control, executive development, and top-level management.³

Economies of Vertical Integration

Vertical mergers seek to gain control over the production process by expanding back toward the output of the raw material or forward to the ultimate consumer. One way to achieve this is to merge with a supplier or a customer.

Vertical integration facilitates coordination and administration. We illustrate via an extreme example. Think of an airline that does not own any planes. If it schedules a flight from Boston to San Francisco, it sells tickets and then rents a plane for that flight from a separate company. This strategy might work on a small scale, but it would be an administrative nightmare for a major carrier, which would have to coordinate hundreds of rental agreements daily. In view of these difficulties, it is not surprising that all major airlines have integrated backward, away from the consumer, by buying and flying airplanes rather than simply patronizing rent-a-plane companies.

When trying to explain differences in integration, economists often stress the problems that may arise when two business activities are inextricably linked. For example, production of components may require a large investment in highly specialized equipment. Or a smelter may need to be located next to the mine to reduce the costs of transporting the ore. It may be possible in such cases to organize the activities as separate firms operating under a long-term contract. But such a contract can never allow for every conceivable change in the way that the activities may need to interact. Therefore, when two parts of an operation are highly dependent on each other, it often makes sense to combine them within the same firm, which then has control over how the assets should be used.⁴

Nowadays the tide of vertical integration seems to be flowing out. Companies are finding it more efficient to outsource the provision of many services and various types of production. For example, back in the 1950s and 1960s, General Motors was deemed to have a cost advantage over its main competitors, Ford and Chrysler, because a greater fraction of the parts used in GM’s automobiles were produced in-house. By the 1990s, Ford and Chrysler had the advantage: they could buy the parts cheaper from outside suppliers. This was partly because the outside suppliers tended to use nonunion labor at lower wages. But it also appears that manufacturers have more bargaining power versus independent suppliers than versus a production facility that’s part of the corporate family. In 1998 GM decided to spin off Delphi, its automotive parts division, as a separate company. After the spin-off, GM continued to buy parts from Delphi in large volumes, but it negotiated the purchases at arm’s length.

Complementary Resources

Many small firms are acquired by large ones that can provide the missing ingredients necessary for the small firms’ success. The small firm may have a unique product but lack the engineering and sales organization required to produce and market it on a large scale. The firm could develop engineering and sales talent from scratch, but it may be quicker and cheaper to merge with a firm that already has ample talent. The two firms have complementary resources—each has what the other needs—and so it may make sense for them to merge. Also, the merger may open up opportunities that neither firm would pursue otherwise.

In recent years many of the major pharmaceutical firms have faced the loss of patent protection on their more profitable products and have not had an offsetting pipeline of promising new compounds. This has prompted an increasing number of acquisitions of biotech firms. For example, in 2012 Syngenta acquired the Belgian biotech Devgen for €403 million. Syngenta calculated that Devgen’s know-how in crop protection technology would enable it to broaden its range of crop protection products. At the same time, Devgen obtained the resources that it needed to bring its products to market.

Surplus Funds

Here’s another argument for mergers: Suppose that your firm is in a mature industry. It is generating a substantial amount of cash, but it has few profitable investment opportunities. Ideally such a firm should distribute the surplus cash to shareholders by increasing its dividend payment or repurchasing stock. Unfortunately, energetic managers are often reluctant to adopt a policy of shrinking their firm in this way. If the firm is not willing to purchase its own shares, it can instead purchase another company’s shares. Firms with a surplus of cash and a shortage of good investment opportunities often turn to mergers financed by cash as a way of redeploying their capital.

Some firms have excess cash and do not pay it out to stockholders or redeploy it by wise acquisitions. Such firms often find themselves targeted for takeover by other firms that propose to redeploy the cash for them. During the oil price slump of the early 1980s, many cash-rich oil companies found themselves threatened by takeover. This was not because their cash was a unique asset. The acquirers wanted to capture the companies’ cash flow to make sure it was not frittered away on negative-NPV oil exploration projects. We return to this free-cash-flow motive for takeovers later in this chapter.

Eliminating Inefficiencies

Cash is not the only asset that can be wasted by poor management. There are always firms with unexploited opportunities to cut costs and increase sales and earnings. Such firms are natural candidates for acquisition by other firms with better management. In some instances “better management” may simply mean the determination to force painful cuts or realign the company’s operations. Notice that the motive for such acquisitions has nothing to do with benefits from combining two firms. Acquisition is simply the mechanism by which a new management team replaces the old one.

A merger is not the only way to improve management, but sometimes it is the only simple and practical way. Managers are naturally reluctant to fire or demote themselves, and stockholders of large public firms do not usually have much direct influence on how the firm is run or who runs it.⁵

If this motive for merger is important, one would expect to observe that acquisitions often precede a change in the management of the target firm. This seems to be the case. For example, Martin and McConnell found that the chief executive is four times more likely to be replaced in the year after a takeover than during earlier years.⁶ The firms they studied had generally been poor performers; in the four years before acquisition their stock prices had lagged behind those of other firms in the same industry by 15%. Apparently many of these firms fell on bad times and were rescued, or reformed, by merger.

Industry Consolidation

The biggest opportunities to improve efficiency seem to come in industries with too many firms and too much capacity. These conditions seem to trigger a wave of mergers and acquisitions, which then force companies to cut capacity and employment and release capital for reinvestment elsewhere in the economy. For example, when U.S. defense budgets fell after the end of the Cold War, a round of consolidating takeovers followed in the defense industry. The consolidation was inevitable, but the takeovers accelerated it.

The banking industry is another example. During the financial crisis many banking mergers involved rescues of failing banks by larger and stronger rivals. But most earlier bank mergers involved successful banks that sought to achieve economies of scale. The United States entered the 1980s with far too many banks, largely as a result of outdated restrictions on interstate banking. As these restrictions eroded and communications and technology improved, hundreds of small banks were swept up into regional or “super-regional” banks. For example, look at Figure 31.2, which shows the dozens of acquisitions by Bank of America and its predecessor companies. The main motive of these mergers was to reduce costs.⁷

   FIGURE 31.2 Part of Bank of America’s family tree.

Sources: Thomson Financial SDC M&A Database and Bank of America annual reports.

Europe also experienced a wave of bank mergers as companies sought to gain the financial muscle to compete in a Europe-wide banking market. These include the mergers of UBS and Swiss Bank Corp (1997), BNP and Banque Paribas (1998), Hypobank and Bayerische Vereinsbank (1998), Banco Santander and Banco Central Hispanico (1999), Unicredit and Capitalia (2007), and Commerzbank and Dresdner Bank (2009).

 31-2   Some Dubious Reasons for Mergers

The benefits that we have described so far all make economic sense. Other arguments sometimes given for mergers are dubious. Here are a few of the dubious ones.

Diversification

We have suggested that the managers of a cash-rich company may prefer to see it use that cash for acquisitions rather than distribute it as extra dividends. That is why we often see cash-rich firms in stagnant industries merging their way into fresh woods and pastures new.

What about diversification as an end in itself? It is obvious that diversification reduces risk. Isn’t that a gain from merging?

The trouble with this argument is that diversification is easier and cheaper for the stockholder than for the corporation. There is little evidence that investors pay a premium for diversified firms; in fact, as we will explain in Chapter 32, discounts are more common. The Appendix to this chapter provides a simple proof that corporate diversification does not increase value in perfect markets as long as investors’ diversification opportunities are unrestricted. This is the value-additivity principle introduced in Chapter 7.

Increasing Earnings per Share: The Bootstrap Game

Some acquisitions that offer no evident economic gains nevertheless produce several years of rising earnings per share. To see how this can happen, let us look at the acquisition of Muck and Slurry by the well-known conglomerate World Enterprises.

The position before the merger is set out in the first two columns of Table 31.2. Because Muck and Slurry has relatively poor growth prospects, its stock’s price–earnings ratio is lower than World Enterprises’ (line 3). The merger, we assume, produces no economic benefits, and so the firms should be worth exactly the same together as they are apart. The market value of World Enterprises after the merger should be equal to the sum of the separate values of the two firms (line 6).

   TABLE 31.2 Impact of merger on market value and earnings per share of World Enterprises.

Note: When World Enterprises purchases Muck and Slurry, there are no gains. Therefore, total earnings and total market value should be unaffected by the merger. But earnings per share increase. World Enterprises issues only 50,000 of its shares (priced at $40) to acquire the 100,000 Muck and Slurry shares (priced at $20).

Since World Enterprises’ stock is selling for double the price of Muck and Slurry stock (line 2), World Enterprises can acquire the 100,000 Muck and Slurry shares for 50,000 of its own shares. Thus World will have 150,000 shares outstanding after the merger.

Total earnings double as a result of the merger (line 5), but the number of shares increases by only 50%. Earnings per share rise from $2.00 to $2.67. We call this the bootstrap effect because there is no real gain created by the merger and no increase in the two firms’ combined value. Since the stock price is unchanged, the price–earnings ratio falls (line 3).

Figure 31.3 illustrates what is going on here. Before the merger $1 invested in World Enterprises bought 5 cents of current earnings and rapid growth prospects. On the other hand, $1 invested in Muck and Slurry bought 10 cents of current earnings but slower growth prospects. If the total market value is not altered by the merger, then $1 invested in the merged firm gives 6.7 cents of immediate earnings but slower growth than World Enterprises offered alone. Muck and Slurry shareholders get lower immediate earnings but faster growth. Neither side gains or loses provided everybody understands the deal.

   FIGURE 31.3 Effects of merger on earnings growth. By merging with Muck and Slurry, World Enterprises increases current earnings but accepts a slower rate of future growth. Its stockholders should be no better or worse off unless investors are fooled by the bootstrap effect.

Source: S. C. Myers, “A Framework for Evaluating Mergers,” in Modern Developments in Financial Management, ed. S. C. Myers (New York: Frederick A. Praeger, Inc., 1976), Figure 1, p. 639. Copyright © 1976 Praeger. Reprinted by permission of ABC-CLIO, Inc., via Copyright Clearance Center.

Financial manipulators sometimes try to ensure that the market does not understand the deal. Suppose that investors are fooled by the exuberance of the president of World Enterprises and by plans to introduce modern management techniques into its new Earth Sciences Division (formerly known as Muck and Slurry). They could easily mistake the 33% postmerger increase in earnings per share for real growth. If they do, the price of World Enterprises stock rises and the shareholders of both companies receive something for nothing.

This is a “bootstrap” or “chain letter” game. It generates earnings growth not from capital investment or improved profitability, but from purchase of slowly growing firms with low price–earnings ratios. If this fools investors, the financial manager may be able to puff up stock price artificially. But to keep fooling investors, the firm has to continue to expand by merger at the same compound rate. Clearly this cannot go on forever; one day expansion must slow down or stop. At this point earnings growth falls dramatically and the house of cards collapses.

This game is not often played these days, but you may still encounter managers who would rather acquire firms with low price–earnings ratios. Beware of false prophets who suggest that you can appraise mergers just by looking at their immediate impact on earnings per share.

Lower Financing Costs

You often hear it said that a merged firm is able to borrow more cheaply than its separate units could. In part this is true. We have already seen (in Section 15-4) that there are significant economies of scale in making new issues. Therefore, if firms can make fewer, larger security issues by merging, there are genuine savings.

But when people say that borrowing costs are lower for the merged firm, they usually mean something more than lower issue costs. They mean that when two firms merge, the combined company can borrow at lower interest rates than either firm could separately. This, of course, is exactly what we should expect in a well-functioning bond market. While the two firms are separate, they do not guarantee each other’s debt; if one fails, the bondholder cannot ask the other for money. But after the merger each enterprise effectively does guarantee the other’s debt; if one part of the business fails, the bondholders can still take their money out of the other part. Because these mutual guarantees make the debt less risky, lenders demand a lower interest rate.

Does the lower interest rate mean a net gain to the merger? Not necessarily. Compare the following two situations:

•  Separate issues. Firm A and firm B each make a $50 million bond issue.

•  Single issue. Firms A and B merge, and the new firm AB makes a single $100 million issue.

Of course AB would pay a lower interest rate, other things being equal. But it does not make sense for A and B to merge just to get that lower rate. Although AB’s shareholders do gain from the lower rate, they lose by having to guarantee each other’s debt. In other words, they get the lower interest rate only by giving bondholders better protection. There is no net gain.

In Section 23-2 we showed that

Merger increases bond value (or reduces the interest payments necessary to support a given bond value) only by reducing the value of stockholders’ option to default. In other words, the value of the default option for AB’s $100 million issue is less than the combined value of the two default options on A’s and B’s separate $50 million issues.

Now suppose that A and B each borrow $50 million and then merge. If the merger is a surprise, it is likely to be a happy one for the bondholders. The bonds they thought were guaranteed by one of the two firms end up guaranteed by both. The stockholders lose in this case because they have given bondholders better protection but have received nothing for it.

There is one situation in which mergers can create value by making debt safer. Consider a firm that covets interest tax shields but is reluctant to borrow more because of worries about financial distress. (This is the trade-off theory described in Chapter 18.) Merging decreases the probability of financial distress, other things equal. If it allows increased borrowing, and increased value from the interest tax shields, there can be a net gain to the merger.⁸

 31-3   Estimating Merger Gains and Costs

Suppose that you are the financial manager of firm A and you want to analyze the possible purchase of firm B.⁹ The first thing to think about is whether there is an economic gain from the merger. There is an economic gain only if the two firms are worth more together than apart. For example, if you think that the combined firm would be worth PVAB and that the separate firms are worth PVA and PVB, then

If this gain is positive, there is an economic justification for merger. But you also have to think about the cost of acquiring firm B. Take the easy case in which payment is made in cash. Then the cost of acquiring B is equal to the cash payment minus B’s value as a separate entity. Thus

The net present value to A of a merger with B is measured by the difference between the gain and the cost. Therefore, you should go ahead with the merger if its net present value, defined as

is positive.

We like to write the merger criterion in this way because it focuses attention on two distinct questions. When you estimate the benefit, you concentrate on whether there are any gains to be made from the merger. When you estimate cost, you are concerned with the division of these gains between the two companies.

An example may help make this clear. Firm A has a value of $200 million, and B has a value of $50 million. Merging the two would allow cost savings with a present value of $25 million. This is the gain from the merger. Thus,

Suppose that B is bought for cash, say, for $65 million. The cost of the merger is

Note that the stockholders of firm B—the people on the other side of the transaction—are ahead by $15 million. Their gain is your cost. They have captured $15 million of the $25 million merger gain. Thus when we write down the NPV of the merger from A’s viewpoint, we are really calculating the part of the gain that A’s stockholders get to keep. The NPV to A’s stockholders equals the overall gain from the merger less that part of the gain captured by B’s stockholders:

Just as a check, let’s confirm that A’s stockholders really come out $10 million ahead. They start with a firm worth PVA = $200 million. They end up with a firm worth $275 million and then have to pay out $65 million to B’s stockholders.¹⁰ Thus their net gain is

Suppose investors do not anticipate the merger between A and B. The announcement will cause the value of B’s stock to rise from $50 million to $65 million, a 30% increase. If investors share management’s assessment of the merger gains, the market value of A’s stock will increase by $10 million, only a 5% increase.

It makes sense to keep an eye on what investors think the gains from merging are. If A’s stock price falls when the deal is announced, then investors are sending the message that the merger benefits are doubtful or that A is paying too much for them.

Right and Wrong Ways to Estimate the Benefits of Mergers

Some companies begin their merger analyses with a forecast of the target firm’s future cash flows. Any revenue increases or cost reductions attributable to the merger are included in the forecasts, which are then discounted back to the present and compared with the purchase price:

This is a dangerous procedure. Even the brightest and best-trained analyst can make large errors in valuing a business. The estimated net gain may come up positive not because the merger makes sense but simply because the analyst’s cash-flow forecasts are too optimistic. On the other hand, a good merger may not be pursued if the analyst fails to recognize the target’s potential as a stand-alone business.

Our procedure starts with the target’s stand-alone market value (PVB) and concentrates on the changes in cash flow that would result from the merger. Ask yourself why the two firms should be worth more together than apart.

The same advice holds when you are contemplating the sale of part of your business. There is no point in saying to yourself, “This is an unprofitable business and should be sold.” Unless the buyer can run the business better than you can, the price you receive will reflect the poor prospects.

Sometimes you may come across managers who believe that there are simple rules for identifying good acquisitions. They may say, for example, that they always try to buy into growth industries or that they have a policy of acquiring companies that are selling below book value. But our comments in Chapter 11 about the characteristics of a good investment decision also hold true when you are buying a whole company. You add value only if you can generate additional economic rents—some competitive edge that other firms can’t match and the target firm’s managers can’t achieve on their own.

One final piece of horse sense: Often two companies bid against each other to acquire the same target firm. In effect, the target firm puts itself up for auction. In such cases, ask yourself whether the target is worth more to you than to the other bidder. If the answer is no, you should be cautious about getting into a bidding contest. Winning such a contest may be more expensive than losing it. If you lose, you have simply wasted your time; if you win, you have probably paid too much.

More on Estimating Costs—What If the Target’s Stock Price Anticipates the Merger?

The cost of a merger is the premium that the buyer pays over the seller’s stand-alone value. How can that value be determined? If the target is a public company, you can start with its market value; just observe price per share and multiply by the number of shares outstanding. But bear in mind that if investors expect A to acquire B, or if they expect somebody to acquire B, the market value of B may overstate its stand-alone value.

This is one of the few places in this book where we draw an important distinction between market value (MV) and the true, or “intrinsic,” value (PV) of the firm as a separate entity. The problem here is not that the market value of B is wrong but that it may not be the value of firm B as a separate entity. Potential investors in B’s stock will see two possible outcomes and two possible values:

If the second outcome is possible, MVB, the stock market value we observe for B, will overstate PVB. This is exactly what should happen in a competitive capital market. Unfortunately, it complicates the task of a financial manager who is evaluating a merger.

Here is an example: Suppose that just before A and B’s merger announcement we observe the following:

Firm A intends to pay $65 million cash for B. If B’s market price reflects only its value as a separate entity, then

However, suppose that B’s share price has already risen $12 because of rumors that B might get a favorable merger offer. That means that its intrinsic value is overstated by 12 × 500,000 = $6 million. Its true value, PVB, is only $44 million. Then

Since the merger gain is $25 million, this deal still makes A’s stockholders better off, but B’s stockholders are now capturing the lion’s share of the gain.

Notice that if the market made a mistake, and the market value of B was less than B’s true value as a separate entity, the cost could be negative. In other words, B would be a bargain and the merger would be worthwhile from A’s point of view, even if the two firms were worth no more together than apart. Of course, A’s stockholders’ gain would be B’s stockholders’ loss, because B would be sold for less than its true value.

Firms have made acquisitions just because their managers believed they had spotted a company whose intrinsic value was not fully appreciated by the stock market. However, we know from the evidence on market efficiency that “cheap” stocks often turn out to be expensive. It is not easy for outsiders, whether investors or managers, to find firms that are truly undervalued by the market. Moreover, if the shares are bargain-priced, A doesn’t need a merger to profit by its special knowledge. It can just buy up B’s shares on the open market and hold them passively, waiting for other investors to wake up to B’s true value.

If firm A is wise, it will not go ahead with a merger if the cost exceeds the gain. Firm B will not consent if A’s gain is so big that B loses. This gives us a range of possible cash payments that would allow the merger to take place. Whether the payment is at the top or the bottom of this range depends on the relative bargaining power of the two participants.

Estimating Cost When the Merger Is Financed by Stock

Many mergers involve payment wholly or partly in the form of the acquirer’s stock. When a merger is financed by stock, cost depends on the value of the shares in the new company received by the shareholders of the selling company. If the sellers receive N shares, each worth PAB, the cost is

Just be sure to use the price per share after the merger is announced and its benefits are appreciated by investors.

Suppose that A offers 325,000 (.325 million) shares instead of $65 million in cash. A’s share price before the deal is announced is $200. If B is worth $50 million stand-alone,¹¹ the cost of the merger appears to be

However, the apparent cost may not be the true cost. A’s stock price is $200 before the merger announcement. At the announcement it ought to go up.

Given the gain and the terms of the deal, we can calculate share prices and market values after the deal. The new firm will have 1.325 million shares outstanding and will be worth $275 million.¹² The new share price is 275/1.325 = $207.55. The true cost is

This cost can also be calculated by figuring out the gain to B’s shareholders. They end up with .325 million shares, or 24.5% of the new firm AB. Their gain is

In general, if B’s shareholders are given the fraction x of the combined firms,

We can now understand the first key distinction between cash and stock as financing instruments. If cash is offered, the cost of the merger is unaffected by the merger gains. If stock is offered, the cost depends on the gains because the gains show up in the postmerger share price.

Stock financing also mitigates the effect of overvaluation or undervaluation of either firm. Suppose, for example, that A overestimates B’s value as a separate entity, perhaps because it has overlooked some hidden liability. Thus A makes too generous an offer. Other things being equal, A’s stockholders are better off if it is a stock offer rather than a cash offer. With a stock offer, the inevitable bad news about B’s value will fall partly on the shoulders of B’s stockholders.

Asymmetric Information

There is a second key difference between cash and stock financing for mergers. A’s managers will usually have access to information about A’s prospects that is not available to outsiders. Economists call this asymmetric information.

Suppose A’s managers are more optimistic than outside investors. They may think that A’s shares will really be worth $215 after the merger, $7.45 higher than the $207.55 market price we just calculated. If they are right, the true cost of a stock-financed merger with B is

B’s shareholders would get a “free gift” of $7.45 for every A share they receive—an extra gain of $7.45 × .325 = 2.42, that is, $2.42 million.

Of course, if A’s managers were really this optimistic, they would strongly prefer to finance the merger with cash. Financing with stock would be favored by pessimistic managers who think their company’s shares are overvalued.

Does this sound like “win-win” for A—just issue shares when overvalued, cash otherwise? No, it’s not that easy, because B’s shareholders, and outside investors generally, understand what’s going on. Suppose you are negotiating on behalf of B. You find that A’s managers keep suggesting stock rather than cash financing. You quickly infer A’s managers’ pessimism, mark down your own opinion of what the shares are worth, and drive a harder bargain.

This asymmetric-information story explains why buying-firms’ share prices generally fall when stock-financed mergers are announced.¹³ Andrade, Mitchell, and Stafford found an average market-adjusted fall of 1.5% on the announcement of stock-financed mergers between 1973 and 1998. There was a small gain (.4%) for a sample of cash-financed deals.¹⁴

 31-4   The Mechanics of a Merger

Buying a company is a much more complicated affair than buying a piece of machinery. Thus we should look at some of the problems encountered in arranging mergers. In practice, these arrangements are often extremely complex, and specialists must be consulted. We are not trying to replace those specialists; we simply want to alert you to the kinds of legal, tax, and accounting issues they deal with.

Mergers, Antitrust Law, and Popular Opposition

Mergers in the United States can get bogged down in the federal antitrust laws. The most important statute here is the Clayton Act of 1914, which forbids an acquisition whenever “in any line of commerce or in any section of the country” the effect “may be substantially to lessen competition, or to tend to create a monopoly.”

Antitrust law can be enforced by the federal government in either of two ways: by a civil suit brought by the Justice Department or by a proceeding initiated by the Federal Trade Commission (FTC).¹⁵ The Hart–Scott–Rodino Antitrust Act of 1976 requires that these agencies be informed of all acquisitions of stock amounting to $15 million or 15% of the target’s stock, whichever is less. Thus, almost all large mergers are reviewed at an early stage.¹⁶ Both the Justice Department and the FTC then have the right to seek injunctions delaying a merger. An injunction is often enough to scupper the companies’ plans. For example, in 2011, when AT&T proposed a $39 billion acquisition of T-Mobile, the Justice Department filed a lawsuit to block the merger. Shortly afterward AT&T threw in the towel and abandoned its bid.

Companies that do business outside the U.S. also have to worry about foreign antitrust laws. For example, GE’s $46 billion takeover bid for Honeywell was blocked by the European Commission, which argued that the combined company would have too much power in the aircraft industry.

Sometimes trustbusters will object to a merger, but then relent if the companies agree to divest certain assets and operations. When Exelon acquired Constellation Energy in 2011, the Justice Department required the companies to sell three electricity-generating plants in Maryland in order to proceed with their $7.9 billion merger.

Mergers may also be stymied by political pressures and popular resentment even when no formal antitrust issues arise. In recent years national governments in Europe have become involved in almost all high-profile cross-border mergers and are likely to intervene actively in any hostile bid. For example, the news in 2005 that PepsiCo might bid for Danone aroused considerable hostility in France. The prime minister added his support to opponents of the merger and announced that the French government was drawing up a list of strategic industries that should be protected from foreign ownership. It was unclear whether yogurt production would be one of these strategic industries.

Economic nationalism is not confined to Europe. In 2005 China National Offshore Oil Corporation (CNOOC) felt obliged to withdraw its bid for Unocal, after what it described as “unprecedented political opposition” in Congress. The following year Congress voiced its opposition to the takeover of Britain’s P&O by the Dubai company DP World. The acquisition went ahead only after P&O’s ports in the United States were excluded from the deal.

The Form of Acquisition

Suppose you are confident that the purchase of company B will not be challenged on antitrust grounds. Next you will want to consider the form of the acquisition.

One possibility is literally to merge the two companies, in which case one company automatically assumes all the assets and all the liabilities of the other. Such a merger must have the approval of at least 50% of the stockholders of each firm.¹⁷

An alternative is simply to buy the seller’s stock in exchange for cash, shares, or other securities. In this case the buyer can deal individually with the shareholders of the selling company. The seller’s managers may not be involved at all. Their approval and cooperation are generally sought, but if they resist, the buyer will attempt to acquire an effective majority of the outstanding shares. If successful, the buyer has control and can complete the merger and, if necessary, toss out the incumbent management.

The third approach is to buy some or all of the seller’s assets. In this case ownership of the assets needs to be transferred, and payment is made to the selling firm rather than directly to its stockholders.

Merger Accounting

When one company buys another, its management worries about how the purchase will show up in its financial statements. Before 2001 the company had a choice of accounting method, but in that year the Financial Accounting Standards Board (FASB) introduced new rules that required the buyer to use the purchase method of merger accounting. This is illustrated in Table 31.3, which shows what happens when A Corporation buys B Corporation, leading to the new AB Corporation. The two firms’ initial balance sheets are shown at the top of the table. Below this we show what happens to the balance sheet when the two firms merge. We assume that B Corporation has been purchased for $18 million, 180% of book value.

   TABLE 31.3 Accounting for the merger of A Corporation and B Corporation assuming that A Corporation pays $18 million for B Corporation (figures in $ millions).

Key: NWC = net working capital; FA = net book value of fixed assets; D = debt; E = book value of equity.

Why did A Corporation pay an $8 million premium over B’s book value? There are two possible reasons. First, the true values of B’s tangible assets—its working capital, plant, and equipment—may be greater than $10 million. We will assume that this is not the reason; that is, we assume that the assets listed on its balance sheet are valued there correctly.¹⁸ Second, A Corporation may be paying for an intangible asset that is not listed on B Corporation’s balance sheet. For example, the intangible asset may be a promising product or technology. Or it may be no more than B Corporation’s share of the expected economic gains from the merger.

A Corporation is buying an asset worth $18 million. The problem is to show that asset on the left-hand side of AB Corporation’s balance sheet. B Corporation’s tangible assets are worth only $10 million. This leaves $8 million. Under the purchase method, the accountant takes care of this by creating a new asset category called goodwill and assigning $8 million to it.¹⁹ As long as the goodwill continues to be worth at least $8 million, it stays on the balance sheet and the company’s earnings are unaffected.²⁰ However, the company is obliged each year to estimate the fair value of the goodwill. If the estimated value ever falls below $8 million, the amount shown on the balance sheet must be adjusted downward and the write-off deducted from that year’s earnings. Some companies have found that this can make a nasty dent in profits. For example, when the new accounting rules were introduced, AOL was obliged to write down the value of its assets by $54 billion.

Some Tax Considerations

An acquisition may be either taxable or tax-free. If payment is in the form of cash, the acquisition is regarded as taxable. In this case the selling stockholders are treated as having sold their shares, and they must pay tax on any capital gains. If payment is largely in the form of shares, the acquisition is tax-free and the shareholders are viewed as exchanging their old shares for similar new ones; no capital gains or losses are recognized.

The tax status of the acquisition also affects the taxes paid by the merged firm afterward. After a tax-free acquisition, the merged firm is taxed as if the two firms had always been together. In a taxable acquisition, the assets of the selling firm are revalued, the resulting write-up or write-down is treated as a taxable gain or loss, and tax depreciation is recalculated on the basis of the restated asset values.

A very simple example will illustrate these distinctions. In 1995 Captain B forms Seacorp, which purchases a fishing boat for $300,000. Assume, for simplicity, that the boat is depreciated for tax purposes over 20 years on a straight-line basis (no salvage value). Thus annual depreciation is $300,000/20 = $15,000, and in 2005 the boat has a net book value of $150,000. But in 2005, Captain B finds that, owing to careful maintenance, inflation, and good times in the local fishing industry, the boat is really worth $280,000. In addition, Seacorp holds $50,000 of marketable securities.

   TABLE 31.4 Possible tax consequences when Baycorp buys Seacorp for $330,000. Captain B’s original investment in Seacorp was $300,000. Just before the merger Seacorp’s assets were $50,000 of marketable securities and one boat with a book value of $150,000 but a market value of $280,000.

Now suppose that Captain B sells the firm to Baycorp for $330,000. The possible tax consequences of the acquisition are shown in Table 31.4. In this case, Captain B may ask for a tax-free deal to defer capital gains tax. But Baycorp can afford to pay more in a taxable deal because depreciation tax shields are larger.

 31-5   Proxy Fights, Takeovers, and the Market for Corporate Control

The shareholders are the owners of the firm. But most shareholders do not feel like the boss, and with good reason. Try buying a share of IBM stock and marching into the boardroom for a chat with your employee, the chief executive officer.

The ownership and management of large corporations are separated. Shareholders elect the board of directors but have little direct say in most management decisions. Agency costs arise when managers or directors are tempted to make decisions that are not in the shareholders’ interests.

As we pointed out in Chapter 1, there are many forces and constraints working to keep managers’ and shareholders’ interests in line. But what can be done to ensure that the board has engaged the most talented managers? What happens if managers are inadequate? What if the board is derelict in monitoring the performance of managers? Or what if the firm’s managers are fine but the resources of the firm could be used more efficiently by merging with another firm? Can we count on managers to pursue policies that might put them out of a job?

These are all questions about the market for corporate control, the mechanism by which firms are matched up with owners and management teams who can make the most of the firm’s resources. You should not take a firm’s current ownership and management for granted. If it is possible for the value of the firm to be enhanced by changing management or by reorganizing under new owners, there will be incentives for someone to make the change.

There are three ways to change the management of a firm: (1) a successful proxy contest in which a group of shareholders votes in a new board of directors who then pick a new management team, (2) a takeover of one company by another, and (3) a leveraged buyout of the firm by a private group of investors. We focus here on the first two methods and postpone discussion of buyouts until the next chapter.

Proxy Contests

Shareholders elect the board of directors to keep watch on management and replace unsatisfactory managers. If the board is lax, shareholders are free to elect a different board.

When a group of investors believes that the board and its management should be replaced, they can launch a proxy contest at the next annual meeting. A proxy is the right to vote another shareholder’s shares. In a proxy contest, the dissident shareholders attempt to obtain enough proxies to elect their own slate to the board of directors. Once the new board is in control, management can be replaced and company policy changed. A proxy fight is therefore a direct contest for control of the corporation. Many proxy fights are initiated by major shareholders who consider the firm poorly managed. In other cases a fight may be a prelude to the merger of two firms. The proponent of the merger may believe that a new board will better appreciate the advantages of combining the two firms.

Proxy contests are expensive and difficult to win. Dissidents who engage in proxy fights must use their own money, but management can use the corporation’s funds and lines of communications with shareholders to defend itself. To level the playing field somewhat, the SEC has proposed new rules to make it easier to mount a proxy fight. In the meantime, shareholders have found that a policy of “just say no” to the reelection of existing directors can send a powerful signal. When Disney shareholders voted 43% of the shares against the reelection of Michael Eisner, the company’s autocratic chairman, he heard the message and resigned the next day.

The threat of a proxy fight may also encourage management to change company policy. For example, in 2008 shareholder activist Carl Icahn indicated his intention to put himself forward for nomination to the board of Motorola. However, Icahn controlled less than 7% of the votes and failed to prevent the reelection of the existing board. Nevertheless the pressure from Icahn had an effect: Motorola agreed to nominate two new board members and, at Icahn’s urging, spun off its handset division as Motorola Mobility.²¹

Takeovers

The alternative to a proxy fight is for the would-be acquirer to make a tender offer directly to the shareholders. If the offer is successful, the new owner is free to make any management changes. The management of the target firm may advise its shareholders to accept the offer, or it may fight the bid in the hope that the acquirer will either raise its offer or throw in the towel.

In the United States the rules for tender offers are set largely by the Williams Act of 1968 and by state laws. The courts act as a referee to see that contests are conducted fairly. The problem in setting these rules is that it is unclear who requires protection. Should the management of the target firm be given more weapons to defend itself against unwelcome predators? Or should it simply be encouraged to sit the game out? Or should it be obliged to conduct an auction to obtain the highest price for its shareholders?²² And what about would-be acquirers? Should they be forced to reveal their intentions at an early stage, or would that allow other firms to piggyback on their good ideas by entering bids of their own?²³ Keep these questions in mind as we review a recent takeover battle.

Oracle Bids for PeopleSoft

Hostile takeover bids tend to be less common in high-tech industries where an acrimonious takeover battle may cause many of the target’s most valued staff to leave. Investors were therefore startled in June 2003 when the software giant, Oracle Corp, announced a $5.1 billion cash tender offer for its rival PeopleSoft. The offer price of $16 a share was only a modest 6% above the recent price of PeopleSoft stock. PeopleSoft’s CEO angrily rejected the bid as dramatically undervaluing the business and accused Oracle of trying to disrupt PeopleSoft’s business and to thwart its recently announced plan to merge with its smaller rival J.D. Edwards & Co. PeopleSoft immediately filed a suit claiming that Oracle’s management had engaged in “acts of unfair trade practices” and had “disrupted PeopleSoft’s customer relationships.” In another suit J.D. Edwards claimed that Oracle had wrongly “interfered with its proposed merger with PeopleSoft” and demanded $1.7 billion in compensatory damages.

   TABLE 31.5 Some key dates in the Oracle/PeopleSoft takeover battle.

Oracle’s bid was the opening salvo in a battle that was to last 18 months. Some of the key dates in this battle are set out in Table 31.5. PeopleSoft had several defenses at its disposal. First, it had in place a poison pill that would allow it to flood the market with additional shares if a predator acquired 20% of the stock. Second, the company instituted a customer-assurance program that offered customers money-back guarantees if an acquirer were to reduce customer support. At one point in the takeover battle the potential liability under this program reached nearly $1.6 billion. Third, elections to the PeopleSoft board were staggered, so that different directors came up for re-election in different years. This meant that it would take two annual meetings to replace a majority of PeopleSoft’s board.

Oracle not only had to overcome PeopleSoft’s defenses, but it also had to clear possible antitrust roadblocks. Connecticut’s attorney general instituted an antitrust action to block Oracle’s bid, in part to protect his state’s considerable investment in PeopleSoft software. Then an investigation of the deal by the U.S. Department of Justice ruled that the deal was anticompetitive. Normally such an objection is enough to kill a deal, but Oracle was persistent and successfully appealed the ruling in a federal court.

While these battles were being fought out, Oracle revised its offer four times. It upped its offer first to $19.50 and then to $26 a share. Then, in an effort to put pressure on PeopleSoft shareholders, Oracle reduced its offer to $21 a share, citing a drop of 28% in the price of PeopleSoft’s shares. Six months later it raised the offer again to $24 a share, warning investors that it would walk away if the offer was not accepted by PeopleSoft’s board or a majority of PeopleSoft shareholders.

Sixty percent of PeopleSoft’s shareholders indicated that they wished to accept this last offer, but before Oracle could gain control of PeopleSoft, it still needed the company to get rid of the poison pill and customer-assurance scheme. That meant putting pressure on PeopleSoft’s management, which had continued to reject every approach. Oracle tried two tactics. First it initiated a proxy fight to change the composition of PeopleSoft’s board. Second, it filed a suit in a Delaware court alleging that PeopleSoft’s management breached its fiduciary duty by trying to thwart Oracle’s offer and not giving it “due consideration.” The lawsuit asked the court to require PeopleSoft to dismantle its takeover defenses, including the poison-pill plan and the customer-assurance program.

PeopleSoft’s CEO had at one point said that he “could imagine no price nor combination of price and other conditions to recommend accepting the offer.” But with 60% of PeopleSoft’s shareholders in favor of taking Oracle’s latest offer, it was becoming less easy for the company to keep saying no, and many observers were starting to question whether PeopleSoft’s management was acting in shareholders’ interest. If management showed itself deaf to shareholders’ interests, the court could well rule in favor of Oracle, or disgruntled shareholders might vote to change the composition of the PeopleSoft board. PeopleSoft’s directors therefore decided to be less intransigent and testified at the Delaware trial that they would consider negotiating with Oracle if it were to offer $26.50 or $27 a share. This was the breakthrough that Oracle was looking for. It upped its offer immediately to $26.50 a share, PeopleSoft lifted its defenses, and within a month 97% of PeopleSoft’s shareholders had agreed to the bid.²⁴ After 18 months of punch and counterpunch the battle for PeopleSoft was over.

Takeover Defenses

What are the lessons from the battle for PeopleSoft? First, the example illustrates some of the stratagems of modern merger warfare. Firms like PeopleSoft that are worried about being taken over usually prepare their defenses in advance. Often they persuade shareholders to agree to shark-repellent changes to the corporate charter. For example, the charter may be amended to require that any merger must be approved by a supermajority of 80% of the shares rather than the normal 50%. Although shareholders are generally prepared to go along with management’s proposals, it is doubtful whether such shark-repellent defenses are truly in their interest. Managers who are protected from takeover appear to enjoy higher remuneration and to generate less wealth for their shareholders.²⁵

Many firms follow PeopleSoft’s example and deter potential bidders by devising poison pills that make the company unappetizing. For example, the poison pill may give existing shareholders the right to buy the company’s shares at half price as soon as a bidder acquires more than 15% of the shares. The bidder is not entitled to the discount. Thus the bidder resembles Tantalus—as soon as it has acquired 15% of the shares, control is lifted away from its reach. These and other lines of defense are summarized in Table 31.6

   TABLE 31.6 A summary of takeover defenses.

Why did PeopleSoft’s management contest the takeover bid? One possible reason was to extract a higher price for the stock, for Oracle was ultimately forced to pay 66% more than its original offer. But the comment by PeopleSoft’s CEO that he could imagine no price at which the merger would be welcome suggests that the defensive tactics may have been intended to defeat the bid and protect managers’ positions with the firm.

Companies sometimes reduce these conflicts of interest by offering their managers golden parachutes, that is, generous payoffs if the managers lose their jobs as a result of a takeover. It may seem odd to reward managers for being taken over. However, if a soft landing overcomes their opposition to takeover bids, a few million may be a small price to pay.

Any management team that tries to develop improved weapons of defense must expect challenge in the courts. In the early 1980s the courts tended to give managers the benefit of the doubt and respect their business judgment about whether a takeover should be resisted. But the courts’ attitudes to takeover battles have shifted. For example, in 1993 a court blocked Viacom’s agreed takeover of Paramount on the grounds that Paramount directors did not do their homework before turning down a higher offer from QVC. Paramount was forced to give up its poison-pill defense and the stock options that it had offered to Viacom. Such decisions have led managers to become more careful in opposing bids, and they do not throw themselves blindly into the arms of any white knight.

At the same time governments have provided some new defensive weapons. In 1987 the Supreme Court upheld state laws that allow companies to deprive an investor of voting rights as soon as the investor’s share in the company exceeds a certain level. Since then state antitakeover laws have proliferated. Many allow boards of directors to block mergers with hostile bidders for several years and to consider the interests of employees, customers, suppliers, and their communities in deciding whether to try to block a hostile bid.

Anglo-Saxon countries used to have a near-monopoly on hostile takeovers. That is no longer the case. Takeover activity in Europe now exceeds that in the United States, and in recent years some of the most bitterly contested takeovers have involved European companies. For example, Mittal’s $27 billion takeover of Arcelor resulted from a fierce and highly politicized five-month battle. Arcelor used every defense in the book—including inviting a Russian company to become a leading shareholder.

Mittal is now based in Europe, but it began operations in Indonesia. This illustrates another change in the merger market: Acquirers are no longer confined to the major industrialized countries. They now include Brazilian, Russian, Indian, and Chinese companies. For example, Tetley Tea, Anglo-Dutch steelmaker Corus, and Jaguar and Land Rover have all been acquired by Indian conglomerate Tata Group. In China Lenovo acquired IBM’s personal computer business and Geely bought Volvo from Ford. The Brazilian mining giant, Vale, purchased Inco, the Canadian nickel producer, while its compatriot, JBS, bought the U.S. meat-packaging company, Swift.

BEYOND THE PAGE

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Cross-border mergers

brealey.mhhe.com/c31

Who Gains Most in Mergers?

As our brief history illustrates, in mergers sellers generally do better than buyers. Andrade, Mitchell, and Stafford found that following the announcement of the bid, selling shareholders received a healthy gain averaging 16%.²⁶ The overall value of the merging firms, buyer and seller combined, increases by about 2% on average. Thus the merging firms are worth more together than apart. But it seems that the stock prices of the acquiring firms decline on average.²⁷ Of course, these are averages; selling shareholders, for example, have sometimes obtained much higher returns. When Hewlett-Packard won its takeover battle to buy data-storage company 3Par, it paid a premium for 3Par’s stock of 230%, or about $1.5 billion.

Why do so many firms make acquisitions that appear to destroy value? One explanation appeals to behavioral traits; the managers of acquiring firms may be driven by hubris or overconfidence in their ability to run the target firm better than its existing management. This may well be so, but we should not dismiss more charitable explanations. For example, McCardle and Viswanathan have pointed out that firms can enter a market either by building a new plant or by buying an existing business. If the market is not growing, it makes more sense for the firm to expand by acquisition. Hence, when it announces the acquisition, firm value may drop simply because investors conclude that the market is no longer growing. The acquisition in this case does not destroy value; it just signals the stagnant state of the market.²⁸

Why do sellers earn higher returns? There are two reasons. First, buying firms are typically larger than selling firms. In many mergers the buyer is so much larger that even substantial net benefits would not show up clearly in the buyer’s share price. Suppose, for example, that company A buys company B, which is only one-tenth A’s size. Suppose the dollar value of the net gain from the merger is split equally between A and B.²⁹ Each company’s shareholders receive the same dollar profit, but B’s receive 10 times A’s percentage return.

The second, and more important, reason is the competition among potential bidders. Once the first bidder puts the target company “in play,” one or more additional suitors often jump in, sometimes as white knights at the invitation of the target firm’s management. Every time one suitor tops another’s bid, more of the merger gain slides toward the target. At the same time, the target firm’s management may mount various legal and financial counterattacks, ensuring that capitulation, if and when it comes, is at the highest attainable price.

Identifying attractive takeover candidates and mounting a bid are high-cost activities. So why should anyone incur these costs if other bidders are likely to jump in later and force up the takeover premium? Mounting a bid may be more worthwhile if a company can first accumulate a holding in the target company. The Williams Act allows a company to acquire a toehold of up to 5% of the target’s shares before it is obliged to reveal its holding and outline its plans. Then, even if the bid is ultimately unsuccessful, the company may be able to sell off its holding in the target at a substantial profit.

Bidders and targets are not the only possible winners. Other winners include investment bankers, lawyers, accountants, and in some cases arbitrageurs such as hedge funds, which speculate on the likely success of takeover bids.³⁰ “Speculate” has a negative ring, but it can be a useful social service. A tender offer may present shareholders with a difficult decision. Should they accept, should they wait to see if someone else produces a better offer, or should they sell their stock in the market? This dilemma presents an opportunity for hedge funds, which specialize in answering such questions. In other words, they buy from the target’s shareholders and take on the risk that the deal will not go through.

 31-6   Mergers and the Economy

Merger Waves

Look back at Figure 31.1, which shows the number of mergers in the United States for each year since 1962. Notice that mergers come in waves. There was an upsurge in merger activity from 1967 to 1969 and then again in the late 1980s and 1990s. Another merger boom got under way in 2003, only to peter out with the onset of the credit crisis.

We don’t really understand why merger activity is so volatile and why it seems to be associated with the level of stock prices. If mergers are prompted by economic motives, at least one of these motives must be “here today and gone tomorrow,” and it must somehow be associated with high stock prices. But none of the economic motives that we review in this chapter has anything to do with the general level of the stock market. None burst on the scene in the 1960s, departed in 1970, and reappeared for most of the 1980s and again in the mid-1990s and early 2000s.

Some mergers may result from mistakes in valuation on the part of the stock market. In other words, the buyer may believe that investors have underestimated the value of the seller or may hope that they will overestimate the value of the combined firm. But we see (with hindsight) that mistakes are made in bear markets as well as bull markets. Why don’t we see just as many firms hunting for bargain acquisitions when the stock market is low? It is possible that “suckers are born every minute,” but it is difficult to believe that they can be harvested only in bull markets.

Merger activity tends to be concentrated in a relatively small number of industries and is often prompted by deregulation and by changes in technology or the pattern of demand. For example, deregulation of telecoms and banking in the 1990s led to a spate of mergers in both industries. Andrade, Mitchell, and Stafford found that about half of the value of all U.S. mergers between 1988 and 1998 occurred in industries that had been deregulated.³¹

Do Mergers Generate Net Benefits?

There are undoubtedly good acquisitions and bad acquisitions, but economists find it hard to agree on whether acquisitions are beneficial on balance. Indeed, since there seem to be transient fashions in mergers, it would be surprising if economists could come up with simple generalizations.

We do know that mergers generate substantial gains to acquired firms’ stockholders and overall gains in the value of the two merging firms. But not everybody is convinced. Some believe that investors react to mergers with short-run enthusiasm and don’t give enough critical attention to long-term prospects.

Since we can’t observe how companies would have fared in the absence of a merger, it is difficult to measure the long-run effects on profitability. Ravenscroft and Scherer, who looked at mergers during the 1960s and early 1970s, argued that productivity declined in the years following a merger.³² But studies of subsequent merger activity suggest that mergers do seem to improve real productivity. For example, Paul Healy, Krishna Palepu, and Richard Ruback examined 50 large mergers between 1979 and 1983 and found an average increase of 2.4 percentage points in the companies’ pretax returns.³³ They argue that this gain came from generating a higher level of sales from the same assets. There was no evidence that the companies were mortgaging their long-term future by cutting back on long-term investments; expenditures on capital equipment and research and development tracked industry averages.³⁴

The most important effect of acquisitions may be felt by the managers of companies that are not taken over. Perhaps the threat of takeover spurs the whole of corporate America to try harder. Unfortunately, we don’t know whether, on balance, the threat of merger makes for active days or sleepless nights.

The threat of takeover may be a spur to inefficient management, but it is also costly. It can soak up large amounts of management time and effort. In addition, the company needs to pay for the services provided by the investment bankers, lawyers, and accountants. These can amount to several million dollars.

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SUMMARY

A merger generates synergies—that is, added value—if the two firms are worth more together than apart. Suppose that firms A and B merge to form a new entity, AB. Then the gain from the merger is

Gains from mergers may reflect economies of scale, economies of vertical integration, improved efficiency, the combination of complementary resources, or redeployment of surplus funds. In some cases the object is to install a more efficient management team or to force shrinkage and consolidation in an industry with excess capacity or too many small, inefficient companies. There are also dubious reasons for mergers. There is no value added by merging just to diversify risks, to reduce borrowing costs, or to pump up earnings per share.

You should go ahead with the acquisition if the gain exceeds the cost. Cost is the premium that the buyer pays for the selling firm over its value as a separate entity. It is easy to estimate when the merger is financed by cash. In that case,

When payment is in the form of shares, the cost naturally depends on what those shares are worth after the merger is complete. If the merger is a success, B’s stockholders will share the merger gains.

The mechanics of buying a firm are much more complex than those of buying a machine. First, you have to make sure that the purchase does not fall afoul of the antitrust laws. Second, you have a choice of procedures: You can merge all the assets and liabilities of the seller into those of your own company; you can buy the stock of the seller rather than the company itself; or you can buy the individual assets of the seller. Third, you have to worry about the tax status of the merger.

Mergers are often amicably negotiated between the management and directors of the two companies; but if the seller is reluctant, the would-be buyer can decide to make a tender offer. We sketched some of the offensive and defensive tactics used in takeover battles. We also observed that when the target firm loses, its shareholders typically win: selling shareholders earn large abnormal returns, while the bidding firm’s shareholders roughly break even. The typical merger appears to generate positive net benefits for investors, but competition among bidders, plus active defense by target management, pushes most of the gains toward the selling shareholders.

Mergers come and go in waves. The most recent wave, which peaked in 2006, consisted mostly of horizontal mergers. Merger activity thrives in periods of economic expansion and buoyant stock prices. Mergers are most frequent in industries that are coping with change, for example, changes in technology or regulation. The wave of mergers in banking and telecoms, for instance, can be traced to deregulation of these industries in the 1990s.

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FURTHER READING

Here are three general works on mergers:

R. Bruner, Applied Mergers and Acquisitions (Hoboken, NJ: John Wiley & Sons, 2004).

J. F. Weston, M. L. Mitchell, and J. H. Mulherin, Takeovers, Restructuring and Corporate Governance, 4th ed. (Upper Saddle River, NJ: Prentice-Hall 2000).

S. Betton, B. E. Eckbo, and K. S. Thorburn, “Corporate Takeovers,” in B. E. Eckbo (ed.), Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), chapter 15.

Recent merger waves are reviewed in:

G. Andrade, M. Mitchell, and E. Stafford, “New Evidence and Perspectives on Mergers,” Journal of Economic Perspectives 15 (Spring 2001), pp. 103–120.

S. J. Everett, “The Cross-Border Mergers and Acquisitions Wave of the Late 1990s,” in R. E. Baldwin and L. A. Winters (eds.), Challenges to Globalization (Chicago: University of Chicago Press, 2004).

J. Harford, “What Drives Merger Waves?” Journal of Financial Economics 77 (September 2005), pp. 529–560.

B. Holmstrom and S. N. Kaplan, “Corporate Governance and Merger Activity in the U.S.: Making Sense of the 1980s and 1990s,” Journal of Economic Perspectives 15 (Spring 2001), pp. 121–144.

Finally, here are some informative case studies:

S. N. Kaplan (ed.), Mergers and Productivity (Chicago: University of Chicago Press, 2000). This is a collection of case studies.

R. Bruner, “An Analysis of Value Destruction and Recovery in the Alliance and Proposed Merger of Volvo and Renault,” Journal of Financial Economics 51 (1999), pp. 125–166.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Merger types Are the following hypothetical mergers horizontal, vertical, or conglomerate?

a.  IBM acquires Dell Computer.

b.  Dell Computer acquires Walmart.

c.  Walmart acquires H. J. Heinz.

d.  H. J. Heinz acquires IBM.

2.  Merger motives Which of the following motives for mergers make economic sense?

a.  Merging to achieve economies of scale.

b.  Merging to reduce risk by diversification.

c.  Merging to redeploy cash generated by a firm with ample profits but limited growth opportunities.

d.  Merging to combine complementary resources.

e.  Merging just to increase earnings per share.

3.  Merger gains and costs Velcro Saddles is contemplating the acquisition of Pogo Ski Sticks, Inc. The values of the two companies as separate entities are $20 million and $10 million, respectively. Velcro Saddles estimates that by combining the two companies, it will reduce marketing and administrative costs by $500,000 per year in perpetuity. Velcro Saddles can either pay $14 million cash for Pogo or offer Pogo a 50% holding in Velcro Saddles. The opportunity cost of capital is 10%.

a.  What is the gain from merger?

b.  What is the cost of the cash offer?

c.  What is the cost of the stock alternative?

d.  What is the NPV of the acquisition under the cash offer?

e.  What is its NPV under the stock offer?

4.  Taxation Which of the following transactions are not likely to be classed as tax-free?

a.  An acquisition of assets.

b.  A merger in which payment is entirely in the form of voting stock.

5.  Mergers True or false?

a.  Sellers almost always gain in mergers.

b.  Buyers usually gain more than sellers.

c.  Firms that do unusually well tend to be acquisition targets.

d.  Merger activity in the United States varies dramatically from year to year.

e.  On the average, mergers produce large economic gains.

f.  Tender offers require the approval of the selling firm’s management.

g.  The cost of a merger to the buyer equals the gain realized by the seller.

6.  Vocabulary Briefly define the following terms:

a.  Purchase accounting

b.  Tender offer

c.  Poison pill

d.  Golden parachute

e.  Synergy

INTERMEDIATE

7.  Merger motives Examine several recent mergers and suggest the principal motives for merging in each case.

8.  Merger gains and costs Examine a recent merger in which at least part of the payment made to the seller was in the form of stock. Use stock market prices to obtain an estimate of the gain from the merger and the cost of the merger.

9.  Merger motives Respond to the following comments.

a.  “Our cost of debt is too darn high, but our banks won’t reduce interest rates as long as we’re stuck in this volatile widget-trading business. We’ve got to acquire other companies with safer income streams.”

b.  “Merge with Fledgling Electronics? No way! Their P/E’s too high. That deal would knock 20% off our earnings per share.”

c.  “Our stock’s at an all-time high. It’s time to make our offer for Digital Organics. Sure, we’ll have to offer a hefty premium to Digital stockholders, but we don’t have to pay in cash. We’ll give them new shares of our stock.”

