title | : | Scientific Financial Management : Advances in Intelligence Capabilities for Corporate Valuation and Risk Assessment
author | : | Glantz, Morton.; Doorley, Thomas L.
publisher | : | AMACOM Books
isbn10 | asin | : | 0814405002
print isbn13 | : | 9780814405000
ebook isbn13 | : | 9780814424605
language | : | English
subject |  | Corporations--Finance--Management, Corporations--Valuation.
publication date | : | 2000
lcc | : | HG4026.G622 2000eb
ddc | : | 658.15
subject | : | Corporations--Finance--Management, Corporations--Valuation.

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Scientific Financial Management

Advances in Intelligence Capabilities for Corporate Valuation and Risk Assessment

Morton Glantz

with a special contribution by Thomas L. Doorley III
Senior Partner Deloitte Consulting/Baxton Associates

Page iv

Disclaimer:
This netLibrary eBook does not include the ancillary media that was packaged with the original printed version of the book.

This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If legal advice or other expert assistance is required, the services of a competent professional person should be sought.

Library of Congress Cataloging-in-Publication Data

Glantz, Morton.
Scientific financial management: advances in intelligence capabilities for
corporate valuation and risk assessment / Morton Glantz with a special
contribution by Thomas L. Doorely III.
p. cm.
Includes bibliographical references and index.
ISBN 0-8144-0500-2
1. CorporationsFinanceManagement. 2. CorporationsValuation.
I. Amacom. III. Title.

HG4026.G622 2000
658.15dc21                                                              00-026632

© 2000 Morton Glantz.
All rights reserved.
Printed in the United States of America.

The material in Chapter 12 draws from the research and methodology contained in Thomas L. Doorely III's book Value-Creating Growth: How to Lift Your Company to the Next Level of Performance, co-authored with John Donovan © Jossey-Bass 1999, San Francisco, 1-800-956-7739 or www.josseybass.com. Adapted by permission of Jossey-Bass, a subsidiary of John Wiley & Sons, Inc

This publication may not be reproduced, stored in a retrieval system, or transmitted in whole or in part, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of AMACOM, a division of American Management Association
1601 Broadway, New York, NY 10019.

Printing number

10 9 8 7 6 5 4 3 2 1

Page v

To my wife Maryann and daughter Felise,
a continuous source of love, patience,
and inspiration.

To Ida Glantz, in her extraordinary
and noble life, a beacon of wisdom
and majesty.

Page vii

Contents

Preface

xi

Acknowledgments

xiii

Chapter 1
Introduction to Scientific Financial Management

1

Nonlinear Financial Models

7

A Quick Look at Data Mining, Neural Networks, and Fuzzy Logic

9

Scientific Financial Management's Road Map

13

Chapter 2
Basic Tools of Financial Risk Management: Portfolios and Options

19

Basics of Modern Portfolio Management

21

Option Pricing Basics

30

The Quintessential Black-Scholes

39

Appendix A: Calculations of Option Values

41

Chapter Two References and Selected Readings

50

Chapter 3
Real Options: Evaluating R&D and Capital Investments

55

The Music Master's Dilemma

56

Flexibility: The Quintessence of Real Options

57

Traditional Methods Versus Real Options

57

The Binomial Model

58

Real Options: Definitions, Examples, and Case Studies

60

Closing Thoughts

79

Chapter Three References and Selected Readings

81

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Chapter 4
Visual Financial Models

85

Background

86

Team Effort

88

Building Effective Models

88

Visual Modeling

92

Analytica: The Nerve Center for Visual Modeling

93

Comparing Spreadsheet Models with Visual Models

94

Visual Display of Model Structure with Influence Diagrams

95

Developing Your Visual Model Step by Step

105

On-Line Demonstration: E-Commerce Start-Up

113

Conclusion

115

Chapter Four References and Selected Readings

115

Chapter 5
Divisional Cash Flow Analysis and Sustainable Growth Problems

117

Cash Flow

117

Cash Flow and Sustainable Growth Problems

129

Chapter Five References and Selected Readings

138

Chapter 6
Statistical Forecasting Methods and Modified Percentage of Sales

139

A "Statistics" Approach to Financial Forecasting

140

A "Sensitivities" Approach to Financial Forecasting

160

Glossary of Forecasting Terms

166

Chapter Six References and Selected Readings

170

Chapter 7
How to Apply Monte Carlo Analysis to Financial Forecasting

173

A "Simulations" Approach to Financial Forecasting

173

Glossary of Distribution Terms

197

Chapter Seven References and Selected Readings

204

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Chapter 8
Neural Networks and Scientific Financial Management

207

Neural Networks

209

Building a Simple Neural Network: The T-C Problem

210

Statistics and Neural Networks

213

Genetic Algorithms

217

Combining Genetic Algorithms with Neural Networks

218

Designing Neural Networks

221

Developing a Neural Network within Excel

223

Chapter Eight References and Selected Readings

228

Chapter 9
Linear Programming, Optimization, and the CFO

233

The Basics of Linear Programming

234

Basic Deterministic Modeling

236

Stochastic Optimization Modeling

256

Tabu Search

257

Numeric Computation and Visualization Optimization Modeling

265

Chapter Nine References and Selected Readings

267

Chapter 10
Risk Analysis of the Corporate Entity and Operating Segments

271

Identifying Systematic Risk

272

Corporate Analysis:

274

Corporate Computerized Risk Rating System

303

Chapter Ten References and Selected Readings

308

Chapter 11
A Primer on Shareholder Value

311

Methods

312

Preparation

318

The Drivers

323

Appendix One to Chapter 11

339

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Appendix Two to Chapter 11

347

Appendix Three to Chapter 11

387

Chapter Eleven References and Selected Readings

397

Chapter 12
The Value-Growth Link

By Thomas L. Doorley III

399

Spectacular Growth/Spectacular Performance: A Global Phenomenon

400

Value Creation Everywhere that Matters

403

Growth-Value: Cautionary Tales

404

Metrics for Success: Guiding Implementation

406

A Vision: The Desired State

410

Index

413

Page xi

Preface

Much literature has been published about valuation. The authors tell us how to derive shareholder value but not how to model value drivers with the latest technology. They advise us how to analyze valuation alternatives and choose the best one but not how to create choices germinal in corporate data. They refer us to quantitative objective functions. They do not give us the means to run up stochastic solutions and thereby improve the chances of ever being able to explain, qualitatively, optimal objectives on which any assessment of valuation must reside. They provide macrostructures but not how microprocesses work, such as leveraging data technology to improve decision making.

In the last 10 years, we have seen finance evolve from a casual discipline to a rigorous science. Just over a decade ago, technologies such as neural nets, stochastic optimization, simulation, fuzzy logic, and data mining were still largely exploratory and at best quite tentative. Algorithms, as a term, rested on the outskirts of financial thought. More than a few financial managers had not even heard of Monte Carlo outside of casinos and travel magazines. Machine learning was in its infancy while shareholder value concepts were encased in the Stone Age logic of earnings multiples and, on more than a few occasions, accounting shenanigans.

Despite dramatic advances in financial techniques and raw computing power, there is still a gap between finance/valuation theory and the utilization of scientific applications. Allow me to quote a wise passage:

We now have a much richer bag of tricks at our disposal, whose effectiveness can be realized using mature networking, database, and desktop technologies. Each one models a different aspect of human reasoning and decision-making. Each technique has a different objective and different character. Collectively, these techniques offer the business community a broad set of tools capable of addressing problems that are much harder or virtually impossible to solve using the more traditional techniques from statistics and operations research.¹

As this paragraph suggests, risk, complexity, and uncertainty will define financial and business well into the millennium. While few of us need challenge standard financial tools (spreadsheets), new financial intelligence capabilities offer a framework to help financial executives cope

¹ Vusant Dhar and Roger Stein, Seven Methods for Transforming Corporate Data Into Business Intelligence (Englewood Cliffs, N. J.: Prentice Hall, 1997).

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with uncertainty. However, the concern is that some managers are resisting computer-actualized solutions. Quantitative methods, such as the use of models or even the use of math, do not alarm sharp professionals. Modeling tools are not black boxes that ignore or inhibit wisdom or that mechanize the decision-making process. However, in many companies, models and, for that matter, change may intimidate financial professionals, inhibiting technological growth and, alas, the requisite skills to participate in strategic decision making at the highest level.

Otherwise capable managers cannot readily quantify and respond to developments in the external environment and find it difficult to creatively deploy advanced techniques to crystallize value drivers, explain optimal capital allocation strategies, and otherwise deliver the goods to CEOs. Knowledge gaps, particularly when it comes to valuation appraisals (and knowing how sensitive your job function is to your firm's value), are detrimental to continued growth both within firms and in advancing careers. This book should help you carry out your financial tasks more succinctly and might even empower you to grab the modeling hardball and to pitch winning games in a domain that is hot, dynamic, complex, and often combative.

Each chapter contains a brief introduction of the topic and then is divided into several "hands-on" sections, with each exhibit and table numbered and titled to facilitate a systematic reading. The book contains a CD that includes (1) a collection of financial models and related software, the author's interactive corporate and divisional risk-rating systems, and (2) software and Internet links donated by adept vendors in evolving valuation disciplines such as financial and real options, optimization, visual modeling, time series/regression, simulation, and neural nets. Most sections are reinforced with problems and examples included on the CD, in the book, or on the Internet. Key concepts are set apart and important equations highlighted. The derivations for equations are provided but are differentiated or appear in appendices. The reader who is not mathematically inclined can skip quantitative passages with no loss of qualitative ideas. A References and Suggested Readings section follows each chapter, and readers can, at their leisure, connect to select Internet sites, access additional material, or download additional software cognate to chapters.

Page xiii

Acknowledgments

The writing of a book on scientific financial management and the interactive computerized systems that combine to power up a firm's value drivers involves the ideas and work of many individuals. Because the subject is so diverse and comprehensive, specialists were consulted, so that in completing this book, I find myself indebted to many for their thoughtful suggestions, critical review, counsel, and encouragement. Thomas L. Doorely III, Senior Partner, Deloitte Consulting/Baxton Associates, for his expertise and contribution as author to chapter 12, The Value-Growth Link. Two individuals were especially helpful: Robert Kissell and Bob Muldowney. Mr. Kissell designed the algorithms contained in the interactive corporate and divisional risk-rating systems and was an important source of wise counsel on issues dealing with statistical matters and neural networks. I thank Mr. Muldowney for the time he took reading the manuscript and above all for his patience as chapters were being prepared. I greatly benefited from his ideas.

I wish to offer a special word of thanks to Gary Lynn, a neural network expert at NeuroDimension, Inc. (a top firm in the field), whom I called on for his insight and knowledge. I also want to thank Gary's colleagues, Neil R. Euliano and Dan Wooten, for donating important sections. Larry Goldman, a product expert at Decisioneering, played an integral role in chapters dealing with simulation, regression, and optimization and coordinated readings of these chapters by the experts at Decisioneering. Keith Woolner, director of marketing, Lumina Decision Systems, Inc., deserves credit for his suggestions on visual modeling. John Noble and Rick Schmitt, Alcar valuation experts, provided valuation exhibits along with Alcar's new release valuation demo. I want to express gratitude to the previously mentioned companies for their support along with the models these firms made available to readers via our CD and/or through Web sites.

I wish to thank Bruce Henderson, who opened up contacts; David Langer, who provided computer support; and Joseph Blake, a financial expert. I am indebted to a number of persons for their interest and encouragement in the preparation of this manuscript. In particular, my appreciation goes to Ray O'Connell, senior acquisitions and planning editor, who first suggested the writing of this book; Andy Ambraziejus, managing editor; and Bruce Owens and Peggy Francomb for their valuable assistance in

Page xiv

editing the manuscript. This does not mean, however, that those listed here or others who were helpful are responsible for errors or omissions; the author must assume such responsibility. Finally, I have acknowledged every source I have been able to identify in footnotes and bibliographies, but some writers and sources may have been missed unintentionally.

Page 1

Chapter One
Introduction to Scientific Financial Management

Kermit Rich along with thirty recent MBA graduates stood on a Long Island cliff overlooking the Atlantic. The five-acre estate promised the graduates both sun, and the possibility of an invitation to join Kermit's wealthy, fast paced firm. Near the edge of the cliff, Kermit addressed the group. ''My execs have enough smarts to turn quarterly profits, but their ideas lack steam to the point where our (business) segments behave like random walks. I need organization, not randomness in my business. I need people with guts, the kind of people that translate randomness into direction and new global challenges. Give me someone like a George Pattonblood, timing and gutsan executive, who grabs the day-to-day stuff, makes sense of it and is not afraid to run past goal posts. If you measure up, take your picka divisional presidency, $4 million in company stock, or, yes, I'll even throw in my estate. Do any of you have what it takes?"

Kermit continued while directing the focus to the impeding cliff. "OK, you guys, inch closer to the edge. See that wicked surf crashing off the cliff. Now, if you can time your dive right and land behind one of those big waves, the surf will carry you right to my schooner. But, heavens forbid, if your timing is off, the rocks will get you fifty feet below. Blood, timing and guts."

As the group headed toward the house, shouts echoed from below. Seconds later a figure drifted toward the schooner.

"You're my kind of guy," Kermit beamed later that afternoon. "Just name ita divisional presidency? Stock? my house?" The red-faced MBA glanced across to the twenty-five-room mansion, and then turned to his bedazzled

Page 2

colleagues hanging about a few feet away. "No, nothing," he replied, "Just find the jerk who pushed me over."¹

Just like the wicked surf crashing off the cliff, engineering one's knowledge is, indeed, a rather strange concept, but that is the idea behind the financial revolutionbridging gaps between traditional, nontechnical (textbook) approaches and modern, asymmetric, real-world solutions that have hit the market.

Recent advances in financial analysis and strategic planning are about dynamic surf patterns, surf timing, rocks, and, yes, surf heights. Dynamic planning is revitalizing financial analysis in areas once thought inaccessible: chaos theory, real options, data mining, artificial intelligence systems such as fuzzy logic and neural networks, plus myriad other powerful models and application builders. These technical advances, virtually unknown a few years back, provide solutions from predicting nonlinearities to solving resource allocation problems. The good part is that most of the software is easily mastered by CFOs for the small price of just a little knowledge engineering.

Behind the technology revolution, at the core, are datasimple though elusive and frequently "chaotic" in nature. However, as random as these data appear, the right software can shape these data bits into distinctive patterns of information. Of course, we may ask, Are the data single or dusted (patterned), short term, and meaningless? The answer may be a little hard to nail down, but one thing is certain: Advances in chaos theory and financial and data mining, together with other financial modeling tools (fuzzy logic and neural nets), show us ways to synthesize and utilize voluminous amounts of data, from customer payment records to production control. Whether our analysis starts with chaos and ends with the same depends not so much on the nature of data but on how it is mined. It goes something like this:

single eventrandom (extremely short term, limited value); ®
genesisextracting patterns (data mining); ® recognizance
value assessment (simulation, fuzzy logic, neural networks); ®
finalizationstrategic planning; long-term planning.

As the flow diagram shows, strategic plans are blueprints for long-term planning; short-term events are basically random (i.e., quarterly profits) and, in isolation, do not add up to corporate intrinsic value. If strategic decisions focus on short-term random events (as in chaos theory), they

¹ Adapted from From Hard Knocks to Hot Stocks, by J. Morton Davis, Michael T. Ford, Louis Rukeyser (New York: William Morrow, 1998). The author wishes to thank J. Morton Davis for his original anecdote about sharks in a pond.

Page 3

tune out genesis (factors), and the result may be as insignificant to the whole as a single dot in a newspaper photo or a measure's worth of notes in a Bach cantata. We are reminded that investor compensation is more or less proportional to risks taken over reasonably sound projection horizons, but this observation excludes investments over arbitrarily short periods.

Which factor will it be: randomness or genesis? Most of us pick genesis, as this offers a greater intrinsic or equity value. Random variables, such as quarterly profits, are trivial, while shareholder value is a definitive strategic concept. Inherently, shareholder value is no less the result of an organic pattern of data that the CFO purifies in a (cash flow) valuation model using modern technology.

While some investors may disagree, quarterly results are random points floating in nonlinear space, influenced by the waywardness of accounting license. We know that financial markets can be stopped coldshort termwhile strategic fundamentals tend to hold a steadier course and will not often thwart goals to maximize shareholder value. A wise person once said, "Fundamental analysis counts when a rising tide isn't floating your firm's earnings." Therefore, suggesting a noncursory look beyond the firm's limited horizons, historically, disorder and chaos will be highlighted.

Let's focus on the analogy in this chapter's opening quotation parable regarding the risk of decision making. If you unwisely risk capital by taking on inferior projects, you will likely plunge against the rocks. On the other hand, by not taking risks and standing by the cliff's edge and watching sunsets ad infinitum, your firm ends up a financial couch potato. Either way, you are dead.

Suppose that you glanced at a solitary wave (random, chaos, like daily profits), and you recorded the time it crashed against the cliff. Hours later you return to repeat the random recording process. The information you "gathered" would be about as useful in predicting the surf as it would be predicting future numbers on a roulette wheel. However, suppose that you activate the latest scientific wave height/pulse measuring equipment. Looking at data configurations, you track recurring timing/depth patterns characteristic to the surf with great accuracy. So go ahead and leap; take Kermit's trophy. The choiceleap or watch sunsetsis chaos (theory) metaphor.

Scientific financial management bridges gaps between chaos theory and financial symmetry. That is, in this new technical age, financial decision making can make or break even the smartest CFOs. That is why smart CFOs feel that it is important to shape data, raw as a clam, in fresh, imaginative ways and ultimately develop strategetic moves that maximize shareholder value. Data mining, fuzzy logic, real options, pricing capital, model building, and a host of other finely tuned management tools offer financial symmety to the corporation; and the scientific road map that

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leads to the end resulta business tuned like a fine watchalmost, without exception, starts with the chaos basics.

Chaos does not necessarily mean "chaotic world economy." Rather, it is associated with tons of information that hit firms daily from all directions; each piece, by itself, is "chaotic." However, if the technology recently developed is applied to all these data, the data cease to be random since patterns emerge (and relationships form) that were hidden beforehand. CFOs who run their shop in a void operate in an environment much like a single sentence operates in a novel. They know how to form words (data) in the sentence and can even read the sentence, but they will not be able to go beyond the single sentence and will not know how the novel turns out. The sentence, with respect to the novel, is itself chaotic.

Think of (the stock market) random walk theory. It is true: while daily price movements are indeed a random walk, long-term trends (bull and bear) are not random, as they are made up of pieces of trend lines. The pieces are chaotic, but not the trend line taken as a whole.

Chaos, rather than being derogatory, actually refers to a really beautiful organizing principle. The organizing principle in finance is no less the gravity that binds in orbit the double star system: valuation and portfolio theory. Andrew Ho stated

The most commonly held misconception about chaos theory is that chaos theory is about disorder. Nothing could be further from the truth. Chaos theory is not about disorder! It does not disprove determinism or dictate that ordered systems are impossible; it does not invalidate experimental evidence or claim that modeling complex systems is useless. The "chaos" in chaos theory is ordernot simply order, but the very essence of order.

Chaos theory, order, and fractals describe new technologies applied to corporate finance, investment analysis, economics, and capital markets. We define chaos theory as discovering patterns out of distinct forms of irregularities that are, in themselves, nonlinear, dynamic, complex, and enigmatic systems (the analogy: quarterly results versus intrinsic value). We can think of "dynamic" as eternally changing complex systems. It forms the crux of most scientific research, along with many varied fieldsphysics, weather forecasting, and finance, to name a few.

Chaos is in everything: raindrops falling on grass, movements in financial markets measured in minutes, and paperwork atop your desk. A sample of the most famous chaos image of all is the Mandelbrot set, named after its discoverer, Benoit Mandelbrot (see Exhibit 11). This image holds a deep fascination, as it can be enlarged over and over with the same patterns emerging.

Exhibit 11.
The Mandelbrot set.

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Exhibit 12.
Clorox 12-month stock price: Illustration of random movement in the stock market.

The point is that tiny changes can produce mammoth fluctuations (of course, we must assume that certain things are held constant). Chaos theory and the effect are just about indistinguishable concepts. If a butterfly in West Africa flaps its wings, the theory goes, a hurricane hits the dunes lining the Long Island coast later on. Chaos theory suggests reactive dependence on original conditions. This means simply that the initial departure point in a system (financial or otherwise) greatly influences its course and destination. This is particularly true if the system(s), be they strategies or businesses, are not appropriately hedged against risk of loss. For example, businesses made up of a portfolio of homogeneous operations are less insulated against macroeconomic shocks than, say, firms that diversify operations along dissimilar businesses. Perhaps financial managers should avoid putting operating/financing strategic eggs in one basket.

While forecasting the ultimate closure of a system is as difficult as predicting Clorox's stock price two years hence, it is possible to model the overall behavior of Clorox's stock (see Exhibits 12 and 13). We know how patterns develop within a financial system, and we often know the end result. The issue is not a system's disorder or unpredictability, which is characteristic of any single component, but rather its natural harmonic structure. If we peered inside a microscope and examined any system, we would see chaos metamorphose to (patterns) and harmony in systems as multifarious as Clorox stock, the cosmos, a Brahms masterpiece, or weather patterns. A butterfly's fit into a bunch of static equations (like the Capital Asset Pricing Model, CAPM) is no better than trifles, but not the dynamic, behavioral nature of our butterfly and its influence within a much larger universe.

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Exhibit 13.
Clorox 14-year stock price: Illustration of long-term market trends.

Stephen Hawking, the great theoretical physicist, agrees with the idea of chaos. He sees nature in terms of particle physics as not fully explicable: Something is missing inside the theories. Hawking believed that chaos theory bridges the gap between particle physics and reality. He stated in his book Black Holes and Baby Universes that "with unstable and chaotic systems, there is generally a time scale on which a small change in an initial state will grow into a change that is twice as big." He goes on to say that "predictability of a system only lasts for a short period of time."

The key point, as Hawking would have it, is time scale and evolving system dynamics. You are asked to prepare your firm's market and production costs in preparation of a fundamental analysis of your firm's strategic plan. You can get away with a cursory analysis if all the boss asks for is a brief update. Nevertheless, the firm's markets are nonlinear, dynamic systems, and chaos theory suggests mathematics that helps evaluate such nonlinear, dynamic systems. For example, intraday sales booked by your firm's Rhode Island division are random with a trend component. Nonlinear systems record the accounts receivable portfolio, itself the product of market, customer, and time frame patterns. Let us connect this to fractals: geometric patterns that are repeated at ever-smaller scales to produce irregular shapes and surfaces. Fractals are self-similar objects, meaning that single parts are linked to the whole. Fractals are used especially in computer modeling of irregular patterns and structures in nature.

Privet bushes are good examples. While the stems get narrower and narrower, each stem is structurally similar to larger and thicker stems and finally to the whole bush. Similarly, you may record daily or intraday divisional sales, sales by product line, national versus regional sales, and sales contribution by customer. Next, you may move on to longer time periods: weekly or monthly sales. The structure (sales) may, at first glance, take on a familiar appearance. However, moving in closer and closer, you see more

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Exhibit 14.
A bifurcation diagram.

and more detail, that repetitive patterns form, and perhaps how minute (sales) detail is connected to larger structures, very much like Feigenbaum's fractal or solutions provided by a fuzzy logic or neural network system. A bifurcation diagram is shown in Exhibit 14.

Chaos theory infers that insignificant dots create patterns and that patterns translate to pictures. Chaotic data, like dots, can splatter around a page; this is why linear models cannot really display, at least not clearly, sine qua non arrays of convergence. We need to nurse along the discipline: nonlinear financial models.

Nonlinear Financial Models

Nonlinear financial models emerged from chaos theory. Meteorologist Edward Lorenz is credited largely with discovering chaos theory. Lorenz developed a set of 12 equations to forecast weather patterns by setting computer algorithms to move in a pattern of sequences. To save time, he ran the program at midpoint rather than at the beginning and discovered that the sequence evolved in a wildly different way. It seemed that Lorenz had typed in only three digits, .506, rather than the number in the original sequence, .506127.

The results that came in were unexpected. A weather forecaster is lucky if he or she can measure accurately to three decimal places. The fourth, fifth, or sixth decimal place was nearly impossible to measure at the time and should not have influenced the experiment in the slightest. Lorenz discovered that this notion was wrong. Lorenz's work came to be known as the "butterfly effect." The amount of variance in the start-up points of the two curves (in his experiment) was so small that we can compare the variance to a butterfly flapping its wings (Lorenz's weather graph is shown).

The flapping of a single butterfly's wing produces a microscopic shift in the atmosphere. Over a period of time, this shift in the world's weather patterns results in a divergence from what might have been.² This phenomenon, common to chaos theory, is

Page 8

also known as sensitive dependence on initial conditions. Just a tiny change in the initial conditions can radically alter the intermediate or even long-term behavior of a systemweather, financial, or otherwise.

Daily share prices are also driven by reactive interdependence on initial and ambient factors as in the fusion of technical, fundamental, and psychological forces that act on the stock between the opening and closing bellall nonlinear phenomena. Most stock analysts agree (at least until recently) that stock prices move in cycles, with each stock, in motion, spinning out ambient factors with its unique set of fingerprints. These are the core fundamentals of fractals that, in a data mining run, reveal the timing and breadth of future cycles existing implicitly in the given stock. In other words, the mining algorithms unearth the "mother" cycle from which underlying cycles gather momentum.

So where is the butterfly? It is in the subject's initial conditions. Slight changes in the starting point of a firm's initial strategic plan can lead to alternative stock (price) outcomes remarkably so if the firm operates in the start-up or rapid growth phase of its life cycle or if operations were not diversified across macroeconomic or industry risk boundries.

Chaotic systems are deterministic and, in the long run, will likely pattern out into intrinsic (shareholder) value. While they appear disorderly, even random (investors pained by the recent roller-coaster S&P averages may argue otherwise), chaotic dots and dashes are not. Underneath lies a sense of harmony, order, and above all grand design. Truly random systems are not chaotic.

To see how this all works, let's look at the weather again. There are numerous variables controlling the weather: temperature, air pressure, wind speed, wind direction, and humidity, to name a few. The equations governing weather patterns involve all these variables. You can enter these variables in an equation and determine a reasonable value of all the variables one, two, or five minutes in the future. These results can be reentered into our computer model, as can the values for the next round, six minutes hence, and so on. Let the computer do the iterations for a month, and you will be able to schedule the lawn party on a sunny day.

Or will you ? Shown here is an image of the Lorenz attractor. Every moment in time is represented by one point on the attractor. However, differential equations cannot merge, so Lorenz realized that he had discovered a mathematical object that was in fact an infinitely complex set of surfaces, never intersecting. Picnic planners know better than to rely on short-term

² Ian Stewart, Does God Play Dice? The Mathematics of Chaos

Page 9

weather forecasts, and meteorologists offer little hope that truly accurate weather predictions for specific places and times will ever be possible.

However, unlike weather equations, financial management formulas are neither infinitely complex nor nonintersecting. Nonetheless, nonlinear solutions, at least in the financial sciences, require analytic power tools. We like to think that some forms of troublesome chaos are things of the past. They will remain so if we dare to start using a few of the scientific financial methods outlined in the rest of this chapter.

A Quick Look at Data Mining, Neural Networks, and Fuzzy Logic

Someone wise recently said, "Chaos can no longer be defined as just a theorychaos is finance trying to be finance without tomorrow's technology." While technology covers a large playing field, a successful financial game plan cannot ignore data mining, neural networking, simulation and stochastic optimization software, and fuzzy logic (some of these applications are detailed later in this book alongside case studies). However, now we again point to the metamorphose: chaos to syllogismrandom to patterns, fixed financial software programs to deductive artificial intelligence. Let's begin with a quick look at data mining, neural networks, and fuzzy logic.

Data mining sifts through large databases, converting meaningless, random information into highly significant if-then patterns. You can then use these patterns to forecast future events and to design "correct" strategies for the firm. Rules or, more correctly, codes fix the limits of data and measure the significance level (reliability) of these rules. These newly discovered codes are then fed back into the mining system to predict more reliable dependent variables and thus new cases. Data models compute the conclusive probability and significance level for each prediction along with prediction errors.

Often, data sets are just too complex to represent in two or even three dimensions. Also, finding valuable data is only half the problem; presenting it in a meaningful way, via advanced visualization, is the other half. Newer techniques simultaneously analyze the behavior of data in many dimensions. For example, within a three-dimensional coordinate system, data can be visualized in up to nine dimensions. By animating the visual display across independent variables that you define, you can observe trends in extremely complex data sets. You can observe the motion on the monitor to check for anomalies or dirty data as well. Dirty data are recognized as anomalies through unexplainable behavior.

What are the basics?³ Suppose that you maintain a data system where each record contains a range of fields about one company, such as name,

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number of employees, industry SIC code, sales, profit, and stock value. Assume that you want to define stock value as the dependent variable, while the other variables represent the independent variable, or "conditions." With the dependent variable being the stock value, the objectives are to reveal the patterns of those companies having a high (or low) stock value and to search out values of the other fields associated with a high (or low) stock value.

A data mining program first reads the data. You then fine-tune trial runs by defining parameters, such as the minimum probability of rules, minimum number of cases in each rule, and the cost of false alarms. Also, software such as WizWhy derives rules assigned to a particular field to predict other fields. The rules are formulated as if-then sentences or mathematical formulas. The user makes predictions on the basis of the rules discovered and applies results to new cases. For example, given the data of a new company, the computer determines its stock value. The key is to derive the rules that reveal the main patterns and the unexpected phenomena in the data.

Data mining can analyze accounts receivable risk (the average collection period, highlighted in many corporate finance books but in practice falling by the wayside). You may want to build accounts receivable models that work with as many as 200 variables. You can deal with accounts receivable data by classifying the information into groups, or cohorts, building models around them.

Self-organizing maps (SOMs) have been used a great deal recently to analyze data. A Belgian company developed a large data set composed of the financial ratios of more than 12,000 Belgian companies.⁴ The study's objective was to explore the role of leasing as a financing tool. Results showed that the nonlinear and robust properties of SOMs yielded a deeper understanding of lease financing than using only accounting data.

As data mining technology (software), such as multidimensional visualization, becomes more accessible, computing requirements for extracting random data and converting the information into meaningful statistical patterns are shrinkingso much so that soon we will see data mining moving from NASA to Main Street.

Alternatively, neural networks processes data by altering the states of networks formed by interconnecting enormous bits of elemental data that interact with one another by exchanging signals, as neurons do in the body's nervous system. Indeed, the best way to visualize neural networking is to think of the human nervous system. The basic processing element in the human nervous system is the neuron. Within the human brain dwell

³ From http://www.wizsoft.com (WizSoft Inc., 6800 Jericho Turnpike, Suite 120W, Syosset, NY 11791).

⁴ Eric de Bodt, Emmanuel-Frederic Henrion, Marie Cottrell, and Charles Van Wymeersch, Self-Organizing Maps for Data Analysis: An Application to the Belgian Leasing Market.

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treelike networks of nerve fiber that connect to the cell body, where the cell nucleus is located. Extending from the cell body is a single, long fiber called the axon, which eventually branches into strands and substrands and connects to other neurons through junctions.

The transmission of signals from one neuron to another is a complex chemical process in which specific transmitter substances are released from the sending end of the junction. The effect is to lower the electrical potential inside the body of the receiving cell. If the potential reaches a threshold, a pulse is sent down the axon, and we then say that the cell has ''fired."

In a simplified mathematical model of the neuron, the effects are represented by "weights" that modulate the effect of the associated input signals, and the nonlinear characteristics exhibited by neurons are represented by a transfer function. The neuron impulse is computed as the weighted sum of the input signals transformed by the transfer function. The learning capability of an artificial neuron is achieved by adjusting the weights in accordance to the chosen learning algorithm since it is arduous to accurately determine multiple values.

This involves creating a network that randomly determines parameter values. The network is then used to carry out input-to-output transformations for actual problems. The correct final parameters are obtained by modifying the parameters in accordance with the errors that the network makes in the process.

Interconnections between corporate risk rating and neural networks are deeply rooted. We explore the methodology in chapter 8 and 10. Corporate risk rating, along with bond ratings, requires a "neural" label that evaluates the ability of corporation to repay principal and interest. The stumbling block is the somewhat subjective nature of ratings themselves since there are no hard-and-fast rules for determining credit ratings.

Rating agencies, banks, and corporate analysts consider a spectrum of factors before assigning a rating. A leading financial software developer, Alcar, built its reputation around popular products such as Value Planner and Bond Rater. Nonetheless, while input factors such as sales, operating margins, working capital, cost of capital, net fixed asset requirements, and other critical assumptions might be assignable, others are questionable. How do you input your customer's willingness to repay? That is where neural networks come in. Rather than working out a payment history regression (judging ability to repay), risk-rating functions might be appropriately solved by training a network using back-propagation.

A neural network consulting firm (ADS) provides consulting services to large credit financial services companies, developing and testing neural network models for data sets supplied by clients. These firms provide raw data to be processed by computers. For example, a typical data set might have 40,000 records, with each record having between 30 and 100 different

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data fields. These fields contain data such as the credit card holder's age, occupation, salary, phone number, and past payment history.

Data may also include information obtained from credit bureaus, such as the number of charge accounts, the number of times the applicant has applied for credit, and the existence of prior bankruptcies. The system predicts the likelihood of a potential credit card holder being assigned a risk classification of good, criticized, or charged off. Finally, the neural system provides a report detailing factors that correlate highly to the forecast.

Like neural nets, fuzzy logic is another fine-edged tool that generates solutions closer to the way our brains work. That is, in our mind we form a number of partial truths that we aggregate further into higher truths that in turn, when certain thresholds are exceeded, cause certain further results, such as motor reaction. Fuzzy logic does not mean system ambiguity. Rather, it is a multivalued logic that allows intermediate values to be defined between conventional evaluations such as yes/no, true/false, black/white, and so on. Notions such as "sort of warm" or "fairly chilly" can be transformed mathematically and processed by computers. In this way, a more human-like way of thinking is possible in computer programming. It is useful to chronicle the German BMW Bank GmbH's fuzzy logic application of its "private customers" leasing operation.

The bank's total fuzzy logic system involved hundreds of fuzzy logic rules in three modules. The designing, testing, and verification of the three modules took years to develop. The system is currently in operation at German BMW dealers, and BMW Bank management considers its performance equivalent to an experienced leasing contract expert. Although a detailed cost savings analysis was not published by BMW Bank, the assumed savings is quite substantial.

To automate the risk assessment evaluation for car leasing contracts, BMW Bank GmbH of Germany and Inform Software GmbH of Germany developed a fuzzy-enhanced score card system. The objective of BMW Bank was to take the decision process away from the bank and give it to the car dealer. The arrangement allowed dealers to obtain approval in real time rather than waiting for the BMW Bank to approve a leasing contract.

Exhibit 15 shows the structure of the fuzzy logic risk assessment for private customers. The input variable "ScoreCard" is the result of the scorecard evaluation. The scorecard result is used with the other input variables to compute a risk profile of the leasing customer. An input variable stores the current unemployment rate for the customer's profession. Another input variable comes from a database and rates the relative illiquidity risk for the customer's place of residence. The result of this evaluation, customer profile is one input that computes the risk rating for the current leasing contract. The rule block uses input variables to describe how timely the customer paid on previous leasing contracts and is matched with the customer's past banking history.

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Exhibit 15.
Fuzzy-enhanced score card system. Scientific Financial Management's Road Map

We can see that technique (and software rather than theory) draws the poker hand that snares the chips. Specifically, what is the generic scheme of this book? Clearly, the CFO's goal is value maximization, and this book, to be germane, should focus on this. A lot has been written about share-holder value (just browse www.amazon.com). But this book is atypical. We do not motif value creation along theoretical lines. What is timely and different is the book's direction finder along scientific value driver lines, with chapters organized so that quantitative (scientific) methodology reinforces and strengthens assumptions anchored to each and every value driver.

CFOs want tools that buttress or define his or her firm's strategic direction, employing scientific methods and models found in Fortune 100 work sheds. And the final test? Smart defense of the shareholder value number. Remember that a key progeny associated with financial management is practical application. The CD-ROM working models offer just that, from simulation to neural networks. In addition Web sites and downloads form the basis of analysis in chapters covering option pricing, valuation, and a host of other engineered applications.

We begin our journey to chapter 12, "The Value-Growth Link" from chapter 2 with an introduction to option analysis, the objective being to introduce generic uses of Black and Scholes. CFOs hedge strategies via the N(dl) component of the option-pricing model. In addition, you learn to measure implied volatility, find debt and equity values, and uncover probabilities that options finish "in the money" through the N(d2) component of the option pricing model. Also, you review the model's use in pricing

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and valuation decisions; quantify the trade-off between risk and pricing; determine, under option pricing assumptions, yields associated with the volatility of returns; calculate expected default frequencies (EDFs); and use these benchmarks to price and tag portfolio risk and uncover bond ratings.

Preparing techniques necessary to understand chapter 2 (and beyond), we review statistics ordered in financial and investment decisions. You, the financial doctor, will do the ordering, but like any good practitioner, financial or medical, you need to know what you are doing, or else the patient dies. A good ear specialist must be familiar with the functions of the auditory nerve, the stirrup, and the eardrum before he or she operates. You do need a different set of knowledge basics to operate on a financial level field, but remember that your field has happened on a rapidly changing terrain called science finance.

It is interesting that the connection between chaos theory and portfolio management is an important one, relating to the hypothesis suggesting that the butterfly effect holds true if few offsetting factors are present. For example, emerging companies producing one product are particularly sensitive to the butterfly effect; firms that produce goods and services spanning numerous, diverse industries are less sensitive to macroeconomic or industry shocks. This is the notion behind portfolio management. Current thinking suggests that while chaos marks day-to-day market movements, chaos eventually flattens into the genesis of nonrandom market trends.

Option pricing's role in optimizing investment and financing decisions is only part of the story. Chapter 3, "Real Options Evaluating R&D and Capital Investments," covers the rest. Think of the value drivercapital expenditures. What specific assets should the business acquire? Assets that promise stronger earnings or assets that deliver lower risk, or perhaps a combination of both? Clearing the correct course to shareholder value is often the dominant investment activity: capital outlays. We key in on project analysis with one of option pricing's most powerful application: real options.

Real options analysis, like its cousin stock and commodity options, provides a more flexible approach to valuing research investments than traditional financial analysis because it allows CFOs to evaluate those investments at successive stages of a project. The chapter reviews the differences between financial and real options, discovering flexibility (the quintessence of real options), traditional methods versus real options, the binomial model, implied binomial trees, abandonment options, options to expand or contract, switching and sequencing options, and case studies.

Visual financial models remind us of the old adage "knowledge is in the pudding." Thus, chapter 4, "Visual Financial Models," deals with modeling. Are underlying assumptions leading up to your shareholder value (result) understood by your audience? Fundamentally, a modeling

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application is any tool that helps CFOs collect, analyze, and present information, often in a highly interactive and iterative way. There are many tools in the developer's kit to implement these applications, each owning up to its own strengths and weaknesses. This chapter examines various options for implementing modeling applications, the applicability of these options to various problems, and advantages and disadvantages of each. We begin by creating multidimensional models for strategic planning with the power of intelligent arrays, integrating model documentation, using intuitive influence diagrams, analyzing uncertainties using probability distributions and efficient probabilistic simulation, using graphical interfaces and hierarchical diagrams and rank-order correlation factors, understanding the relationship between uncertain variables using scatter plots, and communicating your model to the CEO.

As practitioners, we easily identify the fundamental force behind shareholder value: cash flow. Chapter 5, "Divisional Cash Flow Analysis and Sustainable Growth Problems," advances the notion of cash flow reengineering that includes applying the sustainable growth model to cash flow analysis. That is what microproject analysis is all about. How do you use cash flow analysis to test the feasibility of projects? This session starts by championing cash flow, one of the most powerful analytical tools in corporate analysis. Cash flow raises questions dealing with ways that projects generate and absorb cash, with unresolved, serious issues forming the basis of do-or-die allocation decisions. The sustainable growth model keeps the cash flows of rapid growth firms in a prudent mode.

Next we develop uncertainty forecast models that sell. In chapter 6, "Statistical Forecasting Methods and Modified Percentage of Sales," projections hit hard when it comes to working out the equity value figure. Thoughtful projections promote departmental interaction, aid in reassessing guidelines for standard practices, and define performance levels. More important, projections evaluate constraints within an organization such as its size, growth rate, debt capacity, and fixed asset allocation. Financial projections are cornerstones determining shareholder value and uncovering "value gaps," the unequivocal prerequisite to good decision making. We learn to choose the best forecast method in which to authenticate value drivers. The "E" and "F" equations add an intuitive dimension along with the sustainable growth model, which is used to find the maximum rate at which a company's sales can grow without depleting financial resources and again stopping the butterfly effect dead in its tracks. Futhermore, with all that financial data flowing into office computers, we need to sort the important from the superflous. That is where data mining technique (software) plays out.

On a still more technical note, using the CD-ROM included in this book or downloaded from the internet, along with case studies, we unearth statistically complex methods of time-series forecasting and multiple linear regression. Using time-series forecasting, we work around

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chaos factors that I discussed previously, using linear smoothing and seasonal smoothing methods. Linear smoothing includes a variety of averaging and exponential smoothing techniques. Seasonal smoothing includes regular decomposition methods and percentage growth models. Multiple linear regression lets you input a range of data for a dependent variable and a series of ranges of data for independent variables. Once the computer model determines the mathematical relationship, it forecasts each independent variable and then applies the mathematical relationship to forecast the dependent variable.

Applying Monte Carlo to shareholder value has become the hallmark of solid financial thinking. CEOs require more and more justification of critical assumpations now that the technology is available. This notion is the guts and fury behind chapter 7, "How to Apply Monte Carlo Analysis to Financial Forecasting." Monte Carlo, one of the valuable tools testing and validating the value drivers, goes far beyond traditional sensitivity analysis, creating spreadsheets that quantify real-world uncertainties. Also it is a true money saver. For example, independent variables having little impact on forecast (dependent) variables need not be arduously researched.

We cover project and research investment analysis. Other key chapter disciplines will help us define assumptions and identify a distribution type, respond to problems with correlated assumptions, work with confidence levels, determine certainty levels for specific value ranges, determine the expected default frequency, and understand probability distributions and descriptive statistics tools. Finally, the board of directors will want to know the degree of risk posed by your strategic plans. You may be able to say, "Hey, not to worry! The probability of shareholder value dropping below zero (i.e., the chance that real asset values fall below real value liabilities) is 3 basis points. Thus, you can see that my strategic plans move the business into a Triple A rating!"

Also consider this: Monte Carlo simulation will go a long way toward interrupting the butterfly effect dead in its tracks.

Chapter 8, "Neural Networks and Scientific Financial Management," deals with the role that neural nets play in determining shareholder value by applying the scientific method to critical value drivers such as working capital management, cost of capital, and investments. While we do not specifically address these topics you can develop neural network application from the software included in the CD. Neural networks actualize time-series prediction by automating the process of discovering neural network architectures and grouping and determines input or (X) variables critical to the forecast. As such, neural systems represent a quantum leap in working out financial time-series problems, as they are multivariate nonlinear analytics, estimating nonlinear relationships with data alone. They are proficient at recognizing patterns that come out of noisy, complex data. For example, neural networks learn the underlying mechanics of time series or, in the case of trading applications, market dynamics, in ways that mimic

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the human brain. Indeed, there are still problems to be worked out with this new technology, but solutions are being worked out at a fast clip. For example, neural networks are now read in Excel. We actually examine financial applications of neural networks in Excel employing NeuroDimension, Inc.'s, neural networking model, NeuroSolutions.

Linear programming is a mathematical technique that is used by savvy CFOs in working out value drivers, planning efficient operations, and allocating scarce resources. Chapter 9, "Linear Programming, Optimization, and the CFO," covers all this. Problems having numeric decision variables and an objective function to be maximized or minimized are called an optimization problem. Linear programs are among the best studied and most easily solved, and they arise frequently in business planning situations. The CFO's model contains three elements: decision variables, objective functions, and constraints. The goal is to find the combination of ingredients that fit your goals, which in many cases means maximizing shareholder value.

Chapter 10, "Risk Analysis of the Corporate Entity and Operating Segments," deals with a very important value driver: debt cost of capital. Our approach will be to employ a corporate interactive credit-scoring model to help you rate your firm and anticipate concerns that suppliers of capital may have. Three essential factors of a risk-rating system are at play. They include the corporate credit grade, the equivalent bond rating, and the expected default factor associated with the grade. In addition, the overall system is a linked matrix of 19 factors that combine to form a risk grade for a financial offering. The system has a grading line of 1 to 10 in which 1 is the best grade and 10 the worst. In certain cases, a grade of 10 will default the overall grade to an unacceptable 10. Via the model, you work with tools contributing to insightful, well-organized presentations to CEOs, investors, and bankers.

Section 2 of chapter 10, "Corporate Segment Analysis," features a divisional interactive risk-rating model that has been optimized to risk rate operating segments and/or divisions. The overall system is a linked matrix of 11 factors that combine to form a divisional risk grade (and bond rating).

Our road map continues on to shareholder value. Chapter 11, "A Primer on Shareholder Value," highlights cash flow equity value. The essence of strategy formulation is to organize the combined disciplines of risk and valuation and to guide the corporation into a new and better future. The key to effective strategic planning, then, has to deal with two relevant dimensions: (1) responding to changes in the external environment and (2) creatively deploying internal resources to improve the competitive position of the firm.⁵ The key to success is to be able to quantify these factors and integrate them into corporate and shareholder valuation,

⁵ Arnoldo C. Hax, professor of management, Sloan School of Management, MIT.

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strategic planning, and formulation. Thus, the exponential growth of analytics interfacing with modern-day disciplinessimulation, stochastic optimization, and visual modeling, to name a fewhas dramatically changed the way that we view valuation and strategic planning. Proceeding chapters fall in place here as readers learn how to reinforce value drivers with both logic and scientific technology.

An appendix to chapter 11, "Developing a Formal Valuation Appraisal Report," was especially developed for readers who operate as financial consultants and advisers. Chapters 1 through 10 focus on developing a solid value driver foundation utilizing the scientific method. Chapter 11 applies these techniques to shareholder value and in doing so serves up a great deal of quantitative methodology to CFOs and the support team; as is the case, shareholder value analysis is no longer the simple trick of multiplying number of shares by the share price. However, equity values and value gaps to CFOs are not quite the same as viewed from the financial consultant's perspective. Thus, the appendix to chapter 11 offers readers who operate as consultants a framework in which to organize, clarify, and write up a formal and comprehensive valuation appraisal for clients.

The analytics driving valuation decisions arms managment with a powerful tool. Now, for the first time, management has the requisite knowledge to enable it to determine the future value embedded in planned actions. The debate around what to do is honed dramatically by this newfound ability to estimate the value impact. This empowers management to make sound strategic decisions, to chart a positive value-creating course. Thus, focus now shifts from analytics of Chapters 111 to practice. Chapter 12, the final chapter, written by Thomas L. Doorley III, Senior Partner, Deloitte Consulting/Braxton Associates, introduces how all these innovative concepts and technologies can lead to actions that create the value management seeks. Translating analytic rigor embedded in scientific financial management into application, in practice, represents the synergy of the art and science of strategice management. Therefore, we close the book with a perspective into how leadership teams can take their newfound knowledge into the competitive battle.

Finally, speaking of value, what is this book's final value-added component? Along with chapter 12's perspective, it may very well be measured by the incremental quality of excellence in your analytics, along with the clear-sighted organization, power, and logic behind your valuation appraisal.

Now it is your turn to stand at cliff's edge. What will you do? You could watch a few lazy sunsets drift by or, as our hero Fox Mulder of the X-Files would have it, go for it: The truth is out there.

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Chapter Two
Basic Tools of Financial Risk Management:
Portfolios and Options

The mathematics of finance contain some of the most beautiful applications of probability and optimization theory. Yet despite its seemingly abstruse mathematics, finance theory over the last two decades has found its way into the mainstream of finance practice. . . . The scientific breakthroughs in financial modeling both shaped and were shaped by the extraordinary flow of financial innovation that coincided with revolutionary changes in the structure of world financial markets and institutions during the past two decades.¹

Multifractals can be put to work to "stress-test" a portfolio. In this technique the rules underlying multifractals attempt to create the same patterns of variability as do the unknown rules that govern actual markets. Multifractals describe accurately the relation between the shape of the generator and the patterns of up-and-down swings of prices to be found on charts of real market data.²

Climbers who ascend atop Mount Everest carry along Damocles' sword, and so do CFOs, who are very much alike. Their footing must be as secure on the slopes, their protective gear as up-to-date, fitness as pressing, and

¹ Robert C. Merton, "Influence of Mathematical Models in Finance on Practice: Past, Present, and Future," Journal of Financial Practice and Education (Spring/Summer 1995).

² Benoit Mandelbrot, Scientific American.

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concern and knowledge of perils as urgent. Financial graveyards are littered with firms stung by Damocles' swordbusinesses that lost their bearings, those that brushed aside or found difficulty measuring early warning signs, and finally strategic couch potatoes who dared not venture up financial trails, let alone mountains.

The issues in this chapter expand on riskdefining, measuring, and pricing it squarely; dealing with it on an optimal scale; and peeking at ways that link to optimal value adding strategies.

Experts generally partition risk into two categories: unsystematic (or default) risk and systematic (or covariance) risk. Unsystematic risk is company specific and likened to the odds of bankruptcy. A sole mountain climber is the mirror analogy (unsystematic risk) versus of the risk of the entire climbing team tumbling down a crevice (systematic). Examples of unsystematic risk include R&D failures, unsuccessful marketing programs, and losing major contractsevents unique to a firm. Bond ratings mirror unsystematic risk. Inasmuch as these events are essentially random, their effects in a portfolio can be eliminated through diversification.

Systematic risk is exogenous and is usually tied to macroeconomic conditions, that is, a firm's sensitivities to economic conditions. Systematic risk stems from wars, unanticipated inflation, recessions, high interest rates, energy prices, and other events that affect all firms in some measure. Groups of climbers up Everest face systematic risk: bad weather and avalanches. Systematic risk can be diversified away as long as portfolios having disparate sensitivities to these systematic factors can be constructed. For example, a portfolio consisting of rental properties would be downside sensitive to unanticipated inflation since rents cannot be raised overnight to compensate for an unanticipated jump in oil prices. Choosing investments with upside sensitivities to unanticipated inflation would conceivably reduce the portfolio's risk. As a result, we can infer that changes in these microeconomic factors affect returns in several ways, depending on how sensitive the firm's return is to each of these factors.