10.  Merger gains and costs Sometimes the stock price of a possible target company rises in anticipation of a merger bid. Explain how this complicates the bidder’s evaluation of the target company.

11.  Merger motives Suppose you obtain special information—information unavailable to investors—indicating that Backwoods Chemical’s stock price is 40% undervalued. Is that a reason to launch a takeover bid for Backwoods? Explain carefully.

12.  Merger gains and costs As CFO of Frankfurter Rindswurst AG (FR) you are investigating the possible acquisition of Nürnberger Rostbratwurst AG (NR). You have the following basic data:

You estimate that investors currently expect a steady growth of about 6% in Nürnberger’s earnings and dividends. Under new management this growth rate would be increased to 8% per year, without any additional capital investment required.

a.  What is the gain from the acquisition?

b.  What is the cost of the acquisition if Frankfurter pays €25 in cash for each share of Nürnberger?

c.  What is the cost of the acquisition if Frankfurter offers one share of Frankfurter for every three shares of Nürnberger?

d.  How would the cost of the cash offer and the share offer alter if the expected growth rate of Nürnberger was not changed by the merger?

13.  The bootstrap game The Muck and Slurry merger has fallen through (see Section 31-2). But World Enterprises is determined to report earnings per share of $2.67. It therefore acquires the Wheelrim and Axle Company. You are given the following facts:

Once again there are no gains from merging. In exchange for Wheelrim and Axle shares, World Enterprises issues just enough of its own shares to ensure its $2.67 earnings per share objective.

a.  Complete the above table for the merged firm.

b.  How many shares of World Enterprises are exchanged for each share of Wheelrim and Axle?

c.  What is the cost of the merger to World Enterprises?

d.  What is the change in the total market value of the World Enterprises shares that were outstanding before the merger?

14.  Taxation Explain the distinction between a tax-free and a taxable merger. Are there circumstances in which you would expect buyer and seller to agree to a taxable merger?

15.  Merger accounting Look again at Table 31.3. Suppose that B Corporation’s fixed assets are reexamined and found to be worth $12 million instead of $9 million. How would this affect the AB Corporation’s balance sheet under purchase accounting? How would the value of AB Corporation change? Would your answer depend on whether the merger is taxable?

CHALLENGE

16.  Takeover tactics Examine a hostile acquisition and discuss the tactics employed by both the predator and the target companies. Do you think that the management of the target firm was trying to defeat the bid or to secure the highest price for its stockholders? How did each announcement by the protagonists affect their stock prices?

17.  Merger regulation How do you think mergers should be regulated? For example, what defenses should target companies be allowed to employ? Should managers of target firms be compelled to seek out the highest bids? Should they simply be passive and watch from the sidelines?

18.  Merger gains and costs Wasabi Mines is contemplating purchase of Haiku, Inc. The market values of the two companies are ¥20 billion and ¥11 billion, respectively. Wasabi thinks that the combined companies can cut operating costs by ¥450 million per year in perpetuity. Wasabi thinks that a successful cash bid will probably cost ¥14 billion. It is also considering offering Haiku shareholders a 33% stake in the merged firm. Suppose the cost of capital is 11%.

a.  What is the NPV to Wasabi? How does the NPV depend on whether the offer is for cash or stock? Should Wasabi go ahead?

b.  Here is a trickier question: Could a decision to offer stock instead of cash for Haiku signal a lack of confidence by Wasabi’s managers in the stock-market valuation of their company? How would this affect the choice of financing and the odds of a successful transaction?

19.  Merger gains In 2012, governments and investors had to cope with serious financial problems in Greece and some other European counties. The euro had fallen by about 20% against U.S. dollar. Other things equal, did the euro’s decline increase the economic gains to takeovers of European companies by U.S. companies? Be careful: How does the euro’s decline affect the value of a European company’s (euro) earnings to a U.S. buyer? Is an acquisition the only way to take advantage of the euro’s decline?

20.  Takeover tactics Find a recent hostile takeover in Europe, and compare European takeover tactics and defenses to tactics and defenses in the U.S.

APPENDIX ● ● ● ● ●

Conglomerate Mergers and Value Additivity

A pure conglomerate merger is one that has no effect on the operations or profitability of either firm. If corporate diversification is in stockholders’ interests, a conglomerate merger would give a clear demonstration of its benefits. But if present values add up, the conglomerate merger would not make stockholders better or worse off.

In this appendix we examine more carefully our assertion that present values add. It turns out that values do add as long as capital markets are perfect and investors’ diversification opportunities are unrestricted.

Call the merging firms A and B. Value additivity implies

where

For example, we might have

and

Suppose A and B are merged into a new firm, AB, with one share in AB exchanged for each share of A or B. Thus there are 1,500,000 AB shares issued. If value additivity holds, then PVAB must equal the sum of the separate values of A and B just before the merger, that is, $300 million. That would imply a price of $200 per share of AB stock.

But note that the AB shares represent a portfolio of the assets of A and B. Before the merger investors could have bought one share of A and two of B for $600. Afterward they can obtain a claim on exactly the same real assets by buying three shares of AB.

Suppose that the opening price of AB shares just after the merger is $200, so that PVAB = PVA + PVB. Our problem is to determine if this is an equilibrium price, that is, whether we can rule out excess demand or supply at this price.

For there to be excess demand, there must be some investors who are willing to increase their holdings of A and B as a consequence of the merger. Who could they be? The only thing new created by the merger is diversification, but those investors who want to hold assets of A and B will have purchased A’s and B’s stock before the merger. The diversification is redundant and consequently won’t attract new investment demand.

Is there a possibility of excess supply? The answer is yes. For example, there will be some shareholders in A who did not invest in B. After the merger they cannot invest solely in A, but only in a fixed combination of A and B. Their AB shares will be less attractive to them than the pure A shares, so they will sell part of or all their AB stock. In fact, the only AB shareholders who will not wish to sell are those who happened to hold A and B in exactly a 1:2 ratio in their premerger portfolios!

Since there is no possibility of excess demand but a definite possibility of excess supply, we seem to have

That is, corporate diversification can’t help, but it may hurt investors by restricting the types of portfolios they can hold. This is not the whole story, however, since investment demand for AB shares might be attracted from other sources if PVAB drops below PVA + PVB. To illustrate, suppose there are two other firms, A* and B*, which are judged by investors to have the same risk characteristics as A and B, respectively. Then before the merger,

where r is the rate of return expected by investors. We’ll assume rA = rA* = .08 and rB = rB* = .20.

Consider a portfolio invested one-third in A* and two-thirds in B*. This portfolio offers an expected return of 16%:

A similar portfolio of A and B before their merger also offered a 16% return.

As we have noted, a new firm AB is really a portfolio of firms A and B, with portfolio weights of ⅓ and ⅔. It is therefore equivalent in risk to the portfolio of A* and B*. Thus the price of AB shares must adjust so that it likewise offers a 16% return.

What if AB shares drop below $200, so that PVAB is less than PVA + PVB? Since the assets and earnings of firms A and B are the same, the price drop means that the expected rate of return on AB shares has risen above the return offered by the A*B* portfolio. That is, if rAB exceeds ⅓rA 1 ⅔rB, then rAB must also exceed ⅓rA* 1 ⅔rB*. But this is untenable: Investors A* and B* could sell part of their holdings (in a 1:2 ratio), buy AB, and obtain a higher expected rate of return with no increase in risk.

On the other hand, if PVAB rises above PVA + PVB, the AB shares will offer an expected return less than that offered by the A*B* portfolio. Investors will unload the AB shares, forcing their price down.

A stable result occurs only if AB shares stick at $200. Thus, value additivity will hold exactly in a perfect-market equilibrium if there are ample substitutes for the A and B assets. If A and B have unique risk characteristics, however, then PVAB can fall below PVA + PVB. The reason is that the merger curtails investors’ opportunity to tailor their portfolios to their own needs and preferences. This makes investors worse off, reducing the attractiveness of holding the shares of firm AB.

In general, the condition for value additivity is that investors’ opportunity set—that is, the range of risk characteristics attainable by investors through their portfolio choices—is independent of the particular portfolio of real assets held by the firm. Diversification per se can never expand the opportunity set given perfect security markets. Corporate diversification may reduce the investors’ opportunity set, but only if the real assets the corporations hold lack substitutes among traded securities or portfolios.

In rare cases the firm may be able to expand the opportunity set. It can do so if it finds an investment opportunity that is unique—a real asset with risk characteristics shared by few or no other financial assets. In this lucky event the firm should not diversify, however. It should set up the unique asset as a separate firm so as to expand investors’ opportunity set to the maximum extent. If Gallo by chance discovered that a small portion of its vineyards produced wine comparable to Chateau Margaux, it would not throw that wine into the Hearty Burgundy vat.

___________

¹See Hewlett Packard press release November 20, 2012.

²Bill Vlasic and Bradley A. Stertz, “Taken for a Ride,” BusinessWeek, June 5, 2000. Reprinted with special permission © The McGraw-Hill Companies, Inc.

³Economies of scale are enjoyed when the average unit cost of production goes down as production increases. One way to achieve economies of scale is to spread fixed costs over a larger volume of production.

⁴There is a large literature on the benefits of control by vertical integration. See, for example, O. Williamson, “The New Institutional Economics: Taking Stock, Looking Ahead,” Journal of Economic Literature 38 (2000), pp. 595–613; and O. Hart, Firms, Contracts, and Financial Structure (Oxford: Clarendon Press), 1995.

⁵It is difficult to assemble a large-enough block of stockholders to effectively challenge management and the incumbent board of directors. Stockholders can have enormous indirect influence, however. Their displeasure shows up in the firm’s stock price. A low stock price may encourage a takeover bid by another firm.

⁶K. J. Martin and J. J. McConnell, “Corporate Performance, Corporate Takeovers, and Management Turnover,” Journal of Finance 46 (June 1991), pp. 671–687.

⁷A study of 41 large bank mergers estimated cost savings with present value averaging 12% of the combined market values of the merging banks. See J. F. Houston, C. M. James, and M. D. Ryngaert, “Where Do Merger Gains Come From? Bank Mergers from the Perspective of Insiders and Outsiders,” Journal of Financial Economics 60 (May/June 2001), pp. 285–331.

⁸This merger rationale was first suggested by W. G. Lewellen, “A Pure Financial Rationale for the Conglomerate Merger,” Journal of Finance 26 (May 1971), pp. 521–537. If you want to see some of the controversy and discussion that this idea led to, look at R. C. Higgins and L. D. Schall, “Corporate Bankruptcy and Conglomerate Merger,” Journal of Finance 30 (March 1975), pp. 93–114; and D. Galai and R. W. Masulis, “The Option Pricing Model and the Risk Factor of Stock,” Journal of Financial Economics 3 (January–March 1976), especially pp. 66–69.

⁹This chapter’s definitions and interpretations of the gains and costs of merger follow those set out in S. C. Myers, “A Framework for Evaluating Mergers,” in Modern Developments in Financial Management, ed. S. C. Myers (New York: Praeger, 1976).

¹⁰We are assuming that PVA includes enough cash to finance the deal, or that the cash can be borrowed at a market interest rate. Notice that the value to A’s stockholders after the deal is done and paid for is $275 – 65 = $210 million—a gain of $10 million.

¹¹In this case we assume that B’s stock price has not risen on merger rumors and accurately reflects B’s stand-alone value.

¹²In this case no cash is leaving the firm to finance the merger. In our example of a cash offer, $65 million would be paid out to B’s stockholders, leaving the final value of the firm at 275 – 65 = $210 million. There would only be one million shares outstanding, so share price would be $210. The cash deal is better for A’s shareholders in this example.

¹³The same reasoning applies to stock issues. See Sections 15-4 and 18-4.

¹⁴See G. Andrade, M. Mitchell, and E. Stafford, “New Evidence and Perspectives on Mergers,” Journal of Economic Perspectives 15 (Spring 2001), pp. 103–120. This result confirms earlier work, including N. Travlos, “Corporate Takeover Bids, Methods of Payment, and Bidding Firms’ Stock Returns,” Journal of Finance 42 (September 1987), pp. 943–963; and J. R. Franks, R. S. Harris, and S. Titman, “The Postmerger Share-Price Performance of Acquiring Firms,” Journal of Financial Economics 29 (March 1991), pp. 81–96.

¹⁵Competitors or third parties who think they will be injured by the merger can also bring antitrust suits.

¹⁶The target has to be notified also, and it in turn informs investors. Thus the Hart–Scott–Rodino Act effectively forces an acquiring company to “go public” with its bid.

¹⁷Corporate charters and state laws sometimes specify a higher percentage.

¹⁸If B’s tangible assets are worth more than their previous book values, they would be reappraised and their current values entered on AB Corporation’s balance sheet.

¹⁹If part of the $8 million consisted of payment for identifiable intangible assets such as patents, the accountant would place these under a separate category of assets. Identifiable intangible assets that have a finite life need to be written off over their life.

²⁰Goodwill is depreciated for tax purposes, however.

²¹Earlier in the chapter we saw how Motorola Mobility was subsequently acquired by Google.

²²In 1986 the directors of Revlon were held to be in breach of their duty of loyalty when they did not accept the highest bid for the firm’s stock. The Delaware Supreme Court held that when it became inevitable that the company will be sold or broken up, the “directors’ role changed from defenders of the corporate bastion to auctioneers charged with getting the best price for the stockholders.”

²³The Williams Act obliges firms who own 5% or more of another company’s shares to tip their hand by reporting their holding in a Schedule 13(d) filing with the SEC.

²⁴Tender offers seldom result in acceptance by every single shareholder, but Delaware corporate law allows companies that have acquired at least 90% of the outstanding shares to compulsorily purchase the remainder. Other states have similar provisions.

²⁵A. Agrawal and C. R. Knoeber, “Managerial Compensation and the Threat of Takeover,” Journal of Financial Economics 47 (February 1998), pp. 219–239; and P. A. Gompers, J. L. Ishii, and A. Metrick, “Corporate Governance and Equity Prices,” Quarterly Journal of Economics 118 (2003), pp. 107–155.

²⁶G. Andrade, M. Mitchell, and E. Stafford, “New Evidence and Perspectives on Mergers,” Journal of Economic Perspectives 15 (Spring 2001), pp. 103–120.

²⁷For example, one recent study found that after closely contested bids, the losing bidder performed significantly better than the winner, on average by some 50% over the three years following the bid. See U. Malmendier, E. Moretti, and F. Peters, “Winning by Losing: Evidence on the Long-Run Effects of Mergers,” NBER Working Paper No. 18024, April 2012.

²⁸K. F. McCardle and S. Viswanathan, “The Direct Entry versus Takeover Decision and Stock Price Performance around Takeovers,” Journal of Business 67 (January 1994), pp. 1–43.

²⁹In other words, the cost of the merger to A is one-half the gain ΔPVAB.

³⁰Strictly speaking, an arbitrageur is an investor who takes a fully hedged, that is, riskless, position. But arbitrageurs in merger battles often take very large risks indeed. Their activities are known as “risk arbitrage.”

³¹See Footnote 26. See also J. Harford, “What Drives Merger Waves?” Journal of Financial Economics 77 (September 2005), pp. 529–560.

³²See D. J. Ravenscraft and F. M. Scherer, “Mergers and Managerial Performance,” in Knights, Raiders, and Targets: The Impact of the Hostile Takeover, ed. J. C. Coffee, Jr., L. Lowenstein, and S. Rose-Ackerman (New York: Oxford University Press, 1988).

³³See P. Healy, K. Palepu, and R. Ruback, “Does Corporate Performance Improve after Mergers?” Journal of Financial Economics 31 (April 1992), pp. 135–175. The study examined the pretax returns of the merged companies relative to industry averages. A study by Lichtenberg and Siegel came to similar conclusions. Before merger, acquired companies had lower levels of productivity than did other firms in their industries, but by seven years after the control change, two-thirds of the productivity gap had been eliminated. See F. Lichtenberg and D. Siegel, “The Effect of Control Changes on the Productivity of U.S. Manufacturing Plants,” Journal of Applied Corporate Finance 2 (Summer 1989), pp. 60–67.

³⁴Maintained levels of capital spending and R&D are also observed by Lichtenberg and Siegel, “The Effect of Control Changes on the Productivity of U.S. Manufacturing Plants,” Journal of Applied Corporate Finance 2 (Summer 1989), pp. 60–67; and B. H. Hall, “The Effect of Takeover Activity on Corporate Research and Development,” in Corporate Takeover: Causes and Consequences, ed. A. J. Auerbach (Chicago: University of Chicago Press, 1988).

Part 10 Mergers, Corporate Control, and Governance

Corporate Restructuring

In the last chapter we described how mergers and acquisitions enable companies to change their ownership and management teams, and often force major shifts in corporate strategy. But this is not the only way that company structure can be altered. In this chapter we look at a variety of other mechanisms for changing ownership and control, including leveraged buyouts (LBOs), spin-offs and carve-outs, nationalizations and privatizations, workouts, and bankruptcy.

The first section starts with a famous takeover battle, the leveraged buyout of RJR Nabisco. The rest of Sections 32-1 and 32-2 offers a general review of LBOs, spin-offs, and privatizations. The main point of these transactions is not just to change control, although existing management is often booted out, but also to change incentives for managers and improve financial performance.

RJR Nabisco was an early example of a private-equity deal. Section 32-3 takes a closer look at how private-equity investment funds are structured and how the private-equity business has developed since the 1980s.

Private-equity funds usually end up holding a portfolio of companies in different industries. In this respect they resemble the conglomerates that dominated takeover activity in the 1960s. These conglomerates are mostly gone—it seems that private equity is a superior financial technology for doing the tasks that conglomerates used to do. Our review of conglomerates’ weaknesses helps us to understand the strengths of private equity.

Some companies choose to restructure but others have it thrust upon them. None more so than those that fall on hard times and can no longer service their debts. The chapter therefore concludes by looking at how distressed companies either work out a solution with their debtors or go through a formal bankruptcy process.

 32-1   Leveraged Buyouts

Leveraged buyouts (LBOs) differ from ordinary acquisitions in two immediately obvious ways. First, a large fraction of the purchase price is financed by debt. Some, if not all, of this debt is junk, that is, below investment-grade. Second, the company goes private and its shares no longer trade on the open market. Equity financing for LBOs comes from private-equity investment partnerships, which we describe later in this chapter. When a buyout is led by existing management, the transaction is called a management buyout or MBO.

In the 1970s and 1980s many MBOs were arranged for unwanted divisions of large diversified companies. Smaller divisions outside the companies’ main line of business sometimes failed to attract top management’s interest and commitment, and divisional management chafed under corporate bureaucracy. Many such divisions flowered when spun off as MBOs. Their managers, pushed by the need to generate cash for debt service and encouraged by a substantial personal stake in the business, found ways to cut costs and compete more effectively.

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LBOs 1997–2011

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Subsequently, LBO activity shifted to buyouts of entire businesses, including large, mature, public corporations. Table 32.1 lists some of the LBOs from recent years. Shortly before the financial crisis struck in 2007, some huge transactions were completed. By 2009 the number of deals was down nearly 90% from the peak. The LBO market began to pick up again in 2010, but the targets were generally tiddlers compared with earlier years.

   TABLE 32.1 Some recent leveraged buyouts. Note the large size of the transactions before the financial crisis (values in $ billions).

The RJR Nabisco LBO

The largest, most dramatic, and best documented LBO of the 1980s was the $25 billion takeover of RJR Nabisco by Kohlberg, Kravis, Roberts (KKR). The players, tactics, and controversies of LBOs are writ large in this case.

The battle for RJR began in October 1988 when the board of directors of RJR Nabisco revealed that Ross Johnson, the company’s chief executive officer, had formed a group of investors that proposed to buy all RJR’s stock for $75 per share in cash and take the company private. RJR’s share price immediately moved to about $75, handing shareholders a 36% gain over the previous day’s price of $56. At the same time RJR’s bonds fell, since it was clear that existing bondholders would soon have a lot more company.¹

Johnson’s offer lifted RJR onto the auction block. Once the company was in play, its board of directors was obliged to consider other offers, which were not long in coming. Four days later, KKR bid $90 per share, $79 in cash plus PIK preferred stock valued at $11. (PIK means “pay in kind.” The company could choose to pay preferred dividends with more preferred shares rather than cash.)

The resulting bidding contest had as many turns and surprises as a Dickens novel. In the end it was Johnson’s group against KKR. KKR bid $109 per share, after adding $1 per share (roughly $230 million) in the last hour.² The KKR bid was $81 in cash, convertible subordinated bonds valued at about $10, and PIK preferred shares valued at about $18. Johnson’s group bid $112 in cash and securities.

But the RJR board chose KKR. Although Johnson’s group had offered $3 a share more, its security valuations were viewed as “softer” and perhaps overstated. The Johnson group’s proposal also contained a management compensation package that seemed extremely generous and had generated an avalanche of bad press.

But where did the merger benefits come from? What could justify offering $109 per share, about $25 billion in all, for a company that only 33 days previously was selling for $56 per share? KKR and other bidders were betting on two things. First, they expected to generate billions in additional cash from interest tax shields, reduced capital expenditures, and sales of assets that were not strictly necessary to RJR’s core businesses. Asset sales alone were projected to generate $5 billion. Second, they expected to make the core businesses significantly more profitable, mainly by cutting back on expenses and bureaucracy. Apparently, there was plenty to cut, including the RJR “Air Force,” which at one point included 10 corporate jets.

In the year after KKR took over, a new management team set out to sell assets and cut back operating expenses and capital spending. There were also layoffs. As expected, high interest charges meant a net loss of nearly a billion dollars in the first year, but pretax operating income actually increased, despite extensive asset sales.

Inside the firm, things were going well. But outside there was confusion, and prices in the junk bond market were declining rapidly, implying much higher future interest charges for RJR and stricter terms on any refinancing. In 1990 KKR made an additional equity investment in the firm and the company retired some of its junk bonds. RJR’s chief financial officer described the move as “one further step in the deleveraging of the company.”³ For RJR, the world’s largest LBO, it seemed that high debt was a temporary, not a permanent, virtue.

RJR, like many other firms that were taken private through LBOs, enjoyed only a short period as a private company. In 1991 it went public again with the sale of $1.1 billion of stock. KKR progressively sold off its investment, and its last remaining stake in the company was sold in 1995 at roughly the original purchase price.

Barbarians at the Gate?

The RJR Nabisco LBO crystallized views on LBOs, the junk bond market, and the takeover business. For many it exemplified all that was wrong with finance in the late 1980s, especially the willingness of “raiders” to carve up established companies, leaving them with enormous debt burdens, basically in order to get rich quick.⁴

There was plenty of confusion, stupidity, and greed in the LBO business. Not all the people involved were nice. On the other hand, LBOs generated large increases in market value, and most of the gains went to the selling shareholders, not to the raiders. For example, the biggest winners in the RJR Nabisco LBO were the company’s stockholders.

The most important sources of added value came from making RJR Nabisco leaner and meaner. The company’s new management was obliged to pay out massive amounts of cash to service the LBO debt. It also had an equity stake in the business and therefore strong incentives to sell off nonessential assets, cut costs, and improve operating profits.

LBOs are almost by definition diet deals. But there were other motives. Here are some of them.

The Junk Bond Markets LBOs and debt-financed takeovers may have been driven by artificially cheap funding from the junk bond markets. With hindsight, it seems that investors underestimated the risks of default in junk bonds. Default rates climbed painfully, reaching 10.3% in 1991.⁵ The market also became temporarily much less liquid after the demise in 1990 of Drexel Burnham, the investment banking firm that was the chief market maker in junk bonds.

Leverage and Taxes Borrowing money saves taxes, as we explained in Chapter 18. But taxes were not the main driving force behind LBOs. The value of interest tax shields was simply not big enough to explain the observed gains in market value.⁶ For example, Richard Ruback estimated the present value of additional interest tax shields generated by the RJR LBO at $1.8 billion.⁷ But the gain in market value to RJR stockholders was about $8 billion.

Of course, if interest tax shields were the main motive for LBOs’ high debt, then LBO managers would not be so concerned to pay down debt. We saw that this was one of the first tasks facing RJR Nabisco’s new management.

Other Stakeholders We should look at the total gain to all investors in an LBO, not just to the selling stockholders. It’s possible that the latter’s gain is just someone else’s loss and that no value is generated overall.

Bondholders are the obvious losers. The debt that they thought was secure can turn into junk when the borrower goes through an LBO. We noted how market prices of RJR debt fell sharply when Ross Johnson’s first LBO offer was announced. But again, the losses suffered by bondholders in LBOs are not nearly large enough to explain stockholder gains. For example, Mohan and Chen’s estimate of losses to RJR bondholders was at most $575 million⁸—painful to the bondholders, but far below the stockholders’ gain.

Leverage and Incentives Managers and employees of LBOs work harder and often smarter. They have to generate cash for debt service. Moreover, managers’ personal fortunes are riding on the LBO’s success. They become owners rather than organization men and women.

It’s hard to measure the payoff from better incentives, but there is some evidence of improved operating efficiency in LBOs. Kaplan, who studied 48 MBOs during the 1980s, found average increases in operating income of 24% three years after the buyouts. Ratios of operating income and net cash flow to assets and sales increased dramatically. He observed cutbacks in capital expenditures but not in employment. Kaplan concludes that these “operating changes are due to improved incentives rather than layoffs.”⁹

We have reviewed several motives for LBOs. We do not say that all LBOs are good. On the contrary, there have been many mistakes, and even soundly motivated LBOs are risky, as the bankruptcies of a number of highly leveraged transactions have demonstrated. Yet, we do quarrel with those who portray LBOs solely as undertaken by Wall Street barbarians breaking up the traditional strengths of corporate America.

Leveraged Restructurings

The essence of a leveraged buyout is of course leverage. So why not take on the leverage and dispense with the buyout? Here is one well-documented success story of a leveraged restructuring.¹⁰

In 1989 Sealed Air was a very profitable company. The problem was that its profits were coming too easily because its main products were protected by patents. When the patents expired, strong competition was inevitable, and the company was not ready for it. The years of relatively easy profits had resulted in too much slack:

We didn’t need to manufacture efficiently; we didn’t need to worry about cash. At Sealed Air, capital tended to have limited value attached to it—cash was perceived as being free and abundant.

The company’s solution was to borrow the money to pay a $328 million special cash dividend. In one stroke the company’s debt increased 10 times. Its book equity went from $162 million to minus $161 million. Debt went from 13% of total book assets to 136%. The company hoped that this leveraged restructuring would “disrupt the status quo, promote internal change,” and simulate “the pressures of Sealed Air’s more competitive future.” The shakeup was reinforced by new performance measures and incentives, including increases in stock ownership by employees.

It worked. Sales and operating profits increased steadily without major new capital investments, and net working capital fell by half, releasing cash to help service the company’s debt. The stock price quadrupled in the five years following the restructuring.

Sealed Air’s restructuring was not typical. It is an exemplar chosen with hindsight. It was also undertaken by a successful firm under no outside pressure. But it clearly shows the motive for most leveraged restructurings. They are designed to force mature, successful, but overweight companies to disgorge cash, reduce operating costs, and use assets more efficiently.

LBOs and Leveraged Restructurings

The financial characteristics of LBOs and leveraged restructurings are similar. The three main characteristics of LBOs are:

1.  High debt. The debt is not intended to be permanent. It is designed to be paid down. The requirement to generate cash for debt service is intended to curb wasteful investment and force improvements in operating efficiency. Of course, this solution only makes sense in the case of companies that are generating lots of cash and have few investment opportunities.

2.  Incentives. Managers are given a greater stake in the business via stock options or direct ownership of shares.

3.  Private ownership. The LBO goes private. It is owned by a partnership of private investors who monitor performance and can act right away if something goes awry. But private ownership is not intended to be permanent. The most successful LBOs go public again as soon as debt has been paid down sufficiently and improvements in operating performance have been demonstrated.

Leveraged restructurings share the first two characteristics but continue as public companies.

 32-2   Fusion and Fission in Corporate Finance

Figure 32.1 shows some of AT&T’s acquisitions and divestitures. Before 1984, AT&T controlled most of the local and virtually all of the long-distance telephone service in the United States. (Customers used to speak of the ubiquitous “Ma Bell.”) Then in 1984 the company accepted an antitrust settlement requiring local telephone services to be spun off to seven new, independent companies. AT&T was left with its long-distance business plus Bell Laboratories, Western Electric (telecommunications manufacturing), and various other assets. As the communications industry became increasingly competitive, AT&T acquired several other businesses, notably in computers, cellular telephone service, and cable television. Some of these acquisitions are shown as the green incoming arrows in Figure 32.1.

AT&T was an unusually active acquirer. It was a giant company trying to respond to rapidly changing technologies and markets. But AT&T was simultaneously divesting dozens of other businesses. For example, its credit card operations (the AT&T Universal Card) were sold to Citicorp. AT&T also created several new companies by spinning off parts of its business. For example, in 1996 it spun off Lucent (incorporating Bell Laboratories and Western Electric) and its computer business (NCR). Only six years earlier AT&T had paid $7.5 billion to acquire NCR. These and several other important divestitures are shown as the green outgoing arrows in Figure 32.1.

Figure 32.1 is not the end of AT&T’s story. In 2004, AT&T was acquired by Cingular Wireless, which retained the AT&T name. In 2005, that company in turn merged with SBC Communications, Inc., a descendant of Southwestern Bell. In 2006, that company merged with BellSouth. There’s not much left of the original AT&T, but the name survives.¹¹

   TABLE 32.1 The effects of AT&T’s antitrust settlement in 1984, and a few of AT&T’s acquisitions and divestitures from 1991 to 2003. Divestitures are shown by the outgoing green arrows. When two years are given, the transaction was completed in two steps.

In the market for corporate control, fusion—that is, mergers and acquisitions—gets most of the attention and publicity. But fission—the sale or distribution of assets or operating businesses—can be just as important, as the top half of Figure 32.1 illustrates. In many cases businesses are sold in LBOs or MBOs. But other transactions are common, including spin-offs, carve-outs, divestitures, asset sales, and privatizations. We start with spin-offs.

Spin-offs

A spin-off (or split-up) is a new, independent company created by detaching part of a parent company’s assets and operations. Shares in the new company are distributed to the parent company’s stockholders.¹² We came across one recent example in the last chapter, where we saw how Motorola was pressured by Carl Icahn into spinning off Motorola Mobility. Motorola’s shareholders received shares in the new company and could trade their Motorola Mobility shares as well as those of the slimmed-down Motorola Solutions.

Motorola was not alone in wanting to split up. Other spinner-offers in 2011–2012 include Abbott Laboratories, Marathon Oil, McGraw-Hill, Kraft, Fortune Brands, ITT, Hewlett-Packard, and Sara Lee.¹³

Spin-offs widen investor choice by allowing them to invest in just one part of the business. More important, they can improve incentives for managers. Companies sometimes refer to divisions or lines of business as “poor fits.” By spinning these businesses off, management of the parent company can concentrate on its main activity. If the businesses are independent, it is easier to see the value and performance of each and to reward managers by giving them stock or stock options in their company. Also, spin-offs relieve investors of the worry that funds will be siphoned from one business to support unprofitable capital investments in another.

When AT&T announced its planned spin-offs of Lucent and NCR, the chairman commented that the

three independent corporations will be able to go after the exploding opportunities of the industry faster than they could as parts of a much larger corporation. The three new companies . . . will be free to pursue the best interests of their customers without bumping into each other in the marketplace. They are designed to be fast and focused, with a capital structure suited to their individual industries.

Investors were apparently convinced, for the announcement of the spin-offs added $10 billion to the value of the stock overnight.

AT&T’s spin-off of Lucent and NCR was unusual in many respects. But scholars who have studied the topic have found that investors generally greet the announcement of a spin-off as good news.¹⁴ Their enthusiasm appears to be justified, for spin-offs seem to bring about more efficient capital investment decisions by each company and improved operating performance.¹⁵

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How Palm was Carved and Spun

  When 3Com acquired U.S. Robotics in 1997, it also became the owner of Palm, a small start-up business developing handheld computers. It was a lucky purchase, for over the next three years the Palm Pilot came to dominate the market for handheld computers. But as Palm began to take up an increasing amount of management time, 3Com concluded that it needed to return to its knitting and focus on its basic business of selling computer network systems. In 2000 it announced that it would carve out 5% of its holding of Palm through an initial public offering, and then spin off the remaining 95% of Palm shares by giving 3Com shareholders about 1.5 Palm shares for each 3Com share that they owned.

The Palm carve-out occurred at close to the peak of the high-tech boom and got off to a dazzling start. The shares were issued in the IPO at $38 each. On the first day of trading the stock price touched $165 before closing at $95. Therefore, anyone owning a share of 3Com stock could look forward later in the year to receiving about 1.5 shares of Palm worth 1.5 × 95 = $142.50. But apparently 3Com’s shareholders were not fully convinced that their newfound wealth was for real, for on the same day 3Com’s stock price closed at $82, or more than $60 a share less than the market value of the shares in Palm that they were due to receive.*

Three years after 3Com spun off its holding in Palm, Palm itself entered the spin-off business by giving shareholders stock in PalmSource, a subsidiary that was responsible for developing and licensing the Palm™ operating system. The remaining business, renamed palmOne, would focus on making mobile gadgets. The company gave three reasons for its decision to split into two. First, like 3Com’s management, Palm’s management believed that the company would benefit from clarity of focus and mission. Second, it argued that shareholder value could “be enhanced if investors could evaluate and choose between both businesses separately, thereby attracting new and different investors.” Finally, it seemed that Palm’s rivals were reluctant to buy software from a company that competed with them in making handheld hardware.

*This difference would seem to present an arbitrage opportunity. An investor who bought 1 share of 3Com and sold short 1.5 shares of Palm would earn a profit of $60 and own 3Com’s other assets for free. The difficulty in executing this arbitrage is explored in O. A. Lamont and R. H. Thaler, “Can the Market Add and Subtract? Mispricing in Tech Stock Carve-Outs,” Journal of Political Economy 111 (April 2003), pp. 227–268.

Carve-outs

Carve-outs are similar to spin-offs, except that shares in the new company are not given to existing shareholders but are sold in a public offering. For example, in 2011 Hong Kong conglomerate Hutchison Whampoa raised US$6 billion by carving out its ports business and listing it on the Singapore Stock Exchange.

Most carve-outs leave the parent with majority control of the subsidiary, usually about 80% ownership.¹⁶ This may not reassure investors who are worried about lack of focus or a poor fit, but it does allow the parent to set the manager’s compensation based on the performance of the subsidiary’s stock price. Sometimes companies carve out a small proportion of the shares to establish a market for the subsidiary’s stock and subsequently spin off the remainder of the shares. The nearby box describes how the computer company, Palm, was first carved and then spun.

Perhaps the most enthusiastic carver-outer of the 1980s and 1990s was Thermo Electron, with operations in health care, power generation equipment, instrumentation, environmental protection, and various other areas. By 1997 it had carved out stakes in seven publicly traded subsidiaries, which in turn had carved out 15 further public companies. The 15 were grandchildren of the ultimate parent, Thermo Electron. The company’s management reasoned that the carve-outs would give each company’s managers responsibility for their own decisions and expose their actions to the scrutiny of the capital markets. For a while the strategy seemed to work, and Thermo Electron’s stock was a star performer. But the complex structure began to lead to inefficiencies, and in 2000 Thermo Electron went into reverse. It reacquired many of the subsidiaries that the company had carved out only a few years earlier, and it spun off several of its progeny, including Viasys Health Care and Kadant, Inc., a manufacturer of papermaking and paper-recycling equipment. Then in November 2006 Thermo Electron merged with Fisher Scientific.

Asset Sales

The simplest way to divest an asset is to sell it. An asset sale or divestiture means sale of a part of one firm to another. This may consist of an odd factory or warehouse, but sometimes whole divisions are sold. Asset sales are another way of getting rid of “poor fits.” Such sales are frequent. For example, one study found that over 30% of assets acquired in a sample of hostile takeovers were subsequently sold.¹⁷

Maksimovic and Phillips examined a sample of about 50,000 U.S. manufacturing plants each year from 1974 to 1992. About 35,000 plants in the sample changed hands during that period. One-half of the ownership changes were the result of mergers or acquisitions of entire firms, but the other half resulted from asset sales, that is, sale of part or all of a division.¹⁸ Asset sales sometimes raise huge sums of money. For example, in 2012 Pfizer announced that it was selling its nutrition business to Nestlé for $11.9 billion. It had acquired the business three years earlier when it bought Wyeth. The sale represented part of a strategy by Pfizer to focus on its core pharmaceutical activities.

Announcements of asset sales are good news for investors in the selling firm and on average the assets are employed more productively after the sale.¹⁹ It appears that asset sales transfer business units to the companies that can manage them most effectively.

Privatization and Nationalization

A privatization is a sale of a government-owned company to private investors. In recent years almost every government in the world seems to have a privatization program. Here are some examples of recent privatization news:

•  Pakistan sells a majority stake in Habib Bank (February 2004).

•  Japan sells the West Japan Railway Company (March 2004).

•  India sells a stake in ONGC, an oil exploration and production company (March 2004).

•  Ukraine sells the steel company Kryvorizhstal (June 2004).

•  Germany privatizes Postbank, the country’s largest retail bank (June 2004).

•  France sells 30% of EDF (Electricité de France; December 2005).

•  China sells Industrial and Commercial Bank of China (October 2006).

•  Poland sells Tauron Polska Energia (March 2011).

•  Portugal sells 40% of its power grid operator to China State Grid and Oman Oil (February 2012).

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Voucher privatization in Czechoslovakia

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Most privatizations are more like carve-outs than spin-offs, because shares are sold for cash rather than distributed to the ultimate “shareholders,” that is, the citizens of the selling country. But several former Communist countries, including Russia, Poland, and the Czech Republic, privatized by means of vouchers distributed to citizens. The vouchers could be used to bid for shares in the companies that were being privatized. Thus the companies were not sold for cash, but for vouchers.²⁰

Privatizations have raised enormous sums for selling governments. China raised $22 billion from the privatization of the Industrial and Commercial Bank of China. The Japanese government’s successive sales of its holding of NTT (Nippon Telegraph and Telephone) brought in $100 billion.

The motives for privatization seem to boil down to the following three points:

1.  Increased efficiency. Through privatization, the enterprise is exposed to the discipline of competition and insulated from political influence on investment and operating decisions. Managers and employees can be given stronger incentives to cut costs and add value.

2.  Share ownership. Privatizations encourage share ownership. Many privatizations give special terms or allotments to employees or small investors.

3.  Revenue for the government. Last but not least.

There were fears that privatizations would lead to massive layoffs and unemployment, but that does not appear to be the case. While it is true that privatized companies operate more efficiently and thus reduce employment, they also grow faster as privatized companies, which increases employment. In many cases the net effect on employment is positive.

On other dimensions, the impact of privatization is almost always positive. A review of research on privatization concludes that the firms “almost always become more efficient, more profitable, . . . financially healthier and increase their capital investment spending.”²¹

The process of privatization is not a one-way street. It can sometimes go into reverse and publicly owned firms may be taken over by the government. For example, as part of his aim to construct a Socialist republic in Venezuela, Hugo Chavez has nationalized firms in the banking, oil, power, telecom, steel, and cement sectors.

In some other countries temporary nationalization has been a pragmatic last resort for governments rather than part of a long-term strategy. For example, in 2008 the U.S. government took control of the giant mortgage companies Fannie Mae and Freddie Mac when they were threatened with bankruptcy.²² In 2012 the Japanese government agreed to provide one trillion yen in return for a majority holding in Tepco, operator of the stricken Fukushima nuclear plant.

 32-3   Private Equity

The years 2006 and 2007 witnessed an exceptional volume of private-equity deals. For example, in April 2007 one of the largest private-equity firms, Blackstone, won a $39 billion bidding contest for Equity Office Properties, the largest owner of office buildings in the United States. In July it invested nearly $12 billion in Biomet, a manufacturer of medical equipment. Three months later Blackstone announced the $27 billion purchase of Hilton, the hotel operator.

Perhaps the most interesting news of 2007 was DaimlerChrysler’s announcement that it was selling an 80% stake in Chrysler to Cerberus Capital Management. Chrysler, one of Detroit’s original Big Three automakers, merged into DaimlerChrysler in 1998, but the expected synergies between the Chrysler and Mercedes-Benz product lines were hard to grasp. The Chrysler division had some profitable years, but lost $1.5 billion in 2006. Prospects looked grim. DaimlerChrysler (now Daimler A. G.) paid Cerberus $677 million to take Chrysler off its hands. Cerberus assumed about $18 billion in pension and employee health-care liabilities, however, and agreed to invest $6 billion in Chrysler and its finance subsidiary.²³ Two years later, Chrysler filed for bankruptcy, wiping out Cerberus’s investment. Subsequently, Chrysler was acquired by Fiat.

With the onset of the credit crisis the LBO boom of 2007 withered rapidly. Although buyout firms entered 2008 with large amounts of equity, the debt market for leveraged buyouts dried up and the volume of deals fell by more than 70%.

Private-Equity Partnerships

Figure 32.2 shows how a private-equity investment fund is organized. The fund is a partnership, not a corporation. The general partner sets up and manages the partnership. The limited partners put up almost all of the money. Limited partners are generally institutional investors, such as pension funds, endowments, and insurance companies. Wealthy individuals may also participate. The limited partners have limited liability, like shareholders in a corporation, but do not participate in management.

   FIGURE 32.2 Organization of a typical private-equity partnership. The limited partners, having put up almost all of the money, get first crack at the proceeds from sale or IPO of the portfolio companies. Once their investment is returned, they get 80% of any profits. The general partners, who organize and manage the partnership, get a 20% carried interest in profits.

Once the partnership is formed, the general partners seek out companies to invest in. Venture capital partnerships look for high-tech startups or adolescent companies that need capital to grow. LBO funds look for mature businesses with ample free cash flow that need restructuring. Some funds specialize in particular industries, for example, biotech, real estate, or energy. However, buyout funds like Blackstone’s and Cerberus’s look for opportunities almost anywhere.

The partnership agreement has a limited term, which is typically 10 years. The portfolio companies must then be sold and the proceeds distributed. So the general partners cannot reinvest the limited partners’ money. Of course, once a fund is proved successful, the general partners can usually go back to the limited partners, or to other institutional investors, and form another one. (We mentioned three of Blackstone’s 2007 deals earlier in this section. These buyouts were funded from Blackstone’s existing investment partnerships. At the same time it was raising $20 billion for a new buyout fund and $10 billion for a new real estate fund.)

The general partners get a management fee, usually 1% or 2% of capital committed,²⁴ plus a carried interest in 20% of any profits earned by the partnership. In other words, the limited partners get paid off first, but then get only 80% of any further returns. The general partners therefore have a call option on 20% of the partnership’s total future payoff, with an exercise price set by the limited partners’ investment.²⁵

You can see some of the advantages of private-equity partnerships:

•  Carried interest gives the general partners plenty of upside. They are strongly motivated to earn back the limited partners’ investment and deliver a profit.

•  Carried interest, because it is a call option, gives the general partners incentives to take risks. Venture capital funds take the risks inherent in start-up companies. Buyout funds amplify business risks with financial leverage.

•  There is no separation of ownership and control. The general partners can intervene in the fund’s portfolio companies any time performance lags or strategy needs changing.

•  There is no free-cash-flow problem: limited partners don’t have to worry that cash from a first round of investments will be dribbled away in later rounds. Cash from the first round must be distributed to investors.

The foregoing are good reasons why private equity grew. But some contrarians say that rapid growth also came from irrational exuberance and speculative excess. These contrarian investors stayed on the sidelines and waited glumly (but hopefully) for the crash.

The popularity of private equity has also been linked to the costs and distractions of public ownership, including the costs of dealing with Sarbanes-Oxley and other legal and regulatory requirements. Many CEOs and CFOs feel pressured to meet short-term earnings targets. Perhaps they spend too much time worrying about these targets and about day-to-day changes in stock price. Perhaps going private avoids public investors’ “short-termism” and makes it easier to invest for the long run. But recall that for private equity, the long run is the life of the partnership, 8 or 10 years at most. General partners must find a way to cash out of the companies in the partnership’s portfolio. There are only two ways to cash out: an IPO or a trade sale to another company. Many of today’s private-equity deals will be future IPOs, thus private-equity investors need public markets. The firms that seek divorce from public shareholders may well have to remarry them later.

Are Private-Equity Funds Today’s Conglomerates?

A conglomerate is a firm that diversifies across several unrelated businesses. Is Blackstone a conglomerate? Table 32.2, which lists some of the companies held by Blackstone funds, suggests that it is. Blackstone funds have invested in dozens of industries.

   TABLE 32.2 The Blackstone Group invests in many different industries. Here are a few of its portfolio holdings in 2012.

Source: The Blackstone Group, www.blackstone.com.

At the start of this chapter, we suggested that private equity today does some of the tasks that public conglomerates used to do. Let’s take a brief look at the history of U.S. conglomerates.

The merger boom of the 1960s created more than a dozen sprawling conglomerates. Table 32.3 shows that by the 1970s some of these conglomerates had achieved amazing spans of activity. The largest conglomerate, ITT, was operating in 38 different industries and ranked eighth in sales among U.S. corporations.

   TABLE 32.3 The largest conglomerates of 1979, ranked by sales compared with U.S. industrial corporations. Most of these companies have been broken up.

Source: A. Chandler and R. S. Tetlow (eds.), The Coming of Managerial Capitalism, p. 772. © 1985 The McGraw-Hill Companies, Inc. Used with permission. See also J. Baskin and P. J. Miranti, Jr., A History of Corporate Finance (Cambridge, UK: Cambridge University Press, 1997), ch. 7.

Most of these conglomerates were broken up in the 1980s and 1990s. In 1995 ITT, which had already sold or spun off several businesses, split what was left into three separate firms. One acquired ITT’s interests in hotels and gambling; the second took over ITT’s automotive parts, defense, and electronics businesses; and the third specialized in insurance and financial services.

What advantages were claimed for the conglomerates of the 1960s and 1970s? First, diversification across industries was supposed to stabilize earnings and reduce risk. That’s hardly compelling, because shareholders can diversify much more efficiently on their own.

Second, a widely diversified firm can operate an internal capital market. Free cash flow generated by divisions in mature industries (cash cows) can be funneled within the company to those divisions (stars) with plenty of profitable growth opportunities. Consequently, there is no need for fast-growing divisions to raise finance from outside investors.

There are some good arguments for internal capital markets. The company’s managers probably know more about its investment opportunities than outside investors do, and transaction costs of issuing securities are avoided. Nevertheless, it appears that attempts by conglomerates to allocate capital investment across many unrelated industries were more likely to subtract value than add it. Trouble is, internal capital markets are not really markets but combinations of central planning (by the conglomerate’s top management and financial staff) and intracompany bargaining. Divisional capital budgets depend on politics as well as pure economics. Large, profitable divisions with plenty of free cash flow may have the most bargaining power; they may get generous capital budgets while smaller divisions with good growth opportunities are reined in.

Internal Capital Markets in the Oil Business Misallocation in internal capital markets is not restricted to pure conglomerates. For example, Lamont found that, when oil prices fell by half in 1986, diversified oil companies cut back capital investment in their non-oil divisions. The non-oil divisions were forced to “share the pain,” even though the drop in oil prices did not diminish their investment opportunities. The Wall Street Journal reported one example:²⁶

Chevron Corp. cut its planned 1986 capital and exploratory budget by about 30% because of the plunge in oil prices. . . . A Chevron spokesman said that the spending cuts would be across the board and that no particular operations will bear the brunt.

About 65% of the $3.5 billion budget will be spent on oil and gas exploration and production—about the same proportion as before the budget revision.

Chevron also will cut spending for refining and marketing, oil and natural gas pipelines, minerals, chemicals, and shipping operations.

Why cut back on capital outlays for minerals, say, or chemicals? Low oil prices are generally good news, not bad, for chemical manufacturing, because oil distillates are an important raw material.

By the way, most of the oil companies in Lamont’s sample were large, blue-chip companies. They could have raised additional capital from investors to maintain spending in their non-oil divisions. They chose not to. We do not understand why.

All large companies must allocate capital among divisions or lines of business. Therefore, they all have internal capital markets and must worry about mistakes and misallocations. But the danger probably increases as the company moves from a focus on one, or a few related industries, to unrelated conglomerate diversification. Look again at Table 32.3: how could top management of ITT keep accurate track of investment opportunities in 38 different industries?

Conglomerates face further problems. Their divisions’ market values can’t be observed independently, and it is difficult to set incentives for divisional managers. This is particularly serious when managers are asked to commit to risky ventures. For example, how would a biotech startup fare as a division of a traditional conglomerate? Would the conglomerate be as patient and risk-tolerant as investors in the stock market? How are the scientists and clinicians doing the biotech R&D rewarded if they succeed? We don’t mean to say that high-tech innovation and risk-taking are impossible in public conglomerates, but the difficulties are evident.

The third argument for traditional conglomerates came from the idea that good managers were fungible; in other words, it was argued that modern management would work as well in the manufacture of auto parts as in running a hotel chain. Thus conglomerates were supposed to add value by removing old-fashioned managers and replacing them with ones trained in the new management science.

There was some truth in this claim. The best of the conglomerates did add value by targeting companies that needed fixing—companies with slack management, surplus assets, or excess cash that was not being invested in positive-NPV projects. These conglomerates targeted the same types of companies that LBO and private-equity funds would target later. The difference is that conglomerates would buy companies, try to improve them, and then manage them for the long run. The long-run management was the most difficult part of the game. Conglomerates would buy, fix, and hold. Private equity buys, fixes, and sells. By selling (cashing out), private equity avoids the problems of managing the conglomerate firm and running internal capital markets.²⁷ You could say that private-equity partnerships are temporary conglomerates.

   TABLE 32.4 Private-equity fund vs. public conglomerate. Both diversify, investing in a portfolio of unrelated businesses, but their financial structures are otherwise fundamentally different.

Source: Adapted from G. Baker and C. Montgomery, “Conglomerates and LBO Associations: A Comparison of Organizational Forms,” working paper, Harvard Business School, Cambridge, MA, July 1996. Used by permission of the authors.

Table 32.4 summarizes a comparison by Baker and Montgomery of the financial structure of a private-equity fund and of a typical public conglomerate. Both are diversified, but the fund’s limited partners do not have to worry that free cash flow will be plowed back into unprofitable investments. The fund has no internal capital market. Monitoring and compensation of management also differ. In the fund, each company is run as a separate business. The managers report directly to the owners, the fund’s partners. Each company’s managers own shares or stock options in that company, not in the fund. Their compensation depends on their firm’s market value in a trade sale or IPO.

In a public conglomerate, these businesses would be divisions, not freestanding companies. Ownership of the conglomerate would be dispersed, not concentrated. The divisions would not be valued separately by investors in the stock market, but by the conglomerate’s corporate staff, the very people who run the internal capital market. Managers’ compensation wouldn’t depend on divisions’ market values because no shares in the divisions would be traded and the conglomerate would not be committed to selling the divisions or spinning them off.

You can see the arguments for focus and against corporate diversification. But we must be careful not to push the arguments too far. For example, GE, a very successful company, operates in a wide range of unrelated industries. Also, in the next chapter we will find that conglomerates, though rare in the U.S., are common, and apparently successful, in many parts of the world.

 32-4   Bankruptcy

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U.S. bankruptcy filings

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Some firms are forced to reorganize by the onset of financial distress. At this point they need to agree to a reorganization plan with their creditors or file for bankruptcy. We list the largest nonfinancial U.S. bankruptcies in Table 32.5. The credit crunch also ensured a good dose of very large financial bankruptcies. Lehman Brothers tops the list. It failed in September 2008 with assets of $691.1 billion. Two weeks later Washington Mutual went the same way with assets of $327.9 billion.

Bankruptcy proceedings in the United States may be initiated by the creditors, but in the case of public corporations it is usually the firm itself that decides to file. It can choose one of two procedures, which are set out in Chapters 7 and 11 of the 1978 Bankruptcy Reform Act. The purpose of Chapter 7 is to oversee the firm’s death and dismemberment, while Chapter 11 seeks to nurse the firm back to health.

   TABLE 32.5 The largest U.S. nonfinancial bankruptcies.

Source: New Generation Research, Inc., www.bankruptcydata.com.

Most small firms make use of Chapter 7. In this case the bankruptcy judge appoints a trustee, who then closes the firm down and auctions off the assets. The proceeds from the auction are used to pay off the creditors. Secured creditors can recover the value of their collateral. Whatever is left over goes to the unsecured creditors, who take assigned places in a queue. The court and the trustee are first in line. Wages come next, followed by federal and state taxes and debts to some government agencies such as the Pension Benefit Guarantee Corporation. The remaining unsecured creditors mop up any remaining crumbs from the table.²⁸ Frequently the trustee needs to prevent some creditors from trying to jump the gun and collect on their debts, and sometimes the trustee retrieves property that a creditor has recently seized.

Managers of small firms that are in trouble know that Chapter 7 bankruptcy means the end of the road and, therefore, try to put off filing as long as possible. For this reason, Chapter 7 proceedings are often launched not by the firm but by its creditors.

When large public companies can’t pay their debts, they generally attempt to rehabilitate the business. This is in the shareholders’ interests; they have nothing to lose if things deteriorate further and everything to gain if the firm recovers. The procedures for rehabilitation are set out in Chapter 11. Most companies find themselves in Chapter 11 because they can’t pay their debts. But sometimes companies have filed for Chapter 11 not because they run out of cash, but to deal with burdensome labor contracts or lawsuits. For example, Delphi, the automotive parts manufacturer, filed for bankruptcy in 2005. Delphi’s North American operations were running at a loss, partly because of high-cost labor contracts with the United Auto Workers (UAW) and partly because of the terms of its supply contract with GM, its largest customer. Delphi sought the protection of Chapter 11 to restructure its operations and to negotiate better terms with the UAW and GM.