Industry characteristics are important as well. Industries are comprised of companies with similar risk characteristics shaped by the nature of a shared or closely related economic function. The economic function influences the industry life cycle, the rapidity of change, and the degree of capital intensity. In addition, competition within the industry greatly determines the success or failure of firms. Therefore, changes in the environment or competitive structure can have an impact on a broad range of companies within an industry. An industry's sensitivity to environmental, or "systematic," factors, such as changes in demand, regulations, taxation, and the cost of key inputs, periodically contributes to surges in business failures. Successful companies adapt their capital structure to suit the challenges of their industry and manage the uncertainty of future profitability. Let's start our climb to base 1 with a review of portfolio management. We start off on a path that we might christen "from chaos theory to portfolio management."

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The connection between risk, chaos theory, and portfolio risk management is noteworthy, relating to the hypothesis inferring that the butterfly effect holds if few offsetting factors present themselves. For example, emerging companies producing one product are particularly sensitive to the butterfly effect; firms that produce goods and services spanning numerous, diverse industries may be far less sensitive to macroeconomic/ industry shocks. While chaos marks day-to-day business events (or stock price movements), chaos eventually flattens into the genesis of nonrandom value, creating financial/operating strategies (market trends).

Moving from chaos to portfolio risk management is somewhat like chaos in astronomy. Astronomers refer to sudden changes in a celestial body's orbit as chaos. A celestial object behaving in a chaotic way may have an orbital eccentricity that deviates cyclically for millions of years, abruptly changing its variation pattern. The resulting sharp break in the body's history no longer helps astronomers predict long-term future behavior. Albert Einstein said that God does not play with dice. Consider antimatter. Antimatter is matter composed of elementary particles that are mirror images of the particles making up ordinary matter. Antimatter is identical to ordinary matter except that the electrical charges are reversed. Their movement as particles is ''chaotic" until the two collide. The result: no more chaos, no more dice. The particles simply annihilate into pure energy and disappear, possibly down the mountain trail to dark matter. No one quite knows.

Most risk-reducing portfolio formulas are limited because they suggest that price changes are statistically independent of one another. Thus, you have to be careful using them. For example, they assume first that today's Wall Street Journal stock price is noninfluential in terms of tomorrow's price (not very realistic). The second presumption is that price changes are apportioned in a pattern that fits a standard bell-shaped curve. The width of the bell (sigma, or standard deviation) depicts how far price changes diverge from the mean; events at the extremes are considered extremely rare. Typhoons are, in effect, defined out of existence (also not very realistic). The point is that no model is perfect. They exist to serve masters of judgmentcommonsense and logic seekers attempting the climb Financial Mountain. That said, welcome to the quantitative approach.

Basics of Modern Portfolio Management

Aside from a few limitations, portfolios reduce systematic risk, as long as someone picks assets so that combined returns are not perfectly correlated. The concepts of correlation are useful in measuring the extent and nature of interrelationships between assets. When investors know the expected return and variance of a portfolio, they can make prudent investment decisions.

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However, we note that diversification is occasionally used as justification for novel or risky investment strategies. That strategy is flawed. Diversification is optimal when portfolio risk ebbs without affecting expected returns.

Corporate managers define diversification as the taking of multiple noncorrelated risks. The process is distinct from hedging, which is taking negatively correlated risks. Hedging reduces a portfolio's risk by actually offsetting one risk against another. With diversification, risks do not offset (we develop option hedge strategies in the next section). Rather, risk is reduced because uncorrelated risks do not behave in lockstep. For example, a single security portfolio will tank if just one security price crashes. Investors holding multiple uncorrelated securities seldom experience calamities, although shelter from all losses is not guaranteed.

We said that portfolios are composed of a diverse array of investments (or assets) that tend to cancel each other's risk component (or as seen earlier, they soften the butterfly effect). How portfolio hedges are constructed will vary according to specific corporate goals. Let's examine a "deal" that illustrates economic cycle risk/hedge strategies and risk assessment methods.

The Deal

Antimatter Beef Co. Inc. operates a producer of high-end Angus beef. High-end beef consumption is remarkably cyclical. During economy booms, returns are excellent, reflecting peak beef consumption. The company (pardon the pun) is a cash cow. When recessions hit, earnings results are dismal as consumers cut back purchases of high-priced beef in favor of less expensive alternatives. Antimatter's CFO is appraising the takeover of a negatively correlated (countercyclical) business to soften the risk of macroeconomic shocks on existing operations.

A little background. The beef cattle industry stabilized during 1997 after a series of shocks and uncertainty during 1996, including a cyclical peak in cattle numbers, severe weather in various regions of the country, and record-high feed grain prices (not to mention a tiff with Oprah). Generally, U.S. beef production has historically ebbed and flowed in 10-year cycles because of a combination of factors. Beef production expands for approximately five years until prices decline to levels that cause producers to suffer significant economic losses. This leads to a reduction in the cowherd and smaller beef supplies until prices return to profitable levels and producers decide to increase production in response to increased net returns.

The most likely acquisition candidate, Matter Poultry Corp., a poultry producer, has a fair market value of $60 million. The poultry industry is countercyclical. Recessions provide excellent returns, as diminished disposable income triggers higher poultry consumption. Conversely, during good economic times, Matter Poultry suffers dearly as consumers cut back poultry purchases, shifting consumption to high-end beef.

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Exhibit 21.
Minimum variance set.

Backing into portfolio theory for a minute, let us assume that Antimatter Beef Co. considered a host of acquisition candidates beforehand and plotted each set (Antimatter Co. together with candidates X, Y, Z, and so on) on Markowitz's efficient frontier. Specifically, we plot the minimum variance set (a set of two investment portfolios that, for each level of return, have the least risk: see Exhibit 21). The minimum variance set of portfolios has a quadratic form and graphs as a parabola. We employ the quadratic equation and focus only on those portfolios that lie above the minimum variance portfolio in order to map a typical efficient set. The efficient set appears on the left, plotted in the risk/return (standard deviation/expected return) space.

A well-behaved utility function gives rise to indifference curves. An indifference curve displays the entire set of risk/return combinations that provides exactly the same utility. Thus, the risk/return combination associated with Portfolio A and that associated with Portfolio B provide the same satisfaction (utility) because they lie along the same indifference curve. However, we want to know the optimal portfolio. By superimposing the firm's indifference map on the efficient set of available (acquisition) portfolios, we can determine which portfolio maximizes the firm's utility. This point reflects the perfect balance between expected returns and risk. The portfolio that maximizes Antimatter's utility is called the optimal portfolio. It occurs at the point of tangency between the CFO's indifference map and the efficient set of portfolios.

Before results are plotted on a portfolio map, Antimatter's financial team determined each firm's return sensitivities to the business cycle. The team assumed economic conditions over five years. Since decision making involves ex ante returns, they quantified uncertainty of these returns. In this regard, we look at the entire probability distribution of returns (see Exhibit 22).³

³ Do not be overly concerned that you might not fully grasp distributions and probability graphics just yet. We cover it all in chapter 7.

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Exhibit 22.
Economic assumptions and probability distributions of Antimatter Beef Company Inc.
and Matter Poultry Corp.

Mean and Standard Deviation Calculations for Antimatter

Since decision making involves ex ante returns, the team quantified uncertainty associated with these returns under varying (economic) conditions. Here we look at the entire probability distribution of returns.

Central tendency of the distribution is captured in its expected value (the weighted average of all possible outcomes where the probability of each outcome is used as weights). The variability, or risk, of the distribution is summarized by its variance. An equivalent risk measure is the standard deviation of the distribution, which is the square root of the variance. For the special case of a normal distribution, the standard deviation takes on special significance. However, it is possible to provide more precise statements about possible future returns and the probabilities of recession if data entered a Monte Carlo simulation (see Exhibit 23).⁴

Before results are plotted on a portfolio map, Antimatter's financial team determined each firm's return sensitivities to the business cycle. The team assumed economic conditions over five years. Since decision making involves ex ante (expected) returns, they quantified the uncertainty of these returns.

⁴ We take up simulations in chapter 7. It is not necessary to detail them now, except to note that they were run to clear up some points in this deal.

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Exhibit 23.
Antimatter's expected return under uncertainty conditions.

Exhibit 24.
Antimatter's variance and standard deviation.

The first significant number is the expected return of Antimatter, Ra = 22.6%. From the example we see that Ra is the sum of each return multiplied by its respective probability associated with expected economic conditions.

To make this clearer, let us look at an example: We visit a casino and flip a coin. The casino offers you $1,000 if the coin comes out heads; tails pay nothing. The expected payoff on the toss is $500 (50% heads multiplied by $1,000 plus 50% tails multiplied by zero). However, say that the casino offers you $300 if you agree not to chance the coin toss. The $300 payoff represents a certainty return. A bank financing this "transaction" would charge the risk free rate. The difference between $500, the expected risky return, and the $300 certainty return is the risk premium that is required chancing a loss.

We extend Exhibit 23 in Exhibit 24.

Antimatter Beef operates in a nonequilibrium environment. Because Ra, the expected risky return, ignores variability, we look to the standard deviation, 0.2389. When data are tightly clustered around a steep bell-shaped curve, the standard deviation is small. When data are sprawled out along a wide bell curve, the standard deviation will be larger. One standard deviation in either direction of the mean accounts for 68% of the area under the curve. Two and three standard deviations on either side represent 95% and over 99%, respectively, of areas under the curve.

While in this example the standard deviation measures the variability, or uncertainty, of returns, uncertainty is not necessarily risk. Risk is a relative measure, and though financial analysts associate a large standard deviation with probability of losses, what constitutes an unacceptable loss or

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shortfall is subjective. As modern portfolio theory suggests, only volatility beyond the firm's target return counts as undue risk. Most important, assets (and investments) are held not in isolation but jointly with other assets.

Thus, risk associated with an asset is influenced by interaction of the pattern of its return with the patterns of return of the other assets held in combination. This is correlation, which can be defined as the linear association between two random variables X and Y. One measure of correlation is the covariancethe standard measure of how returns relate to each other. Before we examine covariance, let's run through Poultry's expected return Rb and standard deviation sb.

Calculations of the Mean and Standard Deviation for Matter Co.

Recall that both the poultry and the beef producers generate identical returns, except that patterns are literally reversed. Matt?r's returns are grossly negative during peak economic vitality but turn around during recessions (see Exhibit 25). The reverse holds for Antimatter Beef. While this example is somewhat far-fetched, it is not totally unrealistic. There are plenty of cyclical businesses out there, including financial companies (such as high-yield credit card issuers) who perform well in economic downturns when consumers need to borrow to replace lost disposable income.

The covariance of Antimatter's return with Matter's is negative, suggesting that, given specific economic conditions, the returns of the two firms move in opposite directions (see Exhibit 26). A simulation tagging the covariance as the forecast variable indicates, within a confidence level of 95%, that under uncertainty the covariance falls between a certainty range from 0.06583 to 0.04848 with the standard error of the mean, 0.00022. Crystal Ball⁵ simulations were run on the deal (see Exhibit 27).

Exhibit 25.
Matter's return, variance, and standard deviation.

Exhibit 26.
Covariance of returns: Antimatter Co. with returns of Matter's.

⁵ Trademark of Decisioneering, a leading financial software firm located in Boulder, Colorado.

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Exhibit 27
Simulations run on correlation coefficient

Since the expected return, standard deviation, and covariance are all tied together, let's combine results by assuming that each firm contributes 50% to total assets. The expected return of the combined business (or this two-investment portfolio) is as follows (assume that each firm has equal weight):

where wa is the investment weight of Antimatter Co. (50%) and wb represents the investment weight of Matter Corp. (50%).

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Recall, that Antimatter Beef Co. realizes a premerger expected return of 22.6%. However, the postmerger return falls to 17%. The standard deviation of returns of the combined entity can be determined. The standard deviation of a two-investment portfolio is as follows:

With a standard deviation of just 1%, the portfolio's risk has been reduced to near zero. The outcome is as follows:

Stand-Alone
Return

Merged
Return

Stand-Alone
Risk

Merged
Risk

Antimatter Beef

0.2260

0.1700

0.2389

0.0100

Matter Poultry

0.1140

0.1700

0.2436

0.0100

Matter Poultry Corp.'s shareholders are clear winners. Increased returns combine with reduced risk.

Note that the standard deviation of returns of the merged companies approached zero, meaning that variability was infinitesimal. We confirm this with another statistic, the correlation coefficient derived by dividing the covariance by the product of the two standard deviations of each firm's returns. This is measured by Pearson's r, such that the value of the coefficient ranges from 1 to +1. A positive value of r means that the association is positive; that is, if X values increases, Y values increase linearly and vice versa. A negative value of r means that the association is contrary; a value of 1 means that the association is diametric. Correlation factors near zero point to little or no relationship between sets of data.

The correlation coefficient of beef returns with poultry is close to 1, indicating an almost perfect negative relationship between the returns of Antimatter and Matter:

Solving for the correlation coefficient:

In our example of Antimatter and Matter:

Following are additional simulations we ran on the deal.

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The forecast's sensitivity is poultry cash flow positive returns in a down economy and positive beef returns in an up economy.

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Economic assumptions and distributions appear here:

Note: again, distributions were meant to illustrate powerful new risk measuring tools. As for simulation, we jump into the subject deeply in chapter 7.

Option Pricing Basics

Portfolios can provide solid protection against risk, as can options. Financial and real options impact capital selection and allocation decisions, risk reduction, and analysis of corporate restructuring.

· Options form an important basis for decision making. Considerable interest in options and option pricing has come as a result of the development of new option markets and new theoretical developments spanning cost of capital.

· Option pricing is employed to value other complex contingent claim assets, such as shareholder equity, making value gap measurments more accurate.

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· The pricing of stock and commodity options is completed trough a variety of models (e.g., Black-Scholes). Black-Scholes is based on the creation of a perfect hedge by simultaneously being long (short) in the underlying security and holding an opposite short (long) position on a number of options.

· Option analysis provides a more flexible approach to valuation than traditional financial analysis. In addition, the resultant pricing determines default probabilities.⁶ Default is caused when a firm's asset (market) value falls below debt (market) claims

Options in the Raw

Options are contracts entitling holders to buy or sell designated securities within a certain time period at a particular price. Each contract trades in 100 share units. When used in relation to financial instruments, options are generally defined as a contract between two parties whereby one party has the right but not the obligation to execute a contract, usually to buy or sell some underlying asset. Having rights without obligations has specific and definitive value, so option holders must purchase these rights, creating assets. Option assets derive value from other assets, and so they are called derivative assets or contingent claim contracts.

Pure options are instruments created by investment bankers and speculators. The two least complex and most widely traded options are puts and calls. In addition, most other options can be valued either as combinations of puts and calls or by the methodology similar to valuing puts and calls. Consequently, we begin this section with a discussion of puts and calls and then we see how options are used to value debt and equity in the context of mergers and acquisitions M&A activities. Table 21 shows the relationship between puts and calls.

Calls

Calls are the most common options. A call grants its purchaser, the option holder, the right to purchase a specified number of units of some underly-

⁶ KMV Corporation developed this concept (www.kmv.com).

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ing asset from the option seller. The option seller is called the option writer or sometimes the option grantor. This right is good for some specified period of time, called the time to expiration or the time to expiry. The precise date on which the option right expires is called the expiration date. The agreed-to price is called the strike price or the exercise price. Calls sold in Europe can generally be exercised only at a particular date. Thus, calls containing this provision are referred to as European calls. American-style options are usually more valuable than European options since the option can be exercised at any time before expiration. There are quasi-American-style options, notably the Nikkei and Topix index options traded in Japan, which can be exercised on one day a week.

Option values are decomposed into two parts: intrinsic value and time value. Intrinsic value of a European call is given by the maximum of either the difference between the security price and the strike price or zero:

Option values are classified into three major types. Options are in the money when intrinsic value is positive, at the money when intrinsic value is zero, and out of the money when intrinsic value is negative. Call values are related to security price, interest rate, time to expiration, and price volatility and are inversely related to strike price.

For example, on January 4, 1999, a call on Sacks' common gave its holder the right to buy one share at an exercise price of $35 good until May 1999. Sacks sold at 31 13/16, the call at $2 and 7/16 per share ($243.75 per contract). The play is out of the money since the exercise price fell below current price. Again, the option can be European or American, and the option value will be characterized by ''in the money," "at the money," or "out of the money." The intrinsic value of a European put option is the maximum of either the difference between the strike price and the security price or zero.

If the stock increased to $40 before expiration and the call is executed, the holder receives a $2.56 profit, excluding broker fees and taxes ($40 stock price less $35 exercise price less the cost of the option, 2 7/16). If the share price rose to only $37, the call owner loses and will not execute the contract since payoff falls below the call's cost.

Puts

Put options are identical to calls except the option purchaser has the right to sell ("put") the underlying asset to the option writer. This sale, if the option purchaser elects to exercise the option, is made at the option's strike price. Again, the option can be European or American, and the option value will be characterized by "in the money," "at the money," or "out of the money." The intrinsic value of a European put option is the

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maximum of either the difference between the strike price and the security price or zero:

Consider, for example, a $28 Sacks put of January 4. The investor who purchased the contract owns the right to sell Sacks to the person who issued the put at $28 a share on or before expiration. Put values are related to strike price, time to expiration, and stock price volatility but inversely related to security price and interest rate.

The BlackScholes Formula (1973)

Few works have influenced modern civilization as much or have come closer to God's metaphysical universe as Black-Scholes.

The original model of Black-Scholes assumes the following:

1. Stock returns are lognormally distributed and can be quantified with a mean and variance.

2. The risk-free interest rate is known and time invariant.

3. There are no cash dividends paid during the life of the option.

4. The option is European.

5. There are no transaction costs. This allows for riskless hedging between the option and its underlying security at no sunk cost.

The BlackScholes formula computes the value of an option on the basis of the strike price, current stock price, risk-free rate, the stock's volatility, and time to expiration. While these parameters can be successfully explained, Black-Scholes merits a brush with statistics and probability theory. In the following example, we'll employ the model to value and price a corporate restructuring of a small-cap firm.

Barns and Mobile Publishing Corp. (B&M), [CD:MODELS/EXCEL/ C2B&MPub] has been in operation since 1969. The firm grew from a small publisher of town weeklies to a respected and widely read New England publisher of health, exercise, and running books. The firm produces a suburban weekly under the wings of its fully owned Connecticut subsidiary. The suburban operation accounts for one-third of the combined business. Both B&M Publishing and the Connecticut operation have loans with First Conn. Bank:

Company

Loan Amount

Years to Maturity

Rate

Amortization

B&M Publishing Co.

$8,000,000

5

8%

None: due at maturity

Connecticut Subsidiary

$4,000,000

5

8%

None: due at maturity

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Connecticut's obligations are guaranteed by its parent. Combined equity market value is $36 million; the standard deviation (s) of percentage returns is .35.

Percentage returns equate to equity investors' market returns and, in any one year, represent increases in the investor's equity value plus dividends divided by the investor's equity value at the beginning of the year. Without the Connecticut operations, the standard deviation of percentage returns equals .45. Over the past few years, different demographics resulted in a correlation coefficient of .5 for the firm.

Significantly, returns of two diverse operations tend to be driven by different supply/demand forces. This scenario pulls the correlation coefficient into play. We saw this earlier in the Antimatter/Matter example. Remember, God does not play with dice. The correlation coefficient is useful in untangling complex statistics such as the covariance. The covariance is a measure of the relationship between two random variables and how one element moves in terms of the other. The correlation coefficient "rescales" the covariance to facilitate comparisons with corresponding values for other pairs of random variables.

For example, if the correlation coefficient approaches 1, B&M and Connecticut returns advance (or contract) in an opposite directions (this is akin to diversification). On a scatter diagram, the two returns will have a "perfectly" negative correlation lying precisely on a straight, downward-sloping line. This means that one portion of the operation has a relatively high return and the other a relatively low return. In this case, risk for both borrower and bank is low.

Contrariwise, a correlation coefficient of +1 suggests that returns of both operations are perfectly correlated ("all the eggs in one basket"). A scatter diagram would show both returns lying directly on a straight, upward-sloping line. When one portion of the operation has a relatively high return, so will the other. Conversely, a relatively low return for one will be the same for the other. A correlation coefficient of +1 involves a high degree of risk and uncertainty for the bank.

B&M opts to sell the Connecticut operation. While the suburban weekly is profitable, the firm recently felt the impact of a decreased circulation rate base and downward trends in advertising. Thus, management wants to redirect its focus to health books. Proceeds will be used to beef up health book operations, the backbone of the company. However, diversification in both health books and newspaper publishing reduces corporate risk, assuming that demand for health books will decline because of social, economic, or demographic changes. Health books are luxury items historically influenced by discretionary income. As the publishing industry has witnessed, the last recession hampered both advertising and circulation revenues, directly affecting the bottom line. The point is that the weekly diversifies total risk by providing a service to different segments of the publishing market. The operation

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supplies considerable local coverage and gives the paper a competitive advantage over medium-size dailies.

B&M's health book publishing market is subject to the business cycle and changing demographics, including a larger ethnic population, the shift of baby boomers into middle age, and an increasing elderly population. Like many businesses, health book publishing faces limited market share and competition. As technology progresses, the medium for health awareness changes. Time brings about oscillations in the needs, demands, and forms of leisure activities. Thus, this publishing firm has planned operating strategies around a "Darwinian philosophy" in order to survive and will argue that the strategy pointing to divestment will be "good for the firm."

The firm called a meeting with the bank to obtain the bank's approval to divest Connecticut as required by the loan covenants. While B&M's CFO, Jack Smith, feels that First Connecticut Bank will likely go along with the request, he wants to approach the bank prepared, that is, to figure out how best to renegotiate the existing rate on the $12 million loan. The bank may not initially be agreeable to the proposed rate, but Smith's strategy will, it is hoped, "convince" loan officers that only a small rate increase is justified.

The bank may argue that the "value" of the bank's exposure will decline because of the higher default risk given the proposed sale of Connecticut. In other words, based on the planned Connecticut divestiture, both the firm's CFO and bank officers may derive a loan yield under option pricing conditions that leaves the bank no worse in terms of risk/reward pricing than before the sale. If Smith approaches the bank with a simplistic pricing scheme in hand, loan officers may say no deal, or, if they make an offer, Smith may not know whether the offer is fair.

Getting back to the correlation coefficient for a moment, the firm's health and popular psychology operations are negatively correlated. By treating the two operations as a portfolio, management determines the risk of the "portfolio." The mean and standard deviation of percentage returns of two operations are examined separately and combined. Recall the powerful equation that we worked out in the earlier example of Matter and Antimatter regarding the standard deviation of a two-investment portfolio. If sp = zero before the planned divestiture, volatility of the combined returns of B&M's two operations (risk) is zero. Thus, the firm is immunized against macroeconomic shocks. If, on the other hand, after divestiture of Connecticut, sp increases, percentage returns are more volatile, giving the bank incentive to raise loan rates since the firm is no longer immunized (from the "all the eggs in one basket" syndrome). Default risk increases.

Evaluating returns of B&M's two business units is accomplished by calculating the covariance, the correlation coefficient, and finally the optimal allocation that identifies the point where the variance is at a minimum. These data allow management to graph the portfolio's (the combined business operations) opportunity set and efficiency set. Given a combination of

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portfolios, the opportunity set provides the minimum variance (or standard deviation) for a given rate of return. The efficiency set represents the locus of all portfolios (business operations) that have the highest return for a given level of risk.

Exhibit 28 plots the efficient frontier derived from an actual portfolio analysis complete on MATLAB software. Analysis produced a graph showing a set of portfolios that maximizes expected return at each level of portfolio risk.⁷

Exhibit 28.
The efficient frontier.

Thus, from the efficiency set, B&M's management can see which "portfolio" gives the highest return for the least risk. However, management needs to know the expected rate of return for each project. If they expect more than the portfolio can provide, they will look to alternative investments opportunities. Management has done their homework.

A fundamental aspect of portfolio analysis is that risk is inherent in a single asset or business unit contained in a "portfolio" (similar to consolidated financials). This is different from the riskiness of assets held in isolation (financials of unaffiliated individual firms). The covariance of the "portfolio" determines the correlation coefficient. Again, employing these techniques, management determines the combination of business units (within the portfolio) that provides the highest return blended with the least risk. The issue facing B&M Publishing is essentially risk/return.

Thus, if stockholders own a single line of business/health books, unique risk is very important. However, once stockholders diversify into a portfolio (business combinations that sum to the consolidated entity), diversification has done the bulk of its work. The result is reduced corporate (and bank) risk. How will portfolio analysis, then, help the CFO and bankers determine the market value of debt, shareholder value, and most important the yields required on restructured loans once the firm executes its strategic plan to sell the suburban weekly operation?

How Option Pricing Works to Complete This Deal

We may need more math to feel comfortable with option pricing's role in corporate decision making. Option pricing has the ability to calculate the

⁷ Reproduced with permission of MATLAB, high-performance Numeric Computation and Visualization Software, The Math Works Inc., Natick, Massachusetts.

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value of equity on combined operations or on a single-entity basis. Savings from economies of scale, managerial motives, complementary strengths, or technical competence will have an overriding influence on a combined operation. Meanwhile, we have enough of an account to understand how the restructuring was completed.

While the theory looks attractive, the value of combined operations is not easy to quantify. The general methodology for the analysis of divestitures requires a study of the results of breaking up the two organizations. This undertaking includes an estimate of the applicable cost of capital and expected returns and the application of valuation principles to formulate estimates of the value of the firms, separately and combined. If the value of the combined firm is greater than the sum of the two operations taken separately, then B&M should not divest itself of its subsidiary. The opportunity cost of capital is a weighted average of the cost of equity and debt capital. Further, it is the return on assets that firms must earn to increase shareholder wealth. Thus, a study of the capital structure of the subsidiary should be undertaken by means of the Option Pricing Model. With estimates of the cost of equity and cost of debt, the capital structures of both the combined firm and B&M on a stand-alone basis are analyzed to estimate the cost of capital. It is now time for B&M's CFO and the financial team to step up the analysis to the level of option pricing. See appendix calculation of option values.