The aim of Chapter 11 is to keep the firm alive and operating while a plan of reorganization is worked out.²⁹ During this period, other proceedings against the firm are halted, and the company usually continues to be run by its existing management.³⁰ The responsibility for developing the plan falls on the debtor firm but, if it cannot devise an acceptable plan, the court may invite anyone to do so—for example, a committee of creditors.

The plan goes into effect if it is accepted by the creditors and confirmed by the court. Each class of creditors votes separately on the plan. Acceptance requires approval by at least one-half of votes cast in each class, and those voting “aye” must represent two-thirds of the value of the creditors’ aggregate claim against the firm.

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Cramdowns

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The plan also needs to be approved by two-thirds of the shareholders. Once the creditors and the shareholders have accepted the plan, the court normally approves it, provided that each class of creditors is in favor and that the creditors will be no worse off under the plan than they would be if the firm’s assets were liquidated and the proceeds distributed. Under certain conditions the court may confirm a plan even if one or more classes of creditors votes against it,³¹ but the rules for a “cram-down” are complicated and we will not attempt to cover them here.

The reorganization plan is basically a statement of who gets what; each class of creditors gives up its claim in exchange for new securities or a mixture of new securities and cash. The problem is to design a new capital structure for the firm that will (1) satisfy the creditors and (2) allow the firm to solve the business problems that got the firm into trouble in the first place.³² Sometimes satisfying these two conditions requires a plan of baroque complexity, involving the creation of a dozen or more new securities.

The Securities and Exchange Commission (SEC) plays a role in many reorganizations, particularly for large, public companies. Its interest is to ensure that all relevant and material information is disclosed to the creditors before they vote on the proposed plan of reorganization.

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Chapter 55

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Chapter 11 proceedings are often successful, and the patient emerges fit and healthy. But in other cases rehabilitation proves impossible, and the assets are liquidated under Chapter 7. Sometimes the firm may emerge from Chapter 11 for a brief period before it is once again submerged by disaster and back in the bankruptcy court. For example, TWA came out of Chapter 11 bankruptcy at the end of 1993, was back again less than two years later, and then for a third time in 2001, prompting jokes about “Chapter 22” and “Chapter 33.”³³

Is Chapter 11 Efficient?

Here is a simple view of the bankruptcy decision: Whenever a payment is due to creditors, management checks the value of the equity. If the value is positive, the firm makes the payment (if necessary, raising the cash by an issue of shares). If the equity is valueless, the firm defaults on its debt and files for bankruptcy. If the assets of the bankrupt firm can be put to better use elsewhere, the firm is liquidated and the proceeds are used to pay off the creditors; otherwise the creditors become the new owners and the firm continues to operate.³⁴

In practice, matters are rarely so simple. For example, we observe that firms often petition for bankruptcy even when the equity has a positive value. And firms often continue to operate even when the assets could be used more efficiently elsewhere. The problems in Chapter 11 usually arise because the goal of paying off the creditors conflicts with the goal of maintaining the business as a going concern. We described in Chapter 18 how the assets of Eastern Airlines seeped away in bankruptcy. When the company filed for Chapter 11, its assets were more than sufficient to repay in full its liabilities of $3.7 billion. But the bankruptcy judge was determined to keep Eastern flying. When it finally became clear that Eastern was a terminal case, the assets were sold off and the creditors received less than $.9 billion. The creditors would clearly have been better off if Eastern had been liquidated immediately; the unsuccessful attempt at resuscitation cost the creditors $2.8 billion.³⁵

Here are some further reasons that Chapter 11 proceedings do not always achieve an efficient solution:

1.  Although the reorganized firm is legally a new entity, it is entitled to the tax-loss carryforwards belonging to the old firm. If the firm is liquidated rather than reorganized, the tax-loss carryforwards disappear. Thus there is a tax incentive to continue operating the firm even when its assets could be sold and put to better use elsewhere.

2.  If the firm’s assets are sold, it is easy to determine what is available to pay creditors. However, when the company is reorganized, it needs to conserve cash. Therefore, claimants are often paid off with a mixture of cash and securities. This makes it less easy to judge whether they receive a fair shake.

3.  Senior creditors who know they are likely to get a raw deal in a reorganization may press for a liquidation. Shareholders and junior creditors prefer a reorganization. They hope that the court will not interpret the creditors’ pecking order too strictly and that they will receive consolation prizes when the firm’s remaining value is sliced up.

4.  Although shareholders and junior creditors are at the bottom of the pecking order, they have a secret weapon—they can play for time. When they use delaying tactics, the junior creditors are betting on a stroke of luck that will rescue their investment. On the other hand, the senior claimants know that time is working against them, so they may be prepared to settle for a lower payoff as part of the price for getting the plan accepted. Also, prolonged bankruptcy cases are costly, as we pointed out in Chapter 18. Senior claimants may see their money seeping into lawyers’ pockets and decide to settle quickly.

But bankruptcy practices do change and in recent years Chapter 11 proceedings have become more creditor-friendly.³⁶ For example, equity investors and junior debtholders used to find that managers were willing allies in dragging out a settlement, but these days the managers of bankrupt firms often receive a key employee retention plan, which provides them with a large bonus if the reorganization proceeds quickly and a smaller one if the company lingers on in Chapter 11. This has contributed to a reduction in the time spent in bankruptcy from nearly two years before 1990 to about 16 months recently.

While a reorganization plan is being drawn up, the company is likely to need additional working capital. It has, therefore, become increasingly common to allow the firm to buy goods on credit and to borrow money (known as debtor in possession, or DIP, debt). The lenders, who frequently comprise the firm’s existing creditors, are liable to insist on stringent conditions and so have considerable influence on the outcome of the bankruptcy proceedings.

As creditors have gained more influence, shareholders of the bankrupt firms have received fewer and fewer crumbs. In recent years the court has faithfully observed the pecking order in about 90% of Chapter 11 settlements.

In 2009 GM and Chrysler both filed for bankruptcy. They were not only two of the largest bankruptcies ever, but they were also extraordinary legal events. With the help of billions of fresh money from the U.S. Treasury, the companies were in and out of bankruptcy court with blinding speed, compared with the normal placid pace of Chapter 11. The U.S. government was deeply involved in the rescue and the financing of New GM and New Chrysler. The nearby box explains some of the financial issues raised by the Chrysler bankruptcy. The GM bankruptcy raised similar issues.

Workouts

If Chapter 11 reorganizations are not efficient, why don’t firms bypass the bankruptcy courts and get together with their creditors to work out a solution? Many firms that are in distress do first seek a negotiated settlement, or workout. For example, they can seek to delay payment of the debt or negotiate an interest rate holiday. However, shareholders and junior creditors know that senior creditors are anxious to avoid formal bankruptcy proceedings. So they are likely to be tough negotiators, and senior creditors generally need to make concessions to reach agreement.³⁷ The larger the firm, and the more complicated its capital structure, the less likely it is that everyone will agree to any proposal.

Sometimes the firm does agree to an informal workout with its creditors and then files under Chapter 11 to obtain the approval of the bankruptcy court. Such prepackaged or prenegotiated bankruptcies reduce the likelihood of subsequent litigation and allow the firm to gain the special tax advantages of Chapter 11.³⁸ For example, in 2010 Six Flags, the amusement park operator, arranged a prepack after reaching agreement with its creditors. Since 1980 about 25% of U.S. bankruptcies have been prepackaged or prenegotiated.³⁹

Alternative Bankruptcy Procedures

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International bankruptcy procedures

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The United States bankruptcy system is often described as a debtor-friendly system. Its principal focus is on rescuing firms in distress. But this comes at a cost, for there are many instances in which the firm’s assets would be better deployed in other uses. Michael Jensen, a critic of Chapter 11, has argued that “the U.S. bankruptcy code is fundamentally flawed. It is expensive, it exacerbates conflicts of interest among different classes of creditors, and it often takes years to resolve individual cases.” Jensen’s proposed solution is to require that any bankrupt company be put immediately on the auction block and the proceeds distributed to claimants in accordance with the priority of their claims.⁴⁰

In some countries the bankruptcy system is even more friendly to debtors. For example, in France the primary duties of the bankruptcy court are to keep the firm in business and preserve employment. Only once these duties have been performed does the court have a responsibility to creditors. Creditors have minimal control over the process, and it is the court that decides whether the firm should be liquidated or preserved. If the court chooses liquidation, it may select a bidder who offers a lower price but better prospects for employment.

The UK is just about at the other end of the scale. When a British firm is unable to pay its debts, the control rights pass to the creditors. Most commonly, a designated secured creditor appoints a receiver, who assumes direction of the firm, sells sufficient assets to repay the secured creditors, and ensures that any excess funds are used to pay off the other creditors according to the priority of their claims.

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Japan Airlines Encounters Turbulence

  In January 2010 Japan Airlines (JAL) filed for bankruptcy under the Japanese Corporate Reorganization Act leaving debts of $28 billion. It was one of Japan’s biggest-ever corporate failures. In a corporate reorganization a judge appoints a trustee, who is expected to weigh the rights and interests of various stakeholders, including employees. Typically, this trustee is a bankruptcy lawyer, whose initial task is to remove existing management and take control of the company.*

Only three months before JAL’s bankruptcy the Enterprise Turnaround Initiative Corporation of Japan (ETIC) was established to help firms that are potentially profitable but that are hampered by excessive debt. ETIC was empowered to negotiate agreements with a firm’s creditors, buy debts from creditors, and make loans. When JAL filed for bankruptcy, ETIC was appointed by the court as a trustee to devise a restructuring plan.**

ETIC’s plan involved drastic cuts in operations; the airline was required to ditch unprofitable routes, cut a third of its work force, and slash pension benefits. Shareholders would be wiped out and unsecured creditors forced to write off over 80% of their claims. Under the turnaround plan, ETIC and the Development Bank of Japan agreed to provide over $6 billion of new financing to keep the airline flying.

JAL’s rehabilitation plan was approved by the Tokyo District Court in November 2010. The court’s approval cleared the way for a capital injection of $4.2 billion from the state-backed Enterprise Turnaround Initiative Corp. In March 2011 the company emerged from bankruptcy, having paid off its creditors and secured more than $3 billion in new loans and capital. A year later it was operating profitably, and in September 2012 it went public again in an $8.5 billion IPO.

*In 2000 the Japanese government enacted an alternative to corporate reorganization, known as Civil Rehabilitation. This provides for management to retain control. Civil rehabilitation is popular with managers who want to keep their jobs, but it also has drawbacks. In particular, a debtor company lacks protection against secured creditors, who can move to regain control of assets that serve as collateral for loans.

**A veteran bankruptcy lawyer was appointed as co-trustee to supervise legal proceedings.

Davydenko and Franks, who have examined alternative bankruptcy systems, found that banks responded to these differences in the bankruptcy code by adjusting their lending practices. Nevertheless, as you would expect, lenders recover a smaller proportion of their money in those countries that have a debtor-friendly bankruptcy system. For example, in France the banks recover on average only 47% of the money owed by bankrupt firms, while in the UK the corresponding figure is 69%.⁴¹

Of course, the grass is always greener elsewhere. In the United States and France, critics complain about the costs of trying to save businesses that are no longer viable. By contrast, in countries such as the UK, bankruptcy laws are blamed for the demise of healthy businesses and Chapter 11 is held up as a model of an efficient bankruptcy system.

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SUMMARY

A corporation’s structure is not immutable. Companies frequently reorganize by adding new businesses or disposing of existing ones. They may alter their capital structure and they may change their ownership and control. In this chapter we looked at some of the mechanisms by which companies transform themselves.

We started with leveraged buyouts (LBOs). An LBO is a takeover or buyout of a company or division that is financed mostly with debt. The LBO is owned privately, usually by an investment partnership. Debt financing is not the objective of most LBOs; it is a means to an end. Most LBOs are diet deals. The cash requirements for debt service force managers to shed unneeded assets, improve operating efficiency, and forego wasteful expenditure. The managers and employees are given a significant stake in the business, so they have strong incentives to make these improvements.

A leveraged restructuring is in many ways similar to an LBO. In this case the company puts itself on a diet. Large amounts of debt are added and the proceeds are paid out to shareholders. The company is forced to generate cash to service the debt, but there is no change in control and the company stays public.

Most investments in LBOs are made by private-equity partnerships. The limited partners, who put up most of the money, are mostly institutional investors, including pension funds, endowments, and insurance companies. The general partners, who organize and manage the funds, receive a management fee and get a carried interest in the fund’s profits. We called these partnerships “temporary conglomerates.” They are conglomerates because they create a portfolio of companies in unrelated industries. They are temporary because the partnership has a limited life, usually about 10 years. At the end of this period, the partnership’s investments must be sold or taken public again in IPOs. Private-equity funds do not buy and hold; they buy, fix, and sell. Investors in the partnership therefore do not have to worry about wasteful reinvestment of free cash flow.

The private-equity market has been growing steadily. In contrast to these temporary conglomerates, public conglomerates have been declining in the United States. In public companies, unrelated diversification seems to destroy value—the whole is worth less than the sum of its parts. There are two possible reasons for this. First, since the value of the parts can’t be observed separately, it is harder to set incentives for divisional managers. Second, conglomerates’ internal capital markets are inefficient. It is difficult for management to appreciate investment opportunities in many different industries, and internal capital markets are prone to overinvestment and cross-subsidies.

Of course, companies shed assets as well as acquire them. Assets may be divested by spin-offs, carve-outs, or asset sales. In a spin-off the parent firm splits off part of its business into a separate public company and gives its shareholders stock in the company. In a carve-out the parent raises cash by separating off part of its business and selling shares in this business through an IPO. These divestitures are generally good news to investors; it appears that the divisions are moving to better homes, where they can be well managed and more profitable. The same improvements in efficiency and profitability are observed in privatizations, which are spin-offs or carve-outs of businesses owned by governments.

Companies in distress may reorganize by getting together with their creditors to arrange a workout. For example, they may agree to a delay in repayment. If a workout proves impossible, the company needs to file for bankruptcy. Chapter 11 of the Bankruptcy Act, which is used by most large public companies, seeks to reorganize the company and put it back on its feet again. However, the goal of paying off the company’s creditors often conflicts with the aim of keeping the business going. As a result, Chapter 11 sometimes allows a firm to continue to operate when its assets could be better used elsewhere and the proceeds used to pay off creditors.

Chapter 11 tends to favor the debtor. But in some other countries the bankruptcy system is designed almost exclusively to recover as much cash as possible for the lenders. While U.S. critics of Chapter 11 complain about the costs of saving businesses that are not worth saving, commentators elsewhere bemoan the fact that their bankruptcy laws are causing the breakup of potentially healthy businesses.

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FURTHER READING

The following paper provides a general overview of corporate restructuring:

B. E. Eckbo and K. S. Thorburn, “Corporate Restructurings: Breakups and LBOs,” in B. E. Eckbo (ed.), Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), Chapter 16.

The papers by Kaplan and Stein, and Kaplan and Stromberg, provide evidence on the evolution and performance of LBOs. Jensen, the chief proponent of the free-cash-flow theory of takeovers, gives a spirited and controversial defense of LBOs:

S. N. Kaplan and J. C. Stein, “The Evolution of Buyout Pricing and Financial Structure (Or What Went Wrong) in the 1980s,” Journal of Applied Corporate Finance 6 (Spring 1993), pp. 72–88.

S. N. Kaplan and P. Stromberg, “Leveraged Buyouts and Private Equity,” Journal of Economic Perspectives 23 (2009), pp. 121–146.

M. C. Jensen, “The Eclipse of the Public Corporation,” Harvard Business Review 67 (September/October 1989), pp. 61–74.

The Summer 2006 issue of the Journal of Applied Corporate Finance includes a panel discussion and several articles on private equity. Privatization is surveyed in:

W. L. Megginson, The Financial Economics of Privatization (Oxford: Oxford University Press, 2005).

The following books and articles survey the bankruptcy process. Bris, Welch, and Zhu give a detailed comparison of bankrupt firms’ experience in Chapter 7 versus Chapter 11.

E. I. Altman, Corporate Financial Distress and Bankruptcy: A Complete Guide to Predicting and Avoiding Distress and Profiting from Bankruptcy, 3rd ed. (New York: John Wiley & Sons, 2005).

E. S. Hotchkiss, K. John, R. M. Mooradian, and K. S. Thorburn, “Bankruptcy and the Resolution of Financial Distress,” in B. E. Eckbo (ed.), Handbook of Empirical Corporate Finance (Amsterdam: Elsevier/North-Holland, 2007), Chapter 14.

L. Senbet and J. Seward, “Financial Distress, Bankruptcy and Reorganization,” in R. A. Jarrow, V. Maksimovic, and W. T. Ziemba (eds.), North-Holland Handbooks of Operations Research and Management Science: Finance, vol. 9 (New York: Elsevier, 1995), pp. 921–961.

J. S. Bhandari, L. A. Weiss, and B. E. Adler (eds.), Corporate Bankruptcy: Economic and Legal Perspectives (Cambridge, UK: Cambridge University Press, 1996).

A. Bris, I. Welch, and N. Zhu, “The Costs of Bankruptcy: Chapter 7 Liquidation versus Chapter 11 Reorganization,” Journal of Finance 61 (June 2006), pp. 1253–1303.

Here are several good case studies on topics covered in this chapter:

B. Burrough and J. Helyar, Barbarians at the Gate: The Fall of RJR Nabisco (New York: Harper & Row, 1990).

G. P. Baker, “Beatrice: A Study in the Creation and Destruction of Value,” Journal of Finance 47 (July 1992), pp. 1081–1120.

K. H. Wruck, “Financial Policy as a Catalyst for Organizational Change: Sealed Air’s Leveraged Special Dividend,” Journal of Applied Corporate Finance 7 (Winter 1995), pp. 20–37.

J. Allen, “Reinventing the Corporation: The Satellite Structure of Thermo Electron,” Journal of Applied Corporate Finance 11 (Summer 1998), pp. 38–47.

R. Parrino, “Spinoffs and Wealth Transfers: The Marriott Case,” Journal of Financial Economics 43 (February 1997), pp. 241–274.

C. Eckel, D. Eckel, and V. Singal, “Privatization and Efficiency: Industry Effects of the Sale of British Airways,” Journal of Financial Economics 43 (February 1997), pp. 275–298.

L. A. Weiss and K. H. Wruck, “Information Problems, Conflicts of Interest, and Asset Stripping: Chapter 11’s Failure in the Case of Eastern Airlines,” Journal of Financial Economics 48 (April 1998), pp. 55–97.

W. Megginson and D. Scannapieco, “The Financial and Economic Lessons of Italy’s Privatization Program,” Journal of Applied Corporate Finance 18 (Summer 2006), pp. 56–65.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Vocabulary Define the following terms:

a.  LBO

b.  MBO

c.  Spin-off

d.  Carve-out

e.  Asset sale

f.  Privatization

g.  Leveraged restructuring

2.  Restructuring True or false?

a.  One of the first tasks of an LBO’s financial manager is to pay down debt.

b.  Once an LBO or MBO goes private, it almost always stays private.

c.  Targets for LBOs in the 1980s tended to be profitable companies in mature industries.

d.  “Carried interest” refers to the deferral of interest payments on LBO debt.

e.  By 2008 new LBO and private-equity transactions were extremely rare.

f.  The announcement of a spin-off is generally followed by a sharp fall in the stock price.

g.  Privatizations are generally followed by massive layoffs.

h.  On average, privatization seems to improve efficiency and add value.

3.  Privatization What are the government’s motives in a privatization?

4.  Conglomerates What advantages have been claimed for public conglomerates?

5.  Conglomerates List the disadvantages of traditional U.S. conglomerates.

6.  Private equity Private-equity partnerships have a limited term. What are the advantages of this arrangement?

7.  Bankruptcy What is the difference between Chapter 7 and Chapter 11 bankruptcies?

8.  Bankruptcy True or false?

a.  When a company becomes bankrupt, it is usually in the interests of stockholders to seek a liquidation rather than a reorganization.

b.  In Chapter 11 a reorganization plan must be presented for approval by each class of creditor.

c.  In a reorganization, creditors may be paid off with a mixture of cash and securities.

d.  When a company is liquidated, one of the most valuable assets to be sold off is the tax-loss carryforward.

9.  Bankruptcy Explain why equity can sometimes have a positive value even when companies file for bankruptcy.

INTERMEDIATE

10.  Restructuring True, false, or “It depends on . . .”?

a.  Carve-out or spin-off of a division improves incentives for the division’s managers.

b.  Private-equity partnerships have limited lives. The main purpose is to force the general partners to seek out quick payback investments.

c.  Managers of private-equity partnerships have an incentive to make risky investments.

11.  Leveraged buyouts For what kinds of firm would an LBO or MBO transaction not be productive?

12.  Leveraged buyouts Outline the similarities and differences between the RJR Nabisco LBO and the Sealed Air leveraged restructuring. Were the economic motives the same? Were the results the same? Do you think it was an advantage for Sealed Air to remain a public company?

13.  Divestitures Examine some recent examples of divestitures. What do you think were the underlying reasons for them? How did investors react to the news?

14.  Leveraged buyouts Read Barbarians at the Gate (Further Reading). What agency costs can you identify? (Hint: See Chapter 12.) Do you think the LBO was well-designed to reduce these costs?

15.  Private equity Explain the structure of a private-equity partnership. Pay particular attention to incentives and compensation. What types of investment were such partnerships designed to make?

16.  Private equity We described carried interest as an option. What kind of option? How does this option change incentives in a private-equity partnership? Can you think of circumstances where these incentive changes would be perverse, that is, potentially value-destroying? Explain.

17.  Privatization “Privatization appears to bring efficiency gains because public companies are better able to reduce agency costs.” Why do you think this may (or may not) be true?

18.  Bankruptcy We described several problems with Chapter 11 bankruptcy. Which of these problems could be mitigated by negotiating a prepackaged bankruptcy?

19. Bankruptcy procedures We have focused mostly on the U.S. bankruptcy law and procedures, except for a brief discussion for other countries at the very end of this chapter. Now it’s time for you to do some further research. Start with the cross-country analyses referenced in footnote 41. These analyses cover France, Germany, the U.K., Sweden and Finland.

a.  Outline the most important differences in the bankruptcy process in these countries vs. the U.S.

b.  In what circumstances do these differences make bankruptcy significantly more or less efficient than in the U.S.? Give a few examples. (You will have to think about how to define “efficiency.”)

20.  Private equity Figure 32.2 shows how a private equity partnership is organized in the U.S. Do you think that this same type of organization will work in other countries with different laws and financial institutions? For a start in thinking about this question, review Section 15.1 and read the following article:

S. Kaplan, F. Martel and P. Stromberg, “How do Legal Institutions and Experience Affect Financial Contracts?” Journal of Financial Intermediation 16 (2007), pp. 273–311.

___________

¹N. Mohan and C. R. Chen track the abnormal returns of RJR securities in “A Review of the RJR Nabisco Buyout,” Journal of Applied Corporate Finance 3 (Summer 1990), pp. 102–108.

²The whole story is reconstructed by B. Burrough and J. Helyar in Barbarians at the Gate: The Fall of RJR Nabisco (New York: Harper & Row 1990)—see especially Chapter 18—and in a movie with the same title.

³C. Anders, “RJR Swallows Hard, Offers $5-a-Share Stock,” The Wall Street Journal, December 18, 1990, pp. C1–C2.

⁴This view persists in some quarters: in April 2005, Franz Müntefering, Chairman of the German Social Democratic Party, branded private-equity investors as a plague of “locusts” bent on devouring German industry. Try an Internet search on “private equity” with “locusts.”

⁵See E. I. Altman and G. Fanjul, “Defaults and Returns in the High Yield Bond Market: The Year 2003 in Review and Market Outlook,” Monograph, Salomon Center, Leonard N. Stern School of Business, New York University, 2004.

⁶There are some tax costs to LBOs. For example, selling shareholders realize capital gains and pay taxes that otherwise would be deferred. See L. Stiglin, S. N. Kaplan, and M. C. Jensen, “Effects of LBOs on Tax Revenues of the U.S. Treasury,” Tax Notes 42 (February 6, 1989), pp. 727–733.

⁷R. J. Ruback, “RJR Nabisco,” case study, Harvard Business School, Cambridge, MA, 1989.

⁸N. Mohan and C. R. Chen, “A Review of the RJR Nabisco Buyout,” Journal of Applied Corporate Finance 3, no. 2 (1990), pp. 102–108.

⁹S. Kaplan, “The Effects of Management Buyouts on Operating Performance and Value,” Journal of Financial Economics 24 (October 1989), pp. 217–254. For more recent evidence on changes in employment, see S. J. Davis, J. Haltiwanger, R. S. Jarmin, J. Lerner, and J. Miranda, “Private Equity and Employment,” U.S. Census Bureau Center for Economic Studies Paper No. CES-WP-08-07, January 2009.

¹⁰K. H. Wruck, “Financial Policy as a Catalyst for Organizational Change: Sealed Air’s Leveraged Special Dividend,” Journal of Applied Corporate Finance 7 (Winter 1995), pp. 20–37.

¹¹The merger with BellSouth did not signal the end of the acquisitions. Over the following years AT&T continued to be active in the market, including a failed $39 billion offer for T-Mobile.

¹²The value of the shares that shareholders receive is taxed as a dividend unless they are given at least 80% of the shares in the new company.

¹³Instead of undertaking a spin-off, some companies have given their shareholders tracking stock tied to the performance of particular divisions. For example, in 2000 AT&T distributed a special class of shares tied to the performance of its wireless business. But tracking stocks did not prove popular with investors, and a year later AT&T went whole hog and spun off AT&T Wireless into a separate company.

¹⁴For example, P. J. Cusatis, J. A. Miles, and J. R. Woolridge, “Restructuring Through Spin-offs: The Stock-Market Evidence,” Journal of Financial Economics 33 (Summer 1994), pp. 293–311.

¹⁵See R. Gertner, E. Powers, and D. Scharfstein, “Learning about Internal Capital Markets from Corporate Spin-offs,” Journal of Finance 57 (December 2003), pp. 2479–2506; L. V. Daley, V. Mehrotra, and R. Sivakumar, “Corporate Focus and Value Creation: Evidence from Spin-offs,” Journal of Financial Economics 45 (August 1997), pp. 257–281; T. R. Burch and V. Nanda, “Divisional Diversity and the Conglomerate Discount: Evidence from Spin-offs,” Journal of Financial Economics 70 (October 2003), pp. 69–78; and A. K. Dittmar and A. Shivdasani, “Divestitures and Divisional Investment Policies,” Journal of Finance 58 (December 2003), pp. 2711–2744. But G. Colak and T. M. Whited argue that apparent increases in value are due to econometric problems rather than actual increases in investment efficiency. See “Spin-offs, Divestitures and Conglomerate Investment,” Review of Economic Studies 20 (May 2007), pp. 557–595.

¹⁶The parent must retain an 80% interest to consolidate the subsidiary with the parent’s tax accounts. Otherwise the subsidiary is taxed as a freestanding corporation.

¹⁷See S. Bhagat, A. Shleifer, and R. Vishny, “Hostile Takeovers in the 1980s: The Return to Corporate Specialization,” Brookings Papers on Economic Activity: Microeconomics, 1990, pp. 1–12.

¹⁸V. Maksimovic and G. Phillips, “The Market for Corporate Assets: Who Engages in Mergers and Asset Sales and Are There Efficiency Gains?” Journal of Finance 56 (December 2001), Table 1, p. 2000.

¹⁹Ibid.

²⁰There is extensive research on voucher privatizations. See, for example, M. Boycko, A. Shleifer, and R. Vishny, “Voucher Privatizations,” Journal of Financial Economics 35 (April 1994), pp. 249–266; and R. Aggarwal and J. T. Harper, “Equity Valuation in the Czech Voucher Privatization Auctions,” Financial Management 29 (Winter 2000), pp. 77–100.

²¹W. L. Megginson and J. M. Netter, “From State to Market: A Survey of Empirical Studies on Privatization,” Journal of Economic Literature 39 (June 2001), p. 381.

²²The credit crisis prompted a number of company nationalizations throughout the world, such as that of Northern Rock in the UK, Hypo Real Estate in Germany, Landsbanki in Iceland, and Anglo-Irish Bank in Ireland.

²³Cerberus had previously purchased a controlling stake in GMAC, General Motors’ finance subsidiary.

²⁴LBO and buyout funds also extract fees for arranging financing for their takeover transactions.

²⁵The structure and compensation of private-equity partnerships are described in A. Metrick and A. Yasuda, “The Economics of Private Equity Funds,” Review of Financial Studies, 23 (2010), pp. 2303–2341.

²⁶O. Lamont, “Cash Flow and Investment: Evidence from Internal Capital Markets,” Journal of Finance 52 (March 1997), pp. 83–109. The Wall Street Journal quotation appears on pp. 89–90. © 1997 Dow Jones & Company, Inc.

²⁷Economists have tried to measure whether corporate diversification adds or subtracts value. Berger and Ofek estimate an average conglomerate discount of 12% to 15%. That is, the estimated market value of the whole is 12% to 15% less than the sum of the values of the parts. The chief cause of the discount seems to be overinvestment and misallocation of investment. See P. Berger and E. Ofek, “Diversification’s Effect on Firm Value,” Journal of Financial Economics 37 (January 1995), pp. 39–65. But not everyone is convinced that the conglomerate discount is real. Other researchers have found smaller discounts or pointed out statistical problems that make the discount hard to measure. See, for example, J. M. Campa and S. Kedia, “Explaining the Diversification Discount,” Journal of Finance 57 (August 2002), pp. 1731–1762; and B. Villalonga, “Diversification Discount or Premium? Evidence from the Business Information Tracking Service,” Journal of Finance 59 (April 2004), pp. 479–506.

²⁸On average there isn’t much left. See M. J. White, “Survey Evidence on Business Bankruptcy,” in Corporate Bankruptcy, ed. J. S. Bhandari and L. A. Weiss (Cambridge, UK: Cambridge University Press, 1996).

²⁹To keep the firm alive, it may be necessary to continue to use assets that were offered as collateral, but this denies secured creditors access to their collateral. To resolve this problem, the Bankruptcy Reform Act makes it possible for a firm operating under Chapter 11 to keep such assets as long as the creditors who have a claim on them are compensated for any decline in their value. Thus, the firm might make cash payments to the secured creditors to cover economic depreciation of the assets.

³⁰Occasionally the court appoints a trustee to manage the firm.

³¹But at least one class of creditors must vote for the plan; otherwise the court cannot approve it.

³²Although Chapter 11 is designed to keep the firm in business, the reorganization plan often involves the sale or closure of large parts of the business.

³³One study found that after emerging from Chapter 11, about one in three firms reentered bankruptcy or privately restructured their debt. See E. S. Hotchkiss, “Postbankruptcy Reform and Management Turnover,” Journal of Finance 50 (March 1995), pp. 3–21.

³⁴If there are several classes of creditors in this simplistic model, the junior creditors initially become the owners of the company and are responsible for paying off the senior debt. They now face exactly the same decision as the original owners. If their newly acquired equity is valueless, they will also default and turn over ownership to the next class of creditors.

³⁵These estimates of creditor losses are taken from L. A. Weiss and K. H. Wruck, “Information Problems, Conflicts of Interest, and Asset Stripping: Chapter 11’s Failure in the Case of Eastern Airlines,” Journal of Financial Economics 48 (April 1998), pp. 55–97.

³⁶For a discussion of these changes see S. T. Bharath, V. Panchapegesan, and I. Werner, “The Changing Nature of Chapter 11,” working paper, Ohio State University, November 2010.

³⁷Franks and Torous show that creditors make even greater concessions to junior creditors in informal workouts than in Chapter 11. See J. R. Franks and W. N. Torous, “How Shareholders and Creditors Fare in Workouts and Chapter 11 Reorganizations,” Journal of Financial Economics 35 (May 1994), pp. 13–33.

³⁸In a prepackaged bankruptcy the debtor gains agreement to the reorganization plan before the filing. In a prenegotiated bankruptcy the debtor negotiates the terms of the plan only with the principal creditors.

³⁹Data from Lynn LoPucki’s Bankruptcy Research Database at http://lopucki.law.ucla.edu.

⁴⁰M. C. Jensen, “Corporate Control and the Politics of Finance,” Journal of Applied Corporate Finance 4 (Summer 1991), pp. 13–33. An ingenious alternative set of bankruptcy procedures is proposed in L. Bebchuk, “A New Approach to Corporate Reorganizations,” Harvard Law Review 101 (1988), pp. 775–804; and P. Aghion, O. Hart, and J. Moore, “The Economics of Bankruptcy Reform,” Journal of Law, Economics and Organization 8 (1992), pp. 523–546.

⁴¹S. A. Davydenko and J. R. Franks, “Do Bankruptcy Codes Matter? A Study of Defaults in France, Germany and the UK,” Journal of Finance 63 (2008), pp. 565–608. For descriptions of bankruptcy in Sweden and Finland, see P. Stromberg, “Conflicts of Interest and Market Illiquidity in Bankruptcy Auctions: Theory and Tests,” Journal of Finance 55 (December 2000), pp. 2641–2692; and S. A. Ravid and S. Sundgren, “The Comparative Efficiency of Small-Firm Bankruptcies: A Study of the U.S. and Finnish Bankruptcy Codes,” Financial Management 27 (Winter 1998), pp. 28–40.

Part 10 Mergers, Corporate Control, and Governance

Governance and Corporate Control Around the World

Much of corporate finance (and much of this book) assumes a particular financial structure—public corporations with actively traded shares and relatively easy access to financial markets. But there are other ways to organize and finance business ventures. The arrangements for ownership, control, and financing vary greatly around the world. In this chapter we consider some of these differences.

Corporations raise cash from financial markets and also from financial institutions. Markets are relatively more important in the United States, United Kingdom, and other “Anglo-Saxon” economies. Financial institutions, particularly banks, are relatively more important in many other countries, including Germany and Japan. In bank-based systems, individual investors are less likely to hold corporate debt and equity directly. Instead ownership passes through banks, insurance companies, and other financial intermediaries.

This chapter starts with an overview of financial markets, financial institutions, and sources of financing. We contrast Europe, Japan, and the rest of Asia to the United States and United Kingdom. Then Section 33-2 looks more closely at ownership, control, and governance. Here we start with the United States and United Kingdom and then turn to Japan, Germany, and the rest of the world. Section 33-3 asks whether these differences matter. For example, do well-functioning financial markets and institutions contribute to economic development and growth? What are the advantages and disadvantages of market-based versus bank-based systems?

Before starting on this worldwide tour, remember that the principles of financial management apply throughout the journey. The concepts and basic tools of the trade do not vary. For example, all companies in all countries should recognize the opportunity cost of capital (although the cost of capital is even harder to measure where stock markets are small or erratic). Discounted cash flow still makes sense. Real options are encountered everywhere. And even in bank-based financial systems, corporations participate in world financial markets—by trading foreign exchange or hedging risks in futures markets, for instance.

 33-1   Financial Markets and Institutions

In most of this book we have assumed that a large part of debt financing comes from public bond markets. Nothing in principle changes when a firm borrows from a bank instead. But in some countries bond markets are stunted and bank financing is more important. Figure 33.1 shows the total values of bank loans, private (nongovernment) bonds, and stock markets in different parts of the world in 2010. To measure these financial claims on a comparable basis, the amounts are scaled by gross domestic product (GDP).¹

   FIGURE 33.1 Value of financial claims in 2010, percentage of GDP.

Sources: Data from Global Financial Stability Report: The Quest for Lasting Stability, April 2012, IMF. We are grateful to Michael Chui for this figure.

Company financing in the United States is different from that in most other countries. The United States not only has a large amount of bank loans outstanding, but there is also a large stock market and a large corporate bond market. Thus the United States is said to have a market-based financial system. Stock market value is also high in the United Kingdom and Asia,² but bank loans are much more important than the bond market in these countries. In Europe³ and Japan, bank financing again outpaces bond markets, but the stock market is relatively small. Most countries in Europe, including Germany, France, Italy, and Spain, have bank-based financial systems. So does Japan.

Let’s look at these regions from a different perspective. Figure 33.2 shows the financial investments made by households, again scaled by GDP.⁴ (“Households” means individual investors.) Household portfolios are divided into four categories: bank deposits, insurance policies and mutual and pension funds, equity securities, and “other.” Notice in Figure 33.2 the differences in the total amounts of financial assets. Summing the columns for each country and region, the amount of financial assets is 278% of GDP in the United States, 288% in the United Kingdom, 286% in Japan, and 185% in Europe. This does not mean that European investors are poor, just that they hold less wealth in the form of financial assets. Figure 33.2 excludes other important investment categories, such as real estate or privately owned businesses. It also excludes the value of pensions provided by governments.

   FIGURE 33.2 Household portfolio allocations, 1995–2010, percentage of GDP.

Sources: Bank of Japan, EUROSTAT, Federal Reserve Board, and the UK Office for National Statistics. We are grateful to Michael Chui for this figure.

In the United States, a large fraction of households’ portfolios is held directly in equity securities, mostly common stocks. Therefore individual investors can potentially play an important role in corporate governance. Direct equity holdings are smaller in the United Kingdom, smaller still in Europe, and smallest in Japan. Japanese households could not play a significant direct role in corporate governance even if they wanted to. They can’t vote shares that they don’t own.

Where direct equity investment is small, household investments in bank deposits, insurance policies, and mutual and pension funds are correspondingly large. In the United Kingdom, the insurance and funds category dominates, with bank deposits in second place. In Europe, bank deposits and insurance and funds run a close race for first. In Japan, bank deposits win by a mile, with insurance and funds in second place and equities a distant third.

Figure 33.2 tells us that in many parts of the world there are relatively few individual stockholders. Most individuals don’t invest directly in equity markets, but indirectly, through insurance companies, mutual funds, banks, and other financial intermediaries. Of course the thread of ownership traces back through these intermediaries to individual investors. All assets are ultimately owned by individuals. There are no Martian or extraterrestrial investors that we know of.⁵

Now let’s look at financial institutions. Figure 33.3 shows the financial assets held by financial institutions, including banks, mutual funds, insurance companies, pension funds, and other intermediaries. These investments are smaller in the United States, relative to GDP, than in other countries (as expected in the U.S. market-based system). Financial institutions in the United Kingdom, Europe, and Japan have invested large sums in loans and in deposits and currency. Holdings of equity are highest in the United Kingdom. These holdings are mainly owned by insurance companies and pension funds.

   FIGURE 33.3 Financial institutions’ portfolio allocations, 1995–2010, percentage of GDP.

Sources: Bank of Japan, EUROSTAT, Federal Reserve Board, and the UK Office for National Statistics. We are grateful to Michael Chui for this figure.

We’ve covered households and financial institutions. Is there any other source for corporate financing? Yes, financing can come from other corporations. Take a look at Figure 33.4, which shows the financial assets held by nonfinancial corporations. Perhaps the most striking feature is the large amount of equity held by firms in Europe. The amount of equity held in Japan and the United Kingdom is also large. In the United States it is relatively small. As we will see, these holdings of shares by other nonfinancial corporations have important implications for corporate ownership and governance.

Another interesting aspect of Figure 33.4 is the large amount of intercompany loans and trade credit (mostly trade credit) in Japan. Many Japanese firms rely heavily on trade-credit financing, that is, on accounts payable to other firms. Of course the other firms see the reverse side of trade credit: They are providing financing in the form of accounts receivable.

Figures 33.1 to 33.4 show that just drawing a line between market-based, “Anglo-Saxon” financial systems and bank-based financial systems is simplistic. We need to dig a little deeper when comparing financial systems. For example, more equity is held directly by households in the United States than in the United Kingdom and the portfolio allocations of households, nonfinancial corporations, and financial institutions are also significantly different. In addition, we noted the large cross-holdings of shares among European corporations. Finally, Japanese households put significantly more of their savings in banks and Japanese corporations use trade credit much more than in other advanced economies.

   FIGURE 33.4 Nonfinancial corporations’ portfolio allocations, 1995–2010, percentage of GDP.

Sources: Bank of Japan, EUROSTAT, Federal Reserve Board, and the UK Office for National Statistics. We are grateful to Michael Chui for this figure.

Investor Protection and the Development of Financial Markets

What explains the importance of financial markets in some countries, while other countries rely less on markets and more on banks and other financial institutions? One answer is investor protection. Stock and bond markets thrive where investors in these markets are protected reasonably well.

Investors’ property rights are much better protected in some parts of the world than others. La Porta, Lopez-de-Silanes, Shleifer, and Vishny have developed quantitative measures of investor protection based on shareholders’ and creditors’ rights and the quality of law enforcement. Countries with poor scores generally have smaller stock markets, measured by aggregate market value relative to GDP, and the numbers of listed firms and initial public offerings are smaller relative to population. Poor scores also mean less debt financing for private firms.⁶

BEYOND THE PAGE

● ● ● ● ●

Country measures of governance

brealey.mhhe.com/c33

It’s easy to understand why poor protection of outside investors stunts the growth of financial markets. A more difficult question is why protection is good in some countries and poor in others. La Porta, Lopez-de-Silanes, Shleifer, and Vishny point to the origin of legal systems. They distinguish legal systems derived from the common-law tradition, which originated in England, from systems based on civil law, which evolved in France, Germany, and Scandinavia. The English, French, and German systems have spread around the world by conquest, imperialism, and imitation. Both shareholders and creditors are better protected by the law in countries that adopted the common-law tradition.

But Rajan and Zingales⁷ point out that France, Belgium, and Germany, which are civil-law countries, had well-developed financial markets early in the twentieth century. Relative to GDP, these countries’ financial markets were then about the same size as markets in the United Kingdom and bigger than those in the United States. These rankings were reversed in the second half of the century, after World War II, although financial markets are now expanding and playing a greater role in European economies. Rajan and Zingales believe that these reversals can be attributed to political trends and shifts in government policy. For example, they recount the backlash against financial markets after the stock market crash of 1929 and the expansion of government regulation and ownership in the Great Depression and after World War II.

It remains to be seen how political factors will fully play out in the wake of the financial crisis of 2007–2009 and the eurozone sovereign debt crisis that started in 2010. These have already had significant effects, and this trend seems likely to continue.

 33-2   Ownership, Control, and Governance

Who owns the corporation? In the United States and United Kingdom, we just say “the stockholders.” There is usually just one class of common stock, and each share has one vote. Some stockholders may have more influence than others, but only because they own more shares. In other countries, ownership is not so simple, as we see later in this section.

What is the corporation’s financial objective? Normally we just say “to maximize stockholder value.” According to U.S. and UK corporation law, managers have a fiduciary duty to the shareholders. In other words, they are legally required to act in the interests of shareholders. Consider the classic illustration provided by an early case involving the Ford Motor Company. Henry Ford announced a special dividend, but then reneged, saying that the cash earmarked for the dividend would be spent for the benefit of employees. A shareholder sued on the grounds that corporations existed for the benefit of shareholders and the management did not have the right to improve the lot of workers at shareholders’ expense. Ford lost the case.⁸

The idea that the corporation should be run in the interests of the shareholders is thus embedded in the law in the United States and United Kingdom. The board of directors is supposed to represent shareholders’ interests. But laws and customs differ in other countries. Now we look at some of these differences. We start with Japan.

Ownership and Control in Japan

Traditionally the most notable feature of Japanese corporate finance has been the keiretsu. A keiretsu is a network of companies, usually organized around a major bank. Japan is said to have a main bank system, with long-standing relationships between banks and firms. There are also long-standing business relationships between a keiretsu’s companies. For example, a manufacturing company might buy most of its raw materials from group suppliers and in turn sell much of its output to other group companies.

The bank and other financial institutions at the keiretsu’s center own shares in most of the group companies (though a commercial bank in Japan is limited to 5% ownership of each company). Those companies may in turn hold the bank’s shares or each other’s shares. Because of the cross-holdings, the number of shares available for purchase by outside investors is much lower than the total number outstanding.

The keiretsu is tied together in other ways. Most debt financing comes from the keiretsu’s main bank or from affiliated financial institutions. Managers may sit on the boards of directors of other group companies, and a “presidents’ council” of the CEOs of the most important group companies meets regularly.

Think of the keiretsu as a system of corporate governance, where power is divided among the main bank, the group’s largest companies, and the group as a whole. This confers certain financial advantages. First, firms have access to additional “internal” financing—internal to the group, that is. Thus a company with a capital budget exceeding operating cash flows can turn to the main bank or other keiretsu companies for financing. This avoids the cost or possible bad-news signal of a public sale of securities. Second, when a keiretsu firm falls into financial distress, with insufficient cash to pay its bills or fund necessary capital investments, a workout can usually be arranged. New management can be brought in from elsewhere in the group, and financing can be obtained, again “internally.”

Hoshi, Kashyap, and Scharfstein tracked capital expenditure programs of a large sample of Japanese firms—many, but not all, members of keiretsus. The keiretsu companies’ investments were more stable and less exposed to the ups and downs of operating cash flows or to episodes of financial distress.⁹ It seems that the financial support of the keiretsus enabled members to invest for the long run, regardless of temporary setbacks.

Corporation law in Japan resembles that in the United States, but there are some important differences. For example, in Japan it is easier for shareholders to nominate and elect directors. Also, management remuneration must be approved at general meetings of shareholders.¹⁰ Nevertheless, ordinary shareholders do not in fact have much influence. Japanese boards traditionally have 40 or 50 members, with only a handful who are potentially independent of management.¹¹ The CEO effectively controls nominations to the board. As long as the financial position of a Japanese corporation is sound, the CEO and senior management control the corporation. Outside stockholders have very little influence.

Given this control, plus the cross-holdings within industrial groups, it’s no surprise that hostile takeovers are exceedingly rare in Japan. Also, Japanese corporations have been stingy with dividends, which probably reflects the relative lack of influence of outside shareholders. On the other hand, Japanese CEOs do not use their power to generate large sums of personal wealth. They are not well paid, compared to CEOs in most other developed countries. (Look back to Figure 12.1 for average top-management compensation levels for Japan and other countries.)

Cross-holdings reached a peak around 1990 when about 50% of corporations’ shares were held by other Japanese companies and financial institutions. Starting in the mid-1990s a banking crisis began to emerge in Japan. This led firms to sell off bank shares because they viewed them as bad investments. Banks and firms in financial distress, such as Nissan, sold off other companies’ shares to raise funds. By 2004 the level of cross-holdings had fallen to 20%. In the next few years, however, cross-holdings rose again as companies in the steel and other industries began to worry about hostile takeovers, which was the original motivation for acquisition of cross-holdings in the 1950s and 1960s.¹²

Ownership and Control in Germany

Traditionally banks in Germany played a significant role in corporate governance. This involved providing loans, owning large amounts of equity directly, and the proxy voting of shares held on behalf of customers. Over time this role has changed significantly. The relationship between the largest German bank, Deutsche Bank, and one of the largest German companies, Daimler AG, provides a good illustration.

Panel a of Figure 33.5 shows the 1990 ownership structure of Daimler, or as it was known then, Daimler-Benz. The immediate owners were Deutsche Bank with 28%, Mercedes Automobil Holding with 25%, and the Kuwait Government with 14%. The remaining 32% of the shares were widely held by about 300,000 individual and institutional investors. But this was only the top layer. Mercedes Automobil’s holding was half owned by holding companies “Stella” and “Stern,” for short. The rest of its shares were widely held. Stella’s shares were in turn split four ways: between two banks; Robert Bosch, an industrial company; and another holding company, “Komet.” Stern’s ownership was split five ways but we ran out of space.¹³

Panel b shows the ownership structure in 2012. It is quite different. Deutsche Bank does not have a direct stake anymore. The Kuwait government still owns a substantial stake of 7.4%, but considerably less than the 14% it owned in 1990. Aabar Investments owns 3.1%. Aabar is itself majority-owned by International Petroleum Investment Company, which is in turn majority-owned by the Abu Dhabi government. In addition, Renault and Nissan each own 1.5%. In stark contrast to the situation in 1990 when only 32% of the stock was widely held, in 2012 86% was widely held. The ownership structure has moved a long way toward the U.S. ownership pattern, where many large companies are entirely widely held.

An important reason for this dramatic change in ownership structure was a tax change that took effect in 2002. This exempted capital gains on shares held for more than one year from corporate taxation. Prior to that, the corporate capital gains rate had been 52%, which made selling shares very costly for corporations.

Daimler was not the only company to experience a significant drop in bank ownership. Dittman, Maug, and Schneider point out that average bank ownership of equity fell from 4.1% in 1994 to .4% in 2005. Board seats held by bank representatives fell from 9.6% to 5.6% of the total. Dittman, Maug, and Schneider’s evidence suggests that banks are now primarily interested in using their board representation to promote their lending and investment banking activities. However, the companies on whose boards the bankers sit appear to perform worse than similar companies without such a presence.¹⁴

Other countries in continental Europe, such as France and Italy, also have complex corporate ownership structures. These countries have not had a dramatic tax change like that in Germany. However, there has been a steady stream of regulatory changes that have mostly had the effect of making the legal framework for corporate governance more similar to that in the U.S.¹⁵

European Boards of Directors

Germany has a system of codetermination. Larger firms (generally firms with more than 2,000 employees) have two boards of directors: the supervisory board (Aufsichtsrat) and management board (Vorstand). Half of the supervisory board’s members are elected by employees, including management and staff as well as labor unions. The other half represents stockholders and often includes bank executives. There is also a chairman appointed by stockholders who can cast tie-breaking votes if necessary.

   FIGURE 33.5 (a) Ownership of Daimler-Benz, 1990. (b) Ownership of Daimler, 2012.

Sources: (a) J. Franks and C. Mayer, “The Ownership and Control of German Corporations,” Review of Financial Studies 14 (Winter 2001), Figure 1, p. 949. © 2001 Oxford University Press. Used with permission. (b) www.Daimler.com.

The supervisory board represents the interests of the company as a whole, not just the interests of employees or stockholders. It oversees strategy and elects and monitors the management board, which operates the company. Supervisory boards typically have about 20 members, more than typical U.S. and UK boards but smaller than Japanese boards. Management boards have about 10 members.

In France, firms can elect a single board of directors, as in the United States, United Kingdom, and Japan, or a two-tiered board, as in Germany. The single-tiered board, which is more common, consists mostly of outside directors, who are shareholders and representatives from financial institutions with which the firm has relationships. The two-board system has a conseil de surveillance, which resembles a German supervisory board, and a directoire, which is the management board. As far as employee representation is concerned, partially privatized firms and firms where employees own 3% or more of the shares are mandated to have employee-elected directors.

Shareholders versus Stakeholders

It is often suggested that companies should be managed on behalf of all stakeholders, not just shareholders. Other stakeholders include employees, customers, suppliers, and the communities where the firm’s plants and offices are located.

Different countries take very different views. In the U.S., UK, and other “Anglo-Saxon” economies, the idea of maximizing shareholder value is widely accepted as the chief financial goal of the firm.

In other countries, workers’ interests are put forward much more strongly. In Germany, for example, as discussed above, workers in large companies have the right to elect up to half of the directors to the companies’ supervisory boards. As a result they have a significant role in the governance of the firm and less attention is paid to the shareholders.¹⁶ In Japan managers usually put the interests of employees and customers on a par with, or even ahead of, the interests of shareholders.

Figure 33.6 summarizes the results of interviews with executives from large companies in five countries. Japanese, German, and French executives think that their firms should be run for all stakeholders, while U.S. and UK executives say that shareholders must come first. When asked about the trade-off between job security and dividends, most U.S. and UK executives believe dividends should come first. By contrast, almost all Japanese executives and the majority of French and German executives believe that job security should come first.

   FIGURE 33.6 (a) Whose company is it? The views of 378 managers from five countries.

(b) Which is more important—job security for employees or shareholder dividends? The views of 399 managers from five countries.

Source: M. Yoshimori, “Whose Company is it? The Concept of the Corporation in Japan and the West,” Long Range Planning 28 (August 1995), pp. 2–3, 33–44. Copyright © 1995 with permission from Elsevier Science.

As capital markets have become more global, companies in all countries face greater pressure to adopt wealth creation for shareholders as a primary goal. Some German companies, including Daimler and Deutsche Bank, have announced their primary goal as wealth creation for shareholders. In Japan there has also been some movement in this direction as the proportion of foreign ownership of corporations has significantly increased in recent years.

Ownership and Control in Other Countries

La Porta, Lopez-de-Silanes, and Shleifer surveyed corporate ownership in 27 developed economies.¹⁷ They found relatively few firms with actively traded shares and dispersed ownership. The pattern of significant ownership by banks and other financial institutions is also uncommon. Instead, firms are typically controlled by wealthy families or the state. The ultimate controlling shareholders typically have secure voting control even when they do not have the majority stake in earnings, dividends, or asset values.

Family control is common in Europe and also in Asia. Table 33.1 summarizes a study by Claessens, Djankov, and Lang, who traced ownership in 1996 for a sample of nearly 3,000 Asian companies. Except in Japan, a high proportion of public firms were family controlled. Thus wealthy families control large fractions of many Asian economies. For example, in Hong Kong, the 10 largest family groups control 32% of the assets of all listed firms. In Thailand, the top 10 families control 46% of assets. In Indonesia, they control nearly 58% of assets.¹⁸

   TABLE 33.1 Family control in Asia.

a“Control” means ownership of shares with at least 20% of voting rights. Percentages controlled by financial institutions or corporations are not reported.

bPercentage of total assets of all sample firms in each country.

Source: S. Claessens, S. Djankov, and L. H. P. Lang, “The Separation of Ownership and Control in East Asian Corporations,” Journal of Financial Economics 58 (October/November 2000), Table 6, p. 103, and Table 9, p. 108. © 2000, with permission from Elsevier.

Family control does not usually mean a direct majority stake in the public firm. Control is usually exercised by cross-shareholdings, pyramids, and dual-class shares. We have already discussed cross-holdings. Pyramids and dual-class shares need further explanation.