Black and Scholes pointed out that common shares are call options, or options to take (or retain) the firm's assets by paying off its debt. By putcall parity, we can also say that the value of debt is marked down by the value of a default put: Stockholders can put the assets of the firm to its creditors and walk away without further liability. The exercise price of the put is the face value of the publishing company's debt. From this, the financial team understood how to price the firm's liabilities.

When creditors place debt, shareholders receive cash by selling assets to creditors plus a call option. At maturity, if the firm's value exceeds the value of debt, stockholders will exercise their call by paying off the firm's $12 million obligation to the bank. However, if spinning off Connecticut causes B&M to belly up, shareholders will not exercise their option. Investors in the firm will walk away as if they purchased stock or commodity options from their broker and stock or commodity values declined below the exercise price.

The bank ends up with the firm's assets, which will be valued below the face amount of the debt. In other words, regarding equity in a levered firm as a call option implies that investments increase the idiosyncratic or diversifiable risk of a firm without changing its expected return. This will benefit the firm's shareholders at the expense of the bank, even though the value of the firm is unaffected. Because idiosyncratic risk is independent of the market portfolio, an increase in this risk will increase the variance of returns for the firm without changing its beta, or expected, return. Thus, the value of the firm will not change.

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However, a redistribution of wealth to shareholders at the expense of the bank may occur because the higher variance will increase the value of the call option held by B&M shareholders. Thus, increasing the riskiness of the firm's operations increases the value of equity but decreases the value of debt. For example, if the bank lent to a firm whose only purpose is to invest in Treasury bills (as strange as this may seem), the yield the bank expects is Treasury based. However, if the firm wised up, sold its Treasury portfolio, and purchased equipment with the proceeds, volatility of percentage returns will increase along with shareholder value. The bank recognizes that they no longer could lend at the risk-free rate because increased volatility, associated with more aggressive business strategies, has increased default risk, reducing debt values.

While Barns & Mobile Publishing Corp.'s bankers cannot be absolutely certain of the firm's new level of risk, Jack Smith and the bank may wisely employ option techniques to derive the appropriate compensation for the bank to relax loan covanents pertaining to changes in the business.

Now let's assume that projections were completed with support of simulation software. The results indicate within a 95% confidence level that the risk of percentage returns (standard deviation) has increased from 35% to 45%. Incorporating this information in our option pricing spread-sheet, the yield on the loan (from within the universe of option pricing) increases 120 basis points, compensating the bank for the higher level of risk. This translates into the bank receiving a compensation of 120 basis points on the restructured term loan for them to agree to waive the loan covenant restricting divestment activity (if the company's risk level increases from .35 to .45).

You can verify the summaries given in Tables 22 and 23 by using the Excel template in the CD. The file, B&MPub.XLS, is an option pricing model. You may also want to experiment by changing the assumption variables.

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Now, we finish. Though default risk increased, the bank agreed to relax loan covenants, allowing the firm to proceed with the divestiture. A rate increase to 9.2% is reasonable compensation for incremental default risk. The $4 million loan to Connecticut was repaid from the proceeds of the sale.

Option pricing is not the only way to price debt and should never be used alone. However, by estimating the probabilities that shareholders' call options finish "in the money," midsize firms and their capital providers (namely, banks) can arbitrate pricing issues on a level playing field, and that is the important issue: the incremental cost of financingloan yields in equilibrium with the volatility of a restructured business. For this reason, option pricing provides significant insight into the relationship between degrees of risk versus degrees of returns working its way in a strategic plan demanded by key suppliers of capital.

The Quintessential Black-Scholes

Einstein once said, "Nature shows us only the tail of the lion. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size." If Einstein is correct, then volatility/yield (risk/reward) in orbit is the "tail of the lion," and the metaphoric lion is higher-dimensional space-time, the optimal financing plan. Perhaps one day people will concede that "useless statisticsthe bane of many financial managers"is the ultimate source of beauty and simplicity.

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Those who have studied portfolio theory no doubt understand how to depict the correlation between assets comprising a portfolio. To readers who are new to these concepts, I hope that the example has shown that the whole is not just the sum of the parts. The correlation between units of a company or stocks in a mutual fund, even if they appear as remote as a butterfly's flight on wind patterns, are very much present and, more important, have a very determinable value.

For example, at any given concert of Beethoven's Eroica, the power and intensity of the music will visibly shake people. If, at the concert's conclusion, you stroll by the orchestra pit and peek at the sheet music, you will likely think that the score of this most towering work is a jumble of scribbles and scrawls. However, to a musician the scribbles come alive and resonate in both mind and soul. A musician actually hears Beethoven's rich, organic sounds simply by looking at the score. Bars, clefs, keys, sharps, and flats are more than a short collection of scrawls on paper.

Like the Eroica, the metaphoric poem of Black-Scholes is much more a collection of bars, clefs, and keys. Rather, like many a great work, this one evokes subtle interactions well beneath the obvious; and, as a poem of sorts, the formula has the potential to transport financial managers to heights of logic and depth. If so, they may see that, like music, the equation evokes a natural progression and a syllogistic reasoning that is anything but opaque. Beautiful mathematics is much like an elegant movement in a symphony.

We develop options further in the next chapter, which focuses on real options. Real options give CFOs a strategic and valuation tool that contributes to R&D and project decisions, ensuring optimum investment opportunities. Real options is a way of thinking and is part of a broad wave of change in financial, product, and corporate investment decisions that requires managers to create value by managing strategic investments squarely, with a minimum of waste, expense, and effort.

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Appendix A:
Calculations of Options Values

Please open Excel file [CD:MODELS/EXCEL/Opt-bs.XLS], a simple 123 spreadsheet for the Black-Scholes option formula, in the models subdirectory on the CD. In the Black-Scholes model, the derivation is based on the creation of a perfect hedge by simultaneously being long (short) in the underlying security and holding an opposite, short (long) position on a number of options. The return on a completely hedged position will then be equal to the risk-free return on the investment in order to eliminate arbitrage opportunities. A call option that can be exercised only on some future maturity date can be evaluated by the following expression:

Example Inc.

Assume that the information in Table 2A1 has been obtained on the Example Inc. stock. Let's begin with the formula:

The value of the option = the stock price multiplied by delta, N(d₁), less the risk-adjusted present value of exercised price XeRfT N(d₂).

This operation is not easy, so let's break the formula down with the B&S formula:

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Step 1
Find eRfT

eRfT is the formula for continuous discounting. For example, .9667 would be invested now in a risk-free investment to receive $1.00 in 199 days with interest at 5%; e is the natural log; Rf = 5% and T = 199 days.

Step 2
Understand N(d₂)

N(d₂) is the probability that the option is in the money; that is, at maturity the stock price is above the strike or exercise price. The probability that the option contract is out of the money is (1N(d₂)). Assume that N(d₂) is .59611.

Step 3
Link Step 2 to Step 1

Receipt of 1.00 is anything but certain unless you invest in a Treasury bill. If there is a .59611 chance that at maturity you hold an in-the-money-option, its expected present value is $1.00(.9667)(.59611) = $.57629, which is the most you would invest to realize $1.00 at maturity. Thus, the exercise price was $45. Its expected present value is $45(0.57629), or $25.95. In other words, the B&S formula risk adjusts the exercise price, and that is what the exercise price is really worth.

Step 4
Determine N(d₁)

N(d₁) is delta, or the partial derivative, the change in the price of the option with respect to the change in the price of the stock. A delta of .40 means that if the price of the stock changes 100%, the price of the option changes 40% (see the next section).

Finally, the expected stock price SN(d₁) less the risk-adjusted exercise price, XeRfT N(d₂), equals C, the option price.

Developing the Quantitative Elements

First find d1:

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This converts to .17401.

Examining the curve above, we can see some interesting properties of normal probability distributions. For any normal distribution, the probability of an outcome falling plus or minus one standard deviation from the mean s is 68.26%. If we take the range within two standard deviations of the mean, the probability of an occurrence within this range is 95.46%, and 99.74% of all outcomes will fall within three standard deviations of the mean.

Thus, from a z table (table of areas under the normal curve), .451406 converts to a value of .17401, the proportion of total area under the normal curve (opt.bs.xls cell B49).

N(d1), or delta, is simply .5 + .167 = .67401 (cell B54). Delta is a partial derivative that infers that a 100% change is the stock price results in a 67%

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change in price of the option. It is now easy to construct the riskless hedge, r = 1/N(d1). In the example, r = 1/.67401 = 1.48366. Thus we write 148.4 options to hedge against 100 shares of stock D.

If the firm hedges foreign currency, or interest rates for their customer, N(d1) provides the currency or interest rate hedge. It is not enough to know what delta is at any given moment. Thus, we also calculate gamma (see definition in Table 2A2).

N(d₂) is the probability that our European option expires in the money:

The computer derives N(d2) = .59611, the probability that the option finishes ''in the money" (S > X). Thus, eRfT = e.062(199/365) = .966762, represents the present value of $1.00 certain to be received in 199 days, $.9667.

However, the $1.00 is anything but certain. There is only a .59611 chance of realizing a $1.00 under these risk conditions; thus, the expected present value is $1.00(.9667)(.59611) = $.57629. Thus, XeRfT N(d₂) = $45 (.5763) = $25.95, the expected present value of the exercise price. The stock price adjusts by N(d1), the reciprocal of the riskless hedge:

Finally, the value of the option: C = SN(d₁)XeRfT N(d₂) = $31.5125.95 = $5.55.

Exhibit 2A1 shows a three-dimensional surface. For each point on the surface, the height (z-value) represents the sum of the gammas for each option in the portfolio weighted by the amount of each option. The x-axis represents changing price, and the y-axis represents time. The plot adds a fourth dimension by showing delta as surface color.⁸

Recall that gamma is the second derivative of the option price relative to the underlying security price. Exhibit 2A2 shows a three-dimensional surface whose z-value is the gamma of an option as price (x-axis) and time

⁸ Reproduced with permission of MATLAB, high-performance Numeric Computation and Visualization Software, The Math Works Inc., Natick, Massachusetts.

Page 45

Exhibit 2A-1.
A plot of gamma as a function of price and time for a
portfolio of ten Black-Scholes options.

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Exhibit 2A2.
A three-dimensional plot showing how gamma changes relative to price
for a Black-Scholes option.

(y-axis) vary. It adds yet a fourth dimension by showing option delta (the first derivative of option price to security price) as the color of the surface.⁹

The Barns & Mobile Publishing Corp. Practice Session

On page 41, we solved the option problem with mathematical formulas. Now we will use the spreadsheet that is more efficient. Table 2A3 lists input data. Tables 2A4 and 2A5 represent the spreadsheet solution.

Download "a simple 123 spreadsheet for the Black-Scholes Option FormulaDividend Adjusted

www.numa.com10

It might be helpful to review again the Barns & Mobile divestiture, this time working with the Black-Scholes template B&Mpub.XLS.

A SIMPLE 123 SPREADSHEET FOR THE BLACK-SCHOLES OPTION FORMULA

⁹ Reproduced with permission of MATLAB, high-performance Numeric Computation and Visualization Software, The Math Works Inc., Natick, Massachusetts.

¹⁰ "You are free to use this spreadsheet as you wish, but we would be grateful if you could include a reference to Numa Financial Systems. Please contact us if you have any comments or suggestions."

Page 47

Page 48

Case One
Original Conditions (Consolidated)

Assumption: Low-Risk Diversified Business

INPUT

Standard deviation

ENTER B6

35

Risk-free rate

ENTER B7

8.0

Days to expiration (5 yrs x 365)

ENTER B8

1825

Total face amount of combined debt*

ENTER B9

12,000,000

Market value of the firm

ENTER B10

36,000,000

*Health book operation face amt. debt

$8,000,000

*Suburban operation face amt. debt

$4,000,000

OUTPUT

Value of common stock

$28,089,626

Present value of combined debt

$7,910,373

Case Two
Divestiture Strategy (Individual)

The Barns & Mobile Publishing Corp. sells its Connecticut subsidiary, thus increasing the standard deviation of percentage returns to 45%.

Assumption: Higher-Risk Concentrated Business

INPUT

Previous: SD 35%

Standard deviation

ENTER B28

45

Risk-free rate

ENTER B29

8.0

Days to expiration (5 yrs x 365)

ENTER B30

1825

Total face amount of combined debt*

ENTER B31

12,000,000

Market value of the firm

ENTER B32

36,000,000

*Health book operation face amt. debt

$8,000,000

*Suburban operation face amt. debt

$4,000,000

OUTPUT

Yield to compensate for higher variance: 9.2% (vs. initial condition yield of 8.0%)

Value of common stock

$18,950,383

Market value of health book operations

$24,000,000

Present value of health operation debt

$5,049,616

Change in value common stock

$223,966

Change in value debt

($223,966)

Basis-point adjustment in yield to compensate for higher risk and reduction in debt value

120.3

Page 49

The Numbers Worked Out

**Reconciliation: 120 basis-point adjustment to compensate for increased risk: The increased risk of the divestment of suburban weekly has raised the market value of equity by $223,996:

Value of equity before divestment of weekly: $28,089,626

Adjustment to reduce firm 1/3.

(2/3 × $28,089,626)
Less: Postequity (higher variance)
Increase in shareholder value

$18,726,417
($18,950,383)
$223,966

The Barns & Mobile Publishing Corp. sells its Connecticut subsidiary, thus increasing the standard deviation of percentage returns to 45%. The market value of the risky debt on the other hand declined by an equal amount:

Market value of debt as determined by the option pricing model before divestment: $7,910,373

Adjustment (2/3 × 7,910,373)

$5,273,582

Value of debt with increase in
   variability to SD .45 from .35
Decrease in the value of debt

($5,0499,616)
223,966

Results

The promised yield to maturity associated with post divestiture debt can be determined by solving for the discount rate that equates maturity value five years hence to the present value of debt determined by Black-Scholes.

Namely:

where Bo represents the present value of debt
F = face value
e = the natural log
T = years to maturity
kb= the required yield

Solving for the yield, we find that creditors require a postdivestiture yield of 0.09269 (in equilibrium with .45 SD) versus an 8% yield before, or 120 basis points increased compensation.

Page 50

Chapter Two
References and Selected Readings

Books and Periodicals

Aliber, R. Z., and B. R. Bruce. (1991). Global portfolios: Quantitative strategies for maximum performance. Homewood, Ill.: Business One Irwin.

Bakshi, G., et al. (1997). "Empirical performance of alternative option pricing models." Journal of Finance, 200349.

Bates, D. S. (1995). "Testing option pricing models." Working paper. National Bureau of Economic Research, 172.

Bates, D. S., and National Bureau of Economic Research. (1995). Testing option pricing models. Cambridge, Mass.: National Bureau of Economic Research.

Bookstaber, R. M. (1987). Option pricing and investment strategies. Chicago: Probus.

Breen, R. (1990). "Binomial option pricing and the conditions for early exercise: An example using foreign exchange options." Economic and Social Review, 15161.

Brenner, M., and Salomon Brothers Center for the Study of Financial Institutions. (1983). Option pricing: Theory and applications. Lexington, Mass: Lexington Books.

Brockman, P., and M. Chowdhury. (1997). "Deterministic versus stochastic volatility: Implications for option pricing models." Applied Financial Economics, 499505.

Butler, J. S., and B. Schachter. (1986). "Unbiased estimation of the Black/Scholes formula" Journal of Financial Economics, 34157.
The authors present an estimator of the Black and Scholes (1973) option pricing formula that is free of the variance-induced bias discussed by Thorp (1976), Boyle and Ananthanarayan (1977), and others.

Chang, C. W., et al. (1998). "Information-time option pricing: Theory and empirical evidence." Journal of Financial Economics, 21142.

Chang, J. S. K., and L. Shanker. (1987). "Option pricing and the arbitrage pricing theory." Journal of Financial Research, 116.

Chriss, N. (1997). Black-Scholes and beyond: Option-pricing models. Chicago: Irwin.

Cox, J. C., et al. (1987). Option pricing theory and its applications. Cambridge: Sloan School of Management, Massachusetts Institute of Technology.

Ferrentino, G. L., and Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science. (1987). An option-pricing model for R&D projects.

Fortune, P. (1996). "Anomalies in option pricing: The Black-Scholes model revisited." New England Economic Review/Federal Reserve Bank of Boston, 1740.

Gilster, J. E., Jr. (1990). "Systematic risk of discretely rebalanced option hedges." Journal of Financial and Quantitative Analysis, 50716.
Demonstrates that Black-Scholes option-pricing model hedge positions that are risk free when rebalanced continuously will frequently exhibit substantial systematic risk when rebalanced at finite intervals. This systematic risk means that the Black-Scholes option-pricing model is inherently inconsistent with the discrete time version of the Capital Asset Pricing Model (CAPM).

Grenadier, S. R., and A. M. Weiss. (1997). "Investment in technological innovations: An option pricing approach." Journal of Financial Economics, 397416.
Develops "a model of the optimal investment strategy for a firm confronted with a sequence of technological innovations."

Haug, E. G. (1998). The complete guide to option pricing formulas. New York: McGraw-Hill.

Hodges, S. D. (1990). Options: Recent advances in theory and practice. Manchester: Manchester University Press.

Jarrow, R. A., and A. Rudd. (1983). Option pricing. Homewood, Ill.: Dow Jones-Irwin.

Johnson, R. S., et al. (1999). "Skewness-adjusted binomial option pricing model: The relevance of the mean." International Review of Economics and Business, 15972.

Page 51

Kroll, Y. and H. Levy. (1984). "Mean-variance versus direct utility maximization." Journal of Finance, 4761.
The authors compare the expected utility of the optimum portfolio for given utility functions with the expected utility of well-selected portfolios from the mean-variance efficient frontier.

Lee, S. H., et al. (1997). "The performance of option pricing models: A comparison." International Journal of Finance (3), 66882.

Leisen, D. P. J. (1998). "Pricing the American put option: A detailed convergence analysis for binomial models." Journal of Economic Dynamics and Control, 141944.

Lo, A. W., and C. Wang. (1993). Implementing option-pricing models when asset returns are predictable. Cambridge: Alfred P. Sloan School of Management, Massachusetts Institute of Technology.

Lo, A. W., and J. Wang. (1994). "Implementing option pricing models when asset returns are predictable." Working Paper. National Bureau of Economic Research, 154.

Lyng, A., and Sloan School of Management. (1986). "Option pricing: A life-cycle evaluation of a project."

Majd, S., and R. S. Pindyck. (1985). "Time to build, option value, and investment decisions." Working Paper. National Bureau of Economic Research, 124.
The authors develop an explicit model of investment projects and use option pricing methods to derive optimal decision rules for investment outlays over the entire construction program.

Majd, S., and Sloan School of Management. (1984). "Applications of option pricing to corporate finance."

Merrill, C., and S. Thorley. (1996). "Time diversification: Perspectives from option pricing theory." Financial Analysts Journal, 1319.

Merton, R. C. (1970). An analytic derivation of the efficient portfolio frontier. Cambridge: MIT Press.

Merton, R. C. (1971). Theory of rational option pricing. Cambridge: MIT Press.

Merton, R. C. (1975). Option pricing when underlying stock returns are discontinuous. Cambridge: Alfred P. Sloan School of Management, Massachusetts Institute of Technology.

Merton, R. C. (1976). The impact on option pricing of specification error in the underlying stock price returns. Cambridge: Alfred P. Sloan School of Management, Massachusetts, Institute of Technology.

Merton, R. C. (1998). "Applications of option-pricing theory: Twenty-five years later." American Economic Review, 32349.
This article is the lecture that Robert C. Merton delivered in Stockholm, Sweden, December 9, 1997, when he received the Alfred Nobel Memorial Prize in Economic Sciences.

Mitchell, D. W. (1990). "Efficient policy frontier under parameter uncertainty and multiple tools." Journal of Macroeconomics, 13745.

Myers S. C., et al. (1983). Calculating abandonment value using option-pricing theory. Cambridge: MIT Press.

Nawalkha, S. K. (1995). "Face value convergence for stochastic bond price processes: A note on Merton's partial equilibrium option pricing model." Journal of Banking and Finance; 15364.

Nelson, D. B., and K. Ramaswamy. (1989). "Simple binomial processes as diffusion approximations in financial models." Working Paper. Rodney L. White Center for Financial Research, University of Pennsylvania, 145.
Presents conditions under which a sequence of binomial processes converges weakly to a diffusion and shows constructively how one can employ a transformation to produce computationally simple binomial processes. In the context of financial models (especially option pricing models), the binomial method numerically solves a partial differential equation (PDE) for the value of some asset. The methods in this paper permit one to solve such PDEs for alternative underlying diffusions.

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Prakash, A. J., et al. (1989). "General proof of Merton's analytic derivation of the efficient portfolio frontier." Quarterly Journal of Business and Economics, 6777.

Quigg, L. (1993). "Empirical testing of real option-pricing models." Journal of Finance, 62140.
Examines the empirical predictions of a real option-pricing model using a large sample of market prices, with empirical support for a model that incorporates the option to wait to develop land.

Rahman, A., and L. Kryzanowski. (1986). "Alternative specifications of the errors in the Black-Scholes option-pricing model and various implied-variance formulas." Economics Letters (1), 6165.

Reiss, A. (1998). "Investment in innovations and competition: An option pricing approach." Quarterly Review of Economics and Finance (Special Issue), 63550.

Rogers, L. C. G., and D. Talay. (1997). Numerical methods in finance. Cambridge: Cambridge University Press.

Seiford, L., and R. M. Thrall. (1990). "Recent developments in DEA: The mathematical programming approach to frontier analysis." Journal of Econometrics, 738.
Discusses mathematical programming approach to efficient frontier estimation known as DEA and the advantages and limitations of a mathematical programming approach to frontier estimation. Annals 19904, a supplement to the Journal of Econometrics.

Sundaram, R. K., et al. (1999).
An introduction to futures and options. This course provides an intuitive introduction to the nature and pricing of derivative instruments. It covers forwards and futures, swaps, and options. An exposition of derivatives pricing using the Binomial option-pricing model is followed by a discussion of the Black-Scholes model and its extensions.

Turnbull, S. M., and F. Milne. (1991). "Simple approach to interest-rate option pricing." Review of Financial Studies (1), 87120.

Whaley, R. E. (1986). "Valuation of American futures options: Theory and empirical tests." Journal of Finance, 12750.
Reviews the theory of futures option pricing and tests the valuation principles on transaction prices from the S&P 500 equity futures option market.

Wilmott, P., J. et al. (1993). Option pricing: Mathematical models and computation. Oxford: Oxford Financial Press.

Other Periodicals

Anders, Ulrich. (1998). "Improving the pricing of options: A neural network approach." Journal of Forecasting, 17 (5 to 6), 369.

Anonymous. (1998). "How to estimate cumulative volatility." Harvard Business Review, 76(4), 58.

Ballestero, E. (1998). "Approximating the optimum portfolio for an investor with particular preferences." Journal of the Operational Research Society, 49(9), 998.

Birge, John R. (1999). "Risk-neutral option pricing methods for adjusting constrained cash flows." The Engineering Economist, 44(1), 36.

Brown, Mark, and Peter Tedstrom. (1995). "Efficient frontier helps maximize returns." Denver Post, March 13, p. C03, Rockies edition.

Carty, C. Michael. (1999). "A new paradigm for structuring portfolios: Planners can reduce the impact of errors in risk and return projections by applying a new method for portfolio selection." Financial Planning, January 1, p. 1.

Chance, Don M. (1999). "Research trends in derivatives and risk management since Black-Scholes." Journal of Portfolio Management (May), 35.

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Corrado, Charles. (1998). "An empirical test of the Hull-White option pricing model." Journal of Futures Markets, 18(4), 363.

Dalio, Ray, and Dan Bernstein. (1996). "A new edge for efficient frontier." Pensions and Investments, 24(19), 12.

Das, Sanjiv Ranjan. (1999). "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model." Journal of Economic Dynamics and Control, 23(3), 333.

Diacogiannis, George P. (1997). "Multi-factor risk-return relationships." Journal of Business Finance and Accounting, 24(3/4), 559.

Dong-Hyun Ahn. (1999). "Pricing discrete barrier options with an adaptive mesh model." Journal of Derivatives, 6(4), 33.

Dreman, David. (1998). "Nobel laureates with black boxes." Forbes, December 14, 283.

Gibbons, Michael R., Stephen A. Ross, and Jay Shanken. (1989). "A test of the efficiency of a given portfolio." Econometrica, 57(5), 1121.

Gollinger, Terri L. (1993). "Calculation of an efficient frontier for a commercial loan portfolio." Journal of Portfolio Management, 19(2), 39.

Grinold, Richard C. (1992). "Are benchmark portfolios efficient?" Journal of Portfolio Management, 19(1), 34.

Guo, Chen. (1998). "Option pricing with heterogeneous expectations." The Financial Review, 33(4), 81.

Herrick, R. C. (1997). "Exploring the efficient frontier." Risk Management, 44(8), 23.

Ma, Chenghu. (1998)." A discrete-time intertemporal asset pricing model: GE approach with recursive utility." Mathematical Finance, 8(3), 249.

Mahieu, Ronald. (1998). "A Bayesian analysis of stock return volatility and trading volume." Applied Financial Economics, 8(6), 671.

Markowitz, Harry M. (1999). "A more efficient frontier." Journal of Portfolio Management (May), 99.

Marmer, Harry S., and F. K. Louis Ng. (1993). "Mean-semivariance analysis of option-based strategies: A tot." Financial Analysts Journal, 49(3), 47.

Mello, Antonio S. (1998). "A portfolio approach to risk reduction in discretely rebalanced option hedges." Management Science, 44(7), 921.

Reitano, Robert R. (1996). "Non-parallel yield curve shifts and stochastic immunization." Journal of Portfolio Management, 22(2), 71.

Rendleman Richard J., Jr. (1999). "Option investing from a risk-return perspectively." Journal of Portfolio Management (May), 109.

Sharma, Maneesh. (1996). "Efficient frontier: The surprising results of shorter relationships." Multinational Business Review, 4(1), 1.

Shing, Chue. (1999). "Interactive decision system in stochastic multiobjective portfolio selection." International Journal of Production Economics, 6061, 187.

Tian, Yisong. (1999). "A flexible binomial option pricing model;" Journal of Futures Markets, 19(7), pg. 817.

Voros, J. (1999). "A note on the kinks at the mean variance frontier." European Journal of Operational Research, 112(1), 236.

Williams, James O. (1999). "A frontier that's more efficient." Financial Planning, October 1, p. 1.

Winston, Kenneth. (1993). "The' efficient index' and prediction of portfolio variance." Journal of Portfolio Management, 19(3), 27.

Ziobrowski, Alan J. (1999). "Mixed-asset portfolio composition with long-term holding periods and uncertainty." Journal of Real Estate Portfolio Management, 5(2), 139.

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Select Internet Library

Rubash, Kevin. A Study of Option Pricing Models.
Extract: Modern option pricing techniques are often considered among the most mathematically complex of all applied areas of finance. Financial analysts have reached the point where they are able to calculate, with alarming accuracy, the value of a stock option. Most of the models and techniques employed by today's analysts are rooted in a model developed by Fischer Black and Myron Scholes in 1973. This paper examines the evolution of option pricing models leading up to and beyond Black and Scholes's model. .

The Big Applet TM (November 18, 1999).
Daniel Sigrist's Black-Scholes Option Calculator implements the Black-Scholes (1973) equation for European calls and puts and produces prices and Greeks. Use it freely, as is, with his compliments. http://www.margrabe.com/OptionPricing.html.

Monte Carlo Algorithm for Option Pricing.
Extract: Monte Carlo simulation is an established numerical tool for pricing of derivative securities. Standard Monte Carlo approach relies on direct stochastic integration of the Langevin equation for the security price process. You will find on this site an improved Monte Carlo option pricing method that generates the probability distribution of security prices using Metropolis algorithm. http://www.napac.syr.edu/users/miloje/HPFA/Option/home.html.

CD

Name

Size

Type

BLACKSCHOLESOPTION PRICING MODELS
1KB
Internet Shortcut

BlackScholes Option Pricing Applet /Margrabe
DerivativesOptionsSwapsRisk ManagementModel Risk/
1KB
Internet Shortcut

C2b&MPub
21KB
Microsoft Excel Worksheet

C2opt-bs
313KB
Microsoft Excel Worksheet

Monte Carlo Option Pricing
1KB
Internet Shortcut

NumaWeb DERIVATIVES Option Calculator
1KB
Internet Shortcut

NumaWeb The Internet Resource Center For Financial Derivatives
1KB
Internet Shortcut

The Mathworks Financial Toolbox
1KB
Internet Shortcut

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Chapter Three
Real Options:
Evaluating R&D and Capital Investments

Capital expenditures that show up on any FASB 95 cash flow statement are de facto collections of options on real assets, or real options. Real options are similar to financial options in that firms with discretionary investment opportunities have the rightbut are under no obligationto acquire expected cash flows by making an investment on or before the date that the (investment) opportunity ceases to exist.

Integrating real options into (capital) investment analysis is a must for CFOs aiming to derive shareholder value with any degree of accuracy. The technique really works because of the correspondence between managing real assets and investing in financial assets. For example, deciding to invest in a particular Disney film is identical to exercising a call on Amazon.com stock. Investors in a Disney production provide funds if they believe that the present value of expected cash flows (from the movie) exceed the present value of development costs. In much the same way, it is smart to exercise a call on Amazon.com if the stock price is greater than the strike price at the time the option is exercised. When to invest in a Disney production is the same question as asking when it is rational to exercise a call optionin this case, an American call option. Identical methods value both financial options and real options.

''Options" refer to flexibility, natural hallmarks of investment, or operating decisions. "Real" distinguishes options available on tangible or intangible assets from options on financial instruments. Real options explicitly recognize and incorporate the value of being able to defer investment,

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expand output, change technologies, or stop investingbe it a new medical technology or, for that matter, conducting a master piano class at one of New York's music conservatories

The Music Master's Dilemma

Financial decision making reinforced with real options is very much like selecting protégés for music master classestwo highly complicated unpredictable events. Walk into the master's studio on any given day, and you will find the rare protégé who plays superbly. Any master teacher would pick this student immediately. At the other extreme, aspirants attend the selection process with knees shaking so badly that the whole piano vibrates. While mild anxiety is normal when a pianist performs, some suffer from terminal levels of fear. They experience palpitations, rapid breathing, and a loss of control over their ability to manage what can be described only as sheer terror. Few master teachers would bother to pick them. Extremesnow or neverare easy decisions. Alas, music and finance inhabit identical space-time boundaries.

Between the two bands (of option space-time) upper and lower, hopeful protégés position themselves, each with varying prospects. Some demonstrate adequate skills but no debilitating performance anxiety. These pianists might benefit from more time on the vine. Our master teacher could rush "the decision" and pick them now to prevent competing schools from pirating these young Artur Rubinsteins. Or, if this were simply a case of nonfatal performance anxiety, some prospects might recover enough to return to music's Holy Grail: preparation, planning, and presence. Before the next audition, the talented ones may well keep anxiety under control so that the master will not exercise his or her implicit option to abandon. Such is the world of uncertainty.

Protégés needing additional refinementno point picking them now. These pianists are sufficiently far along and willing to let time give them the upper hand. With more work (and luck), knowing the harmonic structure, grasping the musical form of masterpieces, anticipating where each phrase begins and ends, and performing with the musical understanding to bring out the rich tonalities, they will be reconsideredperhaps.

Option theory is, in one form or another, everywhere, framing the totality of art, business, medicine, furniture repair, teaching, and just about anything calling for intelligent decision making. Naturally, accounts differ, as well they should. Music space-time hardly resembles R&D space-time. However, master piano teachers, like their finance counterparts, are always searching out the right options that mightand that is the important wordmaximize value.

If this parable sounds a bit complicated, it is. Just try solving the master's dilemma using standard approaches such as net present value or inter-

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nal rate of return! Of course, the key to solving the master's dilemma is an options deployment problem, meaning the explicit valuation of flexibility.

Flexibility:
The Quintessence of Real Options

Flexibility is purchased and, like a home insurance policy, adds value and is very much sought after. Special features embedded in capital expansion programs are often elastic, are open to negotiation, and can be purchased, for example, flexible manufacturing systems, options to change the product mix in oil refineries, or opportunities to temporarily shut down and restart plant facilities. Other examples are choices permitting you to switch production across borders, beneficial labor conditions, demand, and currency fluctuations. Contracts contain other elastic features, such as the right to deliver natural gas or electricity, whichever is cheaper (switching options). In many cases, flexibility is a largely predictable phenomenon with minor uncertainty.

For example, electrical generators might be used during hours of peak demand, on certain times of day, or in certain seasons. This additional capacity is purchased for the probability of exceeding a "known" benchmark and demonstrates a firm's need for elastic options. However, the exact demand of generated power is unknown, and in fact the actual market price may be so low that little or no power will be generated.

Flexibility internal to the project allows you to modify capital expenditures as external conditions change. These include expansion, alteration or even abandonment. For example, if you are looking to buy a new computer, you might be satisfied if the only real requirement is word processing and spreadsheets. You simply purchase a low priced model. However, you'll purchase high-end if speed and memory is what you require.

The other type is external-, or "project-," dependent flexibility or elasticity. Deciding to embark on a specific project makes possible a second project not feasible without the first. For example, your boss gives you a big bonus, and you go purchase a beach house near your favorite resort. Without the house, you are limited in how often you can get away to relax since local resort hotels are always booked. Purchasing the home gives you flexibility to go sunning and swimming whenever. You are no longer at the mercy of hotels. Elasticity is value. Projects that let managers shift gears midstreamlike abandoning a project that will turn out badlyare worth a lot more than investments without this feature.

Traditional Methods Versus Real Options

Traditional methods such as net present value, internal rate of return, payback period, and so on will hardly be applauded by the board of directors

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if a particular spending program is important to the firm's continuing value. Consider these issues. A firm chooses between static input-output technology and one allowing for dynamic input-output substitution. This means that when conditions change, management modifies the (project's) key value drivers because uncertainties change expectations about the viability of a new technology and thus its explicit value.

If alternative strategies are cleanly quantified and reasoned out, management can make spending adjustments when technology is still in R&D stages. For this reason option value rejuvenates in its own space-time and is thus a much better technique than traditional measures we have been using out of habit. Remember that net-present-value analysis disregards opportunities to alter the game plan and consequently undervalues projects that are explicitly elastic. As we can see in the following example, this is precisely what happened to the CFO at New Technologies as he worked up the numbers dealing with the firm's important, groundbreaking project.

New Technologies has drawn blueprints for a CD-Recordable disk that operates twice as fast as existing models. Production requirements call for significant outlays, drawing cash flow from alternative high-tech projects. The CD project can start now or nine months hence, keeping in mind that deferred investments can find themselves in deep trouble if alternative projects rival for the available cash flows.

The CFO, unfamiliar with real options, called for traditional valuation (net present value, modified internal rate of return, and payback period). He failed to realize that traditional (valuation) methods could easily undervalue the project. Specifically, these methods are not set up to pinpoint (discount) rate/risk volatility implicit in the production and marketing of CD-Recordables, nor can these methods easily identify investment alternatives to alter cash flows. Furthermore, traditional methods ignore abandonment, switching, and sequencing options that are indespensable to planning this pivotal and strategic product.

Without proper decision-making tools, the firm's CFO not only will kill the project out of hand but is destined to open doors to competitors with foresight enough to employ real options analysis. Our CFO, like managers who otherwise feel comfortable trading financial options, could not (or did not want to) perceive the tie between financial and real options. Market options are a known entity; their terms are clearly stated. Real options deal with subliminal corporate issues, complicated by real-world peculiarities and involving more than a few layers of uncertainty.

The Binomial Model

A quick review of the CoxRubinstein binomial model will help you understand what are termed "implied binomial trees." This important option-pricing model was developed using a similar approach to

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BlackScholes, except here the underlying asset follows a binomial distribution. The benefit of the binomial model is that it can be used to evaluate options with an American-style exercise, relevant in our study of real options because we use the binomial distribution to value capital expansion strategies. Since American options can be exercised at any time prior to maturity, they are more valuable than their European counterparts that allow exercise only on the expiration date.

The binomial model works by dividing the time to expiration into specified time intervals. Over each time period, the price of the underlying contract moves either up or down using a specified probability, thus producing a binomial distribution for the price of the underlying asset. This distribution generates a recombining lattice or tree of underlying prices. Each of these prices combines with their respective probabilities to calculate a fair option value. Being able to value the option at each point on the tree, you can determine whether you should exercise before the option expires.

Implied Binomial Tree

A progression of prices for the asset underlying the options with different strike prices starts with the asset's current price and evolves period by period through a bifurcation process. The locations of the nodes of the tree conform to the relationship between the options' implied volatility and strike prices. The implied binomial tree is interpreted as the expected or implied probability distribution of the underlying asset (see Exhibit 31).

The principal defect of a single-period binomial option pricing model is overcome by extending it through a number periods (as shown in

Exhibit 31.
A multiple-period binomial model.

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Exhibit 31) by constructing a recombining binomial tree of asset prices working forward from the present. One path through the tree represents a single sample drawn from the universe of possible future outcomes. The current option value is then calculated by inverting this process and working backward from the end of the tree, being careful at each node to consider the possibility of early exercise.

When you determine the value of options, you require specific information. This information differs from that required for, say, a net present or interval rate of return analysis (see Table 31). Real options differ from financial options (see Table 32).

Real Options:
Definitions, Examples, and Case Studies

Abandonment Options

Firms usually close up projects that destroy value. We recognize the discretionary strategy as abandonment, or termination, options. Abandonment options are similar to American puts giving the holder the right to sell (the project's) cash flows at any time over its remaining life for a determinable

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salvage value The decision to exercise abandonment options or to let them expire is directly influenced by spreads between the asset's liquidation and its ongoing cash flow value; the greater the spread, the greater the temptation to pull out.

Abandonment options form an integral part of the analysis of large capital-intensive projects such as mining, pipelines and aircraft, and investments associated with product introductions in an uncertain marketplace. A copper mine may decide at any time to cease operation at a particular location. Before making a decision to mothball the operation, management might consider the following issues:

· Potential environmental liability associated with closing a mine. Environmental protection laws tie directly into expected values of related projects. Thus, management will exercise (abandonment) put options to avoid potentially substantial liability, but they need to quantify the contingency's expected value. Obviously, mining firms are quite familiar with environmental guidelines and risks, and they take advantage of this knowledge by utilizing dynamic option analysis. A recent case in point:

A Federal District Court in West Virginia found late in 1999 that clean water and surface mining laws were being violated in the blocking of hundreds of miles of streams by rock waste dumped into nearby valleys during the strip mining of mountaintops. The technique involves shearing the mountaintops with explosives to get at the underlying low-sulfur coal, with mining wastes bull-dozed into surrounding valleys.

The court ordered the authorities to curb much of the waste dumping to protect vital waterways. Also, the court found that state regulators had loosely interpreted environmental law to allow the waste dumping in vital streams that flow much of the year and are supposed to be protected by buffer zones. Under a valley fill, the water quality of the stream becomes zero. Because there is no stream, there is no water quality. The end result was grinding a local industry to a virtual halt. In carrying out the ruling, only 3 of 62 previous mountaintop mining projects could go forward.

· Leases. It is important to accurately appraise landowner leases and any ongoing liabilities.

· Maintenance requirements. The costs of decommissioning can be greatly reduced if a mining firm accepts ongoing maintenance responsibility. This being the case, what role (and weight) will maintenance commitments have on abandonment option value?

· Return to service and associated values linked to reactivation. If there is any chance that the mine might return to service, management will organize maintenance of mining equipment, elevators, and tracks. The goal to minimize recommissioning costs.

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Regarding the final issue, let's look at an example. Felise Toys plans to introduce a new line of preteen games. To simplify matters, assume that the project has a two-year life. An initial investment of $70 million (cash flows in millions) is required to fund a one-year-long development phase. At the end of the year, a further $75 million investment will be needed for production. Cash sales (net of selling expenses) are expected at the end of the second year.

There is some uncertainty about cash inflows since it is unclear whether the market will embrace the new games. Management believes that there is an 80% chance the games will succeed. They also believe that the demand pattern will become clearer over the next year. Moreover, they believe that there is a 70% probability that the demand direction established over the next year will continue in the subsequent year. Required return is 11%.

As can be seen from the binomial distribution tree shown in Table 33 and Exhibit 32, there are a total of four probable outcomes (shown as the four nodes on the right side of the diagram). If the games catch on, the best-case scenario in year 2 puts cash flow at $240 million, while the worst case (within the successful scenario year 2) results in $140 million cash flow. If the toy fails, the highest cash flow possible in year 2 is only $80 million, but losses (the worst case in the failure scenario) could be as high as $130 million.

If Felise Toys uses the net-present-value method, the project returns E(NPV) = (12.1) million. The project is rejected out of hand since the present value of inflows minus original investment outlays is negative:

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Exhibit 32.
Project cash flows.

Because both investments occur at time 2, they are discounted at the same rate, 1.11.

Now suppose that the firm has the option to abandon the project after the first year. In this case, the second phase of the project would proceed only if the market direction were favorable over the first year. If unfavorable, management abandons the investment since moving forward costs an additional $75 and the expected present value (at time period 1) of the cash inflows are (0.3 × 80 + 0.7 × 130)/1.11, or (60.36).

Now consider the option to abandon. The expected NPV is as follows:

The expected net present value is positive; the project should proceed. What is the value of having the flexibility to make the investment decision next year rather than having to invest either now or never? The option's

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value is the difference between the two NPVs, or $12.30 less $12.09, or $24.39. You can infer that the firm would be willing to pay $24.39 more for the opportunity to invest either now or next year versus now or never. In real option space-time, the project is as shown in Exhibit 32.

Shutdown Options

Shutdown options are almost identical to abandonment options, except the firm expects to restart production if conditions become favorable. It may not be feasible to operate a plant if revenues fail to justify costs. For example, if oil prices fall below extraction costs, it might be practical to close down until the price recovers. Shutdown options are valuable assets in agribusiness whereby options are exercised if growing and harvesting costs exceed revenues.

Operating Scale Options

These options give the holder the right (flexibility) to expand or scale down operations, for example, the right to expand production under favorable conditions, such as excess capacity. The ''put" side can be exercised by forgoing future expenditures. This would indicate contracting operations or the project itself. The (put) option can be quite valuable.

Option to Expand Operations

Plant capacity can accumulate incrementally or in large blocks. One large facility might be constructed or several smaller ones assembled-depending on the timing and magnitude of future demand. For example, a key factor is often economies of scale. One large facility might cost less than four times that of four smaller facilities, each producing one-quarter the output of the big plant. For example, at Happy Doll Industries, revenues from a "dancing doll" may increase exponentially or move in the opposite direction, depending on the nature, timing, and demand of, say, the "happy doll fad."

While Happy Doll Enterprises cannot be sure exactly how sales will track, management is confident that plant expansion is the correct strategy. Two options are available: (1) begin with a small expansion program, building up capacity slowly; and (2) invest in large-scale production right then and there. If Happy starts small, the firm implicitly holds valuable options since large-scale facilities require substantial financing before the first sales dollar appears. High debt levels increase financial risk, which might block addition funding, just when it is needed most. As leverage jumps, funds are redirected away from investment activities to service debt, cannibalizing operating cash flows.

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Real options fit the bill nicely. If demand picks up, the option to expand can be exercised. If demand drops off, the option is out of the money, and so management will not exercise the option. If Happy Doll builds a large facility immediately, all options are exercised at once.

The way to go on this: A binomial tree systematizes the array in space-time by quantifying the trade-off between revenues resulting from immediate expansion (the tree's upper space) and reduced expected losses associated with slower expansion rates (referred to as operating leverage risk in the finance literature). Thus, real options has defined the optimal strategy. A conservative expansion strategy maximized the value associated with an immediate large-scale investment.

Contractual Options

These options contain specific contract terms that change the risk profile faced by asset owners. For example, venture capitalists frequently include contract terms that give them priority in liquidation (downside protection) and rights to invest alongside follow-on investors (protection against dilution of the upside potential).

Switching Options

The most general situationoptions giving the holder the right to either expand or contract is analogous to a portfolio of puts and calls. Restarting production when facilities are currently shut down is a call option, while shutting down an on-line facility is a put. Projects that can be dynamically turned on and off are more valuable than identical ones without switching elasticity. Perhaps management may elect to build a facility at reduced (initial) construction costs carrying higher maintenance in order to acquire the flexibility to scale down maintenance if sales fall below projections.

Here is an example. AppNetworks Corp. must construct a new facility to produce portable hard drives able to plug into PCMCIA slots of laptops. Sales projections show a highly uncertain market that is spread across three geographic areas. A NPV approach indicated that two production facilities would cost less to build and operate. However, much higher yields result if three plants are constructed, one at each location, thus creating an option to switch production as needed.

Learning Options

The firm invests to learn more about technology or resources. Oil and Gas Development Corp. is engaged in the exploration, development, and production of oil and gas, primarily in the Southwest. To finance

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these activities, the company sponsors its own private placement drilling programs through a network of third-party brokerdealers nationwide. On behalf of these programs, the company performs all services relating to the subject properties from the acquisition of leasehold through the marketing production. Income from this process is earned from drilling the subject wells, operating the well, and the sale of the hydrocarbon production.

The company also owns and operates a natural gas gathering and transmission company. The firm enjoys rights to various oil and gas fields without knowing exactly how many resources they contains. Rather than trying to predetermine a particular level of production capacity, management allocates funds to measure the actual extent of the reserves. It then develops the field without wasting resources by building facilities to process more natural resources than is actually there. Alternatively, management is willing to defer profits by holding back operations for fear of depleting reserves that actually hold more oil and gas than the firm realizes.

Sequencing or Compound Options

These options, when exercised, create other options; that is, compound options involve sequenced investments. Completing one project provides management with the right to make a second investment, which in turn confers the right to make a third and so on.

Sequencing projects remains an important corporate strategy. To illustrate, successful marketing of consumer products may be tied to brand-name recognition. Suppose that a firm produces consumer products whereby the success of the first line leads to production of a second and so on. Brand recognition builds naturally. It is smart to implement the projects sequentially rather than side by side because by pursuing development of a single product, the firm resolves uncertainty surrounding its ability to establish brand identity. Once management confirms the first product's success, they can exercise the option to develop the next one. Thus, by producing a series of related (and dependent) products at once, management has already spent financial resources, and the value of the option not to spend is lost.

Option to Begin or Forgo Investment

Some projects are engineered in such a way that production starts in later periods or, if events make production infeasible, work is canceled altogether. The right to cancel or shrink production is equivalent to exercising a put option. Projects carrying these options are worth more. Let's see how Dix Gauge worked the numbers.

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Case Study:
Option to Begin or Forgo Investment
Determining the Feasibility and Value of New Technology¹

Dix Gauge Corporation produces high-end digital thermometer and thermostats, the only digital sensor that can maintain an accuracy of ±2°C throughout the 3V to 5V power range. By combining economies of scale and cost without sacrificing digital accuracy and flexibility, the firm provides premium thermal management in space-and weight-constrained applications.

Applications for the product include disk drives in PCs, servers, and workstations; environmental and biomedical diagnostic equipment; hand-held instruments, such as cellular telephones; or any thermally sensitive, electronically controlled system.

The firm's growth plans call for greater presence in the biomedical diagnostics market, a highly competitive environment. Development of a new type of thermal laser sensor is on the drawing boards. To keep the case simple, let's assume that the thermal laser can be evaluated in a single trials phase so that we can lower the range of possible outcomes. Once understood, the approach and calculations are easy to extend to as many phases and outcomes as are appropriate. [CD:MODELS/EXCEL/C3DGCaseSim/ScenOne]

Let's also assume that the company contemplates an R&D project with an initial research phase followed by a development phase. Suppose that the company is contemplating an R&D project with an initial research phase followed by a development phase. Initial research costs $1.4 million, takes a year, and has three possible outcomes, each with a degree of probability that can be extrapolated from similar research projects in the past. The chance of creating a highly effective laser sensor (or one that will be used widely) is 9%, a moderately effective laser sensor (or one with a narrower range of uses) is also 9%, and no laser sensor production at all is 80%. If researchers come up with a new laser sensor, the project will enter the developmental phase, also lasting a year, at a cost of $4 million. There are two possible outcomes at this juncture: The laser sensor will either pass the safety tests (40% probability) or fail them (60% probability). (In a more complex example, the company might have the option of accelerating the test phase, perhaps in response to competitive pressure, by laying out more money.)

Should the laser sensor pass the safety tests, it can be marketed. The company estimates that a highly effective laser sensor would reap annual revenues of $18.5 million. For the sake of simplicity, assume that this would continue in perpetuity and that the company's risk adjusted cost of capital is 9.5% (real options have not been employed yet, so management cannot argue for an interest rate reduction associated with lower project risk). The

¹ This case was thoroughly reworked and expanded, and original spreadsheets were developed. My inspiration came from an excellent short example titled "R&D in pharmaceuticals," Thomas E. Copeland and Philip T. Keenan, appearing in "Making Real Options Real," The McKinsey Quarterly, no. 3 (1998).

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project has a present value of $194.7 million at the start of the marketing phase: We'll examine four phases of analysis covering ground from naive NPVdecision tree analysis all the way to real options incorporating Monte Carlo simulations (see Table 34).

Analysis Phase 1
Expected NPVDecision Tree Analysis:
Most Likely Scenario

Should the company go ahead with the project? Not yet aware of real options, management works out traditional approaches: NPV and decision trees. Realizing that the problem is too complex for a single-scenario NPV calculation, management computes several scenarios. For a great product, the expected NPV is $52.3 million (see Table 34) since cash flows (before discounting at the 9.5% cost of capital) are minus $1.4 million in year 0, minus $4 million in year 1, and $194.7 million less $126 million in year 2.

Using the same analysis, a moderately effective laser sensor would generate income of $13 million and have a present value of $136.8 million. Needless to say, all these revenues lie at least two years in the future and are thus uncertain. The marketing department suggests that a great product might generate annual revenues ranging from $16 million to $20.3 million and a mediocre one from $11.7 million to $14.3 million. Building a factory to produce the laser sensor will cost about $127 million (see Table 35).

For a mediocre product, the expected NPV is $113.6 thousand (see Table 35). Then again, there could be no product at all, which would generate a present

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value loss of $1.4, or an NPV of minus 1.1 million, depending on whether the company carried the project into the development phase (see Table 3-6).

Next, the company combines these scenarios into a single probability-weighted NPV by drawing a decision tree (see Exhibit 33). There is a 3.6% chance (9% in the research phase times 40% in the development phase) of creating a great product with an NPV of $52.3 million and a 4% chance of creating a mediocre product with an NPV of $3.2 million. The chance that the research will be an utter failure costing the company $1.4 million is 80%.