Pyramids Pyramids are common in Asian countries as well as several European countries.¹⁹ In a pyramid, control is exercised through a sequence of controlling positions in several layers of companies. The actual operating companies are at the bottom of the pyramid. Above each operating company is a first holding company, then a second one, then perhaps others still higher in the pyramid.²⁰ Consider a three-tier pyramid and a single operating company. Assume that 51% of the votes confer control at each tier. Suppose that the second holding company—the highest one in the pyramid—holds a 51% controlling stake in a lower holding company, which in turn holds a 51% controlling stake in the operating company. A 51% stake in the highest holding company is really only a 26% stake in the operating company (.51 × .51 = .26, or 26%). Thus an investor in the top holding company could control an operating company worth $100 million with an investment of only $26 million. By adding another layer, the required investment falls to .51 × 26 = $13 million.

Dual-Class Equity Another way to maintain control is to hold stock with extra voting rights. Extra votes can be attached to a special class of shares. For example, a firm’s Class A shares could have 10 votes and the Class B shares only 1. Dual-class equity occurs frequently in many countries, including Brazil, Canada, Denmark, Finland, Germany, Italy, Mexico, Norway, South Korea, Sweden, and Switzerland. Stocks with different voting rights also occur (but less frequently) in Australia, Chile, France, Hong Kong, South Africa, the United Kingdom, and the United States.²¹ For example, the Ford Motor Company is still controlled by the Ford family, who hold a special class of shares with 40% of the voting power. Many new technology companies, such as Google, Facebook, and Linkedln, have dual-class shares that give the founders a considerable degree of control.

As we briefly discussed in Chapter 14, there is a wide variation in the value of votes across countries. Table 33.2 shows Tatiana Nenova’s estimates of the value of controlling blocks in different countries, calculated as a fraction of firms’ market values. These values are calculated from the differences in prices between ordinary shares and shares with extra votes. The range of values is large. For example, the Scandinavian countries have uniformly low premiums for control. South Korea and Mexico have very high control premiums.

   TABLE 33.2 The value of control-block votes as a proportion of firm value.

Source: T. Nenova, “The Value of Corporate Voting Rights and Control: A Cross-Country Analysis,” Journal of Financial Economics 68 (June 2003), Table 4, p. 336. © 2003, with permission from Elsevier.

Why is shareholder control valuable? For two reasons, one positive and one negative. The controlling shareholder may maximize value by monitoring management and making sure that the firm pursues the best operating and investment strategies. On the other hand, a controlling shareholder may be tempted to capture value by extracting private benefits at other shareholders’ expense. In this case the control premium is really a discount on the shares with inferior voting rights, a discount reflecting the value that these shareholders cannot expect to receive.

Conglomerates Revisited

Of course there are also examples of U.S. companies that are controlled by families or by investors holding large blocks of stock. But in these cases control is exercised for a single firm, not a group of firms. Elsewhere in the world, and particularly in countries without fully developed financial markets, control extends to groups of firms in several different industries. These industrial groups are really conglomerates.

In Korea, for example, the 20 largest conglomerates own about 40% of the country’s total corporate assets. These chaebols are also strong exporters: names like Samsung and Hyundai are recognized worldwide. Conglomerates are also common in Latin America. One of the more successful, the Chilean holding company Quinenco, is a dizzying variety of businesses, including hotels and brewing, mobile telephone services, banking, and the manufacture of copper cable. Widely diversified groups are also common in India. The largest, the Tata Group, spans 80 companies in various industries, including steel, electric power, real estate, telecommunications, and financial services. All of these companies are public, but control rests with the group and ultimately with the Tata family.

The United States had a conglomerate merger wave in the 1960s and 1970s, but diversification didn’t deliver value in the longer run, and most of the conglomerates of that era have dissolved. But conglomerates survive and grow in developing economies. Why?

Family ownership is part of the answer. A wealthy family can reduce risk, while maintaining control and expanding the family business into new industries. Of course the family could also diversify by buying shares of other companies. But where financial markets are limited and investor protection is poor, internal diversification can beat out financial diversification. Internal diversification means running an internal capital market, but if a country’s financial markets and institutions are substandard, an internal capital market may not be so bad after all.

“Substandard” does not just mean lack of scale or trading activity. It may mean government regulations limiting access to bank financing or requiring government approval before bonds or shares are issued.²² It may mean poor information. If accounting standards are loose and companies are secretive, monitoring by outside investors becomes especially costly and difficult, and agency costs proliferate.

Internal diversification may also be the only practical way to grow. You can’t be big and focused in a small, closed economy, because the scale of one-industry companies is limited by the local market. Size can be an advantage if larger companies have easier access to international financial markets. This is important if local financial markets are inefficient.

Size also means political power, which is especially important in managed economies or in countries where the government economic policy is unpredictable. In Korea, for example, the government has controlled access to bank loans. Bank lending has been directed to government-approved uses. The Korean conglomerate chaebols have usually been first in line.

Many widely diversified business groups have been efficient and successful, particularly in countries like Korea that have grown rapidly. But there is also a dark side. Sometimes conglomerate business groups tunnel resources between the group companies at the expense of outside minority shareholders. Group company X can transfer value to Y by lending it money at a low interest rate, buying some of Y’s output at high prices or selling X’s assets to Y at low prices. Bertrand, Mehta, and Mullainathan found evidence of widespread tunneling in India.²³ Johnson, Boone, Breach, and Friedman note that the temptation to tunnel is stronger during a recession or financial crisis and argue that tunneling—and poor corporate governance in general—contributed to the Asian crisis of 1997–1998.²⁴

 33-3   Do These Differences Matter?

A good financial system appears to accelerate economic growth.²⁵ In fact, at least rudimentary finance may be necessary for any growth at all. Raghu Rajan and Luigi Zingales give the example of a bamboo-stool maker in Bangladesh, who needed 22 cents to buy the raw materials for each stool. Unfortunately, she did not have the 22 cents and had to borrow it from middlemen. She was forced to sell the stools back to the lenders in repayment for the loans and was left with only 2 cents’ profit. Because of a lack of finance, she was never able to break out of this cycle of poverty. In contrast, they give the example of Kevin Taweel and Jim Ellis, two Stanford MBAs, who were able to purchase their own business soon after graduating. They had insufficient capital of their own but were able to raise seed funding to search for the right acquisition, and then additional funding to complete it.²⁶ Taweel and Ellis were the beneficiaries of a modern financial system, including a sophisticated private-equity market.

It is easy to understand the connection between financial and economic development by considering a very simple financial decision. Suppose you need to decide whether to extend credit to a small business. If you are in the United States, you can almost instantaneously pull down a Dun and Bradstreet report via the Internet on any one of several million businesses. This report will show the company’s financial statements, the average size of its bank balances, and whether it pays its bills on time. You will also receive an overall credit score for the company. Such widely available credit information reduces the cost of lending and increases the availability of credit. It also means that no one lender has a monopoly of information, which increases competition among suppliers of credit and reduces the costs to borrowers. In contrast, good credit information is not readily available in most developing economies, and lenders to small businesses are both few and expensive.

Of course finance matters. But does the nature of a country’s financial system matter as long as it is advanced? Does it matter whether a developed country has a market-based or bank-based system? Both types are effective, but each has potential advantages.

Risk and Short-termism

If you look back to Figure 33.2, you will see that in different countries the amount of risk borne by households in their financial portfolios varies significantly. At one extreme is Japan, where households hold over half of their financial assets in bank accounts. Much of the remainder is in insurance and pension funds, which in Japan mainly make fixed payments and are not linked to the stock market. Only a small proportion of household portfolios are linked to the stock market and to the business risk of Japanese corporations. European households also have relatively little direct exposure to the risks of the corporate sector. At the other extreme, households in the United States have large investments in shares and mutual funds.

Of course someone has to bear business risks. The risks that are not borne directly by households are passed on to banks and other financial institutions, and finally to the government. In most countries, the government guarantees bank deposits either explicitly or implicitly. If the banks get into trouble, the government steps in and society as a whole bears the burden. This is what happened in the crisis of 2007–2009.²⁷

Some people argue that firms are free to “invest for the long run” in bank-based systems where financial institutions absorb business risks and few individuals invest directly in the stock market. The close ties of Japanese and German companies to banks are supposed to prevent the dreaded disease of short-termism. Firms in the United States and United Kingdom are supposedly held captive by shareholders’ demands for quick payoffs and therefore have to deliver quick earnings growth at the expense of long-term competitive advantage. Many found this argument persuasive in the late 1980s when the Japanese and German economies were especially robust.²⁸ When market-based economies surged ahead in the 1990s, views changed accordingly.

Growth Industries and Declining Industries

Market-based systems seem to be particularly successful in developing brand-new industries. For example, railways were first developed in the United Kingdom in the nineteenth century, financed largely through the London Stock Exchange. In the twentieth century, the United States led development of mass production in the automobile industry, even though the automobile was invented in Germany. The commercial aircraft industry was also mainly developed in the United States, as was the computer industry after World War II, and more recently the biotechnology and Internet industries.²⁹ On the other hand, Germany and Japan, two countries with bank-based financial systems, have sustained their competitive advantages in established industries, such as automobiles.

Why are financial markets better at fostering innovative industries?³⁰ When new products or processes are discovered, there is a wide diversity of opinion about the prospects for a new industry and the best way to develop it. Financial markets accommodate this diversity, allowing young, ambitious companies to search out like-minded investors to fund their growth. This is less likely when financing has to come through a few major banks.

Market-based systems also seem to be more effective at forcing companies in declining industries to shrink and release capital.³¹ When a company cannot earn its cost of capital and further growth would destroy value, stock price drops, and the drop sends a clear negative signal. But in bank-based financial systems, uneconomic firms are often bailed out. When Mazda faltered in the 1970s, Sumitomo Bank guaranteed Mazda’s debts and orchestrated a rescue, in part by exhorting employees within its keiretsu to purchase Mazda cars. Sumitomo Bank had an incentive to undertake the rescue, because it knew that it would keep Mazda’s business when it recovered. In the 1990s, Japanese banks continued to lend to “zombie” firms long after it became clear that prospects for their recovery were hopeless. For example, a coalition of banks kept the Japanese retailer Sogo afloat for years, despite clear evidence of insolvency. When Sogo finally failed in 2000, its debts had accumulated to ¥1.9 trillion.³²

Transparency and Governance

Despite all the advantages of market-based systems, serious accidents happen. Think of the many sudden, costly corporate meltdowns after the telecom and dot.com boom of the late 1990s. In the last chapter we noted the $100 billion bankruptcy of WorldCom (now reorganized as MCI). But the most notorious meltdown was Enron, which failed in late 2001.

Enron started as a gas pipeline company, but expanded rapidly into trading energy and commodities, and made large investments in electricity generation, broadband communications, and water companies. By the end of 2000, its total stock market value was about $60 billion. A year later, it was bankrupt. But that $60 billion wasn’t really lost when Enron failed, because most of that value wasn’t there in the first place. By late 2001, Enron was in many ways an empty shell. Its stock price was supported more by investors’ enthusiasm than by profitable operating businesses. The company had also accumulated large hidden debts. For example, Enron borrowed aggressively through special-purpose entities (SPEs). The SPE debts were not reported on its balance sheet, even though many of the SPEs did not meet the requirements for off-balance-sheet accounting. (The fall of Enron also brought down its accounting firm, Arthur Andersen.)

The bad news started to leak out in the last months of 2001. In October, Enron announced a $1 billion write-down of its water and broadband businesses. In November, it consolidated its SPEs retroactively, which increased the debt on its balance sheet by $658 million and reduced past earnings by $591 million.³³ Its public debt was downgraded to junk ratings on November 28 and on December 2 it filed for bankruptcy.

Enron demonstrated the importance of transparency in market-based financial systems. If a firm is transparent to outside investors—if the investors can see its true profitability and prospects—then problems will show up right away in a falling stock price. That in turn generates extra scrutiny from security analysts, bond rating agencies, and investors. It may also lead to a takeover.

With transparency, corporate troubles generally lead to corrective action. But the top management of a troubled opaque company may be able to maintain its stock price and postpone the discipline of the market. Market discipline caught up with Enron only a month or two before bankruptcy.

Opaqueness is not so dangerous in a bank-based system. Firms will have long-standing relationships with banks, which can monitor the firm closely and urge it to staunch losses or to cancel excessively risky strategies. But no financial system can avoid occasional corporate meltdowns.

Parmalat, the Italian food company, appeared to be a solidly profitable firm with good growth prospects. It had expanded around the world, and by 2003 was operating in 30 countries with 36,000 employees. It reported about €2 billion in debt but also claimed to hold large portfolios of cash and short-term liquid securities. But doubts about the company’s financial strength began to accumulate. On December 19, 2003, it was revealed that a €3.9 billion bank deposit reported by Parmalat had never existed. Parmalat’s stock price fell by 80% in two weeks, and it was placed in administration (the Italian bankruptcy process) on December 24. Investors learned later that Parmalat’s true debts exceeded €14 billion, that additional billions of euros of asset value had disappeared into a black hole, and that its sales and earnings had been overstated.

It’s nice to dream of a financial system that would completely protect investors against nasty surprises like Enron and Parmalat. Complete protection of investors is impossible, however. In fact, complete protection would be unwise and inefficient even if it were feasible. Why? Because outside investors cannot know everything that managers are doing or why they are doing it. Laws and regulations can specify what managers can’t do but can’t tell them what they should do. Therefore managers have to be given discretion to act in response to unanticipated problems and opportunities.

Once managers have discretion, they will consider their self-interest as well as investors’ interests. Agency problems are inevitable. The best a financial system can do is to protect investors reasonably well and to try to keep managers’ and investors’ interests congruent. We have discussed agency problems at several points in this book, but it won’t hurt to reiterate the mechanisms that keep these problems under control:

•  Laws and regulations that protect outside investors from self-dealing by insiders.

•  Disclosure requirements and accounting standards that keep public firms reasonably transparent.

•  Monitoring by banks and other financial intermediaries.

•  Monitoring by boards of directors.

•  The threat of takeover (although takeovers are very rare in some countries).

•  Compensation tied to earnings and stock price.

In this chapter we have stressed the importance of investor protection for the development of financial markets. But don’t assume that more protection for investors is always a good thing. A corporation is a kind of partnership between outside investors and the managers and employees who operate the firm. The managers and employees are investors too: they commit human capital instead of financial capital. A successful firm requires co-investment of human and financial capital. If you give the financial capital too much power, the human capital won’t show up—or if it does show up, it won’t be properly motivated.³⁴

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SUMMARY

It’s customary to distinguish market-based and bank-based financial systems. The United States has a market-based system, because it has large stock and bond markets. The United Kingdom also has a market-based system: its bond market is less important, but the UK stock market still plays a crucial role in corporate finance and governance. Germany and Japan have bank-based systems, because most debt financing comes from banks and these countries’ stock markets are less important.

Of course the simple distinction between banks and markets is far from the end of the story. For example:

•  UK households tend to hold shares indirectly, through equity-linked insurance and pensions. Direct investment in shares is much less common than in the United States.

•  Japanese households bear relatively little equity risk. Most of their savings goes into bank accounts and insurance policies.

•  In Europe, large blocks of a company’s stock are often held by other corporations.

•  In Japan, companies rely heavily on trade-credit financing, that is, on accounts payable to other companies.

In Japan and Germany, the role of banks goes beyond just lending money. The largest Japanese banks are the hubs of keiretsus, large, cooperative groups of firms. Each keiretsu is held together by long-standing ties to the main bank and by extensive cross-shareholdings within group companies. German banks also have traditionally had long-standing ties to their corporate customers (the hausbank system). The banks end up voting shares held for other investors.

Ownership of large, public corporations in the United States and United Kingdom is pretty simple: there is one class of shares, which trade actively, and ownership is dispersed. In Japan, there is usually one class of shares, but a significant fraction of the shares is locked up in cross-shareholdings within keiretsus, although this fraction has decreased since the mid-1990s. Japanese stockholders have little say in corporate governance. European stockholders likewise have little say, given the concentration of ownership by banks and other corporations.

In the United States and United Kingdom, the law puts shareholders’ interests first. Managers and boards of directors have a fiduciary duty to shareholders. But in Germany, the management board, which runs the business, answers to a supervisory board, which represents all employees as well as investors. The company as a whole is supposed to come first.

Outside the largest developed economies, a different pattern of ownership emerges. Groups of companies are controlled by families and sometimes by the state. Control is maintained by cross-shareholdings, pyramids, and issues of shares with extra voting rights to the controlling investors.

Wealthy families control large fractions of the corporate sector in many developing economies. These family groups operate as conglomerates. Conglomerates are a declining species in the United States, but a conglomerate’s internal capital market can make sense where financial markets and institutions are not well-developed. The conglomerates’ scale and scope may also provide political power, which can add value in countries where the government tries to manage the economy or where laws and regulations are enforced erratically.

Concentrated family control can be a good thing, if it is used to force managers to run a tight ship and focus on value-maximizing investments. But concentration of control can also open the door to tunneling of resources out of the firm at the expense of minority investors.

Protection for outside investors varies greatly around the world. Where protection is good, market-based systems flourish. These systems have certain advantages: they appear to foster innovation and to encourage the release of capital from declining industries. On the other hand, market-based systems may end up investing too much in trendy innovations, as the collapse of the dot.com and telecom boom has illustrated. Bank-based systems may be better-suited to established industries. These systems also help shield individuals from direct exposure to stock market risk.

Market-based systems work only when public firms are reasonably transparent to investors. When they are opaque, like Enron, occasional meltdowns can be expected. Bank-based financial systems may have an advantage in monitoring and controlling opaque firms. The banks have long-standing relationships with their corporate customers, and therefore have better information than outside investors.

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FURTHER READING

The following studies survey or compare financial systems:

F. Allen and D. Gale, Comparing Financial Systems (Cambridge, MA: MIT Press, 2000).

M. Aoki, G. Jackson, and H. Miyajima, Corporate Governance in Japan (Oxford: Oxford University Press, 2007).

J. P. Krahnen and R. H. Schmidt (eds.), The German Financial System (Oxford: Oxford University Press, 2004).

R. La Porta, F. Lopez-de-Silanes, and A. Shleifer, “Corporate Ownership around the World,” Journal of Finance 54 (April 1999), pp. 471–517.

For excellent discussions of corporate governance, see:

M. Becht, P. Bolton, and A. Röell, “Corporate Governance and Control” in G. Constantinides, M. Harris, and R. Stulz (eds.), Handbook of the Economics of Finance (Amsterdam: North-Holland, 2003), pp. 1–109.

R. Morck and B. Yeung, “Never Waste a Good Crisis: An Historical Perspective on Comparative Corporate Governance,” Annual Review of Financial Economics 1 (2009), pp. 145–179.

A. Shleifer and R. W. Vishny, “A Survey of Corporate Governance,” Journal of Finance 52 (June 1997), pp. 737–783.

For discussions of the role of law, politics, and finance see:

R. LaPorta, F. Lopez-de-Silanes, and A. Shleifer, “The Economic Consequences of Legal Origins,” Journal of Economic Literature 46 (2008), pp. 285–332.

R. Rajan and L. Zingales, Saving Capitalism from the Capitalists (New York: Crown Business, 2003).

For the evidence on why finance matters for growth, see:

R. Levine, “Financial Development and Economic Growth: Views and Agenda,” Journal of Economic Literature 35 (1997), pp. 688–726.

R. Rajan and L. Zingales, “Financial Dependence and Growth,” American Economic Review 88 (June 1998), pp. 559–586.

Finally, if you’d like to read about corporate governance gone wrong . . .

P. Healy and K. Palepu, “The Fall of Enron,” Journal of Economic Perspectives 17 (Spring 2003), pp. 3–26.

S. Johnson, R. La Porta, F. Lopez-de-Silanes, and A. Shleifer, “Tunneling,” American Economic Review 90 (May 2000), pp. 22–27.

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PROBLEM SETS

Select problems are available in McGraw-Hill’s Connect Finance. Please see the preface for more information.

BASIC

1.  Financial system structure Which countries have

a.  The largest stock markets?

b.  The largest bond markets?

c.  The smallest direct holdings of shares by individual investors?

d.  The largest holdings of bank deposits by individual investors?

e.  The largest holdings of shares by other corporations?

f.  The largest use of trade credit for financing?

In each case, define “largest” or “smallest” as total value relative to GDP.

2.  Financial system structure What is a keiretsu? Give a brief description.

3.  Corporate governance Do Japanese investors play an important role in corporate financial policy and governance? If not, could they?

4.  Corporate governance German banks often control a large fraction of the shareholder votes for German businesses. How do they get that voting power?

5.  Corporate governance What is meant by the German system of codetermination?

6.  Ownership form What is the most common form of ownership of corporations worldwide?

7.  Pyramids Suppose that a shareholder can gain effective control of a company with 30% of the shares. Explain how a shareholder might gain control of company Z by setting up a holding company X2 that holds shares in a second holding company X, which in turn holds shares in Z.

8.  Real effects of financial systems Why may market-based financial systems be better in supporting innovation and in releasing capital from declining industries?

9.  Corporate governance What is tunneling? Why does the threat of tunneling impede the development of financial markets?

INTERMEDIATE

10.  Corporate governance Agency problems are inevitable. That is, we can never expect managers to give 100% weight to shareholders’ interests and none to their own.

a.  Why not?

b.  List the mechanisms that are used around the world to keep agency problems under control.

11.  Finance by intermediaries Banks are not the only financial intermediary from which corporations can obtain financing. What are the other intermediaries? How much financing do they supply, relative to banks, in the United Kingdom, Germany, and Japan?

12.  Corporate governance Why is transparency important in a market-based financial system? Why is it less important in a bank-based system?

13.  Corporate governance What is meant by dual-class equity? Do you think it should be allowed or outlawed?

14.  Financial system structure What kind of industries do you think should thrive in a market-based financial system? In a bank-based system?

15.  Pyramids Why are pyramids common in many countries but not in the United States or United Kingdom?

16.  Financial system structure What are some of the advantages and disadvantages of Japanese keiretsus?

17.  Corporate governance “Globalization” means, among other things, more international trade, more direct competition among companies in different countries, and more multinational companies. Do you think that globalization will lead to a convergence in systems of corporate governance? Or do you think that international differences in corporate governance are “baked in” by history and differences in legal and financial systems? For a start in thinking about these questions, take a look at the following:

R. Morck, ed., A History of Corporate Governance around the World, University of Chicago Press, 2005.

T. Khanna, J. Kogan and K. Palepu, “Globalization and Similarities in Corporate Governance: A Cross-Country Analysis,” Review of Economics and Statistics 88 (February 2006), pp. 69–90.

___________

¹For more detailed data and discussion of the material in this section, see F. Allen, M. Chui, and A. Maddaloni, “Financial Structure and Corporate Governance in Europe, the USA, and Asia,” in Handbook of European Financial Markets and Institutions, ed. X. Freixas, P. Hartmann, and C. Mayer (Oxford: Oxford University Press, 2008), pp. 31–67.

²Emerging Asia here includes China, Hong Kong SAR, India, Indonesia, Korea, Malaysia, Philippines, Singapore, Taiwan-China, and Thailand.

³Europe here includes Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Slovenia, and Spain.

⁴Data for Asia are not available for this and the following figures that summarize portfolio allocations.

⁵There may be owners not yet present on this planet, however. For example, endowments of educational, charitable, and religious organizations are partly held in trust for future generations.

⁶R. La Porta, F. Lopez-de-Silanes, A. Shleifer, and R. Vishny, “Legal Determinants of External Finance,” Journal of Finance 52 (July 1997), pp. 1131–1150, and “Law and Finance,” Journal of Political Economy 106 (December 1998), pp. 1113–1155.

⁷R. Rajan and L. Zingales, Saving Capitalism from the Capitalists (New York: Crown Business, 2003).

⁸Subsequently it appeared that Henry Ford reneged on the dividend so that he could purchase blocks of shares at depressed prices!

⁹T. Hoshi, A. Kashyap, and D. Scharfstein, “Corporate Structure, Liquidity and Investment: Evidence from Japanese Industrial Groups,” Quarterly Journal of Economics 106 (February 1991), pp. 33–60, and “The Role of Banks in Reducing the Costs of Financial Distress in Japan,” Journal of Financial Economics 27 (September 1990), pp. 67–88.

¹⁰These requirements have led to a unique feature of Japanese corporate life, the sokaiya, who are racketeers who demand payment in exchange for not disrupting shareholders’ meetings.

¹¹In recent years some Japanese companies such as Sony have changed to U.S.-style boards with fewer members and more independent directors.

¹²See H. Miyajima and F. Kuroki, “The Unwinding of Cross-Shareholding in Japan: Causes, Effects and Implications,” in Corporate Governance in Japan: Institutional Change and Organizational Diversity, ed. M. Aoki, G. Jackson, and H. Miyajima (Oxford and New York: Oxford University Press, 2007), pp. 79–124. Also see “Criss-Crossed Capitalism,” The Economist print edition, November 6, 2008.

¹³A five-layer ownership tree for Daimler-Benz is given in S. Prowse, “Corporate Governance in an International Perspective: A Survey of Corporate Control Mechanisms among Large Firms in the U.S., UK, Japan and Germany,” Financial Markets, Institutions, and Instruments 4 (February 1995), Table 16.

¹⁴See I. Dittmann, E. Maug, and C. Schneider, “Bankers on the Boards of German Firms: What They Do, What They Are Worth, and Why They Are (Still) There,” Review of Finance, 14 (2010), pp. 35–71.

¹⁵See L. Enriques and P. Volpin, “Corporate Governance Reforms in Continental Europe,” Journal of Economic Perspectives 21 (2007), pp. 117–140.

¹⁶The following quote from the German banker Carl Fürstenberg (1850–1933) offers an extreme version of how shareholders were once regarded by German managers: “Shareholders are stupid and impertinent—stupid because they give their money to somebody else without any effective control over what this person is doing with it and impertinent because they ask for a dividend as a reward for their stupidity.” Quoted by M. Hellwig, “On the Economics and Politics of Corporate Finance and Corporate Control,” in Corporate Governance, ed. X. Vives (Cambridge, UK: Cambridge University Press, 2000), p. 109.

¹⁷R. La Porta, F. Lopez-de-Silanes, and A. Shleifer, “Corporate Ownership around the World,” Journal of Finance 54 (1999), pp. 471–517.

¹⁸The largest company in the world, Saudi Aramco oil company, is entirely owned by the Saudi royal family.

¹⁹L . A. Bebchuk, R. Kraakman, and G. R. Triantis, “Stock Pyramids, Cross-Ownership, and Dual Class Equity,” in Concentrated Corporate Ownership, ed. R. Morck (Chicago: University of Chicago Press, 2000), pp. 295–318.

²⁰A holding company is a firm whose only assets are controlling blocks of shares in other companies.

²¹Dual-class equity is forbidden in Belgium, China, Japan, Singapore, and Spain.

²²In the United States, the SEC does not have the power to deny share issues. Its mandate is only to assure that investors are given adequate information.

²³M. Bertrand, P. Mehta, and S. Mullainathan, “Ferreting out Tunneling: An Application to Indian Business Groups,” Quarterly Journal of Economics 117 (February 2002), pp. 121–148.

²⁴S. Johnson, P. Boone, A. Breach, and E. Friedman, “Corporate Governance in the Asian Financial Crisis,” Journal of Financial Economics 58 (October/November 2000), pp. 141–186.

²⁵R. Levine, “Financial Development and Economic Growth: Views and Agenda,” Journal of Economic Literature 35 (1997), pp. 688–726; and R. Rajan and L. Zingales, “Financial Dependence and Growth,” American Economic Review 88 (1998), pp. 559–586.

²⁶R. Rajan and L. Zingales, Saving Capitalism from the Capitalists (New York: Crown Business, 2003), pp. 4–8.

²⁷Another possibility is that banks that take a long-run view and are not subject to intense competition can smooth risk across different generations by building up reserves when returns are high and running them down when returns are low. Competition from financial markets prevents this type of intergenerational risk sharing. Generations with high returns want to receive their full returns and will not be willing to have reserves built up. See F. Allen and D. Gale, “Financial Markets, Intermediaries, and Intertemporal Smoothing,” Journal of Political Economy 105 (June 1997), pp. 523–546.

²⁸See M. Porter, “Capital Disadvantage: America’s Failing Capital Investment System,” Harvard Business Review, September/October 1992, pp. 65–82.

²⁹There are counterexamples, such as the development of the chemical industry on a large scale in nineteenth-century Germany.

³⁰See F. Allen and D. Gale, “Diversity of Opinion and the Financing of New Technologies,” Journal of Financial Intermediation 8 (April 1999), pp. 68–89.

³¹See R. Rajan and L. Zingales, “Banks and Markets: The Changing Character of European Finance,” in V. Gaspar, P. Hartmann, O. Sleijpen (eds.), The Transformation of the European Financial System, Second ECB Central Banking Conference, October 2002, Frankfurt, Germany (Frankfurt: European Central Bank, 2003), pp. 123–167.

³²T. Hoshi and A. Kashyap, “Japan’s Financial Crisis and Economic Stagnation,” Journal of Economic Perspectives 18 (Winter 2004), pp. 3–26.

³³Enron faced many further financial problems. For example, it told investors that it had hedged business risks in SPE transactions, but failed to say that many of the SPEs were backed up by pledges of Enron shares. When Enron’s stock price fell, the hedges unraveled. See P. Healy and K. Palepu, “The Fall of Enron,” Journal of Economic Perspectives 17 (Spring 2003), pp. 3–26.

³⁴It is difficult to observe effort and the value of human capital, and therefore difficult to set up compensation schemes that reward effort and human capital appropriately. Thus it can be better to allow managers some leeway to act in their own interests to preserve their incentives. Stockholders can provide this leeway by relaxing some of their rights and committing not to interfere if managers and employees capture private benefits when the firm is successful. How to commit? One way is to take the firm public. Direct intervention by public stockholders in the operation of the firm is difficult and therefore rare. See M. Burkart, D. Gromb, and F. Panunzi, “Large Shareholders, Monitoring and the Value of the Firm,” Quarterly Journal of Economics 112 (1997), pp. 693–728; S. C. Myers, “Outside Equity,” Journal of Finance 55 (June 2000), pp. 1005–1037; and S. C. Myers, “Financial Architecture,” European Financial Management 5 (July 1999), pp. 133–142.

Part 11 Conclusion

Conclusion: What We Do and Do Not Know about Finance

It is time to sign off. Let us finish by thinking about some of the things that we do and do not know about finance.

 34-1   What We Do Know: The Seven Most Important Ideas in Finance

What would you say if you were asked to name the seven most important ideas in finance? Here is our list.

1. Net Present Value

When you wish to know the value of a used car, you look at prices in the secondhand car market. Similarly, when you wish to know the value of a future cash flow, you look at prices quoted in the capital markets, where claims to future cash flows are traded (remember, those highly paid investment bankers are just secondhand cash-flow dealers). If you can buy cash flows for your shareholders at a cheaper price than they would have to pay in the capital market, you have increased the value of their investment.

This is the simple idea behind net present value (NPV). When we calculate an investment project’s NPV, we are asking whether the project is worth more than it costs. We are estimating its value by calculating what its cash flows would be worth if a claim on them were offered separately to investors and traded in the capital markets.

That is why we calculate NPV by discounting future cash flows at the opportunity cost of capital—that is, at the expected rate of return offered by securities having the same degree of risk as the project. In well-functioning capital markets, all equivalent-risk assets are priced to offer the same expected return. By discounting at the opportunity cost of capital, we calculate the price at which investors in the project could expect to earn that rate of return.

Like most good ideas, the net present value rule is “obvious when you think about it.” But notice what an important idea it is. The NPV rule allows thousands of shareholders, who may have vastly different levels of wealth and attitudes toward risk, to participate in the same enterprise and to delegate its operation to a professional manager. They give the manager one simple instruction: “Maximize net present value.”

2. The Capital Asset Pricing Model

Some people say that modern finance is all about the capital asset pricing model. That’s nonsense. If the capital asset pricing model had never been invented, our advice to financial managers would be essentially the same. The attraction of the model is that it gives us a manageable way of thinking about the required return on a risky investment.

Again, it is an attractively simple idea. There are two kinds of risk: risks that you can diversify away and those that you can’t. You can measure the nondiversifiable, or market, risk of an investment by the extent to which the value of the investment is affected by a change in the aggregate value of all the assets in the economy. This is called the beta of the investment. The only risks that people care about are the ones that they can’t get rid of—the nondiversifiable ones. This is why the required return on an asset increases in line with its beta.

Many people are worried by some of the rather strong assumptions behind the capital asset pricing model, or they are concerned about the difficulties of estimating a project’s beta. They are right to be worried about these things. In 10 or 20 years’ time we may have much better theories than we do now. But we will be extremely surprised if those future theories do not still insist on the crucial distinction between diversifiable and nondiversifiable risks—and that, after all, is the main idea underlying the capital asset pricing model.

3. Efficient Capital Markets

The third fundamental idea is that security prices accurately reflect available information and respond rapidly to new information as soon as it becomes available. This efficient-market theory comes in three flavors, corresponding to different definitions of “available information.” The weak form (or random-walk theory) says that prices reflect all the information in past prices. The semistrong form says that prices reflect all publicly available information, and the strong form holds that prices reflect all acquirable information.

Don’t misunderstand the efficient-market idea. It doesn’t say that there are no taxes or costs; it doesn’t say that there aren’t some clever people and some stupid ones. It merely implies that competition in capital markets is very tough—there are no money machines or arbitrage opportunities, and security prices reflect the true underlying values of assets.

Extensive empirical testing of the efficient-market hypothesis began around 1970. By 2012, after more than 40 years of work, the tests have uncovered dozens of statistically significant anomalies. Sorry, but this work does not translate into dozens of ways to make easy money. Superior returns are elusive. For example, only a few mutual fund managers can generate superior returns for a few years in a row, and then only in small amounts.¹ Statisticians can beat the market, but real investors have a much harder time of it.

4. Value Additivity and the Law of Conservation of Value

The principle of value additivity states that the value of the whole is equal to the sum of the values of the parts. It is sometimes called the law of the conservation of value.

When we appraise a project that produces a succession of cash flows, we always assume that values add up. In other words, we assume

We similarly assume that the sum of the present values of projects A and B equals the present value of a composite project AB.² But value additivity also means that you can’t increase value by putting two whole companies together unless you thereby increase the total cash flow. In other words, there are no benefits to mergers solely for diversification.

5. Capital Structure Theory

If the law of the conservation of value works when you add up cash flows, it must also work when you subtract them.³ Therefore, financing decisions that simply divide up operating cash flows don’t increase overall firm value. This is the basic idea behind Modigliani and Miller’s famous proposition 1: In perfect markets changes in capital structure do not affect value. As long as the total cash flow generated by the firm’s assets is unchanged by capital structure, value is independent of capital structure. The value of the whole pie does not depend on how it is sliced.

Of course, MM’s proposition is not The Answer, but it does tell us where to look for reasons why capital structure decisions may matter. Taxes are one possibility. Debt provides a corporate interest tax shield, and this tax shield may more than compensate for any extra personal tax that the investor has to pay on debt interest. Also, high debt levels may spur managers to work harder and to run a tighter ship. But debt has its drawbacks if it leads to costly financial distress.

6. Option Theory

In everyday conversation we often use the word “option” as synonymous with “choice” or “alternative”; thus we speak of someone as “having a number of options.” In finance option refers specifically to the opportunity to trade in the future on terms that are fixed today. Smart managers know that it is often worth paying today for the option to buy or sell an asset tomorrow.

Since options are so important, the financial manager needs to know how to value them. Finance experts always knew the relevant variables—the exercise price and the exercise date of the option, the risk of the underlying asset, and the rate of interest. But it was Black and Scholes who first showed how these can be put together in a usable formula.

The Black–Scholes formula was developed for simple call options and does not directly apply to the more complicated options often encountered in corporate finance. But Black and Scholes’s most basic ideas—for example, the risk-neutral valuation method implied by their formula—work even where the formula doesn’t. Valuing the real options described in Chapter 22 may require extra number crunching but no extra concepts.

7. Agency Theory

A modern corporation is a team effort involving a number of players, such as managers, employees, shareholders, and bondholders. For a long time economists used to assume without question that all these players acted for the common good, but in the last 30 years they have had a lot more to say about the possible conflicts of interest and how companies attempt to overcome such conflicts. These ideas are known collectively as agency theory.

Consider, for example, the relationship between the shareholders and the managers. The shareholders (the principals) want managers (their agents) to maximize firm value. In the United States the ownership of many major corporations is widely dispersed and no single shareholder can check on the managers or reprimand those who are slacking. So, to encourage managers to pull their weight, firms seek to tie the managers’ compensation to the value that they have added. For those managers who persistently neglect shareholders’ interests, there is the threat that their firm will be taken over and they will be turfed out.

Some corporations are owned by a few major shareholders and therefore there is less distance between ownership and control. For example, the families, companies, and banks that hold or control large stakes in many German companies can review top management’s plans and decisions as insiders. In most cases they have the power to force changes as necessary. However, hostile takeovers in Germany are rare.

We discussed the problems of management incentives and corporate control in Chapters 12, 14, 32, and 33, but they were not the only places in the book where agency issues arose. For example, in Chapters 18 and 24 we looked at some of the conflicts that arise between shareholders and bondholders, and we described how loan agreements try to anticipate and minimize these conflicts.

Are these seven ideas exciting theories or plain common sense? Call them what you will, they are basic to the financial manager’s job. If by reading this book you really understand these ideas and know how to apply them, you have learned a great deal.

 34-2   What We Do Not Know: 10 Unsolved Problems in Finance

Since the unknown is never exhausted, the list of what we do not know about finance could go on forever. But, following Brealey, Myers, and Allen’s Third Law (see Section 29-5), we list and briefly discuss 10 unsolved problems that seem ripe for productive research.

1. What Determines Project Risk and Present Value?

A good capital investment is one that has a positive NPV. We have talked at some length about how to calculate NPV, but we have given you very little guidance about how to find positive-NPV projects, except to say in Section 11-2 that projects have positive NPVs when the firm can earn economic rents. But why do some companies earn economic rents while others in the same industry do not? Are the rents merely windfall gains, or can they be anticipated and planned for? What is their source, and how long do they persist before competition destroys them? Very little is known about any of these important questions.

Here is a related question: Why are some real assets risky and others relatively safe? In Section 9-3 we suggested a few reasons for differences in project betas—differences in operating leverage, for example, or in the extent to which a project’s cash flows respond to the performance of the national economy. These are useful clues, but we have as yet no general procedure for estimating project betas. Assessing project risk is therefore still largely a seat-of-the-pants matter.

2. Risk and Return—What Have We Missed?

In 1848 John Stuart Mill wrote, “Happily there is nothing in the laws of value which remains for the present or any future writer to clear up; the theory is complete.” Economists today are not so sure about that. For example, the capital asset pricing model is an enormous step toward understanding the effect of risk on the value of an asset, but there are many puzzles left, some statistical and some theoretical.

The statistical problems arise because the capital asset pricing model is hard to prove or disprove conclusively. It appears that average returns from low-beta stocks are too high (that is, higher than the capital asset pricing model predicts) and that those from high-beta stocks are too low; but this could be a problem with the way that the tests are conducted and not with the model itself.⁴ We also described the puzzling discovery by Fama and French that expected returns appear to be related to the firm’s size and to the ratio of the book value of the stock to its market value. Nobody understands why this should be so; perhaps these variables are related to variable x, that mysterious second risk variable that investors may rationally take into account in pricing shares.⁵

Meanwhile scholars toil on the theoretical front. We discussed some of their work in Section 8-4. But just for fun, here is another example: Suppose that you love fine wine. It may make sense for you to buy shares in a grand cru chateau, even if doing so soaks up a large fraction of your personal wealth and leaves you with a relatively undiversified portfolio. However, you are hedged against a rise in the price of fine wine: Your hobby will cost you more in a bull market for wine, but your stake in the chateau will make you correspondingly richer. Thus you are holding a relatively undiversified portfolio for a good reason. We would not expect you to demand a premium for bearing that portfolio’s undiversifiable risk.

In general, if two people have different tastes, it may make sense for them to hold different portfolios. You may hedge your consumption needs with an investment in wine making, whereas somebody else may do better to invest in a chain of ice cream parlors. The capital asset pricing model isn’t rich enough to deal with such a world. It assumes that all investors have similar tastes: The hedging motive does not enter, and therefore they hold the same portfolio of risky assets.

Merton has extended the capital asset pricing model to accommodate the hedging motive.⁶ If enough investors are attempting to hedge against the same thing, the model implies a more complicated risk–return relationship. However, it is not yet clear who is hedging against what, and so the model remains difficult to test.

So the capital asset pricing model survives not from a lack of competition but from a surfeit. There are too many plausible alternative risk measures, and so far no consensus exists on the right course to plot if we abandon beta.

In the meantime we must recognize the capital asset pricing model for what it is: an incomplete but extremely useful way of linking risk and return. Recognize too that the model’s most basic message, that diversifiable risk doesn’t matter, is accepted by nearly everyone.

3. How Important Are the Exceptions to the Efficient-Market Theory?

The efficient-market theory is strong, but no theory is perfect; there must be exceptions.

Now some of the apparent exceptions could simply be coincidences, for the more that researchers study stock performance, the more strange coincidences they are likely to find. For example, there is evidence that daily returns around new moons have been roughly double those around full moons.⁷ It seems difficult to believe that this is anything other than a chance relationship—fun to read about but not a concern for serious investors or financial managers. But not all exceptions can be dismissed so easily. We saw that the stocks of firms that announce unexpectedly good earnings continue to perform well for a couple of months after the announcement date. Some scholars believe that this may mean that the stock market is inefficient and investors have consistently been slow to react to earnings announcements. Of course, we can’t expect investors never to make mistakes. If they have been slow to react in the past, perhaps they will learn from this mistake and price the stocks more efficiently in the future.

Some researchers believe that the efficient-market hypothesis ignores important aspects of human behavior. For example, psychologists find that people tend to place too much emphasis on recent events when they are predicting the future. If so, we may find that investors are liable to overreact to new information. It will be interesting to see how far such behavioral observations can help us to understand apparent anomalies.

During the dot.com boom of the late 1990s stock prices rose to astronomic levels. The Nasdaq Composite Index rose 580% from the beginning of 1995 to its peak in March 2000 and then fell by nearly 80%. Such gyrations were not confined to the United States. For example, stock prices on Germany’s Neuer Markt rose 1,600% in the three years from its foundation in 1997, before falling by 95% by October 2002.

This is not the only occasion that asset prices have reached unsustainable levels. In the late 1980s there was a surge in the prices of Japanese stock and real estate. In 1989 at the peak of the real estate boom, choice properties in Tokyo’s Ginza district were selling for about $1 million a square foot. Over the next 17 years Japanese real estate prices fell by 70%.⁸

Maybe such extreme price movements can be explained by standard valuation techniques. However, others argue that stock prices are liable to speculative bubbles, where investors are caught up in a scatty whirl of irrational exuberance.⁹ Now that may be true of your Uncle Harry or Aunt Hetty, but why don’t hard-headed professional investors bail out of the overpriced stocks? Perhaps they would do so if it was their money at stake, but maybe there is an agency problem that stems from the way that their performance is measured and rewarded that encourages them to run with the herd.¹⁰ (Remember the remark by the CEO of Citigroup: “As long as the music is playing, you’ve got to get up and dance.”)

These are important questions. Much more research is needed before we have a full understanding of why asset prices sometimes get so out of line with what appears to be their discounted future payoffs.

4. Is Management an Off-Balance-Sheet Liability?

Closed-end funds are firms whose only asset is a portfolio of common stocks. One might think that if you knew the value of these common stocks, you would also know the value of the firm. However, this is not the case. The stock of the closed-end fund often sells for substantially less than the value of the fund’s portfolio.¹¹

All this might not matter much except that it could be just the tip of the iceberg. For example, real estate stocks appear to sell for less than the market values of the firms’ net assets. In the late 1970s and early 1980s the market values of many large oil companies were less than the market values of their oil reserves. Analysts joked that you could buy oil cheaper on Wall Street than in West Texas.

All these are special cases in which it was possible to compare the market value of the whole firm with the values of its separate assets. But perhaps if we could observe the values of other firms’ separate parts, we might find that the value of the whole was often less than the sum of the values of the parts.

Whenever firms calculate the net present value of a project, they implicitly assume that the value of the whole project is simply the sum of the values of all the years’ cash flows. We referred to this earlier as the law of the conservation of value. If we cannot rely on that law, the tip of the iceberg could turn out to be a hot potato.

We don’t understand why closed-end investment companies or any of the other firms sell at a discount on the market values of their assets. One explanation is that the value added by the firm’s management is less than the cost of the management. That is why we suggest that management may be an off-balance-sheet liability. For example, the discount of oil company shares from oil-in-the-ground value can be explained if investors expected the profits from oil production to be frittered away in negative-NPV investments and bureaucratic excess. The present value of growth opportunities (PVGO) was negative!

We do not mean to portray managers as leeches soaking up cash flows meant for investors. Managers commit their human capital to the firm and rightfully expect a reasonable cash return on these personal investments. If investors extract too great a share of the firm’s cash flow, the personal investments are discouraged, and the long-run health and growth of the firm can be damaged.

In most firms, managers and employees co-invest with stockholders and creditors—human capital from the insiders and financial capital from outside investors. So far we know very little about how this co-investment works.

5. How Can We Explain the Success of New Securities and New Markets?

In the last 40 years companies and the securities exchanges have created an enormous number of new securities: options, futures, options on futures; zero-coupon bonds, floating-rate bonds; bonds with collars and caps, asset-backed bonds; catastrophe bonds, . . . the list is endless. In some cases, it is easy to explain the success of new markets or securities; perhaps they allow investors to insure themselves against new risks or they result from a change in tax or in regulation. Sometimes a market develops because of a change in the costs of issuing or trading different securities. But there are many successful innovations that cannot be explained so easily. Why do investment bankers continue to invent, and successfully sell, complex new securities that outstrip our ability to value them? The truth is we don’t understand why some innovations in markets succeed and others never get off the ground.

And then there are the innovations that do get off the ground but crash later, including many of the complex and over-rated securities backed by subprime mortgages. Subprime mortgages are not intrinsically bad, of course: they may be the only route to home ownership for some worthy people. But subprime loans also put many homeowners in nasty traps when house prices fell and jobs were lost. Securities based on subprime mortgages caused enormous losses in the banking industry. A number of new securities and derivatives went out of favor during the crisis. It will be interesting to see which will remain permanently consigned to the dustbin, and which will be dusted off and recover their usefulness.

6. How Can We Resolve the Payout Controversy?

We spent all of Chapter 16 on payout policy without being able to resolve the payout controversy. Many people believe dividends are good; others point out that dividends attract more tax and therefore it is better for firms to repurchase stock; and still others believe that, as long as the firm’s investment decisions are unaffected, the payout decision is irrelevant.

Perhaps the problem is that we are asking the wrong question. Instead of inquiring whether dividends are good or bad, perhaps we should be asking when it makes sense to pay high or low dividends. For example, investors in mature firms with few investment opportunities may welcome the financial discipline imposed by a high dividend payout. For younger firms or firms with a temporary cash surplus, the tax advantage of stock repurchase may be more influential. But we don’t know enough yet about how payout policy should vary from firm to firm.

The way that companies distribute cash has been changing. An increasing number of companies do not pay any dividends, while the volume of stock repurchases has mushroomed. This may partly reflect the growth in the proportion of small high-growth firms with lots of investment opportunities, but this does not appear to be the complete explanation. Understanding these shifts in company payout policy may also help us to understand how that policy affects firm value.

7. What Risks Should a Firm Take?

Financial managers end up managing risk. For example,

•  When a firm expands production, managers often reduce the cost of failure by building in the option to alter the product mix or to bail out of the project altogether.

•  By reducing the firm’s borrowing, managers can spread operating risks over a larger equity base.

•  Most businesses take out insurance against a variety of specific hazards.

•  Managers often use futures or other derivatives to protect against adverse movements in commodity prices, interest rates, and exchange rates.

All these actions reduce risk. But less risk can’t always be better. The point of risk management is not to reduce risk but to add value. We wish we could give general guidance on what bets the firm should place and what the appropriate level of risk is.

In practice, risk management decisions interact in complicated ways. For example, firms that are hedged against commodity price fluctuations may be able to afford more debt than those that are not hedged. Hedging can make sense if it allows the firm to take greater advantage of interest tax shields, provided the costs of hedging are sufficiently low.

How can a company set a risk management strategy that adds up to a sensible whole?

8. What Is the Value of Liquidity?

Unlike Treasury bills, cash pays no interest. On the other hand, cash provides more liquidity than Treasury bills. People who hold cash must believe that this additional liquidity offsets the loss of interest. In equilibrium, the marginal value of the additional liquidity must equal the interest rate on bills.

Now what can we say about corporate holdings of cash? It is wrong to ignore the liquidity gain and to say that the cost of holding cash is the lost interest. This would imply that cash always has a negative NPV. It is equally foolish to say that, because the marginal value of liquidity is equal to the loss of interest, it doesn’t matter how much cash the firm holds. This would imply that cash always has a zero NPV. We know that the marginal value of cash to a holder declines with the size of the cash holding, but we don’t really understand how to value the liquidity service of cash and therefore we can’t say how much cash is enough or how readily the firm should be able to raise it. To complicate matters further, we note that cash can be raised on short notice by borrowing, or by issuing other new securities, as well as by selling assets. The financial manager with a $100 million unused line of credit may sleep just as soundly as one whose firm holds $100 million in marketable securities. In our chapters on working-capital management we largely finessed these questions by presenting models that are really too simple or by speaking vaguely of the need to ensure an “adequate” liquidity reserve.

A better knowledge of liquidity would also help us to understand better how corporate bonds are priced. We already know part of the reason that corporate bonds sell for lower prices than Treasury bonds—companies in distress have the option to walk away from their debts. However, the differences between the prices of corporate bonds and Treasury bonds are too large to be explained just by the company’s default option. It seems likely that the price difference is partly due to the fact that corporate bonds are less liquid than Treasury bonds. But until we know how to price differences in liquidity, we can’t really say much more than this.

Here is another problem. You are a partner in a private-equity firm contemplating a major new investment. You have a forecast of the future cash flows and an estimate of the return that investors would require from the business if it were a publicly traded company. But how much extra return do you need to compensate for the fact that the stock cannot be traded? An addition of 1 or 2 percentage points to the discount rate can make a huge difference to the estimated value.

The crisis of 2007–2009 has again demonstrated that investors seem to value liquidity much more highly at some times than at others. Despite massive injections of liquidity by central banks, many financial markets effectively dried up. For example, banks became increasingly reluctant to lend to one another on an unsecured basis, and would do so only at a large premium. In the spring of 2007 the spread between LIBOR and the interest rate on Treasury bills (the TED spread) was .4%. By October 2008 the market for unsecured lending between banks had largely disappeared and LIBOR was being quoted at more than 4.6% above the Treasury bill rate.¹²

Financial markets work well most of the time, but we don’t understand well why they sometimes shut down or clog up, and we can offer relatively little advice to managers as to how to respond.

9. How Can We Explain Merger Waves?

Of course there are many plausible motives for merging. If you single out a particular merger, it is usually possible to think up a reason why that merger could make sense. But that leaves us with a special hypothesis for each merger. What we need is a general hypothesis to explain merger waves. For example, everybody seemed to be merging in 1998–2000 and again in 2006–2007, but in the intervening years mergers went out of fashion.

There are other instances of apparent financial fashions. For example, from time to time there are hot new-issue periods when there seem to be an insatiable supply of speculative new issues and an equally insatiable demand for them. We don’t understand why hard-headed businessmen sometimes seem to behave like a flock of sheep, but the following story may contain the seeds of an explanation.

It is early evening and George is trying to decide between two restaurants, the Hungry Horse and the Golden Trough. Both are empty and, since there seems to be little reason to prefer one to the other, George tosses a coin and opts for the Hungry Horse. Shortly afterward Georgina pauses outside the two restaurants. She somewhat prefers the Golden Trough, but observing George inside the Hungry Horse while the other restaurant is empty, she decides that George may know something that she doesn’t and therefore the rational decision is to copy George. Fred is the third person to arrive. He sees that George and Georgina have both chosen the Hungry Horse, and, putting aside his own judgment, decides to go with the flow. And so it is with subsequent diners, who simply look at the packed tables in the one restaurant and the empty tables elsewhere and draw the obvious conclusions. Each diner behaves fully rationally in balancing his or her own views with the revealed preferences of the other diners. Yet the popularity of the Hungry Horse owed much to the toss of George’s coin. If Georgina had been the first to arrive or if all diners could have pooled their information before coming to a decision, the Hungry Horse might not have scooped the jackpot.

Economists refer to this imitative behavior as a cascade.¹³ It remains to be seen how far cascades or some alternative theory can help to explain financial fashions.

10. Why Are Financial Systems So Prone to Crisis?

The crisis that started in 2007 was an unwelcome reminder of the fragility of financial systems. One moment everything seems to be going fine; the next moment markets crash, banks fail, and before long the economy is in recession. Carmen Reinhart and Kenneth Rogoff have documented the effects of banking crises in many countries.¹⁴ They find that systemic banking crises are typically preceded by credit booms and asset price bubbles. When the bubbles burst, housing prices drop on average by 35% and stock prices fall by 55%. Output falls by 9% over the following two years and unemployment rises by 7% over a period of four years. Central government debt nearly doubles compared with its precrisis level.

At the start of 2010, the increased government debt in Greece and a number of other periphery eurozone countries caused the crisis to change into a sovereign debt crisis. First Greece, and later Ireland and Portugal, required a bailout from the IMF and other eurozone countries. In June 2012, Spain sought a bailout for its banks. At the time of this writing, this sovereign debt phase of the crisis is far from over. The interaction of politics and economics is particularly important but relatively little is understood about this aspect.