Finally, the project has a 13% chance of running aground during the development phase, for a present value loss of $5 million, throwing off a weighted ($656.8) thousand NPV (see Table 37).

Thus, the overall value of the R&D project, calculated with decision trees directed at a probability-weighted NPV, comes to $218.5 thousand. The individual completing the analysis recommended that the firm move forward and develop the project (see Table 38).

Analysis Phase 2
Expected NPV:
Run Monte Carlo Simulations

(We will study Monte Carlo simulations in chapter 7. For now, we will run the tests and accept the conclusions.)

The CFO was not at all satisfied that the previous analysis went far enough. The probability-weighted NPV was close to breakeven, leaving very little room for error. Senior management wanted simulations run and will not proceed until important issues dealing with uncertainty were put to rest.

The standard forecasting model outlined previously relied on a set of assumptions leading to only one-outcome: the base case. The project is

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Exhibit 33.
The project's decision tree analysis: Phase 1.

complicated; an analysis cannot proceed to real options until the firm runs Monte Carlo simulations centered around at least two different assumption variables: projected income under very successful product conditions and projected income under moderately successful product conditions. In short, it is exceedingly difficult to know which strategic options the firm should pursue since we do not yet know the ranges and distributions of outcomes and the most likely scenario associated with each optiongo/no go (see Tables 39 to 312).

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Recall from scenario 1 that the probability-weighted NPV was $218.5 thousand, which was-close to breakeven. But what a week approach scenario 1 is! The CFO is concerned more with defining the probabilities of losses, lest the project be selected in a categorically restricted and blind spacetime. As the Monte Carlo simulation shows a 63% probability of losses with certainty range ($700,000) to $500,000. Ordinarily, these results suggest that the firm should not undertake the initial research phase by investing $1.4 million.

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Analysis Phase 3
Real Options Analysis

[CD:MODELS/EXCEL/C3CaseSim/RealOption]

A real options analysis conducted without the benefit of Monte Carlo simulation places its value at $3.9 million. This suggests that the company should (1) undertake the initial research phase by investing $1.4 million and (2) take a wait-and-see position until the expiration date of their option a year from today. If conditions are favorable, the firm will exercise their options to invest further in the project. If conditions are unfavorable, the firm produces no digital sensors. Setting up the option, we note the information given in Table 313.

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The real option valuation is so much higher than that arrived at through a decision tree or probability-weighted NPV that it changes the recommendation from no go to go. There are several reasons for this.

First, real option valuation maps out all available possibilities, including those not readily apparent in the decision tree. Although there are two important sources of uncertainty, technological and product market, tradi-

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tional analysis focuses solely on the former, ignoring the latter by focusing too narrowly on the expected value of cash flows. As we saw, the real option valuation takes into account an important element of flexibility: the possibility of not marketing the laser sensor, even if it passes the safety testing phase, should the revised product market outlook seem gloomy. The higher the uncertainty surrounding potential cash flows, the higher the real option valuation. Traditional approaches ignore this kind of uncertainty and management's ability to respond to it.

Also, real option valuation differs from the one arrived at through a decision by varying the discount rate appropriately throughout the tree instead of using a single rate, such as the weighted average cost of capital. Thus, it accounts properly for the relative level of risk that different cash flows involve. Where real options represent substantial leverage, this impact on the discount rate may be enormous; not the difference between 9% and 12% but rather between 9% and 40% (or minus 40%, depending on the nature of the option).

Moreover by varying the discount rate appropriately throughout the binomial tree instead of using a single rate, such as the WACC (weighted-average cost of capital), a real option valuation differs from a traditional technique valuation (NPV, IRR, MIRR). Thus, a real option valuation accounts properly for the relative level of risk that different cash flows involve. Where real options represent substantial leverage is where the volatility of the discount rate may be enormous, reflected not in the difference between 9% and 12% but rather the difference between 9% and 40% (or minus 40% depending on the nature of the option).

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Thus, real option valuation identifies the optimal course for the company at each stage in the process. The initial recommendation is to undertake the research at a cost of $1.4 million. If the research fails, there is no development phase. The company in a sense exercises its put option on further development. Even if the research succeeds, the real option valuation demonstrates that it is sometimes unwise to proceed with development, particularly if the laser sensor in question is a mediocre one and the revised market forecast for the coming year is less optimistic than originally expected. Should the development phase proceed successfully, it is still not always wise to market a laser sensor, for when forecasts turn pessimistic, even a great laser sensor may not cover its costs. By factoring in all alternatives appropriately, the real option approach uncovers additional value that can change recommendations for projects at several stages in their evolution.

Summary, Analysis Phase 3:
Real Options Analysis

Tables 314 to 319 summarize this phase.

Analysis Phase 4
Real Options Analysis Running Monte Carlo Monte Carlo Simulations
[CD:MODELS/EXCEL/C3CaseSim/Phase4Sim]

Table 320 depicts Phase 4 simulation assumption variables.

Assume that the firm exercised its one-year option to begin or forgo investment in this project. A real option and Monte Carlo simulation analysis completed by Crystal Ball would certainty call for a ''move forward" decision. Why? The certainty level at a 95% confidence reveals that the expected NPV range is from $2.1 million to $5.3 million. The entire range is from $1.5 million to $6.4 million (see Table 321).

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Closing Thoughts

Management's ability to alter future action in response to changing market conditions can profoundly affect the decision to invest since investment opportunities are collections of options on real assets. Remarkably, real option value and equity value fit as needle and thread because capital projects are, in many industries, a firm's most important value driver.

Without real options analysis, management forgoes the chance to evaluate (new) information that might change investment strategies. Lost information is an opportunity cost that has to be considered when investments are valued.

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Finally, as technology unfolds at an increasing rate with an increasingly large number of firms focused on returns to the providers of capital, management will take a new hard look at shareholder value and how the number was derived. CFOs, CEOs, and the board want visionary analytics, not old standard bearers delivering this number. Thus, real options have come of age and are no longer looked on as just another business school theory.

So far, we have developed capital investment analysis using two mediums: the vernacular (Word) with help from Excel, a wonderful but

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flat two-dimensional model. We leave this chapter with our analyses stuck between two insentient, inorganic environments no matter how brilliant the result may appear. Real options are indeed real; they operate in a kinetic, dynamic medium. For that reason, we will transport project analysis from flat-plane, two-dimensional space to higher-dimension real time-visual modeling.

Chapter Three
References and Selected Readings

Books and Periodicals

Amram, M., and N. Kulatilaka. (1999). "Real options: Managing strategic investment in an uncertain world." Financial Management Association survey and synthesis series. Boston: Harvard Business School Press, x, 246. Campbell R., C. Harvey, and S. Gray. "International project evaluation, real options and mergers and acquisitions." Global Financial Management.

Chan-Lau, J. A., et al. (1998). "Fixed investment and capital flows: A real options approach." Washington, D.C.: International Monetary Fund Research Department.

Childs, P. D., et al. (1998). "Capital budgeting for interrelated projects: A real options approach." Journal of Financial and Quantitative Analysis, 30534.

Cortazar, G., and J. Casassus. (1998). "Optimal timing of a mine expansion: Implementing a real options model." Quarterly Review of Economics and Finance (Special Issue), 75569.

Davis, G. A. (1998). "Estimating volatility and dividend yields when valuing real options to invest or abandon." Quarterly Review of Economics and Finance (Special Issue), 72554.

Luehrman, T. A. (1998). "Investment opportunities as real options: Getting started on the numbers." Harvard Business Review, 5167.
Here's a way to apply option pricing to strategic decisions without hiring an army of Ph.D.'s.

Luehrman, T. A. (1998). "Strategy as a portfolio of real options." Harvard Business Review, 8999.

Neely, J. E. (1998). "Improving the valuation of research and development: A composite of real options, decision analysis and benefit valuation frameworks."

Pinches, G. E., and D. M. Lander (1998). "Challenges to the practical implementation of modeling and valuing real options." Quarterly Review of Economics and Finance (Special Issue), 53767.

Rose, S. (1998). "Valuation of interacting real options in a tollroad infrastructure project." Quarterly Review of Economics and Finance (Special Issue), 71123.

Sanchez, R. A. (1991). "Strategic flexibility, real options, and product-based strategy."

Sick, G., et al. (1990). Capital budgeting with real options. New York: Salomon Brothers Center for the Study of Financial Institutions, Leonard N. Stern School of Business, New York University.

Trigeorgis, L. (1995). Real options in capital investment: Models, strategies, and applications. Westport, Conn.: Praeger.

Trigeorgis, L. (1996). Real options: Managerial flexibility and strategy in resource allocation. Cambridge: MIT Press.

Williams, J. T. (1993). "Equilibrium and options on real assets." Review of Financial Studies, 82550.

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Other Periodicals

Alleman, James. (1999). "Real options: Management flexibility and strategy in resource allocation." Information Economics and Policy, 11(2), 229.

Alvarez, Luis H. R. (1999). "Optimal exit and valuation under demand uncertainty: A real options approach." European Journal of Operational Research, 114(2), 320.

Anonymous. (1998). "Capital investmentA new approach." Management Accounting, 76(5), 28.

Anonymous. (1999). "Survival: The very real option." Professional Engineering, 12(6), 57.

Benaroch, Michel. (1999). "A case for using real options pricing analysis to evaluate information technology project investments." Information Systems Research, 10(1), 70.

Bollen, Nicholas B. P. (1999). "Real options and product life cycles." Management Science, 45(5), 670.

Cortazar, Gonzalo. (1998). "Optimal timing of a mine expansion: Implementing a real options model." Quarterly Review of Economics and Finance, 38, 755.

Coy, Peter. (1999). "Exploiting uncertainty; The 'real-options' revolution in decision-making." Business Week, June 7, p. 118, Industrial/Technology edition.

Dangl, Thomas. (1999). "Investment and capacity choice under uncertain demand." European Journal of Operational Research, 117(3), 415.

Esty, Benjamin C. (1999). "Improving techniques for valuing large-scale projects." Journal of Project Finance, 5(1), 9.

Garud, Raghu. (1998). "Real options or fool's gold? Perspective makes the difference." The Academy of Management Review, 23(2), 212.

Herath, Hemantha S. B. (1999). "Economic analysis of R&D projects: An options approach." The Engineering Economist, 44(1), 1.

Jagle, Axel J. (1999). "Shareholder value, real options, and innovation in technology-intensive companies." R & D Management, 29(3), 271.

Kensinger, John. (1999). "International investment-Value creation and appraisal: A real options approach." Journal of Finance, 54(6), 2387.

Kingley, Jay. (1999). "Six steps to exercising real options at work." 12(17), 52.

Leslie, Keith, (1998). "The real power of real options." Corporate Finance (158), 13.

Mayo, H. (1999). "Real options: Managing strategic investments, in an uncertain world." Choice, 36(10), 1833.

McGrath, Rita Gunther. (1998). "Only fools rush in? Using real options reasoning to inform the theory of technology strategy: Response to Garud, Kumaraswamy, and Nayyar." The Academy of Management Review, 23(2), 214.

Panayi, Sylvia. (1998). "Multi-stage real options: The cases of information technology infrastructure and international bank expansion." Quarterly Review of Economics and Finance, 38, 675.

Perlitz, Manfred. (1999). "Real options valuation: The new frontier in R&D project evaluation?" R & D Management, 29(3), 255.

Rose, Simone. (1998). "Valuation of interacting real options in a tollroad infrastructure project." Quarterly Review of Economics and Finance, 38, 711.

Select Internet Library

Real Options: Others Classical Papers
The following selection complements the "Real Options Classical Papers" list and also contributed with important insights into real options approach. There are comments, for each paper, available by clicking their titles (under construction). The papers in this page are in chronological order. http://www.puc-rio.br/marco.ind/non-tabl/bib_cla2.html.

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Finance Site List
These Web links are placed here for those interested in understanding and teaching financial ideas. The Journal of Finance maintains the site. http://www.cob.ohio-state.edu/dept/fin/journal/jofsites.htm.

Real Options Group
NIAS/Royal Netherlands Academy of Arts and Sciences Bocconi University, Univer-sity of Calgary, Erasmus University, Northwestern University Last Updated: May 17, 1999 http://www.realoptions.org/.

Real Options Bibliography
The following publications provide a good introduction to the theory and application of real options thinking. Admittedly, some is rather esoteric, but most is accessible to nonspecialists. (Notes: Registration is required to access the McKinsey Quarterly; PDF files require Acrobat Reader software.) http://www.modus-group.com/realoptionbiblio.htm.

The Real Options Contributions Page!
This page is dedicated to contributions from the readers. Working papers, abstracts, dissertations, comments of papers, multimedia materials, and so on, related to real options approach (even if is not petroleum specific). http://www-rpa.puc-rio.br/marco.ind/contribl.html.

Real Options Softwares Webpage
I divided the real options software into three groups: (1) Spreadsheet applications, market currently dominated by Excel; (2) mathematical softwares applications, such as Mathcad, Mathematica Matlab, and Mapple; and (3) computer programming lan-guages, for more professional applications, with highlights for C++ and Java. http://www-rpa.puc-rio.br/marco.ind/software.html.

A Case for Using Real Options Pricing Analysis to Evaluate Information Technology
Project Investments http://sominfo.syr.edu/facstaff/mbenaroc/resume/PAPERS/OPM-ISR/WWW-PAPR.html.

CD

Name

Size

Type

C3DGBaseSim

229KB

Microsoft Excel Worksheet

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Chapter Four
Visual Financial Models

Recently, the profileration of finance technology has been enomous. A few short years from now, our perceptions will not have changed, but "explosion" will be the proper word, not "profileration." Corporate valuation analysis and the spreadsheet will have since parted company; visual modeling will be the lead tool showing CEOs and board members the way through value gap analytics, and office computers will accommodate one or two gigabytes of memory, at most, having been made obsolete by the live wire. And the Web and Internet will go unmatched as the sustaining force behind a new brand of technologic science that we will come to know as finance.

Todaystill, a good assortment of models can dissect and evaluate deals and financial problemssome assorted other corporate assignments, some quite complicated. But few models loaded on our workstations or graduate school computers are capable of offering an optimal architecture for, say, the completion of a divisional "make or break" restructuring analysis or an acquisition/divestiture position paper up for review by the CFO or board. In truth, modern visual modeling, not rows and columns, may well be the vehicle of choice to get the deal structured, understood, and above all sold. So the question we might ask is, "Can your software handle the firm's voluminous data and its dynamic environment?" Often not, unless you work with nonlinear models. Linear models have been in use a long time with little empirical testing of their inherent, internal two-dimensional structure. The result is that they force linearity assumptions on nonlinear data.

As an analogy, imagine a two-dimensional world with mythical two-dimensional people called Flatpeople. To keep their children from straying from a playground, Flatpeople simply draw a circle around them. No

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matter which way the children move, they hit the impenetrable circle. However, it is a trival task for us to spring the children from the playground.¹ We just reach down, grab the flat children, peel them off their two-dimensional world, and redeposit them elsewhere on their world. To other children, it appears as though one of them has mysteriously vanished into thin air. This feat, quite ordinary in three dimensions, appears fantastic in two dimensions. Most of our cash flow projections, valuations, and inventory optimization methods have been living in "flat" linear dependence almost since finance was invented.

You may have run across valuation problems that you attemped to puzzle out with "a straight line," for example, working the deal under the assumption that variable coefficients are stable over time. Straight lines in our corporate valuations are left in illusional two-dimensional space, like the Flatpeople's playgroundparallelism does not exist in real world business, certainly not in financial analysis. When global influences change, as they must every day, the coefficients of your models must be trained to incorporate that change, or any problem resting on your model's forecast will itself be flawed. Let's investigate, first, a two-dimensional representation: the spreadsheet. From there, we will explore visual modeling.

Background

A modeling application is any tool that helps analysts collect, analyze, and present information, often in an interactive and iterative way. Models help determine the impact of alternative strategies on the operating unit or firm's valuethe least common denominator. For example, CFOs often use financial models to:

· Test the relative risk of a corporate buyout

· Determine equity values given the dynamic nature of value drivers

· Asess debt structures and develop priorities for debt repayment.

· Refine working capital policy.

Financial models usually consists of six components: navigation, data entry, data analysis, calculation, reports and presentations, and storage.

Navigation

This capability allows modelers to move around the model's different parts. It may consist of menus, buttons, toolbars, and wizards and on-line help. These engines vary from very tightly controlled, forcing the analyst

¹ Thank you Dr. Kaku for your wonderful analogy. MICHIO KAKU, HYPERSPACE, a Scientific Odyssey through Parallel Universes, time warps and the Tenth Dimension, Oxford University Press, 1994.

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through set paths, to very open, offering a good deal of freedom. The sophistication of analysts, together with its proposed use, determines which type of navigation mechanism is best.

Data Entry

This is the part of the application into which data (assumptions, numbers, and options) can be entered.

Data Analysis

Very often, interactive analysis is supported as well. This is the ability to immediately see how the input affects the results, often referred to as "what-if" analysis. The calculation engine described next makes this possible.

Calculation

This is where the model implements financial rules. These rules are typically represented by formulas, macros, and processes that operate on the inputs to come up with the best results. The important issue is one of integrity and incorruptibility. For example, flexible spreadsheet models such as Excel allow developers almost total freedom in writing formulas. This is fine for basic models.

However, complex models, models for policy analysis or models that determine equity values are much too important to "fiddle" around with the model's nuclear structure. That is why technology delivered by vendors such as Decisioneering, MATLAB, ALCAR, Mathematica, and particularly the visual modeling base that Lumina offers (plus a host of other reputable developers) have won the support of financial decision makersyou cannot afford to engage your CFO or board questioning a valuation model's structure and integrity.

Reports and Presentations

This is output either printed or viewed on-screen. This may take the form of tables, charts and multidimensional graphs, visual diagrams, and various combinations thereof.

Storage

This is where data are stored for further implementation. Templates are made whereby input values are entered later.

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Team Effort

Modeling is a team effort and requires good communication. Intricate models that are organized by one or two staff members, no matter how talented, may not escape errors, particularly if the original developer is too close to the problem. Poorly structured models or the infamous black box serve no one.

Although software may produce spectacular results in the hands of a skilled analyst, it can also produce spectacular garbage of extraordinary complexity in the hands of an incompetent or careless analyst. The saving grace of such tools is that, if they make it easier to exercise, scrutinize, audit, and critique models, they can facilitate peer review and open debate about policy models, providing a powerful mechanism for improving standards of practice.²

Building Effective Models³

The best financial models are clear, comprehensible, and correct. The key to producing a powerful design is to start with a basic format and progressively refine and extend your model where tests of your initial versions point to improvements. Remember that the whole idea of financial modeling is to help you discover which options will optimize your objectives and the financial assignment you have been asked to complete. How can you go about developing an accomplished and skillful model?

First, identify key decision variables. A decision variable is a variable that you affect directly: which industry to seek an acquisition, how much to bid on the contract, which accounts receivable policy is best, when to start new product marketing, and so on. Occasionally, financial analysts want to build a model just for the sake of furthering understanding, without explicitly considering decisions. Most often, however, the ultimate purpose is to make a better decision. In those cases, the decision variables are where you should start your model.

Next, identify your objectives. Sometimes the objective is simply to maximize expected profit or value, find the optimal financial mix, or minimize costs. Utility theory and multiattribute decision analysis provide an array of methods to help structure and quantify objectives in the form of utility. Whatever approach you take, it is important to represent the objectives in an explicit and quantifiable form if the objectives are to be the basis for recommending one decision option over another. The most common

² Lumina Decision System White Paper. The white paper on the Web site was written by M. Granger Morgan and Max Henrion. Referenced with permission, Lumina Decisions Systems.

³ The section was coauthored with Lumina Decision Systems, home to the Analytica product family and developed with permission. Analytica is the modeling system featured in this chapter.

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mistake in specifying objectives is to select objectives that are too narrow. You might want to think in terms of the smallest common denominatorstart small and build the model to the top. Do not start with the top and try to build down. For example, you will not start at headquarters and work your model down to the divisional level; rather, it is the other way around.

Next you focus on identifying the variables that make clear distinctionsvariables whose interpretations will not change with time or your boss. Extra effort here will be repaid in model accuracy and cogency. At this point, you begin to think about influence diagrams (more on influence diagrams when we actually learn to build our visual model). An influence diagram is a purely qualitative representation of a qualitative information path related to the model. It shows the variables and their dependencies. It is usually best to draw in most or all of the first version of your model as an influence diagram or hierarchy of diagrams before trying to quantify the values and relationships between the variables. In this way, you can concentrate on the essential qualitative issues of what variables to include before having to worry about the details of how to quantify the relationships.

Should you create a simple or an intricate visual model? Financial visual models should be as simple as possible but no simpler. When the model is intended to reflect the views and knowledge of a group of people, it is especially valuable to start by drawing up an influence diagram as a group. For example, a small group can sit around the computer. It is best if you have the means to project the image onto a large screen so that the entire group can see and comment on the diagram as they create it. The ability to focus on the qualitative structure initially lets you involve early in the process participants who might not have the time or interest to be involved in the detailed quantitative analysis, which will most certainly involve dozens of simulation distribution possibilities.

With this approach, you can often obtain valuable insights and early buy-in to the modeling process from key people who would not otherwise be available. Perhaps the most common mistake in modeling is to try to build a model that is too complicated or that is complicated in the wrong ways. Just because the situation you are modeling is complicated does not necessarily mean that your model should be complicated. Every model is unavoidably a simplification of reality; otherwise, it would not be a model. The question is not whether your model should be a simplification but rather how simple it should be. A large model requires more effort to build, takes longer to execute, is harder to test, and is more difficult to understand than a small model, and it may not even be more accurate.

Testing and Debugging a Model

It is rare to create the first draft of a model without mistakes. For example, on your first try, definitions may not express what you really intended. It

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is important to test and evaluate your model to make sure that it expresses what you have in mind. You should design the model specifically to make it as easy as possible to scrutinize model structures and dependencies, to explore model implications and behaviors, and to understand the reasons for them. We will set up our models in Analytica so that we can trust the algorithms. Accordingly, it is relatively easy to debug models once you have identified potential problems.

Test as You Build

You should evaluate variables once you have provided a definition for the variable and all the variables on which it depends, even if many other variables in the model remain to be defined. You should evaluate each variable as soon as you can, immediately after you have provided definitions for the relevant parts of the model. In this way, you will discover problems as soon as possible after specifying the definitions that may have caused them. You can then try to identify the cause and to fix the problem while the definitions are still fresh in your memory. Moreover, you will be less likely to repeat the mistake in other parts of the model. If you wait until you believe that you have completed the model before testing it, it may contain several errors that interact in confusing ways. Then you will have to search through much larger sections of the model to track them down. However, if you have already tested the model components independently, you will have already removed most of the errors, and it will usually be much easier to track down any that remain.

The best way to check that your model is well specified is to check it against reality. Compare its predictions against past empirical observations. For example, if you are trying to predict future changes in the composition of acid rain, you should try to compare its ''predictions" for past years for which you have empirical observations. Or, if you are trying to forecast the future profitability of an existing enterprise, you should first calibrate your model in past years for which accounting data are available. If the model is hard to test against reality in advance of using it and if the consequences of mistakes could be catastrophic, you can borrow a technique that NASA uses widely for the space program. You can get two independent modelers (or two modeling teams) to each build their own model, then check the models against each other. It is important that the modelers be independent and not discuss their work ahead of time to reduce the chance that both will make the same mistake. Test model behavior. Many problems become immediately obvious when you look at sensitivities and results, for example, if it has the wrong sign, the wrong order of magnitude, or the wrong dimensions.

Other problems, of course, are not immediately obvious, for example, if the value is wrong by only a few percentage points. For more thorough testing, it is often helpful to analyze the model behavior by specifying a list

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of alternative values for one or two key inputs. If the model behaves in an unexpected way, this may be a sign of some mistake in the specification. For example, suppose that you are modeling a project finance's real option solution and the net value increases with reduced cash flow. You might suspect a problem in the model.

If analyzing the behavior or sensitivities of your model creates unexpected behavior or unexpected results, there are logically two possibilities: Your model contains an error, in that it does not correctly express what you intended, or your expectations about how the model should behave were wrong.

You should first check the model carefully to make sure that it contains no errors and does indeed express what you intended. Explore the model to try to find out how it generates the unexpected results. If after thorough exploration you can find no mistake and the model persists in its unexpected behavior, do not despair! It may be that your assumptions were wrong in the first place. This discovery should be a cause for celebration rather than disappointment. If models always behaved exactly as expected, there would be little reason to build them. The most valuable insights come from models that behave counterintuitively. When you understand how their behavior arises, you can deepen your understanding and improve your intuition, which is, after all, a fundamental goal of modeling.

Document the Model

Give your variables and modules meaningful titles so that, as you build it, others (or you, when you revisit the model a year later) can more easily understand the model from looking at its variables. It is better to refer to your variable as "Capital Expenditures" rather than "see AD144."

It is also a good idea to document your model as you construct it by completing description and attributes for each variable and module. You may find that entering a line or two of description for each variable, explaining clearly what the variable represents, will help keep you clear about the model.

Entering units of measurement for each variable can help you avoid simple mistakes in model specification. Avoid the temptation to put documentation off until the end of the project, when you may run out of time or may have forgotten key aspects. Most models, once built, spend the majority of their lives being used and modified by people other than their original author. Clear and thorough documentation pays continuing dividends; a model is incomplete without it. Have other people review your model. It is often very helpful to have outside reviewers scrutinize your model. Experts with different views and experiences may have valuable comments and suggestions for improving it.

For example, one of the advantages of using a modeling environment such as Analytica over conventional systems is that it is usually possible

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for an expert in the domain to review the model directly, without additional paper documentation. The reviewer can scrutinize the diagrams, the variables, their definitions, and the behavior of the model electronically. You can share models electronically on diskette or over a network.

Expanding Your Model

The best way to develop a model of appropriate size is to start in stages with a very simple model and then to extend it in stages in those ways that appear to be most important. With this approach, you will have a usable model early on. Moreover, you can analyze the sensitivities of the simple model to find out where the key uncertainties and gaps are and use this to set priorities for expanding the model. If, instead, you try to create a large model from the start, you run the risk of running out of time or computer resources before you have anything usable, and you may end up putting much work into creating an elaborate module for an aspect of the problem that turns out to be of little importance. Remember to:

· Identify ways to expand the model.

· Identify ways to expand a model and improve the model.

· Add variables that you think will be important.

· Add objectives or criteria for evaluating outcomes.

· Expand the number of decision options specified for a decision variable or the number of possible outcomes for a discrete chance variable.

· Expand a single decision into two or more sequential decisions, with the later decision being made after more information is revealed.

· For a dynamic model, expand the time horizon (say, from 10 to 20 years) or reduce the time steps (say, from annual to quarterly time periods).

Visual Modeling

This is a new and comprehensive three-dimensional methodology that integrates visual programming into traditional spreadsheet. Visual modeling expands the dimensions of spreadsheets by reenineering its basic structure and providing stratums of reality. The methodology captures the enterprise's smallest components (e.g., the uncertainty surrounding inventory policy within an insubstantial operating division) and works the effect up through a series of influence diagrams all the way to the consolidated entityin a compelling way. Visual models are non-spreadsheet-based. This technology "envisions" real-world finance. Indeed, spreadsheets interface as they must, but in two dimensions, but the structure of visual models is optic, or three dimensional.

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Visual models are ideal for financial professionals who use spreadsheets for creating quantitative models "but find them hard to organize, maintain, expand, document, and explain to their colleagues, the firm's executives. Visual models are best for analysts who build large, multi-dimensional models and who find spreadsheets or other modeling packages inflexible and cumbersome. For the financial staff who are called on to work collaboratively, visual models offer connective interfaces of the model's elements and relationships that make possible a shared understanding among the team.

As software becomes more complex, the benefits of developing a comprehensive "blueprint" that enables financial developers to visualize the complete scope of a project increases substantially. Three elements are needed to successfully diagram and visualize a software system: a process, a notation, and a modeling tool.

Analytica:
The Nerve Center for Visual Modeling⁴

You are about to discover a new and powerful tool for real-world modeling and analysis. Analytica embodies the idea of using a white board for problem solving. Using a visual point-and-click approach, you draw nodes and arrows to depict the relationships between model components. This approach allows you to describe the essential qualitative nature of the problem without getting lost in the details. As the model develops and your understanding of the problem becomes more clear, you can define the exact quantitative details of the model.

A key feature of Analytica is its ability to create hierarchies of models. By grouping together related components of a problem into separate sub-models, you can impose a top-down organization to your model. This will help you manage complex relationships and allow other users to more easily grasp important concepts.

Another key feature of Analytica is the use of Intelligent ArraysTM. These enable you to add or remove dimensions, such as time periods, geographic regions, alternative decisions, and so on, with minimal changes to the model structure. Unlike spreadsheets, which require you to repeat formulas with each new dimension, Analytica separates the dimensions from the relationships so that models remain simple. As the dimensions change, Analytica automatically updates, reports, and graphs the results.

⁴ Analytica is a sophisticated modeling tool that uses influence diagrams to communicate the flow of information and harnesses the power of Intelligent ArraysTM to model complex problems. Analytica is a registered trademark of Lumina Decision Systems. Lumina Decision Systems, Analytica Decision Engine, and Intelligent Arrays are trademarks of Lumina Decision Systems. All others are trademarks of their respective companies.

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Each node in an Analytica model has a window that displays the node's inputs and outputs and allows you to enter definitions, descriptions, units of measure, and other documentary information. This self-documenting capability, combined with hierarchical models and Intelligent ArraysTM, makes it easier to understand and communicate how models work. Analytica also features fully integrated risk and sensitivity analysis for analyzing models with uncertain inputs; powerful facilities for time-dependent, dynamic simulations; comprehensive overlay graphs; and over 100 financial, statistical, and scientific functions for calculating just about any type of mathematical expression.

Visual modeling has expanded and will continue to branch into new areas of financial applications, particularly CFOs who are starting to use quantitative decision-support systems for important decisions affecting their firms' competitive positioning and shareholder value. The software hits home for financial professional and/or the firm's advisers who use spreadsheets for creating quantitative models but find them hard to organize, maintain, expand, document, and explain to their colleagues, clients, or managers. In addition, those working collaboratively, as we saw before, need a product that can produce graphical diagrams so as to share the model's elements and relationships among the team.

Financial consultants who build large, multidimensional models may find spreadsheets or other modeling packages inflexible and cumbersome. For example, consider a corporate restructuring. Here, data and analytics are comprehensive and elusive, often requiring a data breakdown into the tiniest operating component. Often these deals mean allocating cash flows down to the business-unit level, benchmarking comparable firms and using internal data. This is very difficult to accomplish using spreadsheets. Now let's put good theory to practice.

Comparing Spreadsheet Models with Visual Models

Despite the drawbacks discussed previously, few of us will question Excel's or Lotus 1-2-3's preeminence in modeling applications. Their spreadsheet formulas and calculation engines are the picture of smoothness as they work effortlessly through applications. Formulas are relatively easy to amend and understand, especially by nontechs. However, spreadsheets have that one additional weakness: documentation. The models themselvesrepresented in spreadsheets or in specialist modeling languagesare rarely suitable as a medium for communication. Spreadsheets operate in a restricted, one-medium environment; they cannot endure without help from support software. First, you create your model on a spreadsheetone medium. Your documentation is written in a second mediumthe word processorand finally your presentation is

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viewed in a third mediuma video show, again two-dimensional modeling, which often falls short when your problem calls for high levels of abstraction and intricacy.

For example, one firm was involved in an assessment of a global telecommunications venture. The firm's decision makers went to their consultants⁵ with a dozen workbooks, each containing 10 to 20 spreadsheets. Just loading all the project's workbooks took more than five minutes. In comparison, their consultants created a model in Analytica with identical functionality that was not only loaded and executed in seconds but fully extendible. The firm's consultants altered market segmentation, assessment time horizon, and the countries under reviewall in minutes rather than the hours, days, or even weeks required to retool the original voluminous spreadsheet models.

While the B&G spreadsheet stands a bit short of Herculean (see Exhibit 41), we can still retool it from being simply a portrayal of a picture to being the picture itself.

Visual Display of Model Structure with Influence Diagrams

Financial professionals communicate with each other all the time, and, when they do, they do not run first to open spreadsheets. At the first go-around meeting, say, to turn out a deal structure, team members will

⁵ Richard Sonnenblick, Ph.D., is president of Enrich Consulting, Inc., a Silicon Valley-based consulting organization that specializes in customized decision support systems built with Analytica.

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sketch out diagrams: lines, bubbles, arrows, assorted shapes, configurations, and sometimes even doodles. Just about every business application works through a visual context: flowcharts, semantic networks, entity-relationship diagrams, fault trees, decision trees, causal networks, belief networks, and systems-dynamics graphs.⁶ The concept of networks of system-dynamic graphs has maturated recently into a brand new technology: influence diagrams. This visual approach provides an especially intuitive and effective way to foster understanding of complex problems.

Influence diagrams constitute the essential core of visual modeling by providing a simple notation for creating and communicating models. This is accomplished by clarifying the qualitative issues of what factors need to be included and how these constituent connect to each other. An analyst can use influence diagrams when working alone, with a single decision maker, or with a group of interested people. Influence diagrams are comprehensible even to people not interested in the details of quantitative relationships. Later in the process, influence diagrams provide a simple intuitive representation for communicating the qualitative structure that reflects the underlying quantitative representations.⁷

When you open a model detail window or a model without input and output nodes, Analytica displays a Diagram window for the model. The Diagram window depicts the model as an influence diagram. An influence diagram is an intuitive graphical view of the structure of a model consisting of nodes and arrows. Each node depicts a variable or a module.

Lumina Decision Systems has provided the opportunity for you to work out the models, exercises and examples themselves. You and your support team are welcome to visit Lumina's web site and sign up for the free 30-day trial of Analytica without any obligation. The site is www.lumina.com. Readers who prefer not to download this model will learn as much by reading through the chapter and linking to pages on the Internet via the CD.

If you open Analytica open the Analytica model IncStatBasicl which is the influence diagram of B&G Corporation Income Statement (Exhibit 42).

A variable is any object that has a value or that can be evaluated. As seen in Exhibit 42, nodes with thin outlines depict variables. A module, with a thick outline, contains its own influence diagram. The arrows in a Diagram window depict the influences among the variables. An influence arrow from one variable to another means that the value of the first variable directly affects the value (or probability distribution).

When working with a group, it is helpful to involve the entire group early on in drawing up initial influence diagrams. The group may draw

⁶ Analytica White Paper (www.lumina.com).

⁷ Analytica White Paper.

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Exhibit 42.
Influence Diagram: B & G Corp. income statement.

diagrams on a physical white board or may use software, such as Analytica, and project the image of the diagram onto a large screen. The skilled analyst will facilitate the group first in structuring objectives and identifying key decision variables that may affect these objectives. Next, the analyst asks about how the decisions may influence the attainment of the objectives and elicits intermediate variables that mediate between the decisions and the objectives. The analyst may elicit this information by asking questions such as, "What other factors might affect these variables?"⁸

Nodes

Each node shape in a diagram represents a different class of objects. Here are the classes and their corresponding node shapes:

An oval node depicts a chance variable, that is, a variable that is uncertain and that the decision maker cannot control directly. A chance variable is usually defined by a probability distribution. For example, Sales are uncertain, falling into a specific range of possibilities.

A hexagonal node depicts an objective variable, that is, a quantity that evaluates the relative desirability of possible outcomes of combinations of decision and chance variables, in this example Profits. Most models should contain a single objective node, although the objective can comprise several subobjectives. A rounded, thick-outline node depicts a module, that is, a collection of nodes organized as a separate diagram. In this example,

⁸ Ibid.

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there are two modules: Cost of Goods Sold and Expenses. Modules can themselves contain nested modules.

A large model may have hundreds or even thousands of variables, far too many to show on a two-dimensional diagram. Analytica extends the traditional influence diagram notation with the addition of a module node. A module node opens up to another influence diagram, containing its own variables and modules, as shown in Exhibit 42. Using modules, you can organize the B&G model into a three-dimensional hierarchy of modules as we see in Exhibit 42. When a diagram gets overcrowded, you can simplify it by creating a new module node and dragging a set of interrelated variables into that module node. A module is depicted as a rounded rectangle with a thick outline. Analytica displays influence arrows to or from a module node to represent influences to or from variables inside the module.

A rounded, thin-outline node depicts a general variable, that is, a quantity whose class is not determined more precisely or a quantity that the decision maker cannot affect directly and that is not defined as probabilistic. Use a general variable initially, if you are not sure what kind of variable you will need, then change the node class later, if appropriate.

A parallelogram-shaped node depicts an index variable. An index is used to define a dimension of an array. For example, Profit Inputs is an index for an array containing input variables that led to profits.

Influence Arcs

Arrows represent influences. Arrows into a deterministic or objective node indicate that the destination node is a function of the origin nodes. An arrow into a chance node expresses that the probability distribution on the chance node is conditioned on the values of the origin node. An arrow into a decision node is an information influence: It indicates that the value of the origin node will be known when the decision is made and thus may affect that decision.

The absence of a direct arrow between two nodes expresses the belief that the variables are independent of each other, conditional on the values of those variables from which they do have arrows. The absence of an influence arrow, which specifies conditional independence, is actually a stronger statement than is the presence of an arrow, which indicates only the possibility of dependence.⁹

An influence arrow does not necessarily represent a causal relationship from one variable to another. Influences express evidential relationships that need not be physical relationships. However, it is often a useful heuristic when eliciting influences to ask about possible causal relationships among the variables. For example see Exhibit 43.

Sales are defined using a triangular distribution whereby the most likely sales are 800,000, maximum sales, 1,000,000 and minimum sales,

⁹ Ibid.

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Exhibit 43.
Object function, B&G Corp. sales.

Exhibit 44.
Diagram, B&G Corp. cost of goods sold.

700,000. Correspondingly, sales results filter down to output variables defined in the exhibit.

Here, CGS variables are "visually" broken out into their component structures. CGS is represented by a trapezoid-shaped node.

A trapezoid-shaped node depicts a constant, that is, a variable whose value is fixed (see Exhibit 44). A fixed value has no inputs and is not

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Exhibit 45.
Object, B&G overhead.

Exhibit 46.
Object, B&G Corp. capital expenditures.

computed. In this example, it is Beginning Inventory. It is good practice to define such values as constants so that you can refer to them by name; otherwise, you must type their numeric values into each expression that includes them and search for the values when you need to change them. Now lets consider overhead, a chance variable.

Overhead is defined in two parts: (1) capital expenditures plus (2) a uniform distribution with a range between 75,000 and 90,000 (see Exhibit 45). Now let us define capital expenditures (see Exhibit 46).

Capital expenditures are the result of sales multiplied by a factor of 12%, plus a chance variable with a mean of 15,000 and standard deviation of 2,000. Note that output leads to purchasesl overhead.

We now define labor costs (see Exhibit 47).

Labor, a component of cost of goods sold has been derived under uncertainty conditions. Set in a triangular distribution, labor minimum =

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Exhibit 47.
Object, B&G Corp. labor.

Exhibit 48.
Diagram, B&G Corp. expenses.

Probability
Profits

0.05
32.3K

0.25
11.45K

0.5
32.46K

0.75
58.55K

0.95
83.02K

Exhibit 49.
Result, probability bands of profits.

sales × 19%, labor most likely = sales × 12%, labor maximum = sales × 19%. Expenses include a number of variables that are much easier to define in a visual model than on the familiar spreadsheet. For example, consider Exhibit 48. Expenses include administration expenses and selling expenses. (We have not broken these expenses out in order to shorten this example. However, this diagram includes correlations inside the ''expenses importance" node.

Probability bands are specified at given percentile values. The model returns an estimate of probability or confidence bands for X if X is probabilistic (see Exhibit 49).

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B&G's profit probability density appears in Exhibit 410.

If the quantity is a continuous probability distribution, Analytica displays a probability density function. The horizontal (x) axis plots possible values of the uncertain quantity. The height of the curve (probability density) is proportional to the likelihood that the quantity will have the x value. The highest point on the curve is the most likely value (the mode). Where the curve is at zero height or invisible, there is zero probability that the quantity will have that value. (For a discrete probability distribution, Analytica graphs the probability mass.)

The rectangular node, Emissions Reduction, is a decision. The ovals are uncertain variables, and the hexagon is the objective to minimize, Total Cost.

The rounded rectangle nodes are deterministic variables, that is, variables that are defined as deterministic values or as deterministic functions of their input variables. In some notations, deterministic nodes are depicted as ovals that have double outlines.

The hexagonal node on the right-labeled Total Cost depicts the objective, that is, a quantity to be optimized (either maximized or minimized, depending on how it is expressed). In decision analysis, this node expresses the utilitythe objectives and valuesof the decision maker. Decision theory prescribes that the decision maker seek the decision that maximizes the expected utility.

Uncertainty in Your Model

Recall that the oval nodes depict chance variables, that is, variables that have an uncertain value that is not under your direct control. We express

Exhibit 410.
Result, B&G Corp. profit profitability density graph.

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the value of each chance variable in terms of a probability distribution, fit-ting it to data or eliciting it from experts. Uncertain variables propagate uncertainty samples during dynamic simulation. If an uncertain variable is used in a dynamic simulation, its uncertainty sample is calculated only once, in the initial time period. If you want to create a new uncertainty sample for each time period (i.e., resample for each time period), place the distribution in the last parameter of the Dynamic() function. You can enter a distribution anywhere in a definition, including in a cell of an edit table. Thus, you can have arrays of distributions. You can choose from an array of distributions, some of which are listed in Table 4-1.¹⁰ If you simply want to ignore the uncertainty, the software will compute and display a mid-value for any quantity, computed deterministically from the median of each input distribution.

¹⁰ Reprinted with permission of Lumina Decisions Systems.

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Developing Your Visual Model Step by Step

Open Class Donuts.ana

In the models subdirectory of the CD (you need to install open Analytica first). The Class Donut model will be your check. However, you can either create a fresh model for practice or simply follow how Class Donuts.ana was constructed:

Selecting Open Model from the File Menu

When you first create a new model, you must enter an identifier and other information, also referred to as documentation, describing its title, description, and author.

Using the Edit Tool (Arrow Pointing Left)

When the Edit tool is selected, a vertical menu of icons is displayed in the Node palette. These icons represent the different node types and allow you to add nodes to the influence diagram. Setting up the influence diagram

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first will enable you to organize it efficiently. The influence diagram is Exhibit 411 and includes all assumption variables that contribute to the forecast variable, profit.

Creating Variables

Each variable has a node type: Select the node type based on what you know about the variable. The first variable we will create is expenses per donut. This is a chance node. We drag the Chance node to a position in the influence diagram. We enter "Expenses per donut" and press the Return key to create a second line.

Saving Your Model

While creating or modifying a model, you should periodically save your changes.

Deleting a Variable

Sometimes you may want to delete a variable that you previously created.

Moving Nodes

When you create a model, you should try to structure the model layout to make the model logic easy to understand. As you refine your model, however, you undoubtedly will want to group nodes in different ways. Click on the Edit Tool icon and try dragging the Donuts Sold per Year Chance node.

Exhibit 411.
Diagram donuts main.

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Editing Variable Titles

We might select Donuts Sold per Year and click again inside the node's title to select its text for editing (see Exhibit 412).

Here we assume a chance variable governed by a normal distribution with a 150,000 mean and 30,000 standard deviation. Sales lead to outputs that follow in Exhibits 412A, 412B, and 412C.

This variable is influenced by two variables: (1) donuts sold per year multiplied by (2) expenses per donut. We also include a description to help "the team" understand the underlying assumptions.

This variable is governed by a normal distribution with a mean of 40 cents and a standard deviation of 10 cents. A good description of the variable is included.

Exhibit 412.
Object, donuts sold per year.

Exhibit 412A.
Chance, expenses per year.

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Exhibit 412B.
Chance, expenses per donut.

Exhibit 412C.
Object, price per donut.

Drawing an Arrow between Nodes

One of Analytica's most powerful features is its ability to show relationships between variables in the influence diagram. Influence arrows are used to specify the dependencies between variables. Because the Donuts Sold per Year variable influences Expenses per Year, we draw an arrow connecting the two nodes.

Deleting an Arrow

Occasionally, you may need to delete an arrow because of an earlier mistake or a change in your understanding of the model. Try pressing the Delete key to delete the arrow. The arrow disappears. Do not forget to replace the arrow.

Connecting Multiple Arrows

When one variable is influenced by many other variables, you can draw multiple arrows at once.

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Entering Attributes Using the Object Window

· When you create a model, you can add documentation of the model and of its variables. The system supports integrated documentation that can be tied to every variable in the model.

· We double-click again on Donuts Sold per Year to open its Object window (Exhibit 412).

· The identifier in the Object window is Donuts Sold per Year. The title is the same. In the description field, we enter. "We expect to sell 150,000, with a standard deviation of 30,000."

· Clicking on the Definition field opens up a field. Click on expr. Select distribution/Normal. Enter "EXACTLY 150,000,30000." Click the Check button. The result is Normal( 150K, 30K)

· Donuts Sold per Year is no longer filled with a diagonal line pattern around its title. The clear node indicates that Donuts Sold per Year now has a definition that is valid and can be computed.

Entering Attributes Using the Attribute Panel

Rather than opening a separate window to alter a variable's attributes, you may prefer to see a variable's attributes in the same window as the model influence diagram (the module icon is surrounded by a bold border). The attribute panel, which appears under the diagram, allows you to edit as well as examine attributes.

Defining a Variable That Is Influenced by Other Variables

·When one variable is influenced by another variable, you must provide a mathematical expression that describes the relationship between the variables. The Expenses per Year node has arrows entering it from two other variables.

·Because Expenses per Year is equal to Expenses per Donut multiplied by Donuts Sold per Year, we enter the following expression into the Definition field: Donuts Sold per Year × Expenses per Donut (from the Inputs window).

·Notice outputs are Donut Profits per Year and Expenses per Year Importance.

Creating a Module

· To simplify complicated diagrams, most complex models use sub-models, called modules. A module is an influence diagram containing variables and their relationships to one another. While the current model is simple enough, we could add a module if we had, say, a New York division and wanted to create a submodel.

· Drag the Module icon to a position in the influence diagram. You may want to experiment here. Enter "NY Division." Select the

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Exhibit 413.
Object, donuts profits per year.

Decision node (this will be very simplistic). Double-click. Enter "100000" in the definition field. Drag an arrow from profits (within the node to the window Donut Profits per Year). Next, double-click on the Donut Profits per Year node. Notice the new input: Profits.

·Finally, we change the definition by adding profits. Click on the Check button to accept your selection.

Completing the Model

Thus far, we have used several methods for moving between windows, documenting variables, and specifying their definitions. In this last step, we double-click on Donut Profits per Year. The result is shown in Exhibit 413.

·While selecting Donut Profits per Year, click on the Show Results button (green question mark and exclamation point icon) to evaluate Donut Profits per Year.

The distribution reveals a probability density (Y) of Donut Profits per Year (X). Selecting Result from the main menu gives us a choice, for example, midvalue of Donut Profits per Year (see Exhibits 414 and 415).

Importance Analysis

Finally, we may want to view correlations. Importance analysis shows the effect that the uncertainty of one or more input variables have on the uncertainty of an output variable. Importance is defined as the rank-order correlation between the sample of output values and the sample for each uncertain input. This is a robust measure of the uncertain contribution

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Exhibit 414.
Probability density (Y) of donut profits per year (X).

Exhibit 415.
Chart of probability density (Y) of donut profits per year (X).

because it is insensitive to extreme values and skewed distributions (see Exhibit 416).

Select Object from the main menu. Select Make Importance. Donut Profits per Year Importance is measured on the y-axis, while Donut Profits per Year inputs appear in the x-axis. Expenses per Donut is the most important variable, while Price is less important.

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Exhibit 4-16.
Midvalue of donut profits per year importance.

Exhibit 4-17.
Diagram, business opportunity analysis.
(See On-Line Demo)

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On-Line Demonstration:
E-Commerce Start-Up

Readers may find this model at Lumina's site http://www.lumina.com/demos/demomodels.html.¹¹ Explore this model and many of Analytica's features by clicking on the nodes in the diagram or the buttons on the toolbar. More detailed descriptions of model elements are provided in Exhibit 417 Diagram-Business Opportunity Analysis. The exhibits that follow are samples of the E-Commerce Start Up Analytica case taken from the Lumina web address (see Exhibits 418, 419, and 420).

Model description: Consistent profitability remains elusive in the rapidly changing and highly competitive Internet commerce arena. This model allows the entrepreneur to explore key factors that will affect profits and to do it early on, before huge investments are made. Particular attention is paid to determining the potential number of visitors to the site and potential sources of revenue. A variety of financial outputs are generated for evaluating the venture, including financial statements (balance sheet, income statement, and cash flow statement), NPV and IRR, maximum cash out position and timing, and market valuation estimates.

Exhibit 418.
Sample E-Commerce, business opportunity income statement.

¹¹ Used with the kind permission of Lumina Decision Systems.

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Exhibit 4-19.
Sample E-Commerce, business opportunity balance sheet.

Exhibit 4-20.
Sample E-Commerce, business opportunity IRR.

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Conclusion

Analytica is a new and powerful visual modeling tool that embodies the notion of problem solving using a white board. Downloading the model or linking to the model via site locations listed on the CD, we learned how to draw nodes and arrows to depict the relationships between model components, and thus, were able to develop the qualitative nature of financial problems without getting lost in details.

We discovered how to create hierarchies in our models. By grouping together related components of a problem into separate sub models, we imposed a top-down organization and factored this into our models. Far more than spreadsheet models, this permitted us to work out and manage complex relationships and, if other members of the team were involved, could easily allow them to more easily grasp critical issues and concepts.

Another key feature of Analytica is the use of Intelligent ArraysTM. These enabled you to add or remove dimensions such as time periods, geographic regions, alternative decisions, etc., with minimal changes to the model structure. Unlike spreadsheets, which require you to repeat formulas with each new dimension, this tool separates the dimensions from the relationships so that models remain simple. As the dimensions change, Analytica automatically updates, reports, and graphs the results.

Finally, unlike spreadsheet models, this tool features fully integrated risk and sensitivity analysis for analyzing models with uncertain inputs; powerful facilities for time-dependent, dynamic simulations; comprehensive overlay graphs; and over 100 financial, statistical, and scientific functions for calculating just about any type of mathematical expression.

Chapter Four
References and Selected Readings

Books

Benninga, S., and B. Czaczkes. (1997). Financial modeling. Cambridge: MIT Press.

Bertocchi, M., et al. (1996). Modelling techniques for financial markets and bank management. Heidelberg: Physica-Verlag.

Dattatreya, R. E., and K. Hotta. (1994). Advanced interest rate and currency swaps: State-of-the-art products, strategies and risk management applications. Chicago: Irwin.

D'Ecclesia, R. L., et al. (1994). Operations research models in quantitative finance. Heidelberg: Physica-Verlag.