Our understanding of these financial crises is limited. We need to know what causes them, how they can be prevented, and how they can be managed when they do occur. We reviewed the roots of the latest crisis in Chapter 14. But crisis prevention will have to incorporate principles and practices that we discussed in other chapters, such as the importance of good governance systems, well-constructed compensation schemes, and efficient risk management. Understanding financial crises will occupy economists and financial regulators for many years to come.¹⁵ Let’s hope they figure out the last one before the next one knocks on the door.

 34-3   A Final Word

That concludes our list of unsolved problems. We have given you the 10 uppermost in our minds. If there are others that you find more interesting and challenging, by all means construct your own list and start thinking about it.

It will take years for our 10 problems to be finally solved and replaced with a fresh list. In the meantime, we invite you to go on to further study of what we already know about finance. We also invite you to apply what you have learned from reading this book.

Now that the book is done, we sympathize with Huckleberry Finn. At the end of his book he says:

So there ain’t nothing more to write, and I am rotten glad of it, because if I’d a’ knowed what a trouble it was to make a book I wouldn’t a’ tackled it, and I ain’t a’going to no more.

___________

¹See, for example, R. Kosowski, A. Timmerman, R. Wermers, and H. White, “Can Mutual Fund ‘Stars’ Really Pick Stocks? New Evidence from a Bootstrap Analysis,” Journal of Finance 61 (December 2006), pp. 2551–2595.

²That is, if

and if for each period t, Ct(AB) = Ct(A) + Ct(B), then

³If you start with the cash flow Ct(AB) and split it into two pieces, Ct(A) and Ct(B), then total value is unchanged. In other words, PV[Ct(A)] + PV[Ct(B)] = PV[Ct(AB)]. See Footnote 2.

⁴See R. Roll, “A Critique of the Asset Pricing Theory’s Tests: Part 1: On Past and Potential Testability of the Theory,” Journal of Financial Economics 4 (March 1977), pp. 129–176; and, for a critique of the critique, see D. Mayers and E. M. Rice, “Measuring Portfolio Performance and the Empirical Content of Asset Pricing Models,” Journal of Financial Economics 7 (March 1979), pp. 3–28.

⁵Fama and French point out that small firms, and firms with high book-to-market ratios, are also low-profitability firms. Such firms may suffer more in downturns in the economy. Thus size and book-to-market measures may be proxies for exposure to business-cycle risk. See E. F. Fama and K. R. French, “Size and Book-to-Market Factors in Earnings and Returns,” Journal of Finance 50 (March 1995), pp. 131–155.

⁶See R. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica 41 (1973), pp. 867–887.

⁷K. Yuan, L. Zheng, and Q. Zhu, “Are Investors Moonstruck? Lunar Phases and Stock Returns,” Journal of Empirical Finance 13 (January 2006), pp. 1–23.

⁸See W. Ziemba and S. Schwartz, Invest Japan (Chicago, IL: Probus, 1992), p. 109.

⁹See C. Kindleberger, Manias, Panics, and Crashes: A History of Financial Crises, 4th ed. (New York: Wiley, 2000); and R. Shiller, Irrational Exuberance (Princeton, NJ: Princeton University Press, 2000).

¹⁰Investment managers may reason that if the stocks continue to do well, they will benefit from increased business in the future; on the other hand, if the stocks do badly, it is the customers who incur the losses and the worst that can happen to the managers is that they have to find new jobs. See F. Allen, “Do Financial Institutions Matter?” Journal of Finance 56 (August 2001), pp. 1165–1174.

¹¹There are relatively few closed-end funds. Most mutual funds are open-end. This means that they stand ready to buy or sell additional shares at a price equal to the fund’s net asset value per share. Therefore the share price of an open-end fund always equals net asset value.

¹²See M. Brunnermeier, “Deciphering the Liquidity and Credit Crunch 2007–2008,” Journal of Economic Perspectives 23 (Winter 2009), pp. 77–100.

¹³For an introduction to cascades, see S. Bikhchandani, D. Hirshleifer, and I. Welch, “Learning from the Behavior of Others: Conformity, Fads, and Informational Cascades,” Journal of Economic Perspectives 12 (Summer 1998), pp. 151–170.

¹⁴See C. Reinhart and K. Rogoff, “The Aftermath of Financial Crises,” American Economic Review 99 (May 2009), pp. 466–472.

¹⁵For a review of the current literature on financial crises see F. Allen, A. Babus, and E. Carletti, “Financial Crises: Theory and Evidence,” Annual Review of Financial Economics 1 (2009), pp. 97–116.

Appendix

Answers to Select Basic Problems

CHAPTER 1

1.  (a) Real; (b) executive airplanes; (c) brand names; (d) financial; (e) bonds; (f) investment; (g) capital budgeting; (h) financing.

3.  a. Financial assets, such as stocks or bank loans, are claims held by investors. Corporations sell financial assets to raise the cash to invest in real assets such as plant and equipment. Some real assets are intangible.

b.  Capital budgeting means investment in real assets. Financing means raising the cash for this investment.

c.  The shares of public corporations are traded on stock exchanges and can be purchased by a wide range of investors. The shares of closely held corporations are not traded and are not generally available to investors.

d.  Unlimited liability: investors are responsible for all the firm’s debts. A sole proprietor has unlimited liability. Investors in corporations have limited liability. They can lose their investment, but no more.

CHAPTER 2

1.  $1.00.

3.  374/(1.09)9 = $172.20.

5.  100 × (1.15)8 = $305.90.

7.  PV = 4/(.14 – .04) = $40.

9.  a. 10,000/1.055 = $7,835.26.

b.  You need to set aside (12,000 × 6-year annuity factor) = 12,000 × 4.623 = $55,476.

c.  At the end of 6 years you would have 1.086 × (60,476 – 55,476) = $7,934.

11.  (a) $12.625 million; (b) $12.705 million; (c) $12.712 million.

CHAPTER 3

1.  (a) Does not change; (b) Price falls; (c) Yield rises.

3.  The yield over 6 months is 2.7/2 = 1.35%. Therefore, PV = $3.125/1.0135 + $3.125/(1.0135)2 + . . . + $103.125/(1.0135)36 = $150.35.

5.  a. Fall (e.g., 1-year 10% bond is worth 110/1.1 = 100 if r = 10% and is worth 110/1.15 = 95.65 if r = 15%).

b.  Less (e.g., see 5a).

c.  Less (e.g., with r = 5%, 1-year 10% bond is worth 110/1.05 = 104.76).

d.  Higher (e.g., if r = 10%, 1-year 10% bond is worth 110/1.1 = 100, while 1-year 8% bond is worth 108/1.1 = 98.18).

e.  No, low-coupon bonds have longer durations (unless there is only one period to maturity) and are therefore more volatile (e.g., if r falls from 10% to 5%, the value of a 2-year 10% bond rises from 100 to 109.3 (a rise of 9.3%). The value of a 2-year 5% bond rises from 91.3 to 100 (a rise of 9.5%).

7.  (a) 4%; (b) PV = $1,075.44.

9.  a. r2 = (100/99.523).5 – 1 = 0.24%; r3 = (100/98.937).33 – 1 = 0.35%; r4 = (100/97.904).25 – 1 = 0.53%; r5 = (100/96.034).2 – 1 = 0.81%.

b.  Upward-sloping.

c.  Higher. (The yield on the bond is a complicated average of the separate spot rates.)

11.  a.  False. Duration depends on the coupon as well as the maturity.

b.  False. Given the yield to maturity, volatility is proportional to duration.

c.  True. A lower coupon rate means longer duration and therefore higher volatility.

d.  False. A higher interest rate reduces the relative present value of (distant) principal repayments.

13.  7.01%. (The extra return that you earn for investing for 2 years rather than 1 is 1.062/1.05 – 1 = .0701.)

CHAPTER 4

1.  (a) True; (b) true.

3.  P0 = (5 + 110)/1.08 = $106.48

5.  P0 = 10/(.08 – .05) = $333.33.

7.  15/.08 + PVGO = 333.33; therefore PVGO = $145.83.

9.  (a) False; (b) true.

11.  Free cash flow is the amount of cash left over and available to pay out to investors after all investments necessary for growth. In our simple examples, free cash flow equals operating cash flow minus capital expenditure. Free cash flow can be negative if investments are large.

13.  If PVGO = 0 at the horizon date H, horizon value = earnings forecasted for H + 1 divided by r.

CHAPTER 5

1.  (a) A = 3 years, B = 2 years, C = 3 years; (b) B;
(c) A, B, and C; (d) B and C (NPVB = $3,378; NPVC = $2,405); (e) true; (f) It will accept no negative-NPV projects but will turn down some with positive NPVs. A project can have positive NPV if all future cash flows are considered but still do not meet the stated cutoff period.

3.  (a) $15,750; $4,250; $0; (b) 100%.

5.  (a) Two; (b) – 50% and +50%; (c) yes, NPV = +14.6.

7.  1, 2, 4, and 6.

CHAPTER 6

1.  a, b, d, g, h.

3.  (a) False; (b) false; (c) false; (d) false.

7.  PV cost = 1.5 + .2 × 14.09 = $4.319 million. Equivalent annual cost = $4,318, 788.91/14.09 = $306,514.

9.  Replace at end of 5 years ($80,000 > $72,376).

CHAPTER 7

1.  Expected payoff is $100 and expected return is zero. Variance is 20,000 (% squared) and standard deviation is 141%.

3.  Ms. Sauros had a slightly higher average return (14.6% vs. 14.4% for the market). However, the fund also had a higher standard deviation (13.6% vs. 9.4% for the market).

5.  d

7.  (a) 26%; (b) zero; (c) .75; (d) less than 1.0 (the portfolio’s risk is the same as the market, but some of this risk is specific risk).

9.  A, 1.0; B, 2.0; C, 1.5; D, 0; E, – 1.0.

CHAPTER 8

1.  (a) 7%; (b) 27% with perfect positive correlation; 1% with perfect negative correlation; 19.1% with no correlation; (c) See Figure 1; (d) No, measure risk by beta, not by standard deviation.

3.  Sharpe ratio = 7.3/20.0 = .365.

5.  (a) See Figure 2; (b) A, D, G; (c) F; (d) 15% in C. (e) Put 25/32 of your money in F and lend 7/32 at 12%: Expected return = 7/32 × 12 + 25/32 × 18 = 16.7%; standard deviation = 7/32 × 0 + (25/32) × 32 = 25%. If you could borrow without limit, you would achieve as high an expected return as you’d like, with correspondingly high risk, of course.

7.  (a) True; (b) false (it offers twice the market risk premium); (c) false.

CHAPTER 9

1.  Overestimate.

3.  .49, or 49% of variation, was due to market movements; the remainder—(1 – .49) = .51, or 51% of the variation—was diversifiable. Diversifiable risk shows up in the scatter about the fitted line. The standard error of the estimated beta was .34. If you said that the true beta was 2 × .34 = .68 either side of your estimate, you would have a 95% chance of being right.

5.  Beta of assets = .5 × .15 + .5 × 1.25 = .7.

7.  Suppose that the expected cash flow in year 1 is 100, but the project proposer provides an estimate of 100 × 115/108 = 106.5. Discounting this figure at 15% gives the same result as discounting the true expected cash flow at 8%. Adjusting the discount rate, therefore, works for the first cash flow but it does not do so for later cash flows (e.g., discounting a 2-year cash flow of 106.5 by 15% is not equivalent to discounting a 2-year flow of 100 by 8%).

9.  (a) False; (b) false; (c) true.

CHAPTER 10

1.  (a) False; (b) true; (c) true.

3.  a. Analysis of how project profitability and NPV change if different assumptions are made about sales, cost, and other key variables.

b.  Project NPV is recalculated by changing several inputs to new, but consistent, values.

c.  Determines the level of future sales at which project profitability or NPV equals zero.

d.  An extension of sensitivity analysis that explores all possible outcomes and weights each by its probability.

e.  A graphical technique for displaying possible future events and decisions taken in response to those events.

f.  Option to modify a project at a future date.

g.  The additional present value created by the option to bail out of a project, and recover part of the initial investment, if the project performs poorly.

h.  The additional present value created by the option to invest more and expand output, if a project performs well.

5.  a. Describe how project cash flow depends on the underlying variables.

b.  Specify probability distributions for forecast errors for these cash flows.

c.  Draw from the probability distributions to simulate the cash flows.

7.  Adding a fudge factor to the discount rate pushes project analysts to submit more optimistic forecasts.

CHAPTER 11

1.  (a) False; (b) true; (c) true; (d) false.

3.  First consider whether renting the building and opening the Taco Palace is positive NPV. Then consider whether to buy (instead of renting) based on your optimistic view of local real estate.

5.  The secondhand market value of older planes falls by enough to make up for their higher fuel consumption. Also, the older planes are used on routes where fuel efficiency is relatively less important.

CHAPTER 12

1.  (a) True; (b) true; (c) false; (d) true.

3.  Monitoring is costly and encounters diminishing returns. Also, completely effective monitoring would require perfect information.

5.  ROI = 1.6/20 = .08 or 8%. Net return = 8 – 11.5 = – 3.5%. EVA = 1.6 – (.115 × 20) = – $.7 million. EVA is negative.

7.  Not usually by creative accounting, but by reducing or delaying discretionary advertising, maintenance, R&D, or other expenses.

CHAPTER 13

1.  c

3.  (a) False; (b) false; (c) true; (d) false; (e) false; (f) true.

5.  6 – (– .2 + 1.45 × 5) = – 1.05%.

7.  Decrease. The stock price already reflects an expected 25% increase. The 20% increase conveys bad news relative to expectations.

9.  a. Evidence that two securities with identical cash flows (e.g., Royal Dutch Shell and Shell Transport & Trading) can sell at different prices.

b.  Small-cap stocks and high book-to-market stocks appear to have given above-average returns for their level of risk.

c.  IPOs provide relatively low returns after their first few days of trading.

d.  Stocks of firms that announce unexpectedly good earnings perform well over the coming months.

In each case there appear to have been opportunities for earning superior profits.

CHAPTER 14

1.  (a) False; (b) true; (c) true.

3.  (a) subordinated; (b) floating rate; (c) convertible; (d) warrant; (e) common stock; preferred stock.

CHAPTER 15

1.  a. Further sale of an already publicly traded stock;

b.  U.S. bond issue by foreign corporation;

c.  Bond issue by industrial company;

d.  Bond issue by large industrial company.

3.  a. Financing of start-up companies.

b.  Underwriters gather nonbinding indications of demand for a new issue.

c.  The difference between the price at which the underwriter buys the security from the company and resells it to investors.

d.  Description of a security offering filed with the SEC.

e.  Winning bidders for a new issue tend to overpay.

5.  (a) False; (b) false; (c) true.

7.  a. Number of new shares, 50,000;

b.  Amount of new investment, $500,000;

c.  Total value of company after issue, $4,500,000;

d.  Total number of shares after issue, 150,000;

e.  Stock price after issue, $4,500,000/150,000 = $30;

f.  The opportunity to buy one share is worth $20.

CHAPTER 16

1.  a. A1, B5; A2, B4; A3, B3; A4, B1; A5, B2;

b.  On February 7, the ex-dividend date;

c.  (.83 × 4)/$68 = .0488, or 4.88%;

d.  (.83 × 4)/$6 = .5533, or 55.33%;

e.  The price would fall to 68/1.10 = $61.82.

3.  a. Announcement of a dividend increase signals managers’ confidence in future profits, and thus the stock price rises with the announcement.

b.  On the ex-dividend date the price will fall by approximately the dividend amount ($1).

5.  a. There will still be 1 million shares and the stock price will fall to $10. Shareholders’ wealth, including the cash dividend, will equal $10 + 2 × $12 per share.

b. It will spend $2 million to repurchase 166,667 shares at $12 each, leaving 833,333 shares outstanding. Stock price remains at $12 ($10 million divided by 833,333 shares).

7.  Mr. Milquetoast will have to sell a fraction of his investment or borrow against his holdings with the hope that Mr. Buffet will generate a higher return than the interest cost on the loan.

9.  No, demand from investors that prefer a dividend-paying stock does not necessarily lift the prices of these stocks relative to stocks of companies that pay no dividends but repurchase shares. The supply of dividends should expand to satisfy this clientele, and if the supply of dividends already meets demand, then no single firm can increase its market value simply by paying dividends. Without significant tax differentials, firm value is unaffected by the choice between dividends and repurchases.

11.  First, the CFO must decide how much cash to pay out, and second, whether to pay dividends or repurchase shares. In answer to the first question, the firm must determine the amount of surplus cash. In answer to the second question, the firm must determine whether there are any tax benefits or other market imperfections giving preference to either cash dividends or repurchases.

CHAPTER 17

1.  Note the market value of Copperhead is far in excess of its book value:

Ms. Kraft owns .625% of the firm, which proposes to increase common stock to $17 million and cut short-term debt. Ms. Kraft can offset this by (a) borrowing .00625 × 1,000,000 = $6,250, and (b) buying that much more Copperhead stock.

3.  Expected return on assets is rA = .08 × 30/80 + .16 × 50/80 = .13. The new return on equity will be rE = .13 + (20/60)(.13 – .08) = .147.

5.  a. True;

b.  True (as long as the return earned by the company is greater than the interest payment, earnings per share increase, but the P/E falls to reflect the higher risk);

c.  False (the cost of equity increases with the ratio D/E);

d.  False (the formula rE = rA + (D/E)(rA – rD) does not require rD to be constant);

e.  False (debt amplifies variations in equity income);

f.  False (value increases only if clientele is not satisfied).

7.  See Figure 17.3.

CHAPTER 18

1.  The calculation assumes that the tax rate is fixed, that debt is fixed and perpetual, and that investors’ personal tax rates on interest and equity income are the same.

5.  a. Direct costs of financial distress are the legal and administrative costs of bankruptcy. Indirect costs include possible delays in liquidation (Eastern Airlines) or poor investment or operating decisions while bankruptcy is being resolved. Also the threat of bankruptcy can lead to costs.

b.  If financial distress increases odds of default, managers’ and shareholders’ incentives change. This can lead to poor investment or financing decisions.

c.  See the answer to 5(b). Examples are the “games” described in Section 18-3.

7.  More profitable firms have more taxable income to shield and are less likely to incur the costs of distress. Therefore the trade-off theory predicts high (book) debt ratios. In practice the more profitable companies borrow least.

9.  When a company issues securities, outside investors worry that management may have unfavorable information. If so the securities can be overpriced. This worry is much less with debt than equity. Debt securities are safer than equity, and their price is less affected if unfavorable news comes out later.

A company that can borrow (without incurring substantial costs of financial distress) usually does so. An issue of equity would be read as “bad news” by investors, and the new stock could be sold only at a discount to the previous market price.

11.  Financial slack is most valuable to growth companies with good but uncertain investment opportunities. Slack means that financing can be raised quickly for positive-NPV investments. But too much financial slack can tempt mature companies to overinvest. Increased borrowing can force such firms to pay out cash to investors.

CHAPTER 19

1.  Market values of debt and equity are D = .9 × 75 = $67.5 million and E = 42 × 2.5 = $105 million. D/V = .39. WACC = .09(1 – .35).39 + .18(.61) = .1325, or 13.25%.

3.  (a) False; (b) true; (c) true.

5.  (a) True; (b) false, if interest tax shields are valued separately; (c) true.

7.  a. 12%, of course.

b.  rE = .12 + (.12 – .075)(30/70) = .139; WACC = .075(1 – .35)(.30) + .139(.70) = .112, or 11.2%.

9.  No. The more debt you use, the higher rate of return equity investors will require. (Lenders may demand more also.) Thus there is a hidden cost of the “cheap” debt: it makes equity more expensive.

CHAPTER 20

1.  Call; exercise; put; European.

3.  a. The exercise price of the put option (i.e., you’d sell stock for the exercise price).

b.  The value of the stock (i.e., you would throw away the put and keep the stock).

5.  Buy a call and lend the present value of the exercise price.

7.  (a) See Figure 3; (b) stock price – PV(EX) = 100 – 100/1.1 = $9.09.

9.  (a) Zero; (b) Stock price less the present value of the exercise price.

11.  a. All investors, however risk-averse, should value more highly an option on a volatile stock. For both Exxon Mobil and Google the option is valueless if final stock price is below the exercise price, but the option on Google has more upside potential.

b.  American options can be exercised anytime. However, we know that in the absence of dividends the value of a call option increases with time to maturity. So, if you exercised an American call option early, you would needlessly reduce its value. An American call should not be exercised before maturity.

CHAPTER 21

1. a. Using risk-neutral method, (p × 20) + (1 – p) (– 16.7) = 1, p = .48.

d.  Possible stock prices with call option prices in parentheses:

Option prices were calculated as follows:

3.  Using the replicating-portfolio method:

a.  If month 3 stock price = 341.61, delta = (30 – 0)/(400 – 291.75) = .27714. To replicate call, buy .27714 shares, and borrow PV of those shares if stock declines; PV(291.75 × .27714). Option value = .27714 × 341.61 – 80.8545/1.0086 = 14.51.

b.  If month 3 stock price = 468.37, delta = (178.42 – 30)/(548.42 – 400) = 1. To replicate call, buy 1 share, and borrow PV of those shares if stock declines; PV(400 – 30) = PV(370). Option value = 1 × 468.37 – 370/1.0086 = 101.52.

c.  At month 0 delta = (101.52 – 14.51)/(468.37 – 341.61) = .6864. To replicate call, buy .4518 shares, and borrow PV of those shares if stock declines; PV(341.61 × .6864 – 14.51) = PV(219.98). Option value = .6864 × 400 – 219.98/1.0086 = 56.46.

Using the risk-neutral method:

p × .1709 + (1 – p) × (– 0.146) = 0.0086: p = .4879

a.  If month 3 stock price = 341.61, option value = (.4879 × 30 + .5121 × 0)/1.0086 = 14.51.

b.  If month 3 stock price = 468.37, option value = (.4879 × 178.42 + .5121 × 30)/1.0086 = 101.53.

c.  At month 0, option value = (.4879 × 101.53 + .5121 × 14.51)/1.0086 = 56.48.

There is a slight rounding difference in the two methods.

The put option can be valued using put–call parity:

Value of put = 56.48 + 370/1.0086 – 400 = 23.33.

5.  a. Delta = 100/(200 – 50) = .667.

c.  (p × 100) + (1 – p)(– 50) = 10, p = .4.

e.  No. The true probability of a price rise is almost certainly higher than the risk-neutral probability, but it does not help to value the option.

7.  True; as the stock price rises, the risk of the option falls.

CHAPTER 22

1.  a. Increase value (unless the cash flows from the Mark II needed to be discounted at a higher rate).

b.  Increase value.

c.  Reduce value.

3.  The life of a project is not fixed ahead of time. IM&C has the option to abandon the guano project after 2 or 3 years if performance is poor. If performance is great, exercise of the abandonment option could be delayed well beyond the estimated 7-year life.

5.  Gas turbines can be started up on short notice when spark spreads are high. The turbines’ value comes from flexibility in production.

7.  (a) True; (b) true; (c) true; (d) true; (e) true—the series of smaller plants generates real options, but the large plant may nevertheless be more efficient.

CHAPTER 23

1.  Promised yield = 12.77%; expected yield = 8.56%.

3.  Put option on company’s assets with an exercise price equal to the face value of the bond.

5.  The expected growth in the market value of the assets, the face value and maturity of the debt, and the variability of future asset values. (In practice, compromises need to be made if, for example, the company has issued bonds with different maturities.)

7.  Both bonds are more likely to be downrated.

CHAPTER 24

1.  (a) High-grade utility bonds; (b) industrial holding companies; (c) industrial bonds; (d) railroads; (e) asset-backed security.

3.  a. You would like an issue of junior debt.

b.  You prefer it not to do so (unless it is also junior debt). The existing property may not be sufficient to pay off your debt.

5.  a. Approximately 99.489 + 8.25/12 = 100.18%.

b.  .04125 × 250 = $10.3 million on Feb. 15, 1993.

c.  After making earlier sinking fund payments, $12.5 million remains to be repaid on Aug. 15, 2022.

d.  2008 (but see footnote 18 for some possible complications).

7.  a. False. In the event of default, secured bonds have seniority for the relevant assets.

b.  True, but some new securities (e.g., eurobonds) survive even when the original motive for issuing them disappears.

c.  False. The borrower has the option.

d.  True. But debt issues with weak covenants suffered in such takeovers.

e.  True. The costs of renegotiation are less for private placements.

9.  (a) False; (b) true; (c) false; (d) true.

CHAPTER 25

1.  A, c; B, d or i; C, b or e; D, f; E, a; F, h; G, g.

3.  a. The lessor must charge enough to cover the present value of the costs of owning and operating the asset over its expected economic life. In a competitive leasing market the present value of rentals cannot exceed the present value of costs. The competitive rental payment ends up equal to the lessor’s equivalent annual cost.

b.  The user’s equivalent annual cost is the annual cost to the user of owning and operating the asset. If the operating lease rate is less than this cost, it pays to lease.

5.  If the lease is affirmed, the lessee continues to use the leased asset and must make the full lease payments. If the lease is rejected, the leased asset is returned to the lessor. If the value of the returned asset is not enough to cover the remaining lease payments, the lessor’s loss becomes an unsecured claim on the bankrupt firm.

7.  Lenders have no claim on the lessor if the lessee defaults. The lessor avoids liability in this case. But lenders will demand better terms, for example, a higher interest rate, as compensation for lack of recourse.

CHAPTER 26

1.  a. Price paid for immediate delivery.

b.  Forward contracts are contracts to buy or sell at a specified future date at a specified price. Futures differ from forwards in two main ways. They are traded on an exchange and they are marked to market.

c.  Investors who are long have agreed to buy the asset. Investors who are short have contracted to sell.

d.  The risk that arises because the price of the asset used to hedge is not perfectly correlated with that of the asset that is being hedged.

e.  Profits and losses on a position are settled on a regular basis (e.g., daily).

f.  The advantage from owning the commodity rather than the promise of future delivery less the cost of storing the commodity.

3.  She is asking you to pay money, because your sale is showing a loss.

5.  Northern Refineries has fixed the price that it will receive for its oil (we ignore possible basis risk). Because it now has a certain income, it gives up the possibility of pleasant surprises as well as unpleasant ones.

7.  a. A shortage of heating oil increases net convenience yield and reduces the futures price relative to spot price.

b.  Spot and futures prices decrease. The futures price rises relative to spot because convenience yield falls and storage costs rise.

9.  a. Profit;

b.  If the bank took out a new 4-year swap, it would need to pay an extra $.25 million a year. At the new interest rate of 6.5%, the extra payment has a present value of $856,449.65. This is the amount that the bank should charge to terminate.

11.  Sell short $1.2 million of the market portfolio. In practice rather than “sell the market” you would sell futures on $1.2 million of the market index.

CHAPTER 27

1.  a. 76.735;

b.  76.7162;

c.  Yen is at a premium (dollar is at a discount);

d.  premium = 76.735/76.282 – 1 = .005938, or .5938%;

e.  From interest rate parity, 76.282/76.735 = (1 + ryen)/1.015. Therefore ryen = .994097 × 1.015 – 1, ryen = .009008, or .9008%.

f.  76.6595 yen = $1;

g.  If the real exchange rate is expected to be constant, expected difference in inflation is 76.6595/76.735 – 1 = – .00098, i.e., inflation in Japan over the 3 months is expected to be .098% less than in the United States.

3.  a. 2,419 × 1.3/1.02 = R3,083 = $1. b. Real value of rupiah fell by 3,083/8,325 – 1 = .63, or 63%.

5.  b

7.  It can borrow the present value of €1 million, sell the euros in the spot market, and invest the proceeds in an 8-year dollar loan.

9.  a. NPV = 6.61 × 1.2 = $7.94 million.

c.  It doesn’t. The company can always hedge against a fall in the euro.

CHAPTER 28

5.  The illogical ratios are a, b, d, e, and h. The correct definitions are

7.  a. Sales = 3 × 500,000 = 1,500,000; after-tax interest + net income = .08 × 1,500,000 = 120,000; ROA = 120,000/500,000 = 24%;

b.  Net income = .08 × 3 × 500,000 – (1 – .35) × 30,000 = 100,500. ROE = net income/equity = 100,500/300,000 = .34.

9.  .73.; 3.65%

11.  Assume that new debt is a current liability.

a.  Current ratio goes from 100/60 = 1.67 to 120/80 = 1.50; cash ratio goes from 30/60 = .5 to 50/80 = .63;

b.  Long-term debt ratio is unchanged; total liabilities/total assets goes from 410/600 = .6833 to 430/620 = .6935.

13.  $82 million.

CHAPTER 29

3.  Month 3: 18 + (.5 × 90) + (.3 × 120) + (.2 × 100)
= $119,000.

Month 4: 14 + (.5 × 70) + (.3 × 90) + (.2 × 120)
= $100,000.

5.  a. Table 29.2: Cash = 40, Total current assets = 340; Bank loans = 15; Current liabilities = 150; and Total assets = Total liabilities and net worth = 590.

Table 29.3: Increase (decrease) in short-term debt = – 10; net cash flow from financing activities = – 35; Increase in cash balance = 20.

b.  Table 29.2: Long-term debt = 130; Gross investment = 375; Net fixed assets = 275; Cash = 40; Current assets = 340; and Total assets = Total liabilities and net worth = 615.

Table 29.3: Increase (decrease) in long-term debt = 30 + 40 = 70; Net cash flow from financing activities = – 50 + 40 = – 10; Investment in fixed assets = – (25 + 30) = – 55; Increase in cash balance = 20.

c.  Table 29.1: Operating cost (cost of goods sold + other expenses) = (1,644 + 411) × .9 = 1,850; Pretax income = 2,200 – 1,850 – 20 – 5 = 325; Net income = 325 × .5 = 162.5. If dividend is unchanged, earnings retained in the business = 162.5 – 30 = 132.5.

Table 29.2: assuming inventories are unchanged, Cash = 25 + 132.5 – 30 = 127.5; Current assets = 427.5; Net worth = 452.5; total assets = total liabilities and net worth = 677.5.

Table 29.3: Net income = 162.5; Net cash flow from operating activities = 85 + 102.5 = 187.5; Increase (decrease) in cash balance = 107.5

d.  Table 29.4 changes as follows:

Table 29.5 changes as follows:

e.  Table 29.5 changes as follows:

f.  Table 29.5 changes as follows:

g.  Table 29.5 changes as follows:

7.  (a) $ 2,900,000; (b) $ 225,000; (c) .25.

9.  (a) 8.6%; (b) 13.75%.

CHAPTER 30

1.  151.57 days.

3.  By holding large inventories, the firm avoids the risk of running out of materials and finished goods. It can order materials in larger quantities and arrange longer production runs. On the other hand, inventories tie up capital, must be stored and insured, and may be subject to damage.

Similarly, large cash inventories reduce the risk of running out of cash or having to sell securities at short notice. The firm needs to make less frequent sales of securities and therefore minimize the fixed costs of such sales. On the other hand, inventories of cash tie up capital.

5.  a. Due lag decreases, therefore pay lag decreases.

b.  Due lag increases, therefore pay lag increases.

c.  Terms lag increases, therefore pay lag increases.

7.  a. Expected profit = p(1,200 – 1,050)
– 1,050 (1 – p) = 0

Therefore, grant credit if probability of payment exceeds 87.5%.

b.  Expected profit from selling to slow payer: .8(150) – .2(1,050) = – 90. Break-even point for credit check: (.05 × 90 × units) – 12 = 0. Units = 2.67.

9.  (a) False; (b) false; (c) false—should be collection agency or attorney.

11.  (a) Decrease; (b) decrease; (c) increase.

13.  (a) Less; (b) less; (c) invest the same amount; (d) more.

15.  (a) Repurchase agreements; (b) commercial paper; (c) finance company commercial paper; (d) 3-month bills; (e) Treasury bills; (f) Treasury bills.

17.  The cash conversion cycle will increase by 15.4.

CHAPTER 31

1.  (a) Horizontal; (b) conglomerate; (c) vertical; (d) conglomerate.

3.  (a) $5 million (We assume that the $500,000 saving is an after-tax figure.); (b) $4 million; (c) $7.5 million; (d) +$1 million; (e) – $2.5 million.

5.  (a) True; (b) false; (c) false; (d) true; (e) false (They may produce gains, but “large” is stretching it.); (f) false; (g) true.

CHAPTER 32

1.  a. Purchase of a business using mostly debt financing. The company goes private. Management is given a substantial equity stake.

b.  An LBO undertaken by management.

c.  A parent company creates a new company with part of its assets and operations. Shares in the new business are distributed to the parent’s stockholders.

d.  Like a spin-off, but shares in the new business are sold to investors.

e.  Sale of specific assets rather than entire firm.

f.  A government-owned business is sold to private investors.

g.  A company moves to a much higher debt ratio. Proceeds of additional borrowing are paid out to stockholders.

3.  Increased efficiency, broader share ownership, and revenue for the government.

5.  Internal capital markets often misallocate capital. The market values of the conglomerate’s divisions can’t be observed separately, so it’s hard to set incentives and to reward risk-taking.

7.  Chapter 7 usually leads to liquidation. Chapter 11 protects the firm from its creditors while a reorganization plan is developed.

9.  There is always a chance that the company can recover, allowing creditors to be paid off and leaving something for shareholders. Also, the court may not observe absolute priority, so shareholders may be given some crumbs in a Chapter 11 reorganization.

CHAPTER 33

1.  (a) U.S. and UK; (b) U.S. and UK; (c) Japan and Europe; (d) Japan; (e) Euro area; (f) Japan. (Note: Answers exclude countries not separately shown in Figures 33.1–33.4.)

3.  No. Individual investors hold relatively little common stock directly. Also the cross-holdings of stock by Japanese companies limit the opportunities for individuals to play an important role in governance.

5.  German firms have two boards of directors: a management board and a supervisory board, half of whose members are elected by employees. The supervisory board represents the interests of the company as a whole, not just the interests of employees or stockholders.

7.  The shareholder has a .3 holding in x2. x2 has a .3 holding in x, which has a .3 holding in z. The shareholder really has only a .33 or .027 holding in z.

9.  If firm y has a large stake in x, it may be able to transfer value from x by borrowing from x at a low interest rate, selling materials to x at excessive prices, or buying x’s output at low prices.

Glossary

Notes:

1. Italicized words are listed elsewhere in the glossary.

2. A number of websites contain comprehensive financial glossaries. See, for example, www.finance-glossary.com and www.duke.edu/~charvey/ Classes/wpg/glossary.htm

A

Abnormal return Part of return that is not due to marketwide price movements.

ABS Asset-backed security.

Absolute priority Rule in bankruptcy proceedings whereby senior creditors are required to be paid in full before junior creditors receive any payment.

Accelerated depreciation Any depreciation method that produces larger deductions for depreciation in the early years of a project’s life.

Accounts payable (payables, trade debt) Money owed to suppliers.

Accounts receivable (receivables, trade credit) Money owed by customers.

Accrued interest Interest that has been earned but not yet paid.

ACH Automated Clearing House.

Acid-test ratio Quick ratio.

Adjusted present value (APV) Net present value of an asset if financed solely by equity plus the present value of any financing side effects.

ADR American depository receipt.

Adverse selection A situation in which a pricing policy causes only the less desirable customers to do business, e.g., a rise in insurance prices that leads only the worst risks to buy insurance.

Affirmative covenant Loan covenant specifying certain actions that the borrower must take.

Agency costs Costs that arise when an agent (e.g., a manager) does not act solely in the interests of the principal (e.g., the shareholder).

Agency theory Theory of the relationship between a principal, e.g., a shareholder, and an agent of the principal, e.g., the company’s manager.

Aging schedule Summary of age of receivables that are outstanding from each customer.

AIBD Association of International Bond Dealers.

All-or-none underwriting An arrangement whereby a security issue is canceled if the underwriter is unable to resell the entire issue.

Alpha Measure of portfolio return adjusted for effect of market.

Alt-A mortgage Home loan that is less risky than sub-prime but more risky than A-grade loans.

Alternative minimum tax (AMT) A separately calculated minimum amount of tax that must be paid by corporations or individuals.

American depository receipt (ADR) A certificate issued in the United States to represent shares of a foreign company.

American option Option that can be exercised any time before the final exercise date (cf. European option).

Amortization (1) Repayment of a loan by installments; (2) allowance for depreciation.

AMT Alternative minimum tax.

Angel investor Wealthy individual who provides capital for start-up businesses.

Annual percentage rate (APR) The interest rate per period (e.g., per month) multiplied by the number of periods in a year.

Annuity Investment that produces a level stream of cash flows for a limited number of periods.

Annuity due Annuity whose payments occur at the start of each period.

Annuity factor Present value of $1 paid for each of t periods.

Anticipation Arrangement whereby customers who pay before the final date may be entitled to deduct a normal rate of interest.

Appraisal rights A right of shareholders in a merger to demand the payment of a fair price for their shares, as determined independently.

Appropriation request Formal request for funds for a capital investment project.

APR Annual percentage rate.

APT Arbitrage pricing theory.

APV Adjusted present value.

Arb Shorthand for “arbitrageur.”

Arbitrage Purchase of one security and simultaneous sale of another to give a risk-free profit. Often used loosely to describe the taking of offsetting positions in related securities, e.g., at the time of a takeover bid.

Arbitrage pricing theory (APT) Model in which expected returns increase linearly with an asset’s sensitivity to a small number of pervasive factors.

Arranger Lead underwriter to a syndicated loan.

Articles of incorporation Legal document establishing a corporation and its structure and purpose.

Asian currency units Dollar deposits held in Singapore or other Asian centers.

Asian option Option based on the average price of the asset during the life of the option.

Asked price (offered price) Price at which a dealer is willing to sell (cf. bid price).

Asset-backed security (ABS) Security issued by a special-purpose company that holds a package of assets whose cash flows are sufficient to service the bonds.

Asset beta The beta of the firm if it were unlevered.

Asset stripper Acquirer who takes over firms in order to sell off a large part of their assets.

Asymmetric information Difference in information available to two parties, e.g., a manager and investors.

At-the-money option Option whose exercise price equals the current asset price (cf. in-the-money option, out-of-the-money option).

Auction market Securities exchange in which prices are determined by an auction process, e.g., NYSE (cf. dealer market).

Auction-rate preferred A variant of floating-rate preferred stock where the dividend is reset every 49 days by auction.

Authorized share capital Maximum number of shares that a company can issue, as specified in the firm’s articles of incorporation.

Automated Clearing House (ACH) Private electronic system run by banks for high-volume, low-value payments.

Automatic debit Direct payment.

Availability float Checks deposited by a company that have not yet been cleared.

Aval Bank guarantee for debt purchased by forfaiter.

B

BA Banker’s acceptance.

Backdating Discredited practice of using hindsight to select a grant date for at-the-money executive stock options when the stock price (and therefore exercise price) were unusually low.

Backwardation Condition in which spot price of commodity exceeds price of future (cf. contango).

Balloon payment Large final payment (e.g., when a loan is repaid in installments).

Bank discount Interest deducted from the initial amount of a loan.

Banker’s acceptance (BA) Written demand that has been accepted by a bank to pay a given sum at a future date (cf. trade acceptance).

Barrier option Option whose existence depends on asset price hitting some specified barrier (cf. down-and-out option, down-and-in option).

Basel Accord International agreement on the amount of capital to be maintained by large banks to support their risky loans.

Basis point (bp) .01%.

Basis risk Residual risk that results when the two sides of a hedge do not move exactly together.

Bearer security Security for which primary evidence of ownership is possession of the certificate (cf. registered security).

Bear market Widespread decline in security prices (cf. bull market).

Behavioral finance Branch of finance that stresses aspects of investor irrationality.

Benchmark maturity Maturity of a newly issued Treasury bond.

Benefit–cost ratio One plus profitability index.

Bermuda option Option that is exercisable on discrete dates before maturity.

Best-efforts underwriting An arrangement whereby underwriters do not commit themselves to selling a security issue but promise only to use best efforts.

Beta Measure of market risk.

Bid price Price at which a dealer is willing to buy (cf. asked price).

Big Board Colloquial term for the New York Stock Exchange.

Bill of exchange General term for a document demanding payment.

Bill of lading Document establishing ownership of goods in transit.

Binomial method Method for valuing options that assumes there are only two possible changes in the asset price in any one period.

Blanket lien General lien against all the company’s assets.

Blue-chip company Large and creditworthy company.

Blue-sky laws State laws covering the issue and trading of securities.

Boilerplate Standard terms and conditions, e.g., in a debt contract.

Bond Long-term debt.

Bond rating Rating of the likelihood of bond’s default.

Bookbuilding The procedure whereby underwriters gather nonbinding indications of demand for a new issue.

Book entry Registered ownership of stock without issue of stock certificate.

Book runner The managing underwriter for a new issue. The book runner maintains the book of securities sold.

Bought deal Security issue where one or two underwriters buy the entire issue.

BP Basis point.

Bracket A term signifying the extent of an underwriter’s commitment in a new issue, e.g., major bracket, minor bracket.

Break-even analysis Analysis of the level of sales at which a project would just break even.

Bridge loan Short-term loan to provide temporary financing until more permanent financing is arranged.

Bulldog bond Foreign bond issue made in London.

Bullet payment Single final payment, e.g., of a loan (in contrast to payment in installments).

Bull market Widespread rise in security prices (cf. bear market).

Butterfly spread The purchase of two call options with different exercise prices and simultaneous sale of two calls exercisable at the average of these two exercise prices. Provides a bet that the share price will stay within a narrow range.

Bund Long-term German government bond.

Buyback Repurchase agreement.

C

“C” corporation Any U.S. corporation that is taxed separately from its owners. Most major corporations in the United States are “C” corporations (cf. “S” corporation).

Cable The exchange rate between U.S. dollars and sterling.

Call option Option to buy an asset at a specified exercise price on or before a specified exercise date (cf. put option).

Call premium (1) Difference between the price at which a company can call its bonds and their face value; (2) price of a call option.

Call provision Provision that allows an issuer to buy back the bond issue at a stated price.

Cap An upper limit on the interest rate on a floating-rate note.

CAPEX Capital expenditure.

Capital asset pricing model (CAPM) Model in which expected returns increase linearly with an asset’s beta.

Capital budget List of planned investment projects, usually prepared annually.

Capitalization Long-term debt plus preferred stock plus net worth.

Capital lease Financial lease.

Capital market Financial market (particularly the market for long-term securities).

Capital market line A plot of the set of portfolios with the highest Sharpe ratio. The line passes through the risk-free interest rate and the tangent efficient portfolio of risky assets.

Capital rationing Shortage of funds that forces a company to choose between worthwhile projects.

Capital structure Mix of different securities issued by a firm.

CAPM Capital asset pricing model.

Captive finance company Subsidiary whose function is to provide finance for purchases from the parent company.

Caput option Call option on a put option.

CAR Cumulative abnormal return.

CARDs (Certificates for Amortizing Revolving Debt) Pass-through securities backed by credit card receivables.

Carried interest A proportion of the profits to which private equity partnerships, etc. are entitled.

Carry trade Borrowing in country with low interest rate to relend in another country with a higher rate.

CARs (Certificates of Automobile Receivables) Pass-through securities backed by automobile receivables.

Carve-out Public offering of shares in a subsidiary.

Cascade Rational herding in which each individual deduces that previous decisions by others may have been based on extra information.

Cash and carry Purchase of a security and simultaneous sale of a future, with the balance being financed with a loan or repo.

Cash budget Forecast of sources and uses of cash.

Cash cow Mature company producing a large free cash flow.

Cash cycle The time from a firm’s payment for raw materials until the payment for the finished product from the customer.

Cash-deficiency arrangement Arrangement whereby a project’s shareholders agree to provide the operating company with sufficient net working capital.

Catastrophe bond (CAT bond) Bond whose payoffs are linked to a measure of catastrophe losses such as the level of insurance claims.

CAT bond Catastrophe bond.

CBD Cash before delivery.

CD Certificate of deposit.

CDO Collateralized debt obligation. Also CLO (collateralized loan obligation) and CMO (collateralized mortgage obligation).

CDS Credit default swap.

CEO Chief executive officer.

Certainty equivalent A certain cash flow that has the same present value as a specified risky cash flow.

Certificate of deposit (CD) A certificate providing evidence of a bank time deposit.

CFTC Commodity Futures Trading Commission.

CFO Chief financial officer.

Chaebol A Korean conglomerate.

Chapter 7 Bankruptcy procedure whereby a debtor’s assets are sold and the proceeds are used to repay creditors.

Chapter 11 Bankruptcy procedure designed to reorganize and rehabilitate defaulting firm.

Check conversion When customer writes a check, information is automatically captured and his bank account immediately debited.

Check 21 Check Clearing for the 21st Century Act allows banks to process checks electronically.

CHIPS Clearinghouse Interbank Payments System.

Chooser option Holder decides whether it is a call option or put option.

Classified board Staggered board.

Clean price (flat price) Bond price excluding accrued interest (cf. dirty price).

Clearinghouse Interbank Payments System (CHIPS) An international wire transfer system operated by a group of major banks for high-value dollar payments.

Closed-end fund Company whose assets consist of investments in a number of industrial and commercial companies.

Closed-end mortgage Mortgage against which no additional debt may be issued (cf. open-end mortgage).

CMBS Commercial mortgage-backed security.

CMOs Collateralized mortgage obligations.

CoCo Contingent convertible bond.

COD Cash on delivery.

Collar An upper and lower limit on the interest rate on a floating-rate note.

Collateral Assets that are given as security for a loan.

Collateralized debt obligation (CDO) A security backed by a pool of loans and issued in tranches with different levels of seniority.

Collateralized mortgage obligations (CMOs) A variation on the mortgage pass-through security in which the cash flows from a pool of mortgages are repackaged into several tranches of bonds with different maturities.

Collateral trust bonds Bonds secured by common stocks or other securities that are owned by the borrower.

Collection float Customer-written checks that have not been received, deposited, and added to the company’s available balance (cf. payment float).

Commercial draft (bill of exchange) Demand for payment.

Commercial paper Unsecured notes issued by companies and maturing within nine months.

Commitment fee Fee charged by bank on an unused line of credit.

Common-size financial statements Balance sheet where entries are expressed as proportion of total assets and income statement where entries are expressed as a proportion of revenues.

Common stock Security representing ownership of a corporation.

Company cost of capital The expected return on a portfolio of all the firm’s securities.

Compensating balance Non-interest-bearing demand deposits to compensate banks for bank loans or services.

Competitive bidding Means by which public utility holding companies are required to choose their underwriter (cf. negotiated underwriting).

Completion bonding Insurance that a construction contract will be successfully completed.

Composition Voluntary agreement to reduce payments on a firm’s debt.

Compound interest Reinvestment of each interest payment on money invested to earn more interest (cf. simple interest).

Compound option Option on an option.

Concentration banking System whereby customers make payments to a regional collection center. The collection center pays the funds into a regional bank account and surplus money is transferred to the company’s principal bank.

Conditional sale Sale in which ownership does not pass to the buyer until payment is completed.

Conglomerate merger Merger between two companies in unrelated businesses (cf. horizontal merger, vertical merger).

Consol Name of a perpetual bond issued by the British government. Sometimes used as a general term for perpetuity.

Consumer credit Bills awaiting payment from final customer to a company.

Contango Condition in which spot price of a commodity is below that of the future (cf. backwardation).

Contingent claim Claim whose value depends on the value of another asset.

Contingent convertible bond (CoCo) Typically a bond that converts to equity as issuer approaches financial distress.

Contingent project Project that cannot be undertaken unless another project is also undertaken.

Continuous compounding Interest compounded continuously rather than at fixed intervals.

Controller Officer responsible for budgeting, accounting, and auditing in a firm (cf. treasurer).

Convenience yield The extra advantage that firms derive from holding the commodity rather than the future.

Conversion price Par value of a convertible bond divided by the number of shares into which it may be exchanged.

Conversion ratio Number of shares for which a convertible bond may be exchanged.

Convertible bond Bond that may be converted into another security at the holder’s option. Similarly convertible preferred stock.

Convexity In a plot of a bond’s price against the interest rate, convexity measures the curvature of the line.

Corporate venturing Practice by which a large manufacturer provides financial support to new companies.

Corporation A business that is legally separate from its owners.

Correlation coefficient Measure of the closeness of the relationship between two variables.

Cost company arrangement Arrangement whereby the shareholders of a project receive output free of charge but agree to pay all operating and financing charges of the project.

Cost of (equity) capital Opportunity cost of capital.

Counterparty Party on the other side of a derivative contract.

Coupon (1) Specifically, an attachment to the certificate of a bearer security that must be surrendered to collect interest payment; (2) more generally, interest payment on debt.

Covariance Measure of the co-movement between two variables.

Covenant Clause in a loan agreement.

Covered option Option position with an offsetting position in the underlying asset.

Cramdown Action by a bankruptcy court to enforce a plan of reorganization.

Credit default swap (CDS) Credit derivative in which one party makes fixed payments while the payments by the other party depend on the occurrence of a loan default.

Credit derivative Contract for hedging against loan default or changes in credit risk (e.g., credit default swap).

Credit rating Debt rating assigned by a rating agency such as Moody’s or Standard & Poor’s.

Credit scoring A procedure for assigning scores to borrowers on the basis of the risk of default.

Cross exchange rate Exchange rate between two non-U.S. currencies.

Cross-default clause Clause in a loan agreement stating that the company is in default if it fails to meet its obligation on any other debt issue.

Cum dividend With dividend.

Cum rights With rights.

Cumulative preferred stock Stock that takes priority over common stock in regard to dividend payments. Dividends may not be paid on the common stock until all past dividends on the preferred stock have been paid.

Cumulative voting Voting system under which a stockholder may cast all of his or her votes for one candidate for the board of directors (cf. majority voting).

Current asset Asset that will normally be turned into cash within a year.

Current liability Liability that will normally be repaid within a year.

Current ratio Current assets divided by current liabilities—a measure of liquidity.

Current yield Bond coupon divided by price.

D

Data mining (data snooping) Excessive search to find interesting (but probably coincidental) behavior in a body of data.

DCF Discounted cash flow.

DDM Dividend discount model.

Dealer market Securities exchange in which dealers post offers to buy or sell, e.g., Nasdaq (cf. auction market).

Dealer paper Commercial paper sold through a dealer rather than directly by the company.

Death-spiral convertible Convertible bond exchangeable for shares with a specified market value.

Debenture Unsecured bond.

Debtor-in–possession financing (DIP financing) Debt issued by a company in Chapter 11 bankruptcy.

Debt overhang Shareholder reluctance to provide more capital if the extra cash flows are largely used to pay off debtholders.

Decision tree Method of representing alternative sequential decisions and the possible outcomes from these decisions.

Defeasance Practice whereby the borrower sets aside cash or bonds sufficient to service the borrower’s debt. Both the borrower’s debt and the offsetting cash or bonds are removed from the balance sheet.

Deferred tax Asset or liability that arises from differences between the tax expense shown in the income statement and the tax actually paid.

Degree of operating leverage (DOL) The percentage change in profits for a 1% change in sales.

Delta Hedge ratio.

Depository transfer check (DTC) Check made out directly by a local bank to a particular company.

Depreciation (1) Reduction in the book or market value of an asset; (2) portion of an investment that can be deducted from taxable income.

Depreciation tax shield The extra after-tax income that results from the depreciation deduction from taxable income.

Derivative Asset whose value derives from that of some other asset (e.g., a future or an option).

Designated market maker Member of NYSE responsible for market in specified securities (formerly called “specialist”).

Diff Differential swap.

Differential swap (diff, quanto swap) Swap between two LIBOR rates of interest, e.g., yen LIBOR for dollar LIBOR. Payments are in one currency.

Digital option Option paying fixed sum if asset price is the right side of exercise price, otherwise zero.

Dilution Diminution in the proportion of income to which each share is entitled.

DIP financing Debtor-in–possession financing.

Direct deposit The firm authorizes its bank to deposit money in the accounts of its employees or shareholders.

Direct lease Lease in which the lessor purchases new equipment from the manufacturer and leases it to the lessee (cf. sale and lease-back).

Direct payment (automatic debit, direct debit) The firm’s customers authorize it to debit their bank accounts for the amounts due (cf. direct deposit).

Direct quote For foreign exchange, the number of U.S. dollars needed to buy one unit of a foreign currency (cf. indirect quote).

Dirty price Bond price including accrued interest, i.e., the price paid by the bond buyer (cf. clean price).

Discount bond Debt sold for less than its principal value. If a discount bond pays no interest, it is called a “pure” discount, or zero-coupon, bond.

Discount loan Bank loan where interest is deducted up front.

Discounted cash flow (DCF) Future cash flows multiplied by discount factors to obtain present value.

Discount factor Present value of $1 received at a stated future date.

Discount rate Rate used to calculate the present value of future cash flows.

Discounted payback rule Requirement that discounted values of cash flows should be sufficient to pay back initial investment within a specified time.

Discriminatory price auction Auction in which successful bidders pay the price that they bid (cf. uniform price auction).

Disintermediation Withdrawal of funds from a financial institution in order to invest them directly (cf. intermediation).

Dividend Payment by a company to its stockholders.

Dividend discount model Model showing that the value of a share is equal to the discounted value of future dividends.

Dividend reinvestment plan (DRIP) Plan that allows shareholders to reinvest dividends automatically.

Dividend yield Annual dividend divided by share price.

Dodd-Frank Act 2010 legislation to amend regulation of financial markets and banks.

DOL Degree of operating leverage.

Double-declining-balance depreciation Method of accelerated depreciation.

Double-tax agreement Agreement between two countries that taxes paid abroad can be offset against domestic taxes levied on foreign dividends.

Down-and-in option Barrier option that comes into existence if asset price hits a barrier.

Down-and-out option Barrier option that expires if asset price hits a barrier.

DRIP Dividend reinvestment plan.

Drop lock An arrangement whereby the interest rate on a floating-rate note or preferred stock becomes fixed if it falls to a specified level.

DTC Depository transfer check.

Dual-class equity Shares with different voting rights.

Dual-currency bond Bond with interest paid in one currency and principal paid in another.

Du Pont formula Formula expressing relationship between return on assets, sales-to-assets, profit margin, and measures of leverage.

Duration The average number of years to an asset’s discounted cash flows.

Dutch auction In a Dutch auction investors submit the prices at which they are prepared to buy (or sell) the security. The purchase price is the lowest price that allows the firm to sell (or buy) the specified amount of the security.

E

EBIT Earnings before interest and taxes.

EBITDA Earnings before interest, taxes, depreciation, and amortization.

EBPP Electronic bill presentment and payment.

Economic depreciation Decline in present value of an asset.

Economic exposure Risk that arises from changes in real exchange rates (cf. transaction exposure, translation exposure).

Economic income Cash flow plus change in present value.

Economic rents Profits in excess of the competitive level.

Economic value added (EVA) A measure of residual income implemented by the consulting firm Stern Stewart.

Efficient frontier The set of efficient portfolios with different levels of expected return.

Efficient market Market in which security prices reflect information instantaneously.

Efficient portfolio Portfolio that offers the lowest risk (standard deviation) for its expected return and the highest expected return for its level of risk.

EFT Electronic funds transfer.

Electronic bill presentment and payment (EBPP) Allows companies to bill customers and receive payments via the Internet.

Electronic funds transfer (EFT) Transfer of money electronically (e.g., by Fedwire).

Employee stock ownership plan (ESOP) A company contributes to a trust fund that buys stock on behalf of employees.

Entrenching investment An investment that makes particular use of the skills of existing management.

EPS Earnings per share.

Equipment trust certificate Form of secured debt generally used to finance railroad equipment. The trustee retains ownership of the equipment until the debt is repaid.

Equity (1) Common stock and preferred stock. Often used to refer to common stock only. (2) Net worth.

Equity-linked bond Bond whose payments are linked to a stock market index.

Equivalent annual cash flow (or cost) Annuity with the same present value as the company’s proposed investment.

ESOP Employee stock ownership plan.

ETF Exchange-traded fund.

Euribor Euro interbank offered rate.

Euro interbank offered rate (Euribor) The interest rate at which major international banks in Europe borrow euros from each other.

Eurobond (1) Bond that is denominated in one country’s currency but marketed internationally outside that country. (2) Also used to refer to suggested sovereign bond issues that would be guaranteed by all Eurozone governments.

Eurocurrency Deposit held outside the currency’s issuing country (e.g., euroyen, or eurodollar deposit)

Eurodollar deposit Dollar deposit with a bank outside the United States.

European option Option that can be exercised only on final exercise date (cf. American option).

EVA Economic value added.

Event risk The risk that an unanticipated event (e.g., a takeover) will lead to a debt default.

Evergreen credit Revolving credit without maturity.

Exchange of assets Acquisition of another company by purchase of its assets in exchange for cash or shares.

Exchange of stock Acquisition of another company by purchase of its stock in exchange for cash or shares.

Exchange-traded fund (ETF) A stock designed to track a stock market index.

Ex dividend Purchase of shares in which the buyer is not entitled to the forthcoming dividend (cf. with dividend, cum dividend).

Exercise price (strike price) Price at which a call option or put option may be exercised.

Expectations theory Theory that forward interest rate (forward exchange rate) equals expected spot rate.

Expected return Average of possible returns weighted by their probabilities.

Ex rights Purchase of shares that do not entitle the owner to buy shares in the company’s rights issue (cf. with rights, cum rights, rights on).

Extendable bond Bond whose maturity can be extended at the option of the lender (or issuer).

External finance Finance that is not generated by the firm: new borrowing or an issue of stock (cf. internal finance).

Extra dividend Dividend that may or may not be repeated (cf. regular dividend).

F

Face value Principle.

Factor (1) A common influence on security prices (e.g., the level of interest rates or oil prices); (2) A business providing factoring.

Factoring Arrangement whereby a financial institution buys a company’s accounts receivable and collects the debt.

Fair price provision Appraisal rights.

Fallen angel Junk bond that was formerly investment grade.

FASB Financial Accounting Standards Board.

FCIA Foreign Credit Insurance Association.

FDIC Federal Deposit Insurance Corporation.

Fear index VIX.

Federal funds Non-interest-bearing deposits by banks at the Federal Reserve. Excess reserves are lent by banks to each other.

Fedwire A wire transfer system for high-value payments operated by the Federal Reserve System (cf. CHIPS).

Field warehouse Warehouse rented by a warehouse company on another firm’s premises (cf. public warehouse).

Financial assets Claims on real assets.

Financial engineering Combining or dividing existing instruments to create new financial products.

Financial institution A bank, insurance company, or similar financial intermediary.

Financial intermediary An organization that raises money from many investors and provides financing to individuals, corporations, and other organizations.

Financial lease (capital lease, full-payout lease) Long-term, noncancelable lease (cf. operating lease).

Financial leverage (gearing) Use of debt to increase the expected return on equity. Financial leverage is measured by the ratio of debt to debt plus equity (cf. operating leverage).

Firm commitment Arrangement whereby the underwriter guarantees to sell the entire issue.

Financial markets Markets in which securities are issued and traded.

Fiscal agency agreement An alternative to a bond trust deed. Unlike the trustee, the fiscal agent acts as an agent of the borrower.

Flat price Clean price.

Flipping Buying shares in an IPO and selling immediately.

Float See availability float, collection float, payment float.

Floating lien General lien against a company’s assets or against a particular class of assets.

Floating-price convertible Death-spiral convertible.

Floating-rate note (FRN) Note whose interest payment varies with the short-term interest rate.

Floating-rate preferred Preferred stock paying dividends that vary with short-term interest rates.

Floor planning Arrangement used to finance inventory. A finance company buys the inventory, which is then held in trust by the user.

Flow-to-equity method Discounted value of cash flows to and from equityholders.

Foreign bond A bond issued on the domestic capital market of another country.

Forex Foreign exchange.

Forfaiter Purchaser of promises to pay (e.g., bills of exchange or promissory notes issued by importers).

Forward contract Agreement to buy or sell an asset in the future at an agreed-upon price.

Forward cover Purchase or sale of forward foreign currency in order to offset a known future cash flow.

Forward exchange rate Exchange rate fixed today for exchanging currency at some future date (cf. spot exchange rate).

Forward interest rate Interest rate fixed today on a loan to be made at some future date (cf. spot interest rate).

Forward rate agreement (FRA) Agreement to borrow or lend at a specified future date at an interest rate that is fixed today.

Forward price Agreed-upon price for a forward contract.

FRA Forward rate agreement.

Free cash flow Cash not required for operations or for reinvestment.

Free-rider problem The temptation not to incur the costs of participating in a decision when one’s influence on that decision is small.

FRN Floating-rate note.

Full-payout lease Financial lease.

Full-service lease (rental lease) Lease in which the lessor promises to maintain and insure the equipment (cf. net lease).

Fundamental analysis Security analysis that seeks to detect misvalued securities by an analysis of the firm’s business prospects (cf. technical analysis).

Funded debt Debt maturing after more than one year (cf. unfunded debt).

Futures contract A contract to buy a commodity or security on a future date at a price that is fixed today. Unlike forward contracts, futures are traded on organized exchanges and are marked to market daily.

Futures exchange Exchange where futures contracts are traded.

G

GAAP Generally Accepted Accounting Principles.

Gamma A measure of how the option delta changes as the asset price changes.

Gearing Financial leverage.

General cash offer Issue of securities offered to all investors (cf. rights issue).

Generally Accepted Accounting Principles (GAAP) Procedures for preparing financial statements.

Gilt A British government bond.

Global bond Bond that is simultaneously sold domestically and internationally.

Golden parachute A large termination payment due to a company’s officers if they lose their jobs as a result of a merger.

Goodwill The difference between the amount paid for a firm in a merger and its book value.

Governance The oversight of a firm’s management.

Gray market Purchases and sales of securities that occur before the issue price is set.

Greeks The Greek letters that refer to option characteristics, e.g., delta, vega.

Greenmail Situation in which a large block of stock is held by an unfriendly company, forcing the target company to repurchase the stock at a substantial premium to prevent a takeover.

Greenshoe option Option that allows the underwriter for a new issue to buy and resell additional shares.

Growth stock Common stock of a company that has an opportunity to invest money to earn more than the opportunity cost of capital (cf. income stock).

H

Haircut An additional margin of collateral for a loan.

Hedge fund An investment fund charging a performance fee and open to a limited range of investors. Funds often follow complex strategies including short sales.

Hedge ratio (delta, option delta) The number of shares to buy for each option sold to create a safe position; more generally, the number of units of an asset that should be bought to hedge one unit of a liability.

Hedging Buying one security and selling another to reduce risk. A perfect hedge produces a riskless portfolio.

Hell-or-high-water clause Clause in a lease agreement that obligates the lessee to make payments regardless of what happens to the lessor or the equipment.

Highly leveraged transaction (HLT) Bank loan to a highly leveraged firm (formerly needed to be separately reported to the Federal Reserve Board).

High-yield bond Junk bond.

HLT Highly leveraged transaction.

Holding company Company whose sole function is to hold stock in the firm’s subsidiaries.

Horizontal merger Merger between two companies that manufacture similar products (cf. vertical merger, conglomerate merger).

Horizontal spread The simultaneous purchase and sale of two options that differ only in their exercise date (cf. vertical spread).

Hurdle rate Minimum acceptable rate of return on a project.

I

IBF International Banking Facility.

IMM International Monetary Market.

Immunization The construction of an asset and a liability that have offsetting changes in value.

Implied volatility The volatility implied by option prices.

Imputation tax system Arrangement by which investors who receive a dividend also receive a tax credit for corporate taxes that the firm has paid.

Income bond Bond on which interest is payable only if earned.

Income stock Common stock with high dividend yield and few profitable investment opportunities (cf. growth stock).

Indenture Formal agreement, e.g., establishing the terms of a bond issue.

Indexed bond Bond whose payments are linked to an index, e.g., a consumer price index (see TIPS).

Index fund Investment fund designed to match the returns on a stock market index.

Indirect quote For foreign exchange, the number of units of a foreign currency needed to buy one U.S. dollar (cf. direct quote).

Industrial revenue bond (IRB) Bond issued by local government agencies on behalf of corporations.

Initial public offering (IPO) A company’s first public issue of common stock.

Inside director Director who is also employed by the company.

In-substance defeasance Defeasance whereby debt is removed from the balance sheet but not canceled (cf. novation).

Intangible asset Nonmaterial asset, such as technical expertise, a trademark, or a patent (cf. tangible asset).

Interest cover Times interest earned.

Interest rate parity Theory that the differential between the forward exchange rate and the spot exchange rate is equal to the differential between the foreign and domestic interest rates.

Interest tax shield The extra after-tax income that results from the tax deductibility of interest.

Intermediation Investment through a financial institution (cf. disintermediation).

Internal finance Finance generated within a firm by retained earnings and depreciation (cf. external finance).

Internal growth rate The maximum rate of firm growth without external finance (cf. sustainable growth rate).

Internal rate of return (IRR) Discount rate at which investment has zero net present value.

International banking facility (IBF) A branch that an American bank establishes in the United States to do eurocurrency business.

International Monetary Market (IMM) The financial futures market within the Chicago Mercantile Exchange.

Interval measure The number of days that a firm can finance operations without additional cash income.

In-the-money option An option that would be worth exercising if it expired immediately (cf. out-of-the-money option).

Investment-grade bond Bond rated at least Baa by Moody’s or BBB by Standard and Poor’s or Fitch.

IOSCO International Organization of Securities Commissions.

IPO Initial public offering.

IRB Industrial revenue bond.

IRR Internal rate of return.

IRS Internal Revenue Service.

ISDA International Swap and Derivatives Association.

ISMA International Securities Market Association.

Issued share capital Total amount of shares that are in issue (cf. outstanding share capital).

J

Junior debt Subordinated debt.

Junk bond (high-yield bond) Debt that is rated below an investment-grade bond.

Just-in-time System of inventory management that requires minimum inventories of materials and very frequent deliveries by suppliers.

K

Keiretsu A network of Japanese companies organized around a major bank.

L

Law of one price Two identical cash flows or commodities must sell for the same price in a competitive market.

LBO Leveraged buyout.

Lease Long-term rental agreement.

Legal capital Value at which a company’s shares are recorded in its books.

Legal defeasance Novation.

Lessee User of a leased asset (cf. lessor).

Lessor Owner of a leased asset (cf. lessee).

Letter of credit Letter from a bank stating that it has established a credit in the company’s favor.

Letter stock Privately placed common stock, so called because the SEC requires a letter from the purchaser that the stock is not intended for resale.

Leverage See financial leverage, operating leverage.

Leveraged buyout (LBO) Acquisition in which (1) a large part of the purchase price is debt-financed and (2) the remaining equity is privately held by a small group of investors.

Leveraged lease Lease in which the lessor finances part of the cost of the asset by an issue of debt secured by the asset and the lease payments.

Liabilities, total liabilities Total value of financial claims on a firm’s assets. Equals assets minus net worth.

LIBOR London interbank offered rate.

Lien Lender’s claims on specified assets.

Limited liability Limitation of a shareholder’s losses to the amount invested.

Limited liability company (LLC) Partnership in which all partners have limited liability.

Limited partnership Partnership in which some partners have limited liability and general partners have unlimited liability.

Limit order Order to buy (sell) securities within a maximum (minimum) price (cf. market order).

Linear programming (LP) Technique for finding the maximum value of some objective function subject to stated linear constraints.

Line of credit Agreement by a bank that a company may borrow at any time up to an established limit.

Liquid asset Asset that is easily and cheaply turned into cash—notably cash itself and short-term securities.

Liquidating dividend Dividend that represents a return of capital.

Liquidator Person appointed by unsecured creditors in the United Kingdom to oversee the sale of an insolvent firm’s assets and the repayment of debts.

Liquidity Ability to sell an asset on short notice at close to the market price.

Liquidity-preference theory Theory that investors demand a higher yield to compensate for the extra risk of long-term bonds.

Liquidity premium (1) Additional return for investing in a security that cannot easily be turned into cash; (2) difference between the forward interest rate and the expected spot interest rate.

Liquid yield option note (LYON) Zero-coupon, callable, puttable, convertible bond.

LLC Limited liability company.

Loan origination fee Up-front fee charged by the lending bank.

Lockbox system Form of concentration banking. Customers send payments to a post office box. A local bank collects and processes the checks and transfers surplus funds to the company’s principal bank.

Lockup Restriction on existing shareholders from selling shares until some period after an IPO.

London interbank offered rate (LIBOR) The interest rate at which major international banks in London borrow from each other. (LIBID is London interbank bid rate; LIMEAN is mean of bid and offered rate.)

Long hedge Purchase of a hedging instrument (e.g., a future) to hedge a short position in the underlying asset (cf. short hedge).

Longevity bonds Bonds that pay a higher rate of interest if a high proportion of the population survives to a particular age.

Lookback option Option whose payoff depends on the highest asset price recorded over the life of the option.

LP Linear programming.

LYON Liquid yield option note.

M

MACRS Modified accelerated cost recovery system.

Mail float Time spent by a check in the mail.

Maintenance margin Minimum margin that must be maintained on a futures contract.

Majority voting Voting system under which each director is voted upon separately (cf. cumulative voting).

Make-whole call provision Call provision on a bond where the call price is adjusted to ensure that bond owner is not disadvantaged.

Management buyout (MBO) Leveraged buyout whereby the acquiring group is led by the firm’s management.

Mandatory convertible Bond automatically convertible into equity, usually with a limit on the value of stock received.

Margin Cash or securities set aside by an investor as evidence that he or she can honor a commitment.

Marked to market An arrangement whereby the profits or losses on a futures contract are settled up each day.

Market capitalization Market value of outstanding share capital.

Market capitalization rate Expected return on a security.

Market model Model suggesting a linear relationship between actual returns on a stock and on the market portfolio.

Market order Order to buy or sell securities at the prevailing market price (cf. limit order).

Market risk (systematic risk) Risk that cannot be diversified away.

Market-to-book ratio Ratio of market value to book value of firm’s equity.

Market value added Difference between market value and book value of firm’s equity.

MBO Management buyout.

MBS Mortgage-backed security.

MDA Multiple-discriminant analysis.

Medium-term note (MTN) Debt with a typical maturity of 1 to 10 years offered regularly by a company using the same procedure as commercial paper.

Merger (1) Acquisition in which all assets and liabilities are absorbed by the buyer (cf. exchange of assets, exchange of stock); (2) more generally, any combination of two companies.

MIP (Monthly income preferred security) Preferred stock issued by a subsidiary located in a tax haven. The subsidiary relends the money to the parent.

Mismatch bond Floating-rate note whose interest rate is reset at more frequent intervals than the rollover period (e.g., a note whose payments are set quarterly on the basis of the one-year interest rate).

Modified accelerated cost recovery system (MACRS) Schedule of depreciation deductions allowed for tax purposes.

Modified IRR Internal rate of return calculated by first discounting later cash flows back to earlier periods so that there remains only one change in the sign of the cash flows.

Momentum Characteristic of stocks showing persistent recent high returns.

Money center bank A major U.S. bank that undertakes a wide range of banking activities.

Money market Market for short-term safe investments.

Money-market deposit account (MMDA) A bank account paying money-market interest rate.

Money-market fund Mutual fund that invests solely in short-term safe securities.

Monoline Insurance company that insures debtholders against the risk of default.

Monte Carlo simulation Method for calculating the probability distribution of possible outcomes, e.g., from a project.

Moral hazard The risk that the existence of a contract will change the behavior of one or both parties to the contract; e.g., an insured firm may take fewer fire precautions.

Mortality bonds Bonds that pay a higher rate of interest if there is a sharp rise in the death rate.

Mortgage-backed security (MBS) A security backed by a pool of mortgages.

Mortgage bond Bond secured against plant and equipment.

MTN Medium-term note.

Multiple-discriminant analysis (MDA) Statistical technique for distinguishing between two groups on the basis of their observed characteristics.

Mutual fund Managed investment fund whose shares are sold to investors.

Mutually exclusive projects Two projects that cannot both be undertaken.

N

Naked option Option held on its own, i.e., not used for hedging a holding in the asset or other options.

NASD National Association of Security Dealers.

Nasdaq A U.S. stock exchange whose dealers tend to specialize in high-tech stocks.

Negative pledge clause Clause under which the borrower agrees not to permit an exclusive lien on any of its assets.

Negotiable certificate of deposit (CD) A certificate for a time deposit of $1 million or more that can be sold before maturity.

Negotiated underwriting Method of choosing an underwriter. Most firms may choose their underwriter by negotiation (cf. competitive bidding).

Net lease Lease in which the lessee promises to maintain and insure the equipment (cf. full-service lease).

Net present value (NPV) A project’s net contribution to wealth—present value minus initial investment.

Net working capital Current assets minus current liabilities.

Net worth Book value of a company’s common stock, surplus, and retained earnings.

Nominal interest rate Interest rate expressed in money terms (cf. real interest rate).

Nonrefundable debt Debt that may not be called in order to replace it with another issue at a lower interest cost.

NOPAT Net operating profit after tax.

Normal distribution Symmetric bell-shaped distribution that can be completely defined by its mean and standard deviation.

Note Unsecured debt with a maturity of up to 10 years.

Novation (legal defeasance) Defeasance whereby the firm’s debt is canceled (cf. in-substance defeasance).

NPV Net present value.

NYSE New York Stock Exchange.

O

OAT (Obligation assimilable du Trésor) French government bond.

Odd lot A trade of less than 100 shares (cf. round lot).

Off-balance-sheet financing Financing that is not shown as a liability in a company’s balance sheet.

Offer price Asked price.

OID debt Original issue discount debt.

On the run The most recently issued (and, therefore, typically the most liquid) government bond in a particular maturity range.

Open account Arrangement whereby sales are made with no formal debt contract. The buyer signs a receipt, and the seller records the sale in the sales ledger.

Open-end mortgage Mortgage against which additional debt may be issued (cf. closed-end mortgage).

Open interest The number of currently outstanding futures contracts.

Operating lease Short-term, cancelable lease (cf. financial lease).

Operating leverage Fixed operating costs, so called because they accentuate variations in profits (cf. financial leverage).

Operating profit margin After-tax operating income as a percentage of sales.

Opportunity cost of capital (hurdle rate, cost of capital) Expected return that is foregone by investing in a project rather than in comparable financial securities.

Option See call option, put option.

Option delta Hedge ratio.

Original issue discount debt (OID debt) Debt that is initially offered at a price below face value.

OTC Over-the-counter.

Out-of-the-money option An option that would not be worth exercising if it matured immediately (cf. in-the-money option).

Outstanding share capital Issued share capital less the par value of shares that are held in the company’s treasury.

Oversubscription privilege In a rights issue, arrangement by which shareholders are given the right to apply for any shares that are not taken up.

Over-the-counter (OTC) Informal market that does not involve a securities exchange.

P

Partnership Joint ownership of business whereby general partners have unlimited liability.

Par value Value of a security shown on the certificate.

Pass-through securities Notes or bonds backed by a package of assets (e.g., mortgage pass-throughs, CARs, CARDs).

Path-dependent option Option whose value depends on the sequence of prices of the underlying asset rather than just the final price of the asset.

Payables Accounts payable.

Payback period Time until the cumulative cash flow equals the initial investment.

Payback rule Requirement that project should recover its initial investment within a specified time.

Pay-in-kind bond (PIK) Bond that allows the issuer to choose to make interest payments in the form of additional bonds.

Payment float Company-written checks that have not yet cleared (cf. availability float).

Payout ratio Dividend as a proportion of earnings per share.

PBGC Pension Benefit Guarantee Corporation.

Pension fund Investment plan set up by an employer to provide for employees’ retirement.

P/E ratio Share price divided by earnings per share.

PERC (Preferred equity redemption cumulative stock) Preferred stock that converts automatically into equity at a stated date. A limit is placed on the value of the shares that the investor receives.

Perpetuity Investment offering a level stream of cash flows in perpetuity (cf. consol).

PIK Pay-in-kind bond.

PN Project note.

Poison pill Includes a variety of takeover defenses, notably the right of existing shareholders to acquire stock at a discount if a bidder acquires a minimum number of shares.

Poison put A covenant allowing the bondholder to demand repayment in the event of a hostile merger.

Pooling of interest Method of accounting for mergers (no longer available in the USA). The consolidated balance sheet of the merged firm is obtained by combining the balance sheets of the separate firms (cf. purchase accounting).

Position diagram Diagram showing the possible payoffs from a derivative investment.

Postaudit Evaluation of an investment project after it has been undertaken.

Praecipium Arrangement fee for syndicated loan.

Preemptive right Common stockholder’s right to anything of value distributed by the company.

Preferred stock Stock that takes priority over common stock in regard to dividends. Dividends may not be paid on common stock unless the dividend is paid on all preferred stock (cf. cumulative preferred stock). The dividend rate on preferred is usually fixed at time of issue.

Prenegotiated bankruptcy Chapter 11 bankruptcy where only principal creditors have agreed to the reorganization plan before filing (cf. prepackaged bankruptcy).

Prepack Prepackaged bankruptcy.

Prepackaged bankruptcy (prepack) Bankruptcy proceedings intended to confirm a reorganization plan that has already been agreed to informally.

Present value Discounted value of future cash flows.

Present value of growth opportunities (PVGO) Net present value of investments the firm is expected to make in the future.

Primary issue Issue of new securities by a firm (cf. secondary issue).

Prime rate Benchmark lending rate set by U.S. banks.

Principal Amount of debt that must be repaid.

Principal–agent problem Problem faced by a principal (e.g., shareholder) in ensuring that an agent (e.g., manager) acts on his or her behalf.

Private equity Equity that is not publicly traded and that is used to finance business start-ups, leveraged buyouts, etc.

Private placement Issue of bonds or stock that is placed privately with a few investors and is not then publicly traded.

Privatization Sale of a government-owned company to private investors.

Privileged subscription issue Rights issue.

Production payment Loan in the form of advanced payment for future delivery of a product.

Profitability index Ratio of a project’s NPV to the initial investment.

Pro forma Projected.

Project finance Debt that is largely a claim against the cash flows from a particular project rather than against the firm as a whole.

Project note (PN) Note issued by public housing or urban renewal agencies.

Promissory note Promise to pay.

Prospect theory A theory of asset pricing suggested by the observation of behavioral psychologists that investors have a particular aversion to losses even if very small.

Prospectus Summary of the registration statement providing information on an issue of securities.

Protective put Put option that is combined with holding in the underlying asset.

Proxy vote Vote cast by one person on behalf of another.

Public warehouse (terminal warehouse) Warehouse operated by an independent warehouse company on its own premises (cf. field warehouse).

Purchase accounting Method of accounting for mergers. The assets of the acquired firm are shown at market value on the balance sheet of the acquirer (cf. pooling of interest).

Purchase fund Resembles a sinking fund except that money is used only to purchase bonds if they are selling below their par value.

Put–call parity The relationship between the prices of European put and call options.

Put option Option to sell an asset at a specified exercise price on or before a specified exercise date (cf. call option).

PVGO Present value of growth opportunities.

Pyramid Created by forming a holding company whose only asset is a controlling interest in a second holding company, which in turn has a controlling interest in an operating company.

Q

q Ratio of the market value of an asset to its replacement cost.

QIBs Qualified institutional buyers.

Quadratic programming Variant of linear programming whereby the equations are quadratic rather than linear.

Qualified Institutional buyers (QIBs) Institutions that are allowed to trade unregistered stock among themselves.

Quanto swap Differential swap.

Quick ratio (acid-test ratio) Measure of liquidity: (cash + marketable securities + receivables) divided by current liabilities.

R

Range forward A forward exchange rate contract that places upper and lower bounds on the cost of foreign exchange.

Ratchet bonds Floating-rate bonds whose coupon can only be reset downward.

Rate of return Total income and capital appreciation per period per dollar invested.

Rate-sensitive bonds Bonds whose coupon rate changes as issuer’s credit-rating changes.

Real assets Tangible assets and intangible assets used to carry on business (cf. financial assets).

Real estate investment trust (REIT) Trust company formed to invest in real estate.

Real interest rate Interest rate expressed in terms of real goods, i.e., nominal interest rate adjusted for inflation.

Real option The flexibility to modify, postpone, expand, or abandon a project.

Receivables Accounts receivable.

Receiver A bankruptcy practitioner appointed by secured creditors in the United Kingdom to oversee the repayment of debts.

Record date Date set by directors when making dividend payment. Dividends are sent to stockholders who are registered on the record date.

Recourse Term describing a type of loan. If a loan is with recourse, the lender has a general claim against the parent company if the collateral is insufficient to repay the debt.

Red herring Preliminary prospectus.

Refunding Replacement of existing debt with a new issue of debt.

Registered security Security whose ownership is recorded by the company’s registrar (cf. bearer security).

Registrar Financial institution appointed to record issue and ownership of company securities.

Registration Process of obtaining SEC approval for a public issue of securities.

Registration statement A detailed document prepared for the Securities and Exchange Commission that presents information about a firm’s proposed financing and the firm’s history, existing business, and plans for the future.

Regression analysis In statistics, a technique for finding the line of best fit.

Regular dividend Dividend that the company expects to maintain in the future.

Regulation A issue Small security issues that are partially exempt from SEC registration requirements.

REIT Real estate investment trust.

Rental lease Full-service lease.

Replicating portfolio Package of assets whose returns exactly replicate those of an option.

Repo Repurchase agreement.

Repurchase agreement (RP, repo, buy-back) Purchase of Treasury securities from a securities dealer with an agreement that the dealer will repurchase them at a specified price.

Residual income After-tax profit less the opportunity cost of capital employed by the business (see also Economic Value Added).

Residual risk Specific risk.

Retained earnings Earnings not paid out as dividends.

Return on assets (ROA) After-tax operating income as a percentage of total assets.

Return on capital (ROC) After-tax operating income as a percentage of long-term capital.

Return on equity (ROE) Usually, equity earnings as a proportion of the book value of equity.

Return on investment (ROI) Generally, book income as a proportion of net book value.

Revenue bond Municipal bond that is serviced out of the revenues from a particular project.

Reverse FRN (yield curve note) Floating-rate note whose payments rise as the general level of interest rates falls and vice versa.

Reverse split Action by the company to reduce the number of outstanding shares by replacing two or more of its shares with a single, more valuable share.

Revolving credit Legally assured line of credit with a bank.

Rights issue (privileged subscription issue) Issue of securities offered to current stockholders (cf. general cash offer).

Rights on With rights.

Risk-neutral probability The probability of a future outcome that would be consistent with the value of the security to a risk-neutral investor.

Risk premium Expected additional return for making a risky investment rather than a safe one.

ROA Return on assets.

Road show Series of meetings between a company and potential investors before the company decides on the terms of a new issue.

ROE Return on equity.

ROI Return on investment.

Roll-over CD A package of successive certificates of deposit.

Round lot A trade of 100 shares (cf. odd lot).

RP Repurchase agreement.

R squared (R2) Square of the correlation coefficient—the proportion of the variability in one series that can be explained by the variability of one or more other series.

Rule 144a SEC rule allowing qualified institutional buyers to buy and trade unregistered securities.

S

“S” corporation A U.S. corporation that does not pay tax on income. Instead shareholders (who must be limited in number) report their share of income on their individual tax returns (cf. “C” corporation).

Sale and lease-back Sale of an existing asset to a financial institution that then leases it back to the user (cf. direct lease).

Salvage value Scrap or resale value of plant and equipment.

Samurai bond A yen bond issued in Tokyo by a non-Japanese borrower (cf. bulldog bond, Yankee bond).

Sarbanes-Oxley Act (SOX) 2002 legislation to protect shareholders from misleading accounting and fraudulent practice.

SBIC Small Business Investment Company.

Scenario analysis Analysis of the profitability of a project under alternative economic scenarios.

Season datings Extended credit for customers who order goods out of the peak season.

Seasoned issue Issue of a security for which there is an existing market (cf. unseasoned issue).

SEC Securities and Exchange Commission.

Secondary issue (1) Procedure for selling blocks of seasoned issues of stock; (2) more generally, sale of already issued stock.

Secondary market Market in which one can buy or sell seasoned issues of securities.

Secured debt Debt that, in the event of default, has first claim on specified assets.

Securities Claims on real assets.

Securitization Substitution of tradable securities for privately negotiated instruments.

Security market line (SML) Line representing the relationship between expected return and market risk.

Self-liquidating loan Loan to finance current assets. The sale of the current assets provides the cash to repay the loan.

Self-selection Consequence of a contract that induces only one group (e.g., low-risk individuals) to participate.

Semistrong-form efficient market Market in which security prices reflect all publicly available information (cf. weak-form efficient market and strong-form efficient market).

Senior debt Debt that, in the event of bankruptcy, must be repaid before subordinated debt receives any payment.

Sensitivity analysis Analysis of the effect on project profitability of possible changes in sales, costs, and so on.

Serial bonds Package of bonds that mature in successive years.

Series bond Bond that may be issued in several series under the same indenture.

Shark repellant Amendment to company charter intended to protect against takeover.

Sharpe ratio Ratio of portfolio’s risk premium to its risk (standard deviation).

Shelf registration A procedure that allows firms to file one registration statement covering several issues of the same security.

Shogun bond Non-yen bond issued in Japan by a nonresident.

Short hedge Sale of a hedging instrument (e.g., a future) to hedge a long position in the underlying asset (cf. long hedge).

Short sale Sale of a security the investor does not own.

Sight draft Demand for immediate payment (cf. time draft).

Signal Action that demonstrates an individual’s unobservable characteristics (because it would be unduly costly for someone without those characteristics to take the action).

Simple interest Interest calculated only on the initial investment (cf. compound interest).

Simulation Monte Carlo simulation.

Sinker Sinking fund.

Sinking fund (sinker) Fund established by a company to retire debt before maturity.

SIV (structured investment vehicle) A fund that typically invested in mortgage-backed securities, which it financed by issuing senior and junior tranches of asset-backed commercial paper and longer-term notes.

Skewed distribution Probability distribution in which an unequal number of observations lie below and above the mean.

SML Security market line.

SOX Sarbanes-Oxley Act.

SPE Special-purpose entity.

Special dividend (extra dividend) Dividend that is unlikely to be repeated.

Specialist Designated market maker.

Special-purpose entity Partnerships established by companies to hold certain assets and obtain funding. May be used to obtain off-balance-sheet debt for the parent.

Specific risk (residual risk, unique risk, unsystematic risk) Risk that can be eliminated by diversification.

Spinning The underwriter of an IPO unethically allots a portion of offering to senior management of a client company.

Spin-off Distribution of shares in a subsidiary to the company’s shareholders so that they hold shares separately in the two firms.

Spot exchange rate Exchange rate on currency for immediate delivery (cf. forward exchange rate).

Spot price Price of asset for immediate delivery (in contrast to forward or futures price).

Spot rate Interest rate fixed today on a loan that is made today (cf. forward interest rate).

Spread Difference between the price at which an underwriter buys an issue from a firm and the price at which the underwriter sells it to the public.

Staggered board Board whose directors are elected periodically, instead of at one time.

Standard deviation Square root of the variance—a measure of variability.

Standard error In statistics, a measure of the possible error in an estimate.

Standby agreement In a rights issue, agreement that the underwriter will purchase any stock not purchased by investors.

Step-up bond Bond whose coupon is stepped up over time (also step-down bond).

Stock dividend Dividend in the form of stock rather than cash.

Stock split “Free” issue of shares to existing shareholders.

Stop-out price (yield) The highest price (lowest yield) at which a Treasury bill is sold in auction.

Straddle The combination of a put option and a call option with the same exercise price.

Straight-line depreciation An equal dollar amount of depreciation in each period.

Strike price Exercise price of an option.

Stripped bond (strip) Bond that is subdivided into a series of zero-coupon bonds.

Strong-form efficient market Market in which security prices reflect instantaneously all information available to investors (cf. weak-form efficient market and semistrong-form efficient market).

Structured debt Debt that has been customized for the buyer, often by incorporating unusual options.

Subordinated debt (junior debt) Debt over which senior debt takes priority. In the event of bankruptcy, subordinated debtholders receive payment only after senior debt is paid off in full.

Subprime loans The most risky category of loans.

Sum-of-the-years’-digits depreciation Method of accelerated depreciation.

Sunk costs Costs that have been incurred and cannot be reversed.

Supermajority Provision in a company’s charter requiring a majority of, say, 80% of shareholders to approve certain changes, such as a merger.

Sushi bond A eurobond issued by a Japanese corporation.

Sustainable growth rate Maximum rate of firm growth without increasing financial leverage (cf. internal growth rate).

Swap An arrangement whereby two companies lend to each other on different terms, e.g., in different currencies, or one at a fixed rate and the other at a floating rate.

Swaption Option on a swap.

Sweep program Arrangement whereby bank invests a company’s available cash at the end of each day.

Swingline facility Bank borrowing facility to provide finance while the firm replaces U.S. commercial paper with eurocommercial paper.

Syndicated loan A large loan provided by a group of banks.

Systematic risk Market risk.

T

Take-or-pay In project finance, arrangement where parent company agrees to pay for output of project even if it chooses not to take delivery.

Take-up fee Fee paid to underwriters of a rights issue on any stock they are obliged to purchase.

Tangent efficient portfolio The portfolio of risky assets offering the highest risk premium per unit of risk (standard deviation).

Tangible asset Physical asset, such as plant, machinery, and offices (cf. intangible asset).

Tax-anticipation bill Short-term bill issued by the U.S. Treasury that can be surrendered at face value in payment of taxes.

T-bill Treasury bill.

Technical analysis Security analysis that seeks to detect and interpret patterns in past security prices (cf. fundamental analysis).

TED spread Difference between LIBOR and U.S. Treasury bill rate.

Tender offer General offer made directly to a firm’s shareholders to buy their stock.

10-K Annual financial statements as filed with the SEC.

10-Q Quarterly financial statements as filed with the SEC.

Tenor Maturity of a loan.

Terminal warehouse Public warehouse.

Term loan Medium-term, privately placed loan, usually made by a bank.

Term structure of interest rates Relationship between interest rates on loans of different maturities (cf. yield curve).

Throughput arrangement Arrangement by which shareholders of a pipeline company agree to make sufficient use of pipeline to enable the pipeline company to service its debt.

Tick Minimum amount the price of a security may change.

Time draft Demand for payment at a stated future date (cf. sight draft).

Times-interest-earned (interest cover) Earnings before interest and tax, divided by interest payments.

TIPS (Treasury Inflation Protected Securities) U.S. Treasury bonds whose coupon and principal payments are linked to the Consumer Price Index.

Toehold Small investment by a company in the shares of a potential takeover target.

Tolling contract In project finance, arrangement whereby parent company promises to deliver materials to project for processing and then to repurchase them.

Tombstone Advertisement listing the underwriters to a security issue.

Trade acceptance Written demand that has been accepted by an industrial company to pay a given sum at a future date (cf. banker’s acceptance).

Trade credit Accounts receivable.

Trade debt Accounts payable.

Tranche Portion of a new issue sold at a different point in time or that has different terms.

Transaction exposure Risk to a firm with known future cash flows in a foreign currency that arises from possible changes in the exchange rate (cf. economic exposure, translation exposure).

Transfer agent Individual or institution appointed by a company to look after the transfer of securities.

Translation exposure Risk of adverse effects on a firm’s financial statements that may arise from changes in exchange rates (cf. economic exposure, transaction exposure).

Treasurer Principal financial manager (cf. controller).

Treasury bill (T-bill) Short-term discount debt maturing in less than one year, issued regularly by the government.

Treasury stock Common stock that has been repurchased by the company and held in the company’s treasury.

Trust deed Agreement between trustee and borrower setting out terms of a bond.

Trust receipt Receipt for goods that are to be held in trust for the lender.

Tunneling Actions by a controlling shareholder to transfer wealth out of the firm (e.g., by supplying materials at an inflated price).

U

Underpricing Issue of securities below their market value.

Underwriter Firm that buys an issue of securities from a company and resells it to investors.

Unfunded debt Debt maturing within one year (cf. funded debt).

Uniform price auction Auction in which all successful bidders pay the same price (cf. discriminatory price auction).

Unique risk Specific risk.

Unseasoned issue Issue of a security for which there is no existing market (cf. seasoned issue).

Unsystematic risk Specific risk.

V

Value additivity Rule that the value of the whole must equal the sum of the values of the parts.

Value at risk (VAR) The probability of portfolio losses exceeding some specified proportion.

Value stock A stock that is expected to provide steady income but relatively low growth (often refers to stocks with a low ratio of market-to-book value).

Vanilla issue Issue without unusual features.

VAR Value at risk.

Variable-rate demand bond (VRDB) Floating-rate bond that can be sold back periodically to the issuer.

Variance Mean squared deviation from the expected value; a measure of variability.

Variation margin The daily gains or losses on a futures contract credited to the investor’s margin account.

Vega A measure of how the option price changes as the asset’s volatility changes.

Venture capital Capital to finance a new firm.

Vertical merger Merger between a supplier and its customer (cf. horizontal merger, conglomerate merger).

Vertical spread Simultaneous purchase and sale of two options that differ only in their exercise price (cf. horizontal spread).

VIX (Fear index) A measure of the implied volatility of stocks in the S&P 500 Index.

VRDB Variable rate demand bond.

W

WACC Weighted-average cost of capital.

Warehouse receipt Evidence that a firm owns goods stored in a warehouse.

Warrant Long-term call option issued by a company.

Weak-form efficient market Market in which security prices instantaneously reflect the information in the history of security prices. In such a market security prices follow a random walk (cf. semistrong-form efficient market and strong-form efficient market).

Weighted-average cost of capital (WACC) Expected return on a portfolio of all the firm’s securities. Used as hurdle rate for capital investment.

White knight A friendly potential acquirer sought out by a target company threatened by a less welcome suitor.

Wi. When issued.

Winner’s curse Problem faced by uninformed bidders. For example, in an initial public offering uninformed participants are likely to receive larger allotments of issues that informed participants know are overpriced.

With dividend (cum dividend) Purchase of shares in which the buyer is entitled to the forthcoming dividend (cf. ex dividend).

Withholding tax Tax levied on dividends paid abroad.

With rights (cum rights, rights on) Purchase of shares in which the buyer is entitled to the rights to buy shares in the company’s rights issue (cf. ex rights).

Working capital Current assets and current liabilities. The term is commonly used as synonymous with net working capital.

Workout Informal arrangement between a borrower and creditors.

Writer Option seller.

X

xd Ex dividend.

xr Ex rights.

Y

Yankee bond A dollar bond issued in the United States by a non-U.S. borrower (cf. bulldog bond, Samurai bond).

Yield curve Term structure of interest rates.

Yield curve note Reverse FRN.

Yield to call Yield on a bond assuming that it will be called.

Yield to maturity Internal rate of return on a bond.

Z

Zero-coupon bond Discount bond making no coupon payments.

Z-score Measure of the likelihood of bankruptcy.

Index

Note: Page numbers followed by n indicate material in source notes and footnotes.

A

Abandonment option, 259–261, 568–570

project life and, 569

temporary, 569–570

valuation of, 569

Abbott Laboratories, 842

Abnormal return, 325n, 325–326

ABS (asset-backed securities), 605, 610–611, 623, 628

Absolute priority, 459

Accelerated depreciation, 140–142

Accenture, 134n

Accounting income, tax income versus, 142

Accounting rates of return, 726–728

nature of, 726–728

problems with, 728–729

Accounting standards, 643, 643n, 721, 821

Accounts payable, 756

Accounts payable period, 776–777

Accounts receivable, 755–756, 775

Accounts receivable period, 776

Accrued interest, 608

ACH (Automated Clearing House), 789

Acharya, V. V., 369, 611n

Acid-test ratio, 736

Acquisitions. See Mergers and acquisitions

Adecco, 299

Adjusted present value (APV), 495–499

additions to debt capacity, 497–498

base case, 495

for international projects, 498–499

issue costs and, 496–497

leasing and, 650–651

review of, 500–501

value of interest tax shields, 500–501

Adler, B. E., 857

Administrative costs

in leasing, 641

in pooling risks, 663

Adverse selection risk, 663

Agency costs, 12

Agency for International Development, 794n

Agency problem, 295–314, 862–863, 882–883

agents versus principals, 12

compensation plans, 295–314

costs, 12, 298–300, 462–464, 623

monitoring, 298–300

Ponzi schemes, 11–12

reducing agency costs, 623

risk management and, 660, 661–662

risk taking and, 297–298

subprime mortgage crisis, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

transparency and, 875–876

Agency theory, 862–863

Agent, 12

Aggarwal, R. K., 314, 845n

Aghion, P., 854n

Agrawal, A., 826n

Agrawal, D., 594n

Aguirreamalloa, J., 184

AIG, 51, 366, 512, 589

Airbus, 573–575

Air France-KLM, 298

Aivasian, V., 470n

Alcoa, 387, 727

Allayanis, G., 713

Allen, Franklin, 336n, 369, 421, 443, 765, 860n, 874n, 875n, 878, 883, 885n, 889n

Allen, J., 857

Allen, L., 603

Allied Crude Vegetable Oil Refining Corporation, 627

Allied Irish Bank, 367

Allman-Ward, M., 799

Allocated overhead, in net present value analysis, 135

All-or-none underwriting, 379n

Alpha, 325

Alpine bonds, 616

Alternative minimum tax (AMT), 141–142, 642

Altinkilic, O., 387n

Altman, Edward I., 458n, 598n, 603, 839n, 857

Amazon, 401, 778–779

American Airlines (AMR), 358, 588, 594–595, 641–642, 851

American Greetings, 387

American International Group (AIG), 51, 366, 512, 589

American Jobs Creation Act (JOBS) of 2004, 652n

American options, 513, 520n, 539n, 552–554

American Stores, 65

Amortization, 31, 734n

AMR (American Airlines), 358, 588, 594–595, 641–642, 851

Amran, M., 579, 580

AMT (alternative minimum tax), 141–142, 642

Anders, C., 838n

Andrade, G., 458, 458n, 820, 820n, 827, 827n, 829, 830

Angel investors, 373

Anglo-Irish Bank, 845n

Anglo-Saxon financial system, 721, 827, 860–864, 869

Annual coupon, 46–47

Annual percentage rate (APR), 35–38

Annually compounded rate, 46–47

Annuities, 27–34. See also Equivalent annual cost

defined, 27

growing, 33–34

valuation of, 27–33

annual mortgage payments, 30–31

annuities due, 30

future value, 32

growing annuities, 33–34

installment plan costing, 28–29

lottery winnings, 29

present value, 27–28

Annuity due, 30

Annuity factor, 27–28

Anomalies, 328–332

Anthony, R., 306n

Antikarov, R. S., 580

Antitrust law, mergers and, 820–821

Aoki, M., 878

AOL, 341, 808

Apache, 78, 79

Apax, 837

Apollo Management, 837

Apple Computer Inc., 378n, 418, 419, 513–526, 535–544, 548–549, 552, 791

Appropriation requests, 246–247

APR (annual percentage rate), 35–38

APT (arbitrage pricing theory), 205–206, 325n

APV (adjusted present value), 495–501, 650–651

Aramark, 376

Arbitrage

defined, 57

Delta One desks, 682

limits to, 334–335

market efficiency and, 334–335

money machine and, 57, 698

risk-neutral option valuation and, 537–540

risks of, 681, 682

Arbitrage pricing theory (APT), 205–206

capital asset pricing model versus, 206

defined, 205

Fama-French three-factor model and, 206–208, 325n

Arcelor, 827

Archimedes, 536n

Archipelago, 76n

Argentina, 590n

Arithmetic averages, risk and, 162–163

Arrangers, 626

Arthur Andersen, 875

Articles of incorporation, 5

Ashanti Goldfields, 660n

Asian crisis (1997–1998), 613, 873

Asian financial system, 870–871

Asian (average) options, 554

Asked price, bond, 48

Asked yield to maturity, 48

Asquith, Paul A., 337n, 340, 340n, 462n, 614, 614n

Asset-backed securities (ABS), 605, 610–611, 623, 628

Asset beta

calculating, 225–226

defined, 225

determinants of, 227–229

Asset sales, 844

Asset turnover ratio, 729

Assignment, 626n

Asymmetric information, 467–469, 819–820

Atmos Energy Corp., 86

AT&T, 820, 841, 841n, 842, 842n

At-the-money options, 549n, 550

AT&T Universal Card, 841

AT&T Wireless, 842n

Auction markets

initial public offering, 384–385

nature of, 75–77

types of, 384–385

Auction-rate preferred, 797

Auditors, monitoring by, 299

Auerbach, A. J., 829n

Australia, imputation tax system, 414, 415–416, 416n, 467n

Automated Clearing House (ACH), 789

Automatic debit, 789

Autonomy, 808

Avendaño, L. C., 184

Average collection period, 730, 754

Average days in inventory, 754

Average payment period, 754

Aviation Week, 666

Axa, 622–623

B

BA (bankers’ acceptances), 782, 795, 796

Babus, A., 889n

Bachelier, Louis, 321n, 514

Backdating, 551

Bain Capital, 837

Bait and switch game, in financial distress, 462

Baker, G. P., 850, 850n, 857

Baker, M., 343, 411n, 470n

Balance sheet

common-size, 736–740

debt ratio, 350, 469–470, 491–492, 732–733

described, 722–723

Balloon payments, 624

Banco Central Hispanico, 812

Banco Santander, 812

Bandler, J., 551n

Bank(s). See also Bank loans; specific banks

borrowing and lending via, 363

concentration accounts, 790

in corporate financing, 363

direct payment, 788, 789

in financial markets, 860–865

as intermediaries, 363

international, 791, 793–794

loans. See Bank loans

multicurrency accounts, 791

paying for services, 791

payment mechanism and, 364

pooling risk and, 365

sweep programs, 788

time deposits and certificates of deposit, 794–796

types, 363, 363n

BankAmerica Merrill, 626

Bank Boston, 812

Bankers’ acceptances (BAs), 782, 795, 796

Bankers Trust, 340

Bank for International Settlements, 788n, 789n

Bank holding company, 627n

Bank loans, 2, 624–627, 758

commitment and, 624

debt covenants, 627

interest rates, 624–625

maturity of, 624

security of, 626–627

syndicated, 625–626

Bank of America, 194, 198, 297, 300, 359, 360n, 363, 363n, 366, 612, 727, 812

Bank of America Merrill Lynch, 379

Bank of America National Trust and Savings Association, 608

Bank of International Settlements, 683n

Bank of New England, 812

Bank of New York Mellon, 298, 387

Banking industry, 811–812

Bankruptcy, 850–855

alternative procedures, 854–855

Chrysler, 853–855

costs of, 455–459, 472

direct versus indirect, 458–459

evidence of, 458

nature of, 455–456

workouts, 854

Bankruptcy Reform Act of 1978, 850–851, 851n

BankSouth, 812

Banque Paribas, 812

Barberis, N., 205n, 333n, 342

Barclays Bank, 793

Barclays Capital, 379

Baring Brothers, 297n, 681

Barnett Banks, 812

Barrier options, 554

Barwise, P., 288

Basis point (BP), 616

Basis risk, 679–681

Baskin, J., 848n

Bates, T. W., 750n

Bautista, A. J., 650n

Bayerische Vereinsbank, 812

BBVA, 403

Bearer bonds, 46n, 608

Bear Stearns, 366, 610

Beaver, William H., 597–598, 598n

Bebchuk, L. A., 314, 854n, 870n

Becht, M., 878

Bechtel, 375

Behavioral finance, 333–336

dividend payments in, 403–404, 412

limits to arbitrage, 334–335

market efficiency and, 333–336

market timing and, 470–471

signaling and, 372, 403–405

Bell Laboratories, 841

BellSouth, 841n

Benartzi, L., 205n

Benchmark bills, 795, 796

Benefit-cost ratio, 119n

Benetton, 5

Benmelech, E., 642n

Benveniste, L. M., 384n, 392

Berger, P., 849n

Bergman, N. K., 642n

Berkshire Hathaway, 11n, 287, 401

Bermuda options, 554

Bernard, V. L., 741

Berndt, A., 587n

Bertrand, M., 297n, 471n, 873, 873n

Best-efforts underwriting, 379

Beta

asset, 225–226, 227–229

calculating, 181–182

cash-flow, 227

changes in capital structure and, 436–437

company, 219–220

defined, 708, 881

earnings, 227

estimating, 222–224

impact of borrowing on, 195–197

industry, 224

in market model, 325

market risk and, 178–179

portfolio risk and, 178–182, 198–204

project, 219–222

relevering, 492–493, 494n

unlevering, 492–493, 494n

Betton, S., 830

Bhagat, S., 844n

Bhandari, J. S., 851n, 857

Bharath, S. T., 853n

BHP Billiton, 173, 806

Biases, in profitability measures, 307–313

Biddle, G. C., 339, 339n

Bid price, 48

Big Mac Index, 700, 701

Big-ticket leases, 652

Bikhchandani, S., 889n

Billington, Corey A., 573

Binomial method of option pricing, 540–545

Black-Scholes model and, 549

decision trees and, 544–545

defined, 540

general binomial method, 543–544

two-step, 541–543

Biomet, 845–846

Bizjak, J. M., 304n

BK Vision, 353

Black, B., 374n

Black, Fischer, 201n, 202n, 203n, 209, 536, 536n, 545–551, 546n, 555

Black Monday (1987), 171

Black-Scholes option pricing model, 545–551, 576n, 882

binomial method and, 549

development of, 545–551

using, 546–548

to evaluate implied volatilities, 550–551

for executive stock options, 528, 549, 550, 551

to value portfolio insurance, 550

to value warrants, 549–550

Blackstone Group, 837, 845–848

“Black swans,” 191n

Blitzen Computer, 512

Blue-sky laws, 378

BNP, 812

BNP Paribas, 379, 623n

Board of directors

compensation committee, 303–304

connections with CEO, 298–299, 301–302

control rights and, 348, 352, 865–876

European, 867–869

mergers and, 847–850

role of, 5, 298–299, 303–304

voting procedures and, 352–354

Boatmen’s Bancshares, 812

Bodie, Zvi, 312n

Boeing, 3, 135, 258–259

Bohr, Niels, 13

Bolton, P., 878

Bond(s). See also Bond ratings; Bond valuation

alpine, 616

bearer, 46n, 608

callable, 618–619

catastrophe, 663–664

convertible, 358, 490, 617–623

corporate. See Corporate bonds

coupon, 46–49, 606

eurobonds, 357, 385, 386, 616–617

global bonds, 386, 617

innovation in bond market, 621–623

international, 357, 616–617

registered, 46n, 608

samurai, 616

sold by foreign company, 616–617

Treasury. See Treasury bonds

valuation of. See Bond valuation

yankee, 616

Bond covenants, 613–614

Bond ratings, 65–66, 67, 595–597, 601–602, 609, 623, 628n, 783

Bond valuation, 45–70

convertible bonds, 617–618, 620–621

default risk in, 63–68, 590–602

duration in, 51–53

inflation in, 59–63

interest rates in, 46–53, 59–63

present value formulas in, 46–49

spreadsheet functions, 68

term structure of interest rates in, 53–59

in the U.S., 47–49

volatility in, 53

yield to maturity, 47, 48

Bookbuilding, 384

Book rate of return, 108–109, 727

Book-to-market effect, 203, 203n, 204, 206–208

Book value, 77–78

Boone, P., 873, 873n

Booth, L., 470n

Bootstrap game, in mergers, 813–814

Borison, A., 266

Borrowing and lending. See also Debt financing; Financing decisions; Leasing

banks and, 363

internal rate of return and, 113–114

in portfolio theory, 195–197

role of financial markets in, 364–365

Bort, R., 799

Bortolotti, B., 386n

Bowie, David, 610

Bowie bonds, 610

Boycko, M., 845n

BP, 173, 298, 355, 403

BP (basis point), 616

Bradley, M., 96n, 627n

Branson, Richard, 226

Brasil Telecom, 76

Brau, J. C., 376n

Brav, A., 404n, 421

Brazil, payout policy in, 402

Breach, A., 873, 873n

Break-even analysis, 143, 250–253

defined, 250–251

operating leverage and, 253–254

Break-even points, 253–254

Brealey, Richard A., 630, 765, 883

Brennan, Michael J., 238, 570n, 580, 612n, 630

Bridge loans, 624

Bris, A., 857

British Salt, 806, 807

Brown, S. J., 209

Bruner, R., 830, 831

Brunnermeier, M., 332n, 343, 888n

Bubbles

Chinese warrant, 552

dot.com stocks, 332, 334, 341, 366, 374–375, 380, 381, 383, 885

in Japan, 332, 334, 885

market efficiency and, 331–332

subprime crisis, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

Budget Control Act of 2010, 67

Buffett, Warren, 11n, 26, 287, 682

Bullet payments, 624

Bulow, J. I., 549n

Burch, T. R., 842n

Burger King, 837

Burkart, M., 876n

Burroughs, B., 838n, 857

Business plans, in venture-capital financing, 372

Business valuation process

adjusted present value (APV) in, 497–498

discounted cash flow (DCF) in, 93–97

free cash flow, 484–485

weighted-average cost of capital (WACC) in, 221–226

C

Cable, 694n

Cadbury, 806

Caesar’s Entertainment, 63–65

Callable bonds, 618–619

Call options, 513–515

American calls, 513, 552, 554

defined, 513

European calls, 513, 514–515, 553–554

position diagrams, 514–515

price determinants, 527

relationship between put prices and, 540

selling, 515–516, 518

valuation of, 536–538

Call premium, 612n

Call protection, 611–612

Call provisions, 611–613

Calpine, 851

Campa, J. M., 849n

Campbell, J. Y., 173n, 209, 228n

Campbell Soup, 222–224

Canadian Pacific, 76, 224, 490

Caouette, J. B., 603

Cap, 608

CAPEX (capital expenditures), 2

Capital, defined, 4

Capital asset pricing model (CAPM), 198–204

alternatives to, 204–208

arbitrage pricing theory (APT) versus, 206

assumptions behind, 204

capital structure and, 222–224

cost of equity capital and, 222–226, 499–501

defined, 198

estimates of expected returns in, 197

evidence against market efficiency, 328–329

importance of concept, 881

review of, 199

security market line and, 198, 199–200

statistical issues in, 884

tests of, 201–204

validity and role of, 200–204

Capital budgeting, 2–3. See also Capital budgeting problems; Capital budgeting and risk; Investment decisions; Net present value (NPV), investment decisions and

capital budget, defined, 246

capital investment process for, 246–248

capital rationing in, 119–122, 195

discount rates for international projects, 232

internal rate of return in, 107

in long-term financial planning, 761

net present value analysis in, 105–109, 143–144

payback period in, 107, 109–111

pitfalls of, 273–278

postaudits, 247–248

project authorizations, 246–247

Capital budgeting problems, 245–266. See also Capital budgeting and risk; Net present value (NPV), investment decisions and

capital investment process, 246–248

decision trees, 258–265

forecasting economic rents, 278–288

incentives, 296–297, 412–413

market values in assessing, 273–278

Monte Carlo simulation, 254–258

performance measurement, 304–313

real options, 258–262, 561–580

sensitivity analysis, 248–254

Capital budgeting and risk, 218–238

capital structure and, 222–224

company cost of capital, 219–222

discounted cash flow and, 232–237

project cost of capital, 219–222

Capital constraints, in capital budgeting, 119–122

Capital expenditures

in applying net present value rule, 131

capital expenditure (CAPEX) decisions, 2–3

leasing and, 642

Capital gains taxes, 413–417

Capital investments, 108–109, 246–248. See also Capital budgeting

Capital leases, 643

Capital markets. See also Financial markets

historic performance of, 160–167, 197

Capital rationing, 119–122

defined, 119

example, 119–122

linear programming in, 121, 195

profitability index in, 107, 119–120

quadratic programming in, 195

Capital structure. See also Debt financing; Debt policy; Equity financing; Restructuring

capital asset pricing model (CAPM) and, 222–224

changes in, 436–437

debt ratios, manufacturing industry, 491–492

defined, 4

Modigliani-Miller approach to, 406, 428–430

theory of optimal, 472

trade-off theory of capital structure, 455, 465–467

Capital structure theory, 882

Capitalia, 812

Capitalization, market, 724

CAPM. See Capital asset pricing model (CAPM)

Caput options, 554

Cargill, 375

Carhart, Mark M., 327n

Carletti, E., 369, 889n

Carlyle, Hellman & Friedman, 837

Carried interest, 374, 847

Carrow, K. A., 622n

Carry trades, 710

Carter, D. A., 666, 666n

Carve-outs, 843–844, 845

Cascade, 889

Cash, tracing changes in, 751–754

Cash budgeting, 748, 755–757

inflow, 755–756

outflow, 756–757

Cash conversion cycle, 777–779

Cash conversion period, 754

Cash coverage ratio, 734

Cash cows, 848

Cash cycle, 754

Cash discounts, 782

Cash-flow beta, 227

Cash-flow rights, 348, 351

Cash flows. See also Discounted cash flow (DCF)

in applying net present value rule, 131–133

estimating, 133–135, 755–756

forecasting, 24–25, 107–108, 138, 488

in Monte Carlo simulation, 255–256, 257

in net present value analysis, 24–25, 108–109, 130–137

surplus-funds mergers and, 810–811

Cash in and run game, in financial distress, 462

Cash management, 776–779, 787–791

in collections, 786–787, 790

in disbursement, 756–757

international, 791, 793–794

money-market investments in, 361, 791–797

payment for purchases, 788–790

speeding up collections, 790

Cash on delivery (COD), 781–782

Cash ratio, 736

Catastrophe bonds, 663–664

Celanese, 848

Centerparcs, 848

CEOs. See Chief executive officers (CEOs)

Cerberus Capital Management, 808, 846, 846n, 855

Certainty-equivalent cash flow, 232–233

Certainty equivalents, 232–237, 278, 577

defined, 232

valuation by, 232–233

Certificates of deposit (CDs), 794–796

CFOs. See Chief financial officers (CFOs)

Chaebols, 872

Chain letter game, 814

Chandler, A., 848n

Changyou.com, 386

Chapter 7 bankruptcy, 850–851

Chapter 11 bankruptcy, 850–855

Charge cards, 788

Chava, S., 614n

Chavez, Hugo, 845

Check Clearing for the 21st Century Act (Check 21), 790

Check conversion, 790

Checks, 788, 790

Chen, C. R., 837n, 839, 839n

Chen, H. C., 380, 380n

Chevron Corp., 849

Chew, D. H., Jr., 339n

Chicago Board of Trade (CBOT), 666n, 666–668

Chicago Board Options Exchange (CBOE), 171n, 513n, 550–551, 553

Chicago Mercantile Exchange (CME), 666n, 666–668

Chicago Tribune, 5

Chief executive officers (CEOs)

board of directors and, 298–299, 301–302

compensation of, 295–314

earnings and earnings targets, 312–313

mergers and, 847–850

stock options. See Stock options

Chief financial officers (CFOs)

earnings and earnings targets, 312–313

market reaction to stock issues, 387–389

mergers and, 847–850

stock options. See Stock options

Childs, P. D., 567n, 568n

Chile

conglomerates, 872

payout policy in, 402

short-term capital inflows, 499

China

initial public offerings (IPOs) in, 381, 386

privatizations, 845

warrants bubble, 552

China Animal Healthcare, 848

China Eastern Airlines, 76

China National Offshore Oil Corporation (CNOOC), 821

China Solar Energy, 512

China State Grid, 844

CHIPS, 790

Choi, Bill, 419

Chooser (as-you-like-it) options, 554

Chordia, T., 330n

Choudhry, M., 799

Chrysler, 459, 472, 626, 808, 810, 846, 851, 853–854

Chui, M., 860n

Cigna Corporation, 387

Cingular Wireless, 841

Circular File Company case, 460–461, 590–591

Cisco, 750

Citibank, 379, 626

Citicorp, 841

Citigroup, 222–224, 297, 363, 885

Claessens, S., 871n

Class A stocks, 871–872

Class B stocks, 871–872

Classified boards, 352–353

Clayton, J., 226n

Clayton Act of 1914, 820

Clear Channel Communications, 837

Clinton, K., 714

Closed-end funds, 77n, 361, 886

Closed mortgages, 609n

Closely-held corporations, 5, 840, 855

Close-to-the-money projects, 118n

CME Group, 666n

Coca-Cola, 205, 304n, 332, 725, 727

Cochrane, J. H., 209

Codetermination, in Germany, 867

Coffee, J. C., Jr., 829n

Colak, G., 842n

Cole, R. H., 798

Collars, 608

Collateral, 357–358

bond, 609

Collateralized debt obligations (CDOs), 610, 611n

Collateral trust bonds, 609

Collections, 786–787, 790

Collins, D., 741

Comcast, 806, 807

COMEX (Commodity Exchange Division of NYMEX), 667

Comment, R., 405, 405n

Commercial banks, 363

Commercial drafts, 782

Commercial paper (CP), 627–628, 795, 796

Commerzbank, 812

Commodity Exchange Division of NYMEX (COMEX), 667

Commodity futures contracts, 670–672

Common-size financial statements, 736–740

Common stock, 75–98. See also Equity financing; Equity valuation; Portfolio risk; Stock options; Stock repurchases

classes of, 871–872

dividends. See Dividend(s)

equity financing, 351–356

initial public offerings (IPOs), 375–385

of mergers, 818–819

rights issues, 379n, 389–390

secondary issues, 385–390

trust, 355

venture capital, 371–375

growth stocks, 89, 203–204

historic performance of capital markets, 160–162

trading of, 75–77

valuation of, 77–97, 111–118

value stocks, 203–204

voting procedures, 352–354

Company cost of capital, 219–222. See also Weighted-average cost of capital (WACC)

defined, 219

determining, 219–220

expected return and, 433–434

nature of, 219–220

Company risk, 219–222

Comparables, 78–80, 226–227

Compensating balances, 791

Compensation committees, 303–304

Compensation Discussion and Analysis (CD&A), 304

Compensation plans

accounting measures of performance and, 304–313

chief executive officer, 295–314

golden parachutes, 827

incentives for managers and, 295–314

Competitive advantage, 278–281

economic rents and, 278–281

example, 281–288

Competitors

monitoring by, 300

in real option analysis, 578

Complementary resources, of merger candidates, 809, 810

Compound annual return, risk and, 162–163, 164n

Compound calls, 576

Compounding intervals, 35–38, 46–49

Compound interest

compounding intervals, 35–38

defined, 19

Compound options, 554

Comroad, 374–375

Concentration accounts, 790

Conditional sale, 782

Confidence interval, 222–224

Conglomerates, 226–227

defined, 847

mergers, 807, 833–835

ownership and control of, 872–873

private-equity funds as, 846–850

Conoco, 375

Conrad, Joseph, 712n

Conseco, 851

Conservatism, 333, 469

Consistency, in financial planning, 761–762

Consolidation trend, 811–812

Consols, 26

Constant-growth formulas, dangers of, 87–89

Constellation Energy, 820

Consumer credit, 781

Consumer Price Index (CPI), 59

Continental, 287, 812

Contingency planning, 761

Contingent convertible bonds (cocos), 623

Continuous compounding, 35–38

Control rights, 348, 351, 865–876

Convenience yield, 277n, 670–672

Convergence trading, 334–335, 340

Conversion price, 617

Conversion ratio, 617

Convertible bonds, 358, 490, 617–623

bond-warrant package, 621

dilution and, 620

dividends and, 620

forcing conversion, 618–619

reasons for issuing, 619–620

types of, 618–619

valuation, 617–618, 620–621

Cooper, I. A., 163n, 630

Cooper, M., 332n

Cootner, P. H., 321n

Copeland, T. E., 580

Cornell, B., 183, 228n

Cornell, F., 384n

Cornett, M. M., 388n, 388–389

Corporate bonds, 2, 585–603. See also Bond(s); Bond valuation

bond covenants, 613–614

bond terms, 606–608

call provisions, 611–613

convertible, 617–623

default puts and, 591

default risk, 63–68

domestic and foreign, 616–617

indenture, 608

international security issues, 386

junk, 490, 587, 595–597, 839

private placements, 390–391, 615–616

puttable, 613

ratings, 595–597

security of, 386, 608–609

seniority of, 608–609

sinking funds, 611

types, 608–609

yields on, 66, 585–589

yield spread between Treasury bonds and, 66, 587–589

Corporate financing, 348–369. See also Financing decisions

capital structure and, 491–492

debt, 350, 356–359. See also Corporate bonds

equity. See also Common stock; Equity financing

initial public offerings, 375–385

secondary offerings, 385–390

venture capital, 371–375

financial institutions in, 351–352, 363–367, 864–865

financial markets and, 351–352

internal funds, 349–350

links between short-term financing and, 748–751

patterns, 348–351

Corporate governance, 860–878. See also Ownership and control

differences in, 873–876

financial manager role, 6–7

financial markets and institutions in, 860–865

payout policy and, 418–419

value maximization in, 7–12, 16–17

Corporate tax rate, 453

Corporate venturers, 373

Corporations, 5–12. See also Corporate bonds; Corporate governance; Debt financing; Equity financing; Shareholders; Taxes, on corporations

closely-held, 5, 840, 855

defined, 5

financial manager in, 6–7

nature of, 5–6

restructuring by. See Restructuring

separation of ownership and management, 5, 12, 823, 865–876

Corus Steel, 807, 827

Corwin, S. A., 390n

Cost of capital. See Opportunity cost of capital

Cost of debt, in company cost of capital, 221

Cost of equity, in company cost of capital, 221

Cost of equity capital, 222–226, 499–501. See also Opportunity cost of capital

defined, 781

estimating, 84–89

leverage and, 435–436

Costco, 778

Counterparty risk, 665

Countrywide Financial Corp., 3–4, 812

Coupon, bond

annual, 46–47

defined, 46, 46n

semiannual, 47–49, 606

Coval, J. D., 610n

Covariance

beta and, 181–182

in calculating portfolio risk, 175–176, 181–182

defined, 175, 175n

Cowgill, B., 338n

Coy, P., 573n

Cram-down, 852

Credit analysis, 783

Credit cards, 788

Credit decision, 783–786

Credit default swaps, 588–589

Credit insurance, 786

Credit management, 781–787

collection policy in, 786–787

credit analysis in, 783

credit decision in, 783–786

promise to pay and, 782

terms of sale in, 781–782

CreditMetrics, 601, 601n

Credit risk, 585–603

bank loan, 626

bond ratings, 65–66, 67, 595–597, 601–602, 609, 623, 628n

option to default, 590–602

value at risk (VAR), 601–602

yields on corporate debt, 585–589

Credit scoring, 597–599

Credit Suisse, 379, 623

Credit transfer, 788

Cross-border leasing, 652

C&S Sovran, 812

CSX, 224

Cum dividend (with dividend), 402

Cumulative capital requirements, 748–751

Cumulative preferred stock, 356

Cumulative voting, 353

Currency futures market, 695

Currency risk. See Foreign exchange risk

Currency swaps, 675–676

Current assets, 722, 750

Current liabilities, 489, 723

Current ratio, 735–736

Current yield, 47

Cusatis, P. J., 842n

Cutoff date, in payback period, 109–111

Cyclicality, asset beta and, 227

D

Dabora, E., 330n

Daimler AG, 846, 867–869

Daimler-Benz, 3, 808, 867n, 868

DaimlerChrysler, 4, 846

Dakota, Minnesota & Eastern Railroad, 278n

Daley, J. P., 767

Daley, L. V., 842n

Dalian Commodity Exchange (China), 667

Danone, 820

Data-mining/data snooping, 204, 597–599

Davidson, S. M., 11n

Davis, S. J., 839n

Davydenko, S. A., 855, 855n

DAX index, 669, 670

Dealer markets, 76

DeAngelo, H., 417n, 421

DeAngelo, L., 417n, 421

Death-spiral, 622

Debentures, 608

Debit cards, 788

Debt capacity, additions to, 497–498

Debt covenants, 613–614, 627

Debt-equity ratio (D/E), 439–440, 493–494

Debt financing, 356–359, 585–603. See also Bond(s); Corporate bonds; Debt valuation; Financial leases; Leasing

asset-backed securities, 605, 610–611, 623, 628

capital structure changes and, 491–492

debt ratios, 350, 469–470, 491–492, 732–733

forms of debt, 356–358, 605–630

international security issues, 386

long-term, 606–617

choosing a plan, 765

contingency planning, 761

example, 762–764

need for, 761–762

pitfalls in model design, 764

short-term financing versus, 356–357, 458

private placements, 390–391, 615–616

secondary offerings, 385–390

short-term, 757–760

bank loans, 758

commercial paper, 627–628

long-term financing versus, 356–357

medium-term notes (MTNs), 628–629, 795, 796

short-term financing plan, 757–760

stretching payables, 756, 758

Debt policy, 427–443, 448–474

costs of financial distress, 455–467

agency costs, 462–464

bankruptcy, 455–459, 472

without bankruptcy, 459

nature of financial distress, 455

trade-off theory of capital structure, 455, 465–467

varying with type of asset, 464–465

effect of leverage in competitive tax-free economy, 428–434

pecking order of financing choices, 467–472

default risk, 609

financial slack, 471, 472, 484–486

impact of asymmetric information, 467–469

implications of, 462

trade-off theory versus, 470–471

taxes and, 449–454

interest tax shields and stockholders’ equity, 450

personal taxes, 452–454

Debt ratios, 350, 469–470, 491–492, 732–733

Debt valuation, 606–617

convertible securities, 617–618, 620–621

default risk in, 590–602

credit ratings, 65–66, 595–597

government loan guarantees, 594–595

junk bonds, 595–597

duration in, 51–53

inflation in, 59–63

interest rate risk and, 53–59

nominal rate of interest and, 59–63

real rate of interest and, 59–63

term structure of interest rates and, 53–59

volatility in, 53

yields on corporate debt, 66, 585–589

Debtor in possession (DIP), 853

Decision trees, 258–265

abandonment option, 259–261

binomial method of option pricing and, 544–545

defined, 258–259

example of use, 262–265

expansion option, 258–259

pros and cons of, 265

uses of, 258–265

Declining industries, 874–875

Deep-in-the-money projects, 118n

Default puts, 591

Default risk, 590–602. See also Bankruptcy

calculating probability of default, 597–600

corporate bond, 63–68

credit ratings, 65–66, 595–597

credit scoring and, 597–599

market-based risk models, 599–600

sovereign bonds, 66–68

value at risk (VA), 601–602

yield to maturity, 592–594

yields on money-market investments, 793

Defense industry, 811

Deferred taxes, 488n

Defined-contribution plans, 362, 362n

Deflation, 60, 62n

DeGeorge, F., 312–313, 313n

Degree of operating leverage (DOL), 228n, 253–254, 254n

Degrees of freedom, 168n

De Jong, A., 330n

Dell Computer, 781

Del Monte Foods, 837

Delphi, 810, 851

Delta Air Lines, 666, 727

Demirguc-Kunt, A., 470n

Denis, D. J., 401n, 615n, 616n, 624n

Depreciation

accelerated, 140–142

biases in calculating returns, 309–310

investment decisions and, 140–142

salvage value, 135, 137, 651

straight-line, 137, 142, 642

tax shield, 140–142, 641, 644n, 648, 651

Derivatives. See also Forward contracts; Futures contracts; Option(s); Swaps

in risk management, 662, 665–677

Descartes, René, 114n

Deutsche Bank, 76, 173, 322–323, 325, 379, 809, 867, 869

Deutsche Börse, 76

Deutsche Telecom, 623, 848

Devarajan, S., 277n

Devgen, 810

Dewenter, K. L., 404n

Diamond, D., 357n

DIAMONDS, 361

Diet deals, 838–839

Digital (binary or cash-or-nothing) options, 554

Dill, D. A., 650n

Dilution, in convertible valuation, 620

Dimitrov, O., 332n

Dimon, James, 405

Dimson, E., 60n, 64n, 160n, 160–161, 161n, 162n, 165, 165n, 168n, 171n, 183, 702n

DIP (debtor-in-possession) debt, 853

Direct debit, 789

Direct leases, 640

Directors. See Board of directors

Direct payment, 788, 789

Direct quote, 694, 695n

Dirksen, Everett, 605n

Disbursements, controlling, 756–757

Discount, bond, 47

Discounted cash flow (DCF)

in business valuation, 93–97

in calculating present value, 24–25

in common stock valuation, 80–89, 111–118

dangers of constant-growth formulas, 87–89

defined, 24

problems in option pricing, 536

rate of return and. See Internal rate of return (IRR)

in real option valuation, 577–578

risk and, 232–237

multiple risk-adjusted discount rates and, 235–237

single risk-adjusted discount rate and, 234–237

in setting gas and electricity prices, 85–87

spreadsheet functions, 37–38

Discounted-cash-flow rate of return. See Internal rate of return (IRR)

Discounted payback rule, 110–111

Discount factor, 20, 56–57

Discount notes, 795, 796

Discount rate. See also Opportunity cost of capital

avoiding fudge factors in, 227, 230, 232, 247, 247n

multiple, 235–237

single, 234–237

Discriminatory auctions, 385

Disney, 65, 222–224, 387, 824

Dittmann, I., 867, 867n

Dittmar, A. K., 799, 842n

Diversifiable (specific) risk, 174, 174n, 178–179, 190, 229–230

Diversification

arbitrage pricing theory and, 206

internal, 873

limits to, 177–178

market risk and, 171–174

mergers and, 812–813, 848

portfolio risk and, 171–174, 182

value additivity and, 182

Divestiture, 841, 844

Dividend(s). See also Payout policy

in business valuation, 93

in common stock valuation, 80–89, 111–118

in convertible valuation, 620

free cash flow and, 96–97

information content of, 403–404

methods of paying, 402

in option pricing, 553–554

payout ratio, 85, 412–413

preferred stock, 356, 372

taxes on capital gains versus, 413–417

types of, 402

in warrant valuation, 620

Dividend discount model. See Discounted cash flow (DCF)

Dividend reinvestment plans (DRIPs), 402

Dividends per share, 84n

Dividend yield, 77, 84, 85, 166–167

Dixit, A. K., 266, 570n, 580

Djankov, S., 871n

Doherty, N. A., 663n

Dollar loans, 696

Dot.com stocks, 332, 334, 341, 366, 374–375, 380, 381, 383, 885

Douglas, R., 587n

Dow Chemical, 78, 79, 172, 193, 194, 195, 198, 588

Dow Jones Industrial Average, 172, 361

DP World, 821

Dresdner Bank, 812

Dresdner Kleinwort, 379

Drexel Burnham, 839

Dual-class equity, 354, 871–872

Duffie, D., 587n, 603

Duke Energy, 806, 809

Dun and Bradstreet, 783

Du Pont, 375

Du Pont formula, 731

Du Pont system, 730–732

Durand, David, 429n

Duration

in bond valuation, 51–53

in hedging, 678–679

Dutch auction, 403

E

eAccess, 848

Earnings announcements, 329

Earnings before interest and taxes (EBIT), 79n, 597, 733–734

Earnings beta, 227

Earnings per share (EPS)

in equity valuation, 77, 78–79, 89–92

forecasting, 312–313

mergers and, 813–814

Earnings-price ratio, 90

Easterbrook, F., 412n

Eastern Airlines, 458, 852–853

Eastman Kodak, 78

eBay, 380–381, 383

EBITDA (earnings before interest, taxes, and depreciation), 79n, 597, 733–734

Ebner, Martin, 353

Eckbo, B. E., 325n, 392, 830, 857

Eckel, C., 857

Eckel, D., 857

Economic depreciation, 309–310

Economic exposure, 705–706

Economic income, 309–310

Economic order quantity (EOQ), 780

Economic profit (EP), 306

Economic rents

competitive advantage and, 278–281

example, 281–288

forecasting, 278–288

Economic value added (EVA), 305–307, 725–726

applying to companies, 305–306

calculating, 305–306, 726

defined, 726

problems of, 728–729

pros and cons of, 306–307

Economies of scale, in mergers, 809

Economies of vertical integration, 809–810

Economist, The, 335, 353, 809

EDF (Electricité de France), 844

Efficiency ratios, 729–730

Efficient-market hypothesis, 319–332

anomalies and financial managers, 328–332

behavioral finance and, 333–336

evidence against efficient markets, 328–332

evidence for efficient markets, 321–324

exceptions to, 884–885

forms of market efficiency, 324–325

importance of concept, 881

irrelevance of dividends and, 406–411

lessons of market efficiency, 336–341

mispricing and, 341

payout policy in, 406–411

price changes as random, 321–324

random walk hypothesis and, 321–324, 526n

trading opportunities versus, 340

Efficient portfolios

borrowing and lending in, 195–197

defined, 195, 199

Ehrbar, A., 307n, 314

Eichholtz, P., 226n

Eight O’Clock Coffee, 807

Einstein, Albert, 321n

Eisner, Michael, 823–824

Eiteman, D. K., 713

Electronic bill presentation and payment (EBPP), 789

Electronic communication networks (ECFs), 76

Ellis, Jim, 873

Ellis, K., 377n

Ellison, Larry, 302, 549

Elton, E. J., 209, 594n

Embedded options, 512

Empire building, 296

Enriques, L., 867n

Enron, 376, 458, 465, 597, 606, 851, 875, 875n, 875–876

Entergy, 303

Entrenching investment, 296

Equal real interest rates, 703–704

Equifax, 597n

Equipment trust certificates, 609

Equity financing. See also Equity valuation

common stock, 75–98, 351–356

initial public offerings (IPOs), 375–385

mergers and, 818–819

rights issues, 379n, 389–390

secondary issues, 385–390

trust, 355

venture capital, 371–375

in financial distress situations, 461

financing decisions and, 4

international security issues, 386

partnership, 355

preferred stock, 356, 372

rights issues, 379n, 389–390

venture capital, 371–375

Equity investors, 4

Equity Office Properties, 837, 845

Equity valuation, 77–97

in business valuation process, 93–97

comparables in, 78–80, 226–227

discounted-cash-flow (DCF) formula in, 75, 80–89, 111–118

dividends and, 80–89, 111–118

earnings per share (EPS) in, 77, 78–79, 89–92

estimating capitalization rate, 781

stock price in, 75–77

Equivalent annual cash flow, 147–148

cost of excess capacity, 148–149

defined, 148

inflation, 147

long- versus short-lived equipment, 147–148

net present value analysis, 147–148

in replacement decisions, 148

taxes and, 148

technological change, 147

Equivalent annual cost, operating leases and, 644–646

Equivalent loans, 649–650

Erb, C., 710n

Esty, B. C., 630

Eurex Exchange, 668

Euribor (euro interbank offered rate), 625n, 793

Euler LÖsungen

Eurobonds, 357, 385, 386, 616–617

Eurocurrency, 357, 793

Eurodollars, 793

Euro interbank offered rate, 625n, 793

Euronext, 76, 76n

European Central Bank, 67

European Monetary Union (EMU), 694n, 793

European options, 513–515, 539–540, 553–554

Euros, 357, 694n

Eurozone debt, 67–68, 367

EVA Dimensions, 724, 728–729

Evans, M. D., 714

Everett, S. J., 830

Evergreen credit, 624

Excess capacity, equivalent annual cash flow and, 148–149

Exchange rates. See also Foreign exchange risk

changes in, 698

interest rates and, 696–697

Exchange-traded funds (ETFs), 77, 361–362

Ex dividend, 402

Execucomp, 301n

Executive stock options. See Stock options

Exelon, 820

Exotic securities

asset-backed securities, 605, 610–611, 623, 628

innovation in bond market, 621–623

and violation of Modigliani-Miller approach to capital structure, 440

Expansion option, 258–259, 512–513, 761

exploiting new technology in, 281–288

flexible production, 571–572

follow-on investment opportunities, 561–565

forecasting market values in, 273–278

purchases in, 573–575

Expectations theory of exchange, 697

Expectations theory of forward rates, 699–700

Expectations theory of term structure, 57–59

Expected returns

capital asset pricing model and, 198–204, 224–226

estimates of, 198–199

traditional approach to capital structure and, 433–434

Experian, 597n

Export-Import Bank, 786

Express Scripts, 806

External financing, 765–766

Extra dividends, 402

Exxon Mobil, 3, 4, 7, 175–177, 191–193, 194, 198, 205, 359, 360n, 401, 402, 461, 725, 727, 728, 806

Ezzell, R., 494n, 502

F

Fabozzi, F. J., 70, 630, 654, 799

Facebook, 871

Face value, defined, 46

Factoring, 786

Fair Isaac & Co. (FICO), 597n, 783n

Fair market rent, 275n

Faleye, O., 353n

Fallen angels, 595–597

Fama, Eugene F., 166n, 203n, 207, 207n, 327n, 342, 343, 466n, 470n, 700n, 884, 884n

Fama-French three-factor model, described, 206–208, 325n

Fanjul, G., 839n

Fannie Mae, 51, 336, 366, 611, 794, 845

Fawcett, S. E., 376n

FCX, 135

FDA (U.S. Food and Drug Administration), 262–265, 578

Federal agency securities, 794, 795

Federal Deposit Insurance Corporation (FDIC), 595

Federal Express, 375

Federal Family Education Loan (FFEL), 595

Federal Home Loan Mortgage Corporation (Freddie Mac), 51, 336, 366, 611, 794, 845

Federal National Mortgage Association (FNMA; Fannie Mae), 51, 336, 366, 611, 794, 845

Federal Power Commission v. Hope Natural Gas Company, 85n

FedEx, 258–259, 375

Fedwire, 790, 790n

Ferguson, M., 587n

Fernandez, P., 184

Fiat, 5, 173

Fiduciary duty, 865

FIFO (first-in, first-out inventory), 339

Financial Accounting Standards Board (FASB), 643, 643n, 821

Financial analysis, 719–741

financial ratios, 719–720, 729–741

financial statements, 720–729

Financial assets, 2. See also Marketable securities

Financial Assistance Corporation, 794n

Financial crisis of 2007–2009, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

Financial distress, 455–467. See also Bankruptcy

without bankruptcy, 459

incentives and, 459–460

leasing and, 641–642

nature of, 455

risk management and, 660–661

trade-off theory of capital structure, 455, 470–471

type of asset and, 464–465

Financial engineering, 522

Financial intermediaries, 351–352, 363–367

role of, 360, 364–367

types of, 363–364. See also Bank(s); Underwriters

Financial leases, 646–652, 732n

advantages of, 640–642, 651–652

defined, 640

example, 647

net value of lease, 648–650, 733n

ownership of asset, 647–648

salvage value for depreciation, 651

as source of financing, 640

taxes and, 648

valuing, 646–652

Financial leverage

cost of equity capital and, 435–436

defined, 428, 732

effect in competitive tax-free economy, 428–433

Modigliani-Miller approach, 428–430

traditional approach, 428

impact on expected stream of earnings per share, 433–434

leverage ratios, 732–734

measuring, 732–734

Financial managers, 6–7

compensation and incentive plans for, 295–314

lessons of market efficiency and, 336–341

market anomalies and, 328–332

separation of ownership and management and, 5, 12, 823, 865–876

value maximization and, 7–12, 16–17, 245–266

Financial markets, 359–360, 860–865. See also International finance

crisis of 2007–2009, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

current versus future consumption and, 16

financial institutions in, 360, 363–367, 864–865

information provided by, 365–366

initial public offerings (IPOs), 375–385

international capital markets, 386, 860–865

investor protection and, 864–865

nature of, 8, 8n

pooling risk and, 365, 662–664

as source of financing, 364–367

Financial planning, 748–767

growth and external financing, 765–766

long-term, 748, 760–765

models for, 748–751

pitfalls of model design, 764

short-term. See Short-term financial planning

Financial ratios, 719–720, 729–741

Du Pont system, 730–732

efficiency, 729–730

for Home Depot, 737, 740, 741

interpreting, 736–741

leverage, 732–734

liquidity, 735–736

median ratios for Standard & Poor’s Composite Index, 739

Financial risk, 433–437

Financial slack

defined, 471

free cash flow and, 93–94, 96–97, 471, 484–486

Financial statements, 720–729

balance sheet, 722–723

common-size, 736–740

income statement, 723

in merger analysis, 821–822

Financial structure. See Capital structure

Financing decisions. See also Capital structure; Corporate financing; Debt financing; Efficient-market hypothesis; Equity financing; Leasing; Mergers and acquisitions

adjusted present value (APV), 495–499

adjusting discount rate through weighted average cost of capital (WACC), 479–483

defined, 2

examples, 3, 4–5

investing decisions versus, 5, 136–137, 139, 321

mergers and, 814–815

net present value and, 136–137, 139

valuing businesses, 483–488

weighted-average cost of capital in, 479–502

First Data, 837

First Gibraltar, 812

First-in, first-out (FIFO) inventory, 339

First Solar, 298

First-stage financing, 372

Fisher, A. C., 277n

Fisher, F., 509n

Fisher, Irving, 62–63, 699n

Fitch credit ratings, 65–66, 595, 628n

Fitzpatrick, Dan, 4n

Fixed-income market, 47

Fixed-rate debt, 357

Flat (clean) price, 48n

FleetBoston, 812

Fleet Financial Group, 812

Floating charge, 626

Floating-price convertibles, 622

Floating-rate debt, 357, 588, 588n, 673–675

Floating-rate notes, 608

Floating-rate preferred stock, 797, 797n

Floor, 608

Flow-to-equity method of valuing companies, 488

Forcing conversion, 618–619

Ford, Henry, 865, 865n

Ford Credit, 472, 628

Ford Motor Company, 37, 172, 178–179, 194, 198, 302, 471, 472, 628, 712, 810, 865

Forecasts

cash flow, 24–25, 107–108, 138, 488

earnings per share, 312–313

economic rents in, 278–288

market values in, 273–278

prediction markets, 338

Foreign bonds, 616–617

Foreign Credit Insurance Association (FCIA), 786

Foreign exchange risk, 693–710

basic relationships, 695–704

economic exposure, 705–706

foreign exchange market, 693–710

hedging currency risk, 704–706

international investment decisions, 706–710

transaction exposure, 705–706

Forelle, C., 551n

Fortis, 367

Fortune Brands, 842

Forward contracts, 665

forward exchange rates, 694–695

forward market, defined, 694

forward rate agreements (FRAs), 672

homemade, 672

simple, 665

speculation in, 681–683

Forward exchange rates, 694–695

Forward interest rate, 672

Forward premium, 697

Forward prices, 665

Forward rate, expectations theory of, 699–700

Forward rate agreements (FRAs), 672

Forward rate of interest, 58n

France

compounding intervals in, 46–47

corporations in, 5n

government bond valuation, 46–47

nominal versus real exchange rates, 701–703

ownership and control in, 869

Frank, M., 470n

Franks, J. R., 458n, 650n, 820n, 854n, 855, 855n, 868n

Fraudulent conveyance, 462

Freddie Mac, 51, 336, 366, 611, 794, 845

Free cash flow (FCF)

financial slack and, 93–94, 96–97, 471, 484–486

net income versus, 485

valuing businesses, 484–485

Free-cash-flow problem, 296

Freescale Semiconductor, 848

French, Kenneth R., 166n, 203n, 207, 207n, 327n, 332n, 343, 466n, 470n, 884, 884n

Fried, J., 314

Friedman, F., 873, 873n

Froot, K. A., 330n, 663n, 684, 700n, 714

Full-payout leases, 640

Full (dirty) price, 48n

Full-service leases, 640

Fürstenberg, Carl, 869n

Futures contracts, 666–672

commodity, 670–672

hedging with, 666–672, 677–679

mechanics of trading, 667–669

speculation in, 681–683

trading and pricing, 669

Future value

of annuity, 32

calculating, 18–19

defined, 18–19

net present value and, 24

Futures exchanges, 666–672

Futures markets, 278, 666–672

G

Gabaix, X., 301n

Gadanecz, B., 626n

Galai, D., 815n

Gale, D., 369, 874n, 875n, 878

Gallinger, G. W., 798

Gambling for redemption, 297, 297n

Gao, P., 628n

Gates, Bill, 26

Gateway Rail, 848

Gavazza, A., 646n

Gearing. See Financial leverage

GE Capital Aviation Services, 639

GE Capital Corporation, 627, 639

Geely, 827

Geithner, Tim, 67n

Geltner, D., 226n

Genentech, 375

General cash offers, 385–390

costs of, 386–387

international security issues, 386

market reaction to, 387–389

shelf registration, 385

General Electric (GE), 75–77, 134, 313n, 401, 820, 850

General Mills, 387

General Motors (GM), 375, 387, 405, 472, 606, 628, 751, 810, 851, 853–854, 855

General Motors Acceptance Corporation (GMAC), 846n

General obligations, 794n

General partnerships, 846

General Services Administration (GSA), 794n

Generali, 298

Generally accepted accounting principles (GAAP), 77–78, 299

Genesee & Wyoming, 224

Genzyme, 806

Geometric average return, 163n

Germany

accounting standards in, 721

agency problem and, 883

CEO compensation, 300, 301–302

corporations in, 5n

futures contracts in, 669, 670

growth and declining industries in, 874–875

inflation in, 63, 64

mergers and, 808

net present value calculations in, 143–144

ownership and control in, 866–869

short-termism in, 874

taxes in, 143–144, 415

Gertner, R., 842n

Gilligan, Thomas W., 641n

Gilson, R., 374n

Ginnie Mae, 794n

Glaxo Smith Kline, 2, 3, 4, 403

Glencore, 806

Global bonds, 386, 617

Global Crossing, 851

Global markets. See International finance

Goetzmann, W. N., 165n, 184, 209

Going-concern value, 78

Gold, 276–278, 660, 660n, 662

Golden parachutes, 827

Goldman Sachs, 6, 11, 12, 363, 363n, 379, 626

Goldreich, D., 384n, 385n

Gompers, P. A., 375n, 392, 826n

Goodrich, 806

Google, 83, 92, 338, 354, 384, 384n, 401, 465, 806, 807, 871

Gordon, M. J., 84n

Governance. See Ownership and control

Government National Mortgage Association (GNMA; Ginnie Mae), 794n

Government regulation, 623. See also names of specific laws and government agencies

Government-sponsored enterprises (GSEs), 794–796

Goyal, V., 470n

Graham, John R., 108, 123, 164n, 201n, 312, 312n, 313, 313n, 314, 404n, 411n, 414n, 421, 454, 454n, 466n, 474, 619, 619n, 641n, 660n, 749n

Grant, R. M., 279n

Gray market, 383n

Great Depression, 60, 335, 367

Greece, 67–68, 367, 589, 889

Greenshoe option, 379

Greenspan, Alan, 334n

Grenadier, S. R., 655

Grinstein, Y., 414n

Gromb, D., 876n

Grossman, S. J., 328n

Growth industries, 874–875

Growth rates

internal, 765–766

sustainable, 766

Growth stocks, 89, 203–204

Gruber, M. J., 209, 327n, 594n

Grullon, G., 404n

Guiso, L., 10n

Gulfport Energy, 387

Gulf & Western Industries, 848

H

Habib, M., 630

Habib Bank, 844

Hall, B. H., 829n

Hall, B. J., 314

Haltiwanger, R. S., 839n

Hamada, R. S., 494n

Hansen, Robert S., 380n, 387n

Hard rationing, 122

Harford, J., 829n, 830

Harper, J. T., 845n

Harrah’s Entertainment, 837

Harris, M., 474

Harris, R. S., 709n, 820n

Hart, O., 352n, 368, 810n, 854n

Hart-Scott-Rodino Antitrust Act of 1976, 820, 820n

Harvey, Campbell R., 108, 123, 164n, 201n, 312, 312n, 313n, 314, 404n, 421, 466n, 474, 619, 619n, 710n, 749n

Haushalter, G. David, 662, 662n

HBOS, 379, 389, 390

Healey, B. P., 798

Healy, Paul M., 403–404, 404n, 741, 829, 829n, 875n, 878

Hedge funds, 11, 335, 340, 362

Hedge ratio, 537, 679–681

Hedging

currency risk, 704–706

economic exposure, 705–706

example, 704

transaction exposure, 705–706

defined, 659–660, 665

fuel costs, 664, 666

with futures contracts, 666–672, 677–679

setting up hedge, 677–681

Heineken, 173

Heinz, 175–177, 179, 191–193, 194, 198

Hellman, T., 374n

Hellwig, M., 869n

Helyar, J., 838n, 857

Hendel, Igal, 641n

Herman Miller Corporation, 307

Hershey, 340n

Hewlett-Packard, 298, 304, 512, 573, 808, 827, 842

Higgins, R. C., 815n

Hill, N. C., 798

Hilton Hotels, 837, 845

Hirshleifer, J., 889n

Historic data

on capital markets, 160–167, 197

on CEO compensation, 300–301

on inflation, 59–60

on mergers, 828–829, 888–889

Hodges, Stewart D., 281n, 650n

Holmes, Max, 615

Holmstrom, B., 831

Home Depot, The, 300, 721–741

Honeywell, 820

Horizontal mergers, 807

Horizon value

estimating, 94–95, 96, 485–487

market-book ratios and, 95

price-earnings ratio and, 95

Hornbeck Offshore Services, 387

Hoshi, T., 866, 866n, 875n

Hotchkiss, E. S., 598n, 603, 852n, 857

Hotelling, Harold, 277n

Houghton Mifflin, 848

Household portfolios, 861–862

Houston, J. F., 812n

Hovnanian, 490

Howe, Christopher D., 257n

Huang, J., 594n

Huang, M., 205n, 333n, 594n

Hudson’s Bay Company, 6

Hull, J. C., 555, 684

Hurdle rate. See Opportunity cost of capital

Hutchison Whampoa, 843

Hypobank, 812

Hypo Group, 367

Hypo Real Estate, 845n

I

Ibbotson, R. G., 184, 392

IBES, 85n

IBM, 62n, 106, 117, 190–191, 194, 198, 232, 304n, 333, 401, 591–592, 677, 827

Icahn, Carl, 299, 824, 842

Ihrig, J., 713

IKEA, 279

Ikenberry, D., 405n

Imputation tax system, 414, 415–416, 416n, 467n

IMS Health, 837

Incentives. See also Stock options

financial distress and, 459–460

for financial managers, 295–314

leveraged buyouts (LBOs) and, 839, 840

payout policy and, 412–413

Incidental effects, 133–134

Inco, 827

Income statement

common-size, 736–740

described, 723

in estimating cash flow, 755–756

leasing and, 643–644

Income stocks, 89

Incomplete contracts, 352n

Incremental net present value, 133

Indenture, bond, 608

Indexed bonds, 61–62

Index funds, 327–328

Index futures, 670

India, conglomerates, 872

Indirect quote, 694

Industrial and Commercial Bank of China, 375, 381, 844–845

Industry beta, 224

Industry betas, 224

Industry consolidation, mergers and, 811–812

Industry costs of capital, 490

Industry structure, components of, 279

Inefficiency

eliminating, 811

mergers and, 811, 845

Inflation rates

in bond valuation, 59–63

Consumer Price Index (CPI), 59

by country, 60, 63, 64

equivalent annual cash flow, 147

exchange rates and, 698

interest rates and, 59–63, 699–704

international rates, 63, 64

in net present value analysis, 135–136

nominal interest rates and, 62–63

in term structure of interest rates, 59

Information asymmetries, 467–469, 819–820

Information effect. See also Signaling

information provided by financial markets, 365–366

investor response to, 326–327

market reaction to stock issues, 387–389

for mergers, 819–820

in payout policy, 403–405

in semistrong market efficiency, 324–325

in sensitivity analysis, 249–250

in stock repurchase plans, 405

in strong form of market efficiency, 325, 326–327

in weak form of market efficiency, 324, 336–337

Information memo, 626

ING, 367

Initial public offerings (IPOs), 375–385

arranging, 376–378

auctions of, 384–385

bookbuilding for, 384

sale of, 380–383

underpricing of, 380–383

underwriters of, 377–381

winner’s curse and, 384–385

Installment plan costing, 28–29

Institutional investors

initial public offerings and, 378–379

private placements and, 390–391, 615–616

Insurance, 662–664

portfolio, 550

risk transfer and, 662–663

Insurance companies, 364, 589

Intangible assets

in mergers, 822

nature of, 18

Intel, 373, 375, 750

Intercontinental Exchange (ICE), 667

Interest coverage, 733–734

Interest rate parity, 696–697, 699

Interest rate risk

in bond valuation, 53–59

hedging, 677–679

Interest rates. See also Term structure of interest rates

on bank loans, 624–625

in bond valuation, 46–53, 59–63

exchange rates and, 696–697

Fisher’s theory of, 62–63, 699n

inflation rates and, 59–63, 699–704

nominal versus real, 59–63

real, 59–63

Interest rate swaps, 673–675

Interest tax shields, 450–454

personal taxes and, 452–454

value of stockholders’ equity, 450

Intermediaries, 360, 363–367

Intermolecular, 387

Internal capital market, 848–850

Internal cash flow, 349

Internal funds, 349–350

Internal growth rate, 765–766

Internal rate of return (IRR), 107, 111–118

calculating, 112–113

internal rate of return rule, 113

in lending versus borrowing, 113–114

modified, 115n

more than one opportunity cost of capital, 117–118

multiple rates of return and, 114–115

for mutually exclusive projects, 115–117

spreadsheet functions, 121

verdict on, 118

Internal Revenue Service (IRS), 142, 488n, 648, 648n, 792, 796

International Accounting Standards Board (IASB), 643n, 721

International banking facilities (IBFs), 794

International finance. See also names of specific countries

accounting standards, 643n, 721

adjusted present value, 498–499

average market risk premiums, 165

banks in, 791, 793–794

bonds in, 357, 616–617

bubbles in, 332

cash management, 791, 793–794

CEO compensation, 300–302, 304

comparative inflation rates, 59–60

discount rates for international projects, 232

dividend policy, 402

dual-class shares, 354, 871–872

exchange risk and, 706–710

financial markets and institutions, 386, 860–865

imputation tax systems, 414, 415–416, 416n, 467n

inflation rates by country, 60, 63, 64

initial public offerings, 381–382

international money markets, 793–794

international security issues, 386

leasing in, 605–606, 652

mergers and acquisitions, 848

net present value in other currencies, 143–144

ownership and control, 865–876

privatization in, 844–845

risks in. See International risks

sovereign debt, 66–68, 367, 589, 889

standard deviations of stocks in, 171

stock market returns, 171

stock repurchases, 403

weighted-average cost of capital (WACC), 221–226

International Financial Reporting Standards (IFRS), 721

International Fisher effect, 699n

International Monetary Fund (IMF), 67, 889

International Petroleum Investment Company, 867

International projects. See Project finance

International risks, 693–714

foreign exchange risk, 693–710

basic relationships, 695–704

economic exposure, 705–706

foreign exchange market, 693–710

hedging currency risk, 704–706

international investment decisions, 706–710

transaction exposure, 705–706

political risk, 710–712

International Securities Exchange (ISE), 513n

International Swap Dealers Association (ISDA), 588n

International Swaps and Derivatives Association, 589, 673n

Internet bubble, 332, 334, 341, 366, 374–375, 380, 381, 383, 385

Intrade, 338

Inventory management, 779–781

Inventory turnover, 730

Investment banks, 363, 381

Investment decisions. See also Capital budgeting; Capital budgeting and risk; Project finance

capital budgeting process for, 246–248

defined, 2

examples, 2–4

financing decisions versus, 5, 136–137, 139, 321

investment trade-off, 9–10

market value in, 274–278

net present value (NPV) and, 105–109, 130–149

alternatives to, 107

book rate of return versus, 108–109

cash flow in, 130–137

cost of excess capacity, 144, 148–149

depreciation and, 135, 137, 140–142

example, 137–144

forecasting economic rents, 278–288

incentives, 295–314

inflation and, 135–136

investment versus financing decisions, 5, 136–137, 139, 321

key points concerning, 107–108

long- versus short-lived projects, 144, 145–148

market values in, 273–278

multiple cash flows, 24–25

payback analysis versus, 109–111

replacement problem, 144, 148

review of basics, 105–109

taxes and, 140–142

timing, 144–145

real estate, 274–276

Investment opportunity, present value of, 20–22

Investment option, 512, 575–577

Involuntary issuers, 389n

Iowa Electronic Markets, 338

Iridium, 3

IRR. See Internal rate of return (IRR)

Irrevocable letter of credit, 782

Ishii, J. L., 826n

ISS, 304

Italy, nominal versus real exchange rates, 701–703

ITT, 842, 848, 849

Ivanhoe, 390n

J

Jackson, G., 878

Jack Wolfskin, 848

Jacquier, E., 163n

Jaguar Land Rover, 807

James, C. M., 812n

James Webb Space Telescope, 135

Japan

bubbles in, 332, 334, 885

company financing in, 863

foreign bonds in, 616

growth and declining industries in, 874–875

just-in-time approach, 781

mergers and, 809

ownership and control in, 865–866, 869

short-termism in, 874

Japan Airlines, 855

Jarmin, R. S., 839n

Jarrell, G., 96n, 405, 405n

JBS, 827

J.C. Penney, 606–608, 608n, 611, 613, 615–617

J.D. Edwards & Co., 824

Jenkinson, T., 392

Jensen, Michael C., 296, 296n, 314, 471, 471n, 839n, 854, 854n, 857

Jobs, Steve, 419

John, K., 857

Johnson, B., 741

Johnson, E. J., 333n

Johnson, Ross, 837–839

Johnson, S., 354n, 873, 873n, 878

Johnson & Johnson, 65, 78, 79, 219–220, 373, 450–452, 466–467, 725, 727, 806

Jorion, P., 165n

J.P. Morgan, 404, 405

JPMorgan Chase, 363, 366, 379, 405, 793

JP Morgan Prime Money Market Fund, 361

Jump risks, 663

Junior debt, 357, 613

Junk bonds, 490, 587, 595–597, 839

Jurek, J., 610n

Just-in-time approach, 781

K

Kadant Inc., 844

Kahle, K. M., 750n

Kahneman, D., 333n

Kalay, A., 421

Kallberg, J. G., 767

Kane, A., 163n

Kaneko, T., 384n

Kansas City Southern Railroad, 224, 490

Kaplan, S. N., 302n, 374n, 458, 458n, 498, 498n, 831, 839, 839n, 857

Kashyap, A., 866, 866n, 875n

Kay, John A., 279n, 308n

Kedia, S., 849n

Keiretsu, 865–866

Kelly, Ned, 37

Kendall, Maurice G., 321n, 321–322, 325

Keown, A., 326n

Kerviel, Jérôme, 682

Kester, W. C., 266

K.G.R. Ökologische Naturdüngemittel GmbH (KGR), 143–144

Kim, Y., 387n

Kinder Morgan, 79–80, 93, 837

Kindleberger, C., 885n

Kinetic Concepts, 837

Kiska, Wendy, 595

KKR (Kohlberg Kravis Roberts & Co.), 837–838

Klein, M., 638n

KLM, 512

Knoeber, C. R., 826n

Kohlberg Kravis Roberts & Co. (KKR), 837–838

Kooyul, Jung, 387n

Korea, conglomerates in, 872–873

Kosowski, R., 327n, 881n

Kothari, S. P., 325n

Kozlowski, Dennis, 12

KPMG, 77

Kraakman, R., 870n

Kraft, 806, 842

Krahnen, J. P., 878

Krigman, L., 377n

Kryvorizhstal, 844

Kulatilaka, N., 571n, 580

Kumar, A., 411n, 414n

Kumar, P., 614n

Kuoni, 706

Kuroki, F., 866n

L

Laclede Group Inc., 86

Lakonishok, J., 405n

Lamont, O. A., 843n, 848–849, 849n

Landier, A., 301n

Land Rover, 827

Landsbanki, 845n

Lang, L. H. P., 871n

La Porta, R., 352n, 419n, 864, 864n, 869n, 869–870, 878

LaSalle Bank, 812

Last-in, first-out (LIFO) inventory, 339

Law of conservation of value, 430–431, 881–882

Law of one price, 54–55, 698n

Lazard, 363

LBOs. See Leveraged buyouts (LBOs)

Leary, M. T., 641n

Leases, 358

Leasing, 358, 639–655

dubious reasons for, 642–644

financial leases, 640, 646–652, 732n

leveraged leases, 605–606, 640, 653

nature of leases, 639–640

as off-balance-sheet financing, 643

operating leases, 640, 644–646

reasons for, 640–642

in theory of optimal capital structure, 472

Lee, D. S., 405n

Leeson, Nick, 297n, 681

Legal systems, 820–821

Lehman Brothers, 5, 51, 366, 441n, 458, 628, 850

Leica, 848

Lemmon, M. L., 304n, 421, 467n, 470n

Lenders, monitoring by, 299

Lerner, J., 375n, 392, 839n

Lessard, D. R., 713

Lessee (user), 639

Lessor (owner), 639

Lettau, M., 173n

Lev, B., 228n

Leverage

cost of equity capital and, 435–436

financial. See Financial leverage

operating, 227–228, 253–254

Leveraged buyouts (LBOs), 462, 498, 733, 836–840

characteristics of, 840

examples, 837–839

incentives and, 839, 840

junk bonds and, 839

other stakeholders and, 839

taxes and, 839

Leveraged leases, 605–606, 640, 653

Leveraged restructurings, 840

Leverage ratios, 732–734

Levi, M. D., 713

Levine, R., 873n, 878

Levi Strauss, 375

Lewellen, W. G., 815n

Lewis, C. M., 620n, 630

Lewis, K. K., 714

Li, F., 579

Liabilities, current, 489

LIBOR (London Interbank Offered Rate), 357, 607–608, 625, 626, 672n, 793

Lichtenberg, F., 829n

Lie, E., 551n

LifeCare Holdings, 585–586

Life cycle of firm, payout policy and, 417–419

LIFFE, 666n

LIFO (last-in, first-out) inventory, 339

Limit orders, 76

Limited liability, 5, 456, 592

Limited liability companies (LLCs), 6

Limited liability partnerships (LLPs), 6

Limited partnership, 355, 846–847

Lindahl, F. W., 339, 339n

Lindt & Sprüngli, 706

Linear programming (LP), 121, 195

LinkedIn, 387, 871

Lintner, John, 198, 198n, 406n

Liquidation value, 78, 487

Liquidity

cash management and, 787

defined, 735

value of, 887–888

Liquidity ratios, 735–736

Litton Industries, 848

Litzenberger, R. H., 415, 415n

Lizzeri, Alessandro, 641n

Ljungqvist, A., 383n, 392

Lockbox systems, 790

Lognormal distributions, 191n

London interbank offered rate (LIBOR), 357, 607–608, 625, 626, 672n, 793

London Metal Exchange (LME), 667

London Stock Exchange, 76, 874

Longevity bonds, 623

Long-lived assets

choice between short-lived assets and, 144, 145–148

investing in, 348–349

multiple risk-adjusted discount rates for, 235–237

single risk-adjusted discount rate for, 234–237

Long Term Capital Management (LTCM), 335

Long-term financial planning, 748, 760–765

contingency planning, 761

example, 762–764

need for, 761–762

pitfalls in model design, 764

spreadsheet functions, 762

Long-term financing decisions. See Corporate financing

Longwei Petroleum, 549–550

Lookback options, 554

Loomis, C., 287n

Lopez-de-Salanes, F., 352n, 419n, 864, 864n, 869n, 869–870, 878

LoPucki, Lynn, 854n

L’Oréal, 5

Lottery winnings, 29

Loughran, R., 330n

Loughran, T., 382n, 383n, 389n, 390n

Lowenstein, L., 829n

Lowe’s Companies, 739–740

LTV, 848

Lu, Qi, 341n

Lucas, Deborah, 595

Lucent Technologies, 841, 842

Luehrman, T. A., 502

Lufthansa, 512, 666

Luxottica Group SpA, 615

LVMH, 3, 3n

M

Macaulay duration, 52, 53n

Mackie-Mason, J., 466n

MacKinlay, A. C., 325n

Macquarie Bank, 363

Maddaloni, A., 860n

Madoff, Bernard, 11–12, 12n

Majd, S., 569n

Majluf, N. S., 388n

Majority voting, 353

Maksimovic, V., 470n, 844, 844n

Malkiel, B. G., 173n, 327n, 342, 343

Malmendier, U., 827n

Malted Herring, 512

Management buyouts (MBOs), 836–840

Mandelker, G. N., 228n

Mann, C., 594n

Mann, S. V., 70, 799

Mannesmann, 301–302

Marathon Oil, 842

Marcus, A. J., 163n

Maremont, Mark, 808n

Margin, in futures trading, 667–669

Margrabe, W., 564n

Marketable securities. See also specific types

as financial assets, 2

management of, 791–797

Market capitalization, 4, 76–77, 724

Market capitalization rate, 81. See also Cost of equity capital

Market efficiency. See Efficient-market hypothesis

Market factor, in three-factor model, 206–208

Market model, 325

Market orders, 76

Market portfolio, stocks in, 202n

Market risk, 881

beta in measuring, 178–179

defined, 174, 174n, 190

portfolio diversification and, 171–174

spreadsheet functions in estimating, 236–237

Market risk premium

defined, 197

expected, 197–198

historic, 160–167, 197

in three-factor model, 207

Market timing, 470–471

Market-to-book ratio, 95, 724–725

Market value, 273–278

Cadillac/movie star parable, 274

in capital budgeting problems, 273–278

in investment decisions, 274–278

Market value added, 724

Market Volatility Index (VIX), 550–551, 553

Markowitz, Harry M., 190, 190n, 195

Mark to market, futures contract, 668

Marriott Corporation, 614, 615, 628

Marsh, P. R., 60n, 64n, 160n, 160–161, 161n, 162n, 165, 165n, 168n, 171n, 183, 288, 337n, 702n

Marston, F. C., 709n

Martin, K. J., 811, 811n

Marvin Enterprises case, 281–288, 371–373, 376–380, 384–385

Marx, Karl, 287

Mason, S. P., 580

Master limited partnership, 355

Masulis, R. W., 392, 815n

Matching maturities, 749

Matthews, J., 610n

Mauer, D. C., 749n

Maug, E., 867, 867n

MaxLinear, 387

Mayer, C., 868n

Mayers, D., 884n

Mazda, 875

MBNA, 812

McCardle, K. F., 828, 828n

McConnell, J. J., 622n, 646n, 655, 811, 811n

McDonald, R. L., 555, 579

McGraw-Hill, 842

McGuire, William, 551

MCI, 875

McKinnell, Henry, 300

McKinsey & Company, 306

McNichols, Maureen F., 597–598, 598n

Medco Health Solutions, 806

Medium-term notes (MTNs), 628–629, 795, 796

Megginson, W., 386n, 391, 845n, 857

Mehra, J., 164n

Mehra, R., 184

Mehrotra, V., 842n

Mehta, P., 873, 873n

Mei, J., 228n

Mercedes Automobil Holding, 867

Merck, 130, 708

Mergers and acquisitions, 806–831

antitrust law and, 820–821

Bank of America, 812

benefits of, 829

board of directors and, 847–850

conglomerate mergers and value additivity, 807, 833–835

dubious motives for, 812–815

economy and, 828–829

estimating gains and costs of, 815–820, 827–828

form of acquisition, 821

junk bonds and, 490, 587, 595–597, 839

mechanics of mergers, 820–823

merger accounting, 821–822

sensible motives for, 807–812

takeover battles and tactics, 826–827

types of, 807

waves of, 828–829, 888–889

Merrill Lynch, 297, 300, 363n, 366, 812

Merton, Robert C., 368, 546n, 580, 592n, 884, 884n

Metrick, A., 391, 826n, 847n

Mexico, put options on oil, 664

Mezzanine financing, 373, 373n

Mian, S. L., 786n, 799

Michaely, R., 377n, 404n, 414n, 421

Microsoft, 4, 322–325, 323n, 401, 412, 413, 465, 725, 727, 728, 729, 806

Mihov, V. T., 615n, 616n, 624n

Mikkelson, W. H., 405n

Miles, J. A., 494n, 502, 842n

Milgrom, P., 392

Mill, John Stuart, 883

Miller, Merton H., 406, 406n, 415, 415n, 429n, 443, 451n, 453, 453n, 491–495, 494n, 623, 660, 882

Miller, N. G., 226n

Miller, S. C., 626n

Miranda, J., 839n

Miranti, P. J., Jr., 848n

Mishler, L., 798

Mishra, D. R., 709n

Mitchell, M., 820, 820n, 827, 827n, 829, 830

Mitsubishi Estate Company, 465n

Mittal Steel, 827

Mittelstaedt, F., 741

Miyajima, H., 866n, 878

Mizuho Bank, 809, 809n

Modified accelerated cost recovery system (MACRS), 140–142

Modified duration, 53

Modified internal rate of return, 115n

Modigliani, F., 406, 406n, 429n, 451n, 491–495, 494n, 660, 882

Modigliani-Miller (MM) approach

to capital structure, 428–430

law of conservation of value, 430–431, 881–882

Proposition 1, 430–434, 438, 441, 450, 451–452, 491–492

Proposition 2, 434–436, 438, 439, 442, 492, 493

rebalancing and, 494n

taxes in, 450–452

violations of, 441

to payout policy, 406–411

Moffett M. H., 713

Mohan, N., 837n, 839, 839n

Mola, S., 390n

Money machines, 57, 698

Money market, 792

Money-market investments, 361, 791–797

calculating yield on, 792

types of, 794–797

yields on, 792, 793

Monte Carlo simulation, 254–258

defined, 254

example, 255–258

Montgomery, C., 850, 850n

Moody’s credit ratings, 65–66, 595, 609, 623, 628n, 783

Moody’s KMV, 600, 600n

Moon, Mark, 584n

Mooradian, R. M., 857

Moore, J., 854n

Moral hazard risk, 663

Morck, R., 878

Moretti, E., 827n

Morgan Stanley, 6, 363, 363n, 379, 386, 626

Morris, J. R., 767

Morrison, A. D., 11n

Mortality bonds, 622–623

Mortgage-backed securities (MBSs), 297, 336, 366–367, 610, 628

subprime crisis of 2007–2009, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

Mortgage bonds, 609

Mortgage pass-through certificates, 610n

Mortgages

calculating annual payments, 30–31

subprime crisis of 2007–2009, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

Motorola, 824, 842

Motorola Mobility, 806, 807

Mulally, Alan, 472

Mulherin, J. H., 830

Mullainathan, S., 297n, 873, 873n

Mullins, David W., Jr., 337n, 340, 340n

Multi Commodity Exchange (India), 667

Murphy, K. J., 314

Murphy, T., 781n

Mutual funds, 360–362

closed-end, 77n, 361, 886

open-end, 77n, 361

Mutually exclusive projects

internal rate of return and, 115–117

net present value rule for, 144–149

Myers, Stewart C., 289, 388n, 470n, 474, 495n, 569n, 650n, 765, 814n, 815n, 876n, 883

N

Nagel, S., 411n

“Naked” call options, 220n

Nanda, V., 383n, 842n

Narayanan, P., 603

Nardelli, Robert, 300

Nasdaq (National Association of Securities Dealers Automated Quotations System), 76, 551

Nasdaq Composite Index, 332, 885

Nationalization, 844–845

Nationally recognized statistical rating organizations (NRSOs), 595n

National Venture Capital Association, 375

NationsBank, 812

NatWest Bancorp, 812

Naveen, L., 304n

Navistar, 299

NBB Bankcorp, 812

NBC Universal, 806, 807

NCR, 841, 842

Negative pledge clause, 608n

Negotiable certificates of deposit (CDs), 794–796

Nenova, Tatiana, 354, 354n, 871–872, 872n

Nestlé, 340n, 705, 706, 844

Net asset value (NAV), 360

Net convenience yield, 670–672

Net current assets, 723

Net income, free cash flow (FCF) versus, 485

Net leases, 640

Net operating profit after tax (NOPAT), 727n

Net present value (NPV), 105–109, 320–321. See also Net present value rule; Present value (PV)

capital budgeting decisions and, 245–266

capital investment process, 246–248

decision trees, 258–265

forecasting economic rents, 278–288

forecasting market values, 273–278

incentives, 296–297, 412–413

Monte Carlo simulation, 254–258

process for, 246–248

real options, 258–262, 561–580

sensitivity analysis, 248–254

defined, 22, 105

financing decisions and, 5, 136–137, 139, 312

importance of concept, 880

investment decisions and, 105–109, 130–149

alternatives to, 107

book rate of return versus, 108–109

cash flow in, 130–137

cost of excess capacity, 144, 148–149

depreciation and, 135, 137, 140–142

example, 137–144

forecasting economic rents, 278–288

incentives, 295–314

inflation and, 135–136

investment versus financing decisions, 136–137, 139, 321

key points concerning, 107–108

long- versus short-lived projects, 144, 145–148

market values in, 273–278

multiple cash flows, 24–25

payback analysis versus, 109–111

replacement problem, 144, 148

review of basics, 105–109

taxes and, 140–142

timing, 144–145

key features, 107–108

leasing and, 650–651

in merger analysis, 815–820

for other countries/currencies, 143–144

present value versus, 22, 22n

production option and, 571–572

project analysis, 142–143

project risk and, 883

review, 105–109

sensitivity analysis and, 249–250

Net present value rule, 130–149

applying, 130–137

statement of, 24

Net return on investment, 305

Netter, J. M., 845n

Net working capital, 723. See also Working capital

investing in, 348–349

Net-working-capital-to-total-assets, 735–736

Neuberger, A. J., 278n

Neuer Markt, 374–375, 885

Nevitt, P. K., 654

New issues

alternative issue procedures, 384–385

costs of, 380

efficient-market hypothesis and, 329–330

hot new-issue periods, 383

primary market, 76, 359–360. See also Initial public offerings (IPOs)

secondary market, 76, 385–390

New Jersey Resources Corp., 86

Newmont Mining, 173–174, 179, 194, 195, 198

New projects. See also Capital budgeting; Capital rationing

incidental effects of, 133–134

New York Mercantile Exchange (NYMEX), 666, 666n, 667

New York Stock Exchange (NYSE), 5, 7, 76, 76n, 201, 303–304, 355

New York Yankees, 301

New Zealand, imputation tax system, 415–416

Ng, C. K., 781n

Nielsen, 848

Nielsen Holdings, 387

Nikkei 225 Index, 332

Nimmo, R., 603

Nippon Telegraph and Telephone (NTT), 375, 845

NiSource Inc., 86

Nissan, 866, 867

Nocco, B. W., 684

Nokia, 512, 617–618

Nominal exchange rates, real exchange rates versus, 701–703

Nominal rates of interest, 59–63

inflation and, 62–63

real rates of interest versus, 59–63

Nominal returns, real returns versus, 699

Nomura (Japan), 363

Nondiversifiable risk. See Market risk

Non-negotiable time deposits, 795, 796

Nonrecourse leases, 653

Norfolk Southern, 224

Norli, Ø, 392

Normal risk, 235–237

Norstar Bancorp, 812

Northern Rock, 845n

Northwest Natural Gas Co., 86

Notes

defined, 608

floating rate, 608

medium-term (MTNs), 628–629, 795, 796

Treasury, 47–49

Notional principal, 673–674

Notional value, 674–675

Novartis, 706

NPV. See Net present value (NPV)

NTT (Nippon Telephone and Telegraph), 375, 845

Nuclear Regulatory Commission, 2

Nycomed, 806

NYSE Euronext, 76, 76n

NYSE Euronext LIFFE, 668

O

OATs (Obligations Assimilables du Trésor), 46–47

Obama, Barack, 67, 301, 338

O’Brien, T. J., 709n

Occupy Wall Street protest, 367

Ofek, E., 332n, 849n

Ofer, A. R., 404n

Off-balance-sheet liabilities, 643, 885–886

Offering price, 380

O’Hara, M., 377n

Oman Oil, 844

Omidyar, Pierre, 383

Onex, 837

ONGC, 844

Open account, 782

Open-end mutual funds, 77n, 361

Open mortgages, 609n

Open repos, 796

Operating expenses, 108–109

Operating leases, 644–646

defined, 640

example, 644–645

lease-or-buy decision and, 645–646

Operating leverage, 253–254

asset beta and, 227–228

break-even points and, 253–254

defined, 253

Operating profit margin, 731

Opler, Tim, 750, 750n

Opportunity cost of capital, 725–726. See also Discount rate

business risk and, 500

calculating, 20–22

company, 219–222, 433–434

defined, 10

discount rates for international projects, 232

example, 25

financing decisions and, 321

historical evidence to evaluate, 163–166

for international investments, 708–709

multiple, 117–118

nature of, 10

net present value and, 108–109, 134–135

payback period and, 107, 109–111

perfect pitch and, 220–221

project, 219–222

Optimization models, 760

Option(s), 512–529. See also Convertible bonds; Option pricing models; Real options; Stock options; Warrants

default puts, 591

reducing risk with, 664

spotting, 521–522

strategies for using, 517–522

types of, 552–554. See also specific types of options

Option delta, 537, 539, 542

Option equivalents, 536–540

Option pricing models, 523–528, 535–555

binomial method, 540–545

Black-Scholes formula, 545–551, 576n, 882

call options, 536–538

dividends in, 553–554

option values at a glance, 552–554

risk and, 527, 537–540, 601

simple option-valuation model, 536–540, 612–613

stock value and, 523–528

types of options, 552–554

Option theory, 882

Option valuation. See Option pricing models

Oracle Corporation, 302, 549, 549n, 824–826

Osaka Securities Exchange (OSE), 668

Oshkosh, 299

Osobov, I., 401n

Overconfidence bias, 333–334, 827–828

Overhead, in net present value analysis, 135

Over-the-counter (OTC) market, 76, 360, 551

Ownership and control. See also Agency problem; Board of directors; Corporate governance

of conglomerates, 872–873

dual-class equity in, 354, 871–872

in France, 869

in Germany, 866–869

in Japan, 865–866, 869

of leased assets, 647–648

pyramids in, 870–871

risk and short-termism and, 874

separation of ownership and management, 5, 12, 823, 865–876

transparency and, 875–876

P

Pacific Gas & Electric, 628, 851

Palepu, Krishna G., 403–404, 404n, 741, 829, 829n, 875n, 878

Panunzi, F., 876n

Paramount, 827

Parkinson, K., 767

Parmalat, 876

Parrino, R., 857

Partch, M. M., 405n

Participation, 626n

Partnerships, 6, 355, 846–850

Pass-through certificates, 610n

Pastor, L., 383n

Patel, J., 312–313, 313n

Pattenden, K., 414n

Paulson, John, 335n

Payback period, 107, 109–111

applying, 109–110

determining, 109–110

payback rule and, 109–111

Payback rule, 109–111

Pay for performance, monitoring, 303–304

Payment mechanism, 364

Payout policy, 400–421

capital structure and, tax-free economy, 428–433

controversy concerning, 406–411, 886–887

irrelevance of dividends, 406–411

pro-dividend payout, 416–417

in corporate governance, 418–419

deciding on, 402–403

efficient-market hypothesis and, 406–411

facts concerning, 401–403

information content of, 403–405

life cycle of the firm and, 417–419

method of payment, 402

Modigliani-Miller approach to, 406–411

payout decision in, 4

pecking order of financing choices and, 469–470

stock repurchase, 403–411

Payout ratio, 85, 412–413. See also Payout policy, controversy concerning

Pecking order of financing choices, 467–472

default risk, 609

financial slack, 471, 472, 484–486

impact of asymmetric information, 467–469

implications of, 469–470

trade-off theory versus, 470–471

Pemex, 664

Penman, S., 741

Penney (J.C.), 606–608, 608n, 611, 613, 615–617

Pension Benefit Guarantee Corporation (PBGC), 594–595, 851

Pension funds, 362, 374, 594–595, 623

PeopleSoft, 824–826

PepsiCo, 332, 820

Percentage of sales model, 764

Performance measurement, 304–313

accounting measures of performance, 304–313

incentives and. See Incentives; Stock options

Performance shares, 302

Perkins, C. A., 579

Perks, 296

Perpetuities, 26–27

defined, 26

growing, 33

valuation of, 26–27

Peso loans, 696

Peters, F., 827n

Petersen, M. A., 787n, 799

Petraeus, David, 302

Petrohawk Energy, 806

Pettway, R., 384n

Peugeot, 5

Pfizer, 194, 198, 300, 844

Pharmaceutical Product Development, 837

Phaup, Marvin, 595

Philadelphia Index, 303

Philips Electronics, 322–323, 325

Phillips, G., 844, 844n

Phillips Petroleum, 115

Piedmont Natural Gas Co., 86

PIK (pay in kind), 837–838

Pindyck, R. S., 266, 570n, 580

Pinkerton, J., 326n

Pinkowitz, L., 750n, 751, 751n, 799

Plains All American Pipeline LP, 355

Playing for time game, in financial distress, 462

P&O, 821

Poison pill defense, 824–826

Poison-put clauses, 614

Poison put defense, 826

Political risk, 710–712

guaranteeing loans against, 712

scores for sample of countries, 711

Ponzi, Charles, 11n

Ponzi schemes, 11n, 11–12, 12n

Pooling risks, 365, 662–664

Porsche, 334–335

Porter, Michael E., 279, 279n, 288, 874n

Portfolio insurance, 550

Portfolio risk, 160–184

beta and, 178–182, 198–204

calculating, 175–178, 181–182

diversification and, 171–174, 182

historic performance of capital markets and, 160–167

individual securities and, 178–182

measuring, 167–174

relationship to return, 197–200

standard deviation in, 167–170, 171, 181–182

variance in, 167–170, 171–174

Portfolio theory, 190–209

birth of, 190–197

borrowing and lending in, 195–197

developing portfolios, 191–195

efficient portfolios in, 195–197, 199

standard deviation and, 190–191, 193n, 196n

variance and, 193n

Portfolio variance, 167–170, 171–174

Position diagrams, 514–515, 516–517

Postaudits, in capital budgeting process, 247–248

Postbank, 844

Poterba, J. M., 332n

Powers, E., 842n

Prediction markets, 338

Preferred stock, 356, 372

floating-rate, 797, 797n

Premium, bond, 47

Prenegotiated bankruptcies, 854

Prepackaged bankruptcies, 854

Prescott, E. C., 184

Present value (PV), 18–39. See also Adjusted present value (APV); Net present value (NPV)

of annuities, 27–28

in bond valuation, 46–49

calculating, 19–20, 20–22

defined, 20

of investment opportunity, 20–22

in Monte Carlo simulation, 258

net present value rule, 24, 130–149

net present value versus, 22, 22n

nominal interest rates and, 59–63

opportunity cost of capital and, 25

of perpetuity, 26–27

present value formula, 26n

rates of return and, 23–24

real interest rates and, 59–63

risk and, 22–23

Present value of growth opportunities (PVGO), 90–92, 259, 886

in business valuation, 95–96

calculating, 91–92

defined, 90–91

examples of growth opportunities, 91–92

President’s Council on Jobs and Competitiveness, 377

Price discovery, 672n

Price-earnings (P/E) ratio, 78–79, 95, 312n

Price-fixing, 380n

Primary issues, 359–360. See also Initial public offerings (IPOs)

Primary markets, 76, 359–360

Prince, Charles, 297, 297n

Principal, 12, 46, 883

Private benefits, 296, 354

Private equity, 845–850

Private-equity deals, 846–850

Private equity investing, 374

Private-equity partnerships, 846–850

Private Export Funding Corporation, 794n

Private placements, 390–391, 615–616

Privatization, 844–845

Privileged subscription issues, 389–390

Probabilities, beliefs about, 333–334

Procter & Gamble (P&G), 2, 3, 4, 340

Procurement, 572

Production option, 261, 571–572

Professional corporations (PC), 6

Profitability index, 107, 119–120

Profitability measures, 113

biases in, 307–313

calculating, 308–310

economic value added (EVA), 305–307

net return on investment, 305

Profit diagrams, 516–517

Profit margin, 731

Profit maximization, 785

Progress Energy, 806, 809

Project analysis, 245–266

capital investment process, 246–248

decision trees, 262–265

Monte Carlo simulation, 254–258

net present value and, 142–143

real options, 258–262

sensitivity analysis, 248–254

Project beta, 219–222

Project cost of capital, 219–222

Project finance

adjusted present value for international investments, 498–499

discount rates for international projects, 232

weighted-average cost of capital (WACC), 221–226

Project life, abandonment value and, 569

Project risk, 883

analyzing, 226–232

capital budgeting and, 219–222

Prospect theory, 333

Prospectus, 378, 380

Prowse, S., 867n

Proxy contests, 353–354, 823–824

PRS Group, Inc., 710–711, 711n

Prudhoe Bay Royalty Trust, 355

Public companies

closely-held companies versus, 5

defined, 5

security sales, 385–390

costs, 386–387

general cash offers, 385–387

international security issues, 386

market reaction to stock issues, 387–389

rights issues, 389–390

Purchase method of merger accounting, 821–822

Purchasing power parity, 698, 698n, 700–703, 705n

Pure plays, 226

Puri, M., 374n

Put-call parity, 520n, 520–521

Put options

in reducing risk, 664

relationship between call prices and, 540

selling, 515–516

valuation of, 539–540

Puttable bonds, 613

PV. See Present value (PV)

PVGO. See Present value of growth opportunities (PVGO)

Pyramids, 870–871

Q

QQQQs, 361

Quadratic programming, 195

Qualified institutional buyers, 391

Qualified opinions, 299

QUBES, 361

Quick ratio, 736

Quiet period, 377n

Quinenco, 872

QVC, 827

R

Raghaven, Anita, 615n

RailAmerica, 224

Rainbow options, 554

Rajan, Raghu G., 296n, 368, 470, 470n, 787n, 799, 864n, 864–865, 873, 873n, 875n, 878

Rajaratnam, Raj, 326n

Rajgopal, S., 312, 312n, 313n, 314

Ramaswamy, K., 415, 415n

Random walk hypothesis, 321–324, 526n

Rate of return rule, statement of, 24

Rates of return. See also specific types of return

accounting, 726–728

bond, 51

book, 108–109, 727

calculating, 160–162

defined, 51

on levered equity, 439–440

present value and, 23–24

Rau, P. R., 332n

Rauh, J. D., 302n

Ravenscroft, D. J., 829, 829n

Ravid, S. A., 855n

Raviv, A., 474

Real assets, 2

value maximization and, 16–17

Real estate

investment decisions for, 274–276

optimal timing for development of, 567–568

Real estate investment trusts (REITs), 226, 226n, 355

Real exchange rates

defined, 703n

nominal exchange rates versus, 701–703

Real options, 258–262, 561–580

abandonment option, 259–261, 568–570

conceptual problems, 577–578

decision trees and, 258–265

default risk, 590–602

defined, 258

expansion option, 258–259, 281–288, 512–513, 561–565, 573–575, 761

investment option, 512, 575–577

production option, 261, 571–572

timing option, 261–262, 565–568

valuing flexibility, 571–575

Real rates of interest, 59–63

in bond valuation, 59–63

determinants of, 62

indexed bonds and, 61–62

nominal rates of interest versus, 59–63

Rebalancing debt, 493–494

Receivables turnover, 730

Record date, 402

Registered bonds, 46n, 608

Registration statement, 377–378

Regular cash dividends, 402

Reinhart, Carmen M., 369, 889, 889n

Relative tax advantage of debt, 452–453

Relevering beta, 492–493, 494n

Renault, 867

Rental leases, 640

Reorder point (two-bin) system, 780n

Replacement decisions, equivalent annual cash flow and, 144, 148

Replicating portfolio, 537

Repurchase agreements (repos), 795, 796

Repurchase programs. See Stock repurchases

Research in Motion, 298

Reserve Primary Fund, 792

Residual claims, 358–359

Residual income. See Economic value added (EVA)

Restricted stock, 302

Restructuring, 836–857

asset sales, 844

of AT&T, 841

bankruptcy, 455–459, 850–855

carve-outs, 843–844, 845

leveraged buyouts, 836–840

leveraged restructurings, 840

privatization, 844–845

spin-offs, 842, 843

Return on assets (ROA), 305n, 597, 727, 728, 731

Return on capital (ROC), 305n, 726, 727–728

Return on equity (ROE), 85–89, 727, 728, 734

Return on investment (ROI)

biases in, 307–313, 312–313

net, 305

Revenue adequacy, 87

Revenue securities, 794n

Reverse repos, 796

Reverse stock splits, 354–355, 355n

Revlon, 824n

Revolving credit, 624

Revsine, L., 741

Rhee, S. G., 228n

Rhie, Jung-Wu, 597–598, 598n

Rice, E. M., 884n

Richardson, M. W., 332n, 369, 611n

Richemont, 706

Riddiough, T. J., 567n, 568n

Rieker, M., 405n

Rights issues, 379n, 389–390

Right to default, 455–456

Rio Tinto, 761

Risk. See also International risks; Portfolio risk

attitudes toward, 333

capital asset pricing model (CAPM) and, 198–204, 224–226

capital budgeting and. See Capital budgeting and risk

company, 219–222

compound annual return and, 162–163, 164n

counterparty, 665

default, 63–68, 590–602

diversifiable (specific), 174, 174n, 178–179, 190, 229–230

expected return and, 197–200

foreign exchange, 693–710

of foreign investments, 232

market. See Market risk

normal, 235–237

option pricing and, 527, 537–540, 601

political, 710–712

pooling, 365, 662–664

portfolio. See Portfolio risk

present value and, 22–23

project, 219–222, 226–232, 333, 883

return and, 883–884

short-termism and, 874

in term structure of interest rates, 58–59

Risk aversion, 8

Risk class, 81

Risk-free rate of interest, 520n

Risk management, 659–684, 887

agency problem, 660, 661–662

derivatives in, 662, 665–677

evidence on, 662

forward contracts, 665

hedging

defined, 659–660, 665

with futures contracts, 666–672, 677–679

setting up hedge, 677–681

insurance, 550, 662–664

international risks in, 693–714

options, 664

reasons for, 659–662

swaps, 673–677

Risk-neutral option valuation, 537–540

Risk premium

calculating, 164

defined, 164n

dividend yields and, 166–167

historic, 197

market. See Market risk premium

in Sharpe ratio, 196, 196n

Risk-return trade-off, financial leverage and, 428–433

Risk shifting game, in financial distress, 460–461

Ritter, J. R., 330n, 380, 380n, 382n, 383n, 389n, 392

Ritz Carlton, 807

RJR Nabisco, 462, 837–839

ROA (return on assets), 305n, 597, 727, 728, 731

Road show, 378

Robert Bosch, 867

Roberts, M. R., 467n, 624n, 627n

ROC (return on capital), 305n, 726, 727–728

Roche, 706–709

Rockefeller Center, 465n

Rockefeller Center Properties, 465n

Rodriguez, Alex, 301

ROE (return on equity), 85–89, 727, 728, 734

Roe, M., 855n

Röell, A., 878

Rogalski, R. J., 620n, 630

Rogers, D. A., 666, 666n

Rogoff, Kenneth, 369, 714, 889, 889n

ROI. See Return on investment (ROI)

Rolfe, David A., 419

Roll, Richard, 329n, 884n

Romaine, C., 509n

Rose-Ackerman, S., 829n

Rosenthal, L., 330n

Ross, Stephen, 205–206

Royal Bank of Scotland, 367

Royal Dutch Petroleum, 330, 335

Royal Dutch Shell, 76, 403

Royal Statistical Society, 321

Ruback, Richard S., 343, 498, 498n, 502, 829, 829n, 839, 839n

Rubinstein, M. E., 343

Rule 10b-18, 403n

Rule 144A, 391, 616

Rule of signs (Descartes), 114n

Russian debt default (1998), 67, 335, 335n, 590n

Rydqvist, K., 382n

Ryngaaert, M. D., 812n

S

Sabathia, C. C., 301

Sacconaghi, A. M., 419

Sagner, J., 799

Sahlman, W. A., 392

Sale and lease-back, 640

Salvage value

abandonment options and, 569–570

depreciation and, 135, 137

leasing and, 651

in net present value analysis, 135, 137

in replacement decisions, 148

Samurai bonds, 616

Sanofi-Aventis, 806

Santos, T., 205n, 333n

Sapienza, P., 10n

Sara Lee, 842

Sarbanes-Oxley Act of 2002 (SOX), 298, 376, 418, 847

Sarkozy, Nicolas, 301

Sartoris, W. L., 798

Saunders, A., 603

Savings banks, 363n

Savor, Pavel, 341n

SBC Communications, Inc., 841

Scannapieco, D., 857

Scenario analysis, 250, 564n

Schaefer, A. M., 70

Schaefer, S. M., 684

Schall, L. D., 815n

Schallheim, J. S., 646n, 654, 655

Scharfstein, D., 684, 842n, 866, 866n

Scherer, F. M., 829, 829n

Scherr, F. C., 798

Schmidt, R. H., 878

Schneider, C., 867, 867n

Schoar, A., 471n

Schofield, Adrian, 666

Scholes, Myron S., 402n, 415, 415n, 536, 536n, 545–551, 546n

Schranzk, D., 587n

Schultze, George J., 855n

Schwartz, E. S., 278n, 570n, 580, 612n, 630, 885n

Schwartz, Eduardo, 584n

Schwartz, S. L., 332, 332n

Schwert, G. W., 343

Sealed Air Corporation, 840

SEC. See U.S. Securities and Exchange Commission (SEC)

Secondary issues, 385–390

Secondary markets, 76, 385–390

Secondary transactions, 360

Second law, Brealey, Myers, and Allen, 231n, 247n

Second-stage financing, 373

Secured debt, 608

Securities. See Marketable securities and specific types

Securities Act of 1933, 377n

Securitization, 610

Security market line

defined, 198

stocks not lying on, 199–200

Security Pacific, 812

Segmented markets, 321

Self-liquidating loans, 624

Semiannual coupons, 47–49, 606

Semiannual interest payment, 47–49, 606

Semistrong form of market efficiency, 324–325

Senbet, L., 857

Senior debt, 608–609

Senior management. See also Board of directors; Chief executive officers (CEOs); Chief financial officers (CFOs)

CEO compensation by country, 300

as off-balance-sheet liability, 885–886

Sensitivity analysis, 143, 248–254

in arbitrage pricing theory, 205–206

break-even analysis, 250–253

defined, 249

limits to, 250

operating leverage and, 253–254

scenario analysis, 250, 564n

in three-factor model, 207–208

value of information, 249–250

Separation of ownership and management, 5, 12, 823, 865–876

Sercu, P., 713

Seuss, Dr., 298–299, 299n, 304

Seward, J. K., 620n, 630, 857

Shanghai Futures Exchange, 667

Shapiro, A. C., 713

Shapiro, E., 84n

Share buybacks, 419

Shareholders

agency problem and, 882–883

limited liability of, 823

minority, 354–355

monitoring by, 299, 304

role of, 823

separation of ownership and management, 5, 12, 823, 865–876

stakeholders versus, 869

value maximization and, 7–12, 16–17, 245–266

Share repurchases. See Stock repurchases

Shark-repellent charter amendments, 826

Sharpe, William F., 198, 198n

Sharpe ratio, 196, 196n

Shaw, W. H., 377n

Shawmut National, 812

Shefrin, H., 412n

Shelf registration, 385

Shell Transport & Trading, 330, 335

Shenzhen Stock Exchange, 552

Shiely, J. S., 314

Shiller, Robert J., 167n, 334n, 343

Shin, B., 638n

Shivakumar, L., 330n

Shivdasani, A., 842n

Shleifer, A., 296n, 343, 352n, 419n, 844n, 845n, 864, 864n, 869n, 869–870, 878

Shortage of capital, 117

Short-lived assets

choice between long-lived assets and, 144, 145–148

investing in, 348–349

Short sales, 334–335

Short squeeze, 334–335

Short-term debt, 489

Short-term financial planning, 748–751, 757–760

cash budgeting, 748, 755–757

evaluating plan, 759–760

example, 758–759

leases in, 640–641

options, 758

short-term financial planning models, 760

sources of short-term borrowing, 757–760

Short-termism, 312, 874

Short-term tax-exempts, 794, 795

Shoven, J. B., 549n

Shyam-Sunder, L., 389n, 470n

“Siamese twins,” 330, 330n

Sidel, R., 405n

Siegel, D. R., 404n, 829n

Sight drafts, 782

Signaling, 372. See also Information effect

dividends and, 403–405

stock repurchase and, 405

Simkins, B. J., 666, 666n, 684

Sindelar, J. L., 392

Singal, V., 857

Singapore Exchange (SGX), 668

Singh, R., 383n

Singleton, K. J., 603

Sinking funds, 611

Sivakumar, R., 842n

Six Flags, 600, 848

Size factor, in three-factor model, 206–208

Skeel, D., 855n

Skinner, Douglas J., 401n, 417n, 419, 421

Skype, 806

Small business. See also Mergers and acquisitions

forms of organization, 6

higher investment returns and, 202–204, 328–329

small-firm effect in three-factor model, 206–208

Small Business Administration (SBA), 595, 794n

Smart, S. B., 386n

Smit, H., 578n, 580

Smith, Clifford W., Jr., 655, 660n, 786n, 799

Smith, J. K., 781n, 782n

Smith, K. V., 798

Smith, R. L., 781n

Smithson, C. H., 684

Société Générale, 681, 682

Soft rationing, 121–122

Sogo, 875

Sole proprietorships, 6

Sony, 76, 133–134, 322–323, 325

Southern California Edison, 628

Southern Company, 3

South Jersey Industries Inc., 86

Southwest Airlines, 778–779

Southwestern Bell, 841

Southwest Gas Corp., 86

Sovereign bonds

default risk, 66–68

sovereign debt crisis, 67–68, 367, 589, 889

Spark spread, 571

SPDRs (Standard & Poor’s Depository Receipts), 361

Special dividends, 402

Special-purpose entities (SPEs), 358, 465, 605–606, 628, 653, 875

Specific (diversifiable) risk, 174, 174n, 178–179, 190, 229–230

Spindt, P. A., 384n

Spinning, 380

Spin-offs, 842, 843

Spitzer, Eliot, 381

Split-ups, 842, 843

Spot prices, 665, 670–672

Spot rate

defined, 54

of exchange, 694, 697

forward premium and, 697

law of one price and, 54–55, 698n

Spread

spark, 571

TED, 625, 888

underwriting, 380, 387

yield, 66, 587–589

Spreadsheet functions

bond valuation, 68

discounting cash flows, 37–38

estimating market risk, 236–237

estimating stock risk, 236–237

internal rate of return, 121

long-term financial planning, 762

Sprint Nextel, 727

Stafford, E., 610n, 820, 820n, 827, 827n, 829, 830

Stakeholders

in leveraged buyouts, 837–839

shareholders versus, 869

value maximization, 7–12

Standard deviation

defined, 167–168

of foreign stocks, 171

in measuring portfolio risk, 167–170

portfolio, 167–170, 171, 175–176

in portfolio theory, 190–191, 193n, 196n

in Sharpe ratio, 196, 196n

Standard error, 162n

of estimated beta, 222–224

Standard of profitability, 113

Standard & Poor’s 500 Index, 322, 322n, 328, 550–551, 553

Standard & Poor’s Composite Index, 163, 331, 361, 551, 609n, 738, 739

Standard & Poor’s credit ratings, 65–66, 67, 595, 596, 601–602, 623, 628n, 783

Standard & Poor’s Depository Receipts (SPDRs), 361

Standards, accounting, 721

Starbucks, 173–174, 194, 198, 601–602

Stars, 848

Statman, M., 412n

Staunton, M., 60n, 64n, 160n, 160–161, 161n, 162n, 165, 165n, 168n, 171n, 183, 702n

Stein, Jeremy C., 341n, 620n, 684, 857

Step-up provision, 623

Stern, J. M., 314, 339n

Stern-Stewart, 305n, 306

Stertz, Bradley A., 808n

Stiglin, L., 839n

Stiglitz, J. E., 328n

Stillwell Financial, 490

Stock dividends, 402, 402n

Stockholders. See Shareholders

Stockholders’ equity, interest tax shields and value of, 450

Stock options, 512–529. See also Option pricing models

Black-Scholes model for valuing, 528, 549, 550, 551

call options, 514–515, 536–538

incentives created by, 302–303

position diagrams, 514–515, 516–517

profit diagrams, 516–517

put options, 515

strategies for using, 517–522

Stock price

dividend payout ratio and, 408–409

dividends and, 80–84

in equity valuation, 75–77

link between earnings per share and, 77, 78–79, 89–92

market reaction to stock issues, 387–389

option values and, 523–528

underpricing of initial public offerings, 380–383

Stock repurchases, 403–411

free cash flow and, 96–97

growth in use, 403

information content of, 405

irrelevance, 406–407

method of using, 403

Stock splits, 402, 402n

reverse, 354–355, 355n

Stohs, M. H., 749n

Stonehill, A. I., 713

Stonier, J. E., 573n, 574n

Stored-value cards, 789

Straight-line depreciation, 137, 142, 642

Stretching payables, 756, 758

Stripped bonds (strips), 55–56, 61

Stromberg, P., 374n, 855n, 857

Strong form of market efficiency, 325, 326–327

Structured investment vehicles (SIVs), 735

Stulz, R. M., 387n, 684, 709n, 750n

Subordinated debt, 357

Subprime mortgage crisis, 297–298, 300–301, 335–336, 366–367, 588–589, 886, 888, 889

Sufi, A., 624n, 626n

Sumitomo Bank, 875

Summit Bancorp, 812

Sundaresan, A., 70

Sundgren, S., 855n

SunGard, 848

Sunk costs, in net present value analysis, 135

SunTrust Banks, 65

Supermajority, 353, 826

Surplus funds, in mergers, 810–811

Sussman, O., 458n

Sustainable growth rate, 766

Swaminathan, B., 404n

Swaps, 673–677

credit default, 588–589

currency, 675–676

interest rate, 673–675

total return, 676–677

Swap trades, 695n

Swatch Group, 5, 705, 706

Sweep programs, 788

Swiss Bank Corp., 812

Swiss Re, 706

Switzerland

foreign bonds in, 616

transaction/economic exposure in, 705–706

voting rights in, 353, 354

Syndicated loans, 625–626

Synergy, 809

Syngenta, 810

Synthes, 806

Systematic risk. See Market risk

T

Taggart, R. A., Jr., 502

Takeda Pharmaceuticals, 806

Takeover premium, 326

Takeovers, 326, 824, 826–827. See also Mergers and acquisitions

Tangible assets, in mergers, 822

Target, 698

Tata Chemicals, 806

Tata Group, 807, 827, 872

Tata Motors, 3, 76

Tauron Polska Energia, 844

Taweel, Kevin, 873

Taxes

on capital gains versus cash dividends, 413–417

on corporations

alternative minimum tax (AMT), 141–142, 642

capital structure and, 449–454

depreciation rules, 140–142

equivalent annual cash flow and, 148

financial leases, 648

innovation in the bond market, 623

Taxes—Cont.

investment decisions and, 140–142

leveraged buyouts (LBOs) and, 839

in merger analysis, 822–823

in Germany, 143–144, 415

imputation tax system, 414, 415–416, 416n, 467n

on individuals, leverage and, 452–454

in net present value analysis, 133

on partnerships, 355

on REITs, 355

weighted-average cost of capital, 225

Tax-exempt municipal notes, 794, 795

Tax preferences, 140–142

Tax Reform Act of 1986, 140–142

Tax shields

depreciation, 140–142, 641, 644n, 648, 651

interest, 450–454

lease, 641

nature of, 449–452

value of interest, 500–501

Taylor, A. M., 714

Taylor, M. P., 714

Technological change

equivalent annual cash flow and, 147

exploiting new technology, 281–288

TED spread, 625, 888

Tehranian, H., 388n, 388–389

Teixeira, Mark, 301

Temporary abandonment, 569–570

10-K, 304, 720

10-Q, 720

Tender offer, 824

Tenneco, 848

Term loans, 624

Terms of sale, 781–782

Term structure of interest rates, 53–59

in bond valuation, 53–59

defined, 53

expectations theory of, 57–59

explaining, 57–59

inflation in, 59

law of one price, 54–55

measuring, 55–56

risk in, 58–59

Tesla Motors, 387

Tetley Tea, 827

Tetlow, R. S., 848n

Texaco, 851

Texas Pacific Group, 837

Thaler, R. H., 205n, 333n, 342, 343, 700n, 843n

Thermo Electron, 843–844

Third Law, Brealey, Myers, and Allen, 765, 883

Thomas Lee, 837

Thorburn, K. S., 830, 857

Thornburg, Karin, 458n

3Com, 843

3G, 837

Three-factor model, 206–208

Tiffany, 778

Tightwad Bank, 363

Time deposits, 794–796

Times-interest-earned ratio, 733–734

Time value of money, 107–108

Time Warner, 341, 727, 808. See also AOL

Timing option, 144–145, 261–262, 565–568

Timmerman, A., 327n, 881n

TIPS (Treasury Inflation-Protected Securities), 61–62

Titman, S., 443, 820n

T-Mobile, 820

Tokyo Financial Futures Exchange (TFX), 668

Tokyo Gas, 809

Tokyo Stock Exchange (TSE), 76, 668

Tomkins, 837

“Too big to fail” mentality, 336

Torous, W. N., 854n

Total capitalization, 726

Total expected profit, 785

Total return swaps, 676–677

Towers Perrin, 300n

Toyota, 302, 781

TPG Capital, 837

Trade acceptances, 782

Trade credit, 781

Trade-off theory of capital structure, 455, 465–467, 470–471

Trade sales, 847

Tranches, 610

Transaction exposure, 705–706

Transfer of value, 409–411

Transparency, 875–876

Transportation costs, in leasing, 641

TransUnion, 597n

Trans World Airlines, 641–642

Travlos, N., 820n

Treasury bills, 47–49, 160–162, 794, 795

Treasury bonds. See also Bond valuation

duration, 52

historic interest rates, 49

historic performance of capital markets, 160–162

indexed, 61–62

present value formulas and, 47–49

stripped, 55–56, 61

yield spread between corporate bonds and, 66, 587–589

yield to maturity trends, 48

Treasury Inflation-Protected Securities (TIPS), 61–62

Treasury notes, semiannual interest, 47–49

Treynor, Jack, 198

Triantis, A. J., 266, 567n, 568n, 870n

Trigeorgis, L., 578n, 580

Trust deed, 608

Trusts, 355

TRW, 848

TSE (Tokyo Stock Exchange), 76, 668

Tufano, Peter, 443, 662, 662n

Tufts Center for the Study of Drug Development, 263n

Tunneling, 354

Tversky, A., 333n

TWA, 852

Twite, T., 414n

TXU, 837

Tyco, 12

U

UBS, 298, 353, 367, 379, 681, 682, 812

Underpricing, 380–383

Underwriters, 363, 377, 378–380, 381

Undiversifiable risk. See Market risk

Unfunded obligations, 358

Unicredit, 812

Uniform-price auctions, 385

Union Pacific, 2, 3, 78, 79, 224n, 224–226

Unique risk. See Specific (diversifiable) risk

United Airlines (UAL), 594n, 666, 851

United Auto Workers (UAW), 851

United Biscuits, 848

United Health Group Inc., 551

United Kingdom

accounting standards in, 721

Anglo-Saxon financial system in, 721, 827, 860–864, 869

bankruptcy laws, 854, 855

company financing in, 863

electricity prices, 571–572

forward currency market, 700

inflation in, 63, 64

nominal versus real exchange rates, 701–703

United States

Anglo-Saxon financial system in, 721, 827, 860–864, 869

bankruptcy regulation, 850–855

company financing in, 861–863

compounding intervals in, 47–49

deficit crisis of 2010, 67

dividend yields, 166–167

historic performance of capital markets, 160–167

inflation in, 59–60, 63, 64

initial public offerings (IPOs) in, 381–382, 383, 384

market risk premia in, 166–167

mergers in, 807

payout policy in, 401, 402

venture capital financing in, 373–375

U.S. Census Bureau, 776n, 778n

U.S. Federal Reserve, 224, 367

U.S. Federal Trade Commission (FTC), 820

U.S. Food and Drug Administration (FDA), 262–265, 578

U.S. Justice Department, 820, 825

U.S. Robotics, 843

U.S. Securities and Exchange Commission (SEC), 11, 303–304, 377–378, 852

accounting and reporting standards, 721

proposed Rule 14a-11, 354n

Rule 10b-18, 403n

Rule 144A, 391, 616

well-known seasoned issuer (WKSI), 385n

U.S. Shoe Corp., 615

U.S. Steel, 65

U.S. Supreme Court, 85n, 827

U.S. Surface Transportation Board (STB), 87

U.S. Trust, 812

United Technologies, 806

Universal Orlando, 848

Unlevering beta, 492–493, 494n

Unlimited liability, 592

Unocal, 821

US Airways Group, Inc., 5n

V

Vale, 3, 827

Va Linux, 380, 381n

Valuation

of abandonment option, 569

annuity. See Annuities

bond. See Bond valuation

business. See Business valuation process

by certainty equivalents, 232–233

by comparables, 78–80, 226–227

debt. See Debt valuation

equity. See Equity valuation

financial lease, 646–652

option, 523–528, 535–555. See also Black-Scholes option pricing model

warrant, 549–550

Valuation horizon, 94–95, 96, 485–487

Value additivity, 430, 881–882

conglomerate mergers and, 833–835

defined, 182

diversification and, 182

economic value added (EVA), 305–307, 725–726

Value at risk (VA), 601–602

Value Line, 85n

Value maximization

agency problem in, 12

as goal of corporation, 7–12, 16–17, 245–266

Value stocks, 203–204

Van Dijk, M. A., 330n

Vanguard 500 Index Fund, 327–328

Vanguard Index Funds, 327–328, 361

Vanguard Total Stock Market index, 361

Variability, measuring, 170–171

Variable-rate demand notes (VRDNs), 795, 796

Variance

defined, 167–168

in measuring portfolio risk, 167–170

portfolio, 167–170, 171–174

in portfolio theory, 193n

Venture capital, 371–375, 377

market for, 373–375

stages of financing, 371–373

Vermaelen, T., 405n

Veronesi, P., 383n

Vertical mergers, 807, 809–810

Viacom, 387, 827

Viasys Health Care, 844

Villalonga, B., 849n

Virgin Atlantic, 226

Virgin Group, 226

Vishny, R. W., 296n, 419n, 844n, 845n, 864, 864n, 878

Viskanta, T., 710n

Viswanathan, S., 828, 828n

Vlasic, Bill, 808n

Volatility. See also Beta

bond, 53

implied, 550–551

Volcker, Paul, 49

Volkswagen (VW), 139, 334–335, 639, 762

Volpin, P., 867n

Voluntary Employees’ Beneficiary Association (VEBA), 855

Volvo, 827

Voting procedures, 352–354

Voting rights, preferred stock, 356

Vulture funds, 362

W

Wakeman, L. M., 655

Wald, J. K., 466n

Wall Street Journal, The, 48, 76n, 375, 626, 849

“Wall Street Walk,” 299

Walmart, 2, 3, 7, 9–10, 65, 178, 194, 198, 725, 727

Walt Disney Company, 65, 222–224, 387, 824

Warga, A., 614n

Warner, J. B., 325n, 458n

Warrants, 358

bond-warrant package, 621

Chinese warrant bubble, 552

valuing, 549–550

Warther, V. A., 404n

Washington Public Power Supply System (WPPSS), 795n

Watts, R. L., 339n

Weak form of market efficiency, 324, 336–337

Weighted-average cost of capital (WACC), 221–226, 437–441, 479–502, 726. See also Company cost of capital

adjusting, 493–494

rebalancing, 493–494

unlevering and relevering cost of equity, 492–493, 494n

after-tax, 225, 441–442, 479–483

in business valuation process, 483–488

calculating, 480–481

common mistakes in using, 490–491

comparing return on capital with, 727–728

defined, 221–222

flow-to-equity valuation method versus, 488

industry costs of capital, 490

in practice, 488–495, 499–501

questions concerning, 499–501

review of assumptions for, 483

to value a project, 481–482

Weiss, Lawrence A., 458, 458n, 851n, 853n, 857

Welch, I., 857, 889n

Well-known seasoned issuer (WKSI), 385n

Wensley, R., 288

Wermers, R., 327n, 881n

Werner, I., 853n

Western Electric, 841

West Japan Railway Company, 844

West Lb, 367

Weston, J. F., 713, 830

WGL Holdings Inc., 86

Whaley, R. E., 553n

White, H., 327n, 881n

White, M. J., 851n

Whited, T. M., 842n

Wilhelm, W. J., Jr., 11n, 392

Williams, J. B., 84n, 406n, 429n

Williams Act of 1968, 824, 824n, 828

Williamson, O., 810n

Williamson, R., 750n, 751, 751n, 799

Wilmott, P., 555

Wilshire 5000 Index, 327

Wingfield, N., 419n

Winner’s curse, 382n, 382–383, 384–385, 385n

Wizman, Thierry, 614, 614n

Wolfers, J., 338n

Wolfson, M. A., 402n

Womack, K. L., 377n

Woolley, S., 289

Woolridge, J. R., 842n

Working capital. See also Working capital management

in applying net present value rule, 132–133

characteristics of, 755–757

defined, 775

in estimating cash flows, 132–133

investments in, 132–133, 139–140

net, 723

short-term borrowing sources, 757–760

Working capital management, 775–799. See also Working capital

cash conversion cycle, 776–779

cash management, 776–779, 787–791

credit management, 781–787

inventory management, 779–781

marketable security management, 791–797

operating cycle, 776

working capital, defined, 775

Workouts, 854

World Bank, 712

WorldCom, 65, 376, 851, 875

Wright, Orville, 287

Wruck, E. G., 314

Wruck, K. H., 458n, 840n, 853n, 857

Wulf, J., 296n

WuLiangYe Corporation, 552

Wurgler, J., 343, 411n, 470n

Wyeth, 844

X

Xiong, Wei, 552n

Xstrata, 806

XTO Energy, 806

Xu, Y., 173n

Y

Yago, G., 443

Yahoo!, 298, 332

Yahoo! Finance, 77n

Yankee bonds, 616

Yasuda, A., 391, 847n

Yermack, D., 551n

Yeung, B., 878

Yield

convenience, 477n, 670–672

on corporate debt, 66, 585–589

current, 47

dividend, 77, 84, 85, 166–167

on money-market investments, 792–793

Yield curve, 55

Yield spread, 66, 587–589

Yield to maturity

bond valuation, 48

default risk and, 592–594

defined, 47

Yoshimori, M., 870n

Yu, Jialin, 552n

Yuan, K., 884n

Yun, H., 628n

Z

Zeckhauser, R., 312–313, 313n

Zell, Sam, 5

Zender, J. F., 467n, 470n

Zero-coupon bonds, 55–56, 61

Zero-dividend companies, 401

Zero-maintenance hedges, 677–679

Zero-stage financing, 371–375

Zero-sum game, 659–660

Zheng, L., 884n

Zhengzhou Commodity Exchange, 667

Zhu, N., 857

Zhu, Q., 884n

Ziemba, W. T., 332, 332n, 885n

Zingales, Luigi, 10n, 368, 459, 459n, 470, 470n, 864n, 864–865, 873, 873n, 875n, 878

Zipcar, 387

Zitzewitz, E., 338n

“Zombie” firms, 875

Z-scores, 598n