Euro Working Group for Financial Modeling, R. L. D'Ecclesia, et al. (1994). Operations research models in quantitative finance. Heidelberg: Physica-Verlag.

Greenstein, S. M., and J. Wade. (1997). Dynamic modeling of the product life cycle in the commercial mainframe computer market, 19681982. Cambridge, Mass.: National Bureau of Economic Research.

Guerard, J., and H. T. Vaught. (1989). The handbook of financial modeling: The financial executive's reference guide to accounting, finance, and investment models. Chicago: Probus.

Ijiri, Y. (1993). Creative and innovative approaches to the science of management. Westport, Conn.: Quorum Books.

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Meyer, H. I., and M. C. Weaver. (1977). Corporate financial planning models. New York, John Wiley & Sons.

Meyer, M. F. (1983). Financial modeling. Gaithersburg, Md.: Aspen Systems.

Morris, J. R. (1987). The Dow Jones-Irwin guide to financial modeling. Homewood, Ill.: Dow Jones-Irwin.

Rothman, P. (1999). Nonlinear time series analysis of economic and financial data. Boston: Kluwer Academic Publishers.

Sheldon, T., Consultative Group to Assist the Poorest, et al. (1998). Business planning and financial modeling for micro finance institutions: A handbook. Washington, D.C.: World Bank CGAP.

Stokes, H. H., and H. M. Neuburger. (1998). New methods in financial modeling: Explorations and applications. Westport, Conn.: Quorum Books.

Varian, H. R. (1993). Economic and financial modeling with mathematica. New York: Springer-Verlag.

Wang, R. Y, et al. (1992). Data quality requirements analysis and modeling. Cambridge: Alfred P. Sloan School of Management, Massachussetts Institute of Technology.

Zopounidis, C., and Euro Working for Financial Modeling. New operational approaches for financial modeling. Heidelberg: Physica-Verlag.

Select Internet Library

Lumina Decision Systems, Analytica: Beyond the Spreadsheet Topics Discussed: The Quantitative Modeling Tool With Visual Ease; Who's Doing What With Analytica; Manage Risk and Uncertainty; Decision Making Within the Enterprise; Build Analytica Models in Three Easy Steps; Instant Access to Every Element of Your Model; Expand Your Models With Intelligent ArraysTM Functions and Operators http://www.lumina.com/brochure/index.html.

Tweedie, L., R. Spence, H. Dawkes, and S. Hua. Externalizing Abstract Mathematical Models. To appear in the ''Proceedings of CHI'96" (Vancouver: ACM Press).
Description: Abstract mathematical models play an important part in engineering design, economic decision making, and other activities. Such models can be externalized in the form of interactive Visualization Artifacts (IVAs). These IVAs display the data generated by mathematical models in simple graphs that are interactively linked. Visual examination of these graphs enables users to acquire insight into the complex relations embodied in the model. In the engineering context, this insight can be exploited to aid design. http://www.ee.ic.ac.uk/research/information/www/LisaDir/CHI96/lt1txt.html.

Using MathWorks Products; The Financial Toolbox 2.0.
Description (1999): The MATLAB Financial Toolbox extends the functionality of MATLAB by providing essential tools for quantitative financial modeling and analytic prototyping. The Financial Toolbox is used for a wide array of applications, including fixed-income pricing, yield, and sensitivity analysis; advanced term structure analysis; coupon cash flow data and accrued interest analysis; and derivative pricing and sensitivity analysis. http://www/mathworks.com/products/finance/.

CD

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ABC Corp
4KB
Analytica Model File

About Analytica
1KB
Internet Shortcut

Analytica Customer List
1KB
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ClassDonuts
4KB
Analytica Model File

Demo Models
1 KB
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Market Model
33KB
Analytica Model File

Njr
10KB
Analytica Model File

Online Demo E-Commerce Model
1KB
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2,515 . . .
Application

tutorial.pdf
1KB
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Chapter Five
Divisional Cash Flow Analysis and Sustainable Growth Problems

This chapter assumes that you have a working knowledge of basic cash flow. The first section reviews cash flow analysis at the basic (divisional) operating level, and the second section reviews advanced cash flow and sustainable growth problems, again at the divisional level.

Consolidated equity value remains the quest for all operating parts. It begins at the subatomic levelthe lowly operating division, its remote cash flow, the genetic capital cost and strategic plan. From these tiny threads, the colossus emerges.

Cash Flow

Cash flow has always been one of the most compelling financial and risk analytical tools, raising questions dealing with how businesses generate and absorb cash.

Accounting:
Fact or Fiction

Warren Buffet calls net income "white lies." Lee Seidler has been known to say, "If push came to shove, if a chairman wants a nickel more a share, any good controller knows where to find it."

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Cash flow is literally the precursor of shareholder value. If an operating unit routinely produces poor cash flow or is inadequately capitalized, it cannot survive long. Indeed, the operating unit may subsist "on a shoestring" by cannibalizing corporate headquarters. However, siphoning off the parent's cash originally earmarked to improve value-creating businesses is not the way to run a shop.

We can draw on IAS 7 to work out the best way to analyze cash flows at the operating unit level:

· The divisional cash flow statement forms the basis of macro corporate analysis.

· Operating units down to the least common denominator should account for changes in cash and cash equivalents for a specific period, monthly or quarterly.

· Cash equivalents are short-term, highly liquid investments subject to insignificant risk of changes in value. The "basic unit" statement should decompose changes in cash and cash equivalents into operating, investing, and financial activities. Cash changes between periods are unimportant. A reconciliation of net cash flow from operations to net income is required using either the direct or the indirect method. Both techniques provide cash from operations. The direct method shows receipts from customers and payments to suppliers, employees, government (taxes), and so on. The indirect method begins with accrual basis net profit or loss and adjusts for major noncash items. Make sure that you segregate intercompany receipts, disbursements, and inventory profits.

· Investing activities: Disclose (separately) cash receipts and payments arising from acquisition or sale of property, plant, and equipment; acquisition or sale of equity or debt instruments of other enterprises (including acquisition or sale of subsidiaries); and advances and loans made to, or repayments from, third parties.

· Financing activities: Disclose cash receipts downstreamed from headquarters and payments upstreamed apart from financing injections obtained from external debt and equity investors.

· Cash flows arising from tax rebates are disclosed apart from operating activities.

· Investing and financing activities that do not give rise to cash flows (a nonmonetary transaction, such as acquisition of property by issuing debt) should be excluded from the cash flow statement but disclosed separately.

The Indirect Method of Cash Reporting:
The In-Depth Cash Flow

In order to take advantage of the power of cash flow, you might adjust the cash flow format so that it is more in line with cash flow valuation models. As

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it stands now, cash flow audits combine working (capital) assets and working (capital) liabilities with gross operating cash flow items. The end result is to arrive at net cash flow from operations. That is too bad, particularly if you are evaluating segment performance. In short, do not combine categories. Rather, separate significant account classes.

Gross operating cash flow (GOCF), categorically, measures the power of the bottom line. Operating units finance growth in two ways: either from parental downstreams and/or through old-fashioned internal cash flow. However, keep in mind that internal cash flow can form simply by selling assets but that the division cannot grow by casting off assets. Strong internal GOCF is the only viable road to value, and there are several signals

You may want to compare GOCF to cash provided by headquarters. This allows you to (1) check operating divisions for internal versus external financing imbalances and (2) make comparisons in financial leverage trends.

Overall, would a business pay stockholder dividends out of GOCF? That is hard to imagine since GOCF must first cover working capital. As far as passing dividends up to the parent, that may be another story. Thus, if working capital sources (increases in accounts payable, accruals, and other working capital accounts) exceed applications (increases in accounts receivable, inventory and other current assets), cash flowing down the income statement will not end up cannibalizing working capital. Rather, it is redirected to finance investment activities, retire debt, and then, perhaps, shoot dividends up to headquarters. Exhibit 51 is an example of a comprehensive cash flow.

Cash Flow:
The Essence

Investing Activities

Investment activities include advances and repayments to subsidiaries, securities transactions, and investments in long-term revenue-producing assets. Cash inflows from investing include proceeds from disposals of equipment and proceeds from the sale of investment securities. Cash outflows include capital expenditures and the purchase of stock of other entities, project financing, capital and operating leases, and master limited partnerships.

Property, Plant, and Equipment (PP&E)

Property, plant, and equipment include acquisitions and purchases, capital leases, and proceeds from any disposals of property, plant, or equipment. Noncash transactions include translation gains and losses, transfers, depreciation, reverse consolidations, and restatements.

You should ensure that accounts are up to date regarding maintenance of existing capacity and expenditures for expansion into new capacity. This

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Exhibit 51.
Cash flow statement.

is important segment disclosure since maintenance and capital expenditures are nondiscretionary outlays. How, then, can a CFO determine whether funds are being allocated for maintenance of existing capacity, replacing rundown equipment, or providing expansion (and often discretionary) outlays? The answer lies the knowing how to take a cash flow apart.

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Unconsolidated Subsidiaries

It is not unusual for operating units to form alliances with outsides to reduce the cost of raw materials and overhead and to improve marketing. These alliances might take shape in equity investments. When a unit purchases between 20% and 50% of another company's stock, the account "Investment in Unconsolidated subsidiary" shows up on the acquiring business's balance sheet. Cash flows from unconsolidated subsidiaries include dividends from subsidiaries, advances and repayments, and acquisition or sale of securities of subsidiaries. Noncash transactions include equity earnings, translation gains and losses, and consolidations.

Investment Project Cash Flows and Joint Ventures

Investments in joint ventures or other separate entities formed to develop projects of various sizes are referred to as project financing and/or joint ventures. Typically, the new entity borrows funds to build a plant or a project with a guarantee of debt repayment furnished by companies that formed the new entity. Cash flows from the project (or joint ventures) are generally passed up to headquarters in the form of dividends. Prudence dictates that you obtain a full disclosure of the project's future cash flow since construction projects may report noncash earnings: construction accounting or equity earnings.

Asset Divestitures

Asset sales can be a positive move for a company, as in the case of an unprofitable division sold off to allow management to focus on the business's core businesses.

Working Capital:
Operating Cash Uses

Accounts Receivable

Increases represent cash drains and are typically financed. A decrease in receivables is associated with cash inflows.

Accounts receivable policy is closely allied to inventory management since both are the two largest current asset accounts. The volume of financial sales and the average collection period determines accounts receivable levels. You should examine receivables at the divisional level as well as on the corporate level. The divisional average collection period like consolidated receivables are influenced partly by economic conditions and partly by a set of controllable factors called financial policy variables and they may differ: divisional versus consolidated. Neural networking, data mining, and fuzzy logic are playing important roles setting credit standards and credit policy and working to optimize cash flows. These new methods really dig up hidden data.

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Inventory

As we saw, inventory is a vital component in cash flow cycles. Good inventory control starts with ongoing tracking of raw materials, work in process, and finished goods. Raw materials levels are based on anticipated production, the seasonality of the business, and the reliability of suppliers. If raw materials are highly salable and commodity-like, this stage is often closer to cash than work-in-process inventory. A buildup of raw material usually indicates speculative activity in anticipation of price increases or shortages.

Work in process is defined as the length of the production cycle. Factors that directly affect work in process include the grade of the equipment, engineering techniques, and the maintenance of highly skilled workers. Exorbitant work-in-process inventory depicts production slow-downs and/or manufacturing inefficiencies, severely hindering cash flow. Finished goods involve coordinating the sales effort. Salability of finished goods depends generally on the type of business operation. If there is a problem in this area, review sales strategy and find out why potential customers do not want to buy your product. This will advise you what inventory stage needs fine-tuning.

Effective inventory management is crucial to good cash flow management. Carrying excessive inventory is both costly and, in certain cases, leads to failure. Inventory control means careful planning plus maintaining open lines of communication within the organization so that inventory adjusts to optimal levels. Just-in-time inventory, economic order quantity, and neural network models do just that.

Operating Cash Sources

The right side of the balance sheet supports assets. Large increases and decreases in current accounts represent substantial inflows and outflows of cash. Operating cash sources generally include non-interest-bearing current liabilities that tend to follow sales increases.

Accounts Payable

Increases in payable are cash sources in the sense that they delay cash outflows into the future. While the division has use of this cash, it can utilize it for daily needs as well as for investment purposes. Generally, decreases from one period to the next represent an amount paid to suppliers in excess of purchases expensed.

Accruals and Taxes Payable

Increases in accruals and taxes payable represent sources of cash since items such as salaries, taxes, and interest are expensed but not paid out. Thus, cash is conserved for a limited period. A decrease in accruals arises from payments in excess of costs expensed. In the current period, therefore, the decrease is subtracted from the cash flow as a use of cash.

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Net Operating Cash Flow

Net operating cash flow denotes the cash available from gross operating cash flow to internally finance a unit's growth after working capital demands are satisfied. One of the great things about the structure of the cash flow format is how pieces of information surface to formulate powerful insights as to whether the business is optimizing its performance. For example, if gross operating cash flow is consistently larger than net cash flow from operations, the traditional sources of working capital, accounts payable and accrual have provided full support to traditional uses of working capital, accounts receivable, and inventory. Thus, precious operating cash income need not be diverted to support working capital and can be rerouted to finance "growth" strategies, such as investments in efficient fixed assets and aggressive R&D programsthe lifeblood of maximizing both divisional and consolidated value.

Cash Flow Analysis

Gross Operating Cash Flow

Operating cash flow should contribute toward an optimal financing strategy. Thus, imbalances between debt and equity usually begin with weak divisional (internal) cash flow. A less obvious situation is the case of a start-up or rapid growth operation. Although income may increase, expansion costs might rise at an even faster rate. Funding increases in receivables, inventories, and capital expenditures might push debt/equity perilously high unless new equity surfaces. What you do not want is crash-and-burn: crash if cash evaporates, burn if investments are written off.

Depreciation is a noncash charge with adjustments made to net income. You may want to question adequacy of reserves, nonrecurring items, and cash versus accrual-based income. If most of profits consist of equity earnings, beware that inadequate operating cash flow may be available for expansion and repayment of obligations. Most important, the division's capital structure may be distorted since "low quality" earnings have artificially propped up equity. Also, if earnings have relied on deferred tax credits, beware. Deferred tax credits may be part of an accounting game to push profits up. Remember that deferred tax reversals do not offer a sustainable source of cash.

Checklist

·The quality, magnitude, and trend of earnings should be analyzed. Check the division's quality of earnings in such areas as adequacy of reserves, nonrecurring items, cash versus accrual-based income, and cash from operations.

·When you analyze earnings trends, pay particular attention to the contribution of income to overall financing. If income is contributing less and less to overall financing, go back and check strategic plans.

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·Net income and dividends should be compared to each other. Are dividends large in proportion to net income? If so, why are they upstreamed?

·Depreciation should be compared with capital expenditures. If depreciation is greater than capital expenditures, assets may be running below optimal levels.

·Although reserves and write-downs such as inventory are add-backs to gross operating cash flow, they should be fully investigated.

Analysis of Operating Cash Uses

Increases in receivables are normal in a growing operating unit as long as the average collection period (aging schedule) remains relatively proportionate to sales increases. However, large increases in receivables accompanied by weak operating performance and unaccountable increases in the average collection period should be checked against (1) financial standards, (2) terms of discount offered, (3) collection policies, (4) concentration, (5) quality, and (6) the receivables aging report. Changes in net income should be cross-referenced with changes in inventory. If your business segment suffers losses, has inventory levels increased? If so, someone may ask why stockpile goods if they cannot be sold off at a profit?

Checklist

· If the average collection period has increased, what is the reason(s)?

·Why aren't you writing down inventory if losses are sizable?

Analysis of Operating Cash Sources

Compare accounts payable with gross operating cash flow. You may want to set up a data or tickler system to ensure that divisions take full advantage of trade discounts. No excuses here, particularly when credit lines are appropriated to operating units and accounts payable are large. The spread between loan pricing and an annualized 37% return associated with anticipating 2/10 net-30 terms multiplied by the payable is nothing to sneeze at. Operating cash flow should be compared with accounts payable. A "bulge" in payables may indicate late payments, particularly if gross operating cash flow is not making an adequate contribution to investment activities or the operating unit is highly leveraged.

Checklist

·Does the payables manager take advantage of trade discounts?

·Does the cash conversion cycle contribute to increased payables balances and late payments?

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Analysis of Net Cash Provided by Operating Activities

Net cash provided by operating activities is the line providing cash to primary expenditures after working capital coverage. Working capital requirements can pull large amounts of cash from the business. This can cut into capital expansions programs, particularly if operating cash flow falls significantly below expectations. Keep in mind that one of the best ways to check quality of earnings is the comparison of net income to net cash flow from operations. For example, if divisional income consistently reaches high levels but little of it remains to cover investment activities, then, what good is income?

Analysis of Investment Activities

Net Fixed Assets

First of all, break investment activities into groups: discretionary and nondiscretionary. Nondiscretionary refers to outlays required to keep a healthy gross margin on the operating unit level. Say, for example, that nondiscretionary investments are covered by the division's internal cash flow. From this, you may discover that financing activities is discretionary. This is a sign of sure strengthyou control the capital structure, unsystematic (company-specific) risk is reduced, and, as far as valuation is concerned, the division can factor in a lower cost of debt when used to discount back free cash flows.

Assets require continuous replacement and upgrading to ensure efficient operations. For example, if XYZ Division fails to maintain property, plant, and equipment, a series of problems could easily ensue. The unit's aging or outmoded machinery would increasingly experience longer periods of downtime, and goods produced could be defective.¹ The operating unit will begin to fall behind its competitors from both a technological and an opportunity cost standpoint. Worse, its products may be perceived by customers as inferior, lower quality, or "old fashioned" compared to those of its competitors.

When depreciation expenses consistently exceed capital expenditures over time, this is an indication of a declining operation. Eventually, it will lead to a decline in earnings and profitability. Capital expenditures represent major nondiscretionary outlays.

Checklist

· Check whether deferred taxes are running off. Deferred taxes usually increase when capital expenditures accelerate.

· Download the most recent capital budgeting schedule. Focus on project cost, net present value, and internal rate of return.

¹ See chapter 7 on simulation. The binomial distribution tracks this. Say, for example, that a particular piece of equipment produces three defective parts out of a hundred runs when the target is one defective part out of a hundred trials. The equipment may need to be replaced.

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· Is fixed-asset turnover (sales/net fixed assets) increasing sharply? This ratio measures the turnover of plant and equipment in relation to sales. The FA-to-T/O ratio is really a form of cash flow in that it indicates how well fixed assets are being utilized.

· Are backlogs increasing without a large pickup in sales? Unresolved backlogs happen only once, and then customers go elsewhere.

· Does work-in-process inventory compare tie-in to a sharply deteriorating inventory turnover? This question reinforces the previous statement.

· Make sure that the gross margin has not trended down over the past few years because of increased labor costs and decreased operating leverage.

· Real options criteria should always be used when applicable.

Investment Project Cash Flows and Joint Ventures

Once the financial merits of a project have been examined, it must be discerned whether the project's cash flow is reasonably understood.

Checklist

· Is the cost of capital appropriate? If it is artificially low, the net present value of the project will be inflated.

· Is the time frame to complete the project realistic, or is it a ''pie in the sky" scenario? Projects may take longer to complete than projected and will invariably cost more than budgeted. This will lower the project's net present value and may lead to an eventual cash crunch for the company.

· What, if any, contingencies have been made by the company in the event that the project costs and/or completion time exceeds the original estimate? If the business can raise additional capital without difficulty, this is a very positive factor from a lender's point of view.

Analysis of Financing Activities:
Debt

Checklist

· Increases in long-term debt should always be examined on a specific issue basis in order to ensure optimal financing. Optimal financing means financing that minimizes the cost of capital, maximizes equity value, and prevents the division's credit grade or bond rating from down-tiering. Make sure that you distinguish real debt increases from accounting debt increases on the cash flow statement. For example, amortization of bond discount results in debt increases, but no cash is involved.

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· Decreases in long-term debt should be matched against increases in long-term debt and the magnitude of gross operating cash flow. For example, in an expanding business, increases in long-term debt may exceed reductions. As long as leverage is within acceptable levels, cash flow is probably contributing its fair share to the overall financing of the business.

· Amortization of bond premiums distorts debt reductions. Find cash decreases by separating bond premiums.

· Long-term debt conversions to equity should be noted since conversion to equity may represent a substantial noncash exchange.

· Increases in long-term debt are examined on a specific-issues basis to understand how a business might plan its future financing.

Analysis of Equity and Other Financing Activities

Checklist

· Dividends should be reviewed to determine whether they are tied to income or whether they are relatively constant. Financial leverage should be examined as well to verify that dividends are reasonable in light of future prospects. It should be determined whether an established partner exists in the business's capital expenditure program.

Benchmarking divisional performance means that you search out weak cash flow operations (see chapter 11 on valuation) and pinpoint value-destroying operations. If cash flow shareholder value falls below liquidation value, you may decide that the business is better off sold than retained. The bigger the spread the faster you will move. Savvy CFOs perform this analysis frequency, and that is when you see the perfect merger of accounting principles and scientific financial methodology.

How to Assess "Cash Flow" Reports Delivered by Your Divisional Heads

Let's face it, everyone wants to put his or her best foot forward, particularly when it comes to proving one's worth. (I am talking at the divisional level.) However, when it comes to headquarters, the consolidated valuation report that you deliver to the board may well serve as the most compelling document published the entire year. More often than not, the numbers in a valuation can easy fall victim to accounting whim. The following section may hold the old adage "garbage in, garbage out" at bay.

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The Divisional Accounting Checklist²

· Cash. Portion restricted; currency fluctuations and uncertainty; currency translations. Check frequently.

· Receivables. Large overdue receivables; large increase with divisional sales flat; overly dependent on one or two customers; related-party receivables; slow receivables turnover (annualize this frequently); right of return exists; change in divisional terms, credit standards, discount, or collections.

· Inventory Salability. Large increase when sales are flat; slow inventory turnover; faddish inventory; inventory collateralized without your signature; watch unjustified LIFO-to-FIFO changes; insufficient insurance; change in divisional inventory valuation methods; increase in the number of LIFO pools; unreasonable intercompany profits; inclusion of inflation profits in inventory; large, unexplained increase in inventory; gross profit trends bad but no markdowns; inclusion of improper costs in inventory; capitalized instead of flow-through.

· Property Plant and Equipment. Outdated equipment and technology; high maintenance and repair expense; declining output level; inadequate depreciation charge; change in depreciation method; lengthening depreciation period; decline in depreciation expense; large write-off of assets; watch distortions regarding currency translations.

· Unconsolidated Investments. Watch switching between current and noncurrent classifications; investments recorded in excess of costs; investmentsreal values along with book.

· Intangibles. Slow amortization period; lengthening amortization period; high ratio of intangibles to total assets and capital; large balance in goodwill even though profits are weak.

· Liabilities and Equity. Liabilities understated; off-balance-sheet liabilities; warranties amortized too fast; amortize warranties quickly; unexpected and/or substantial reserves; worrisome negative cumulative translation adjustments.

· Income Statement. Merchandise shipped out at the end of the year to window-dress the financials; unearned income; shifting sales to future periods via reserves; income smoothing gimmicks; creating gains and losses by selling, retiring debt; hiding losses inside discontinued operations; selling assets after pooling; moving current expenses to later periods by improperly capitalizing costs, amortizing costs too slowly, and failing to write off worthless assets.

² Some of these accounting examples in this section were drawn from an excellent source: Financial Shenanigans, by Howard Schilit (New York: McGraw-Hill). I have added to this source from my own extensive experience dealing with accounting distortions.

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Cash Flow and Sustainable Growth Problems

Too often, maximizing growth seems to take center stage as the single most important business priority. Under certain conditions, expansion strategies can easily prove fatal. Sales might grow exponentially, causing operating leverage (heavy capital expenditure investment) to hit the cash flow hard. How are these big investments financed? Retained profits and new debt generate some cash, but only in limited amounts. Unless the business exercises the equity option via equity carve-outs or draws money from headquarters, it could find itself in a great deal of trouble.

Growth is indispensable to well-being. However, it is possible that growth may come too fast for one's own good, particularly if operations are small or if financial planning expertise is deficient. An old rule states that the faster you grow, the greater the requirement for funds to support growth (see Excel's exponential trendline). Leverage increases might satisfy cash flows on a short-term basis, but eventually headquarters might dam the river if the financial structure is debt saturated. With no cash available, equity value can easily drop below zero with liquidation in hot pursuit. This corporate headache is worse than a migraine and is called imprudent exponential growth. However, if managers mind the shop, meaning that they match growth rates to an optimal (or at least pragmatic) capital structure, growing pains settle down fast.

The sustainable growth rate is the maximum rate sales increase (over the foreseeable future) without depleting financial resources. In simple terms, it means that operating units need money to make money. The primary value of the sustainable growth idea is its emphasis on the need to boost net worth as volume increasesconsolidated along with consolidatingthe results of which maintain equilibrium between liabilities and equity. Since no perfect relationship exists between liabilities and equity (because of the dynamic nature of the capital structure), industry benchmarks are acceptable points of reference. Industry norms reflect the cumulative results of decisions by management, lenders, suppliers, customers, and competitors. Whenever the relationship between liabilities and net worth is significantly below industry standards, questions surface about management competence and the firm's unsystematic risk control. Just look at the spreads between Treasuries and the rates charged on corporate issues sitting in the lowest quartile of their respective industry.

This cash flow model that we call sustainable growth measures the probability that increases (in sales) of highly leveraged rapid-growth companies stress out the financial structure. The model helps identify the portion of growth fueled through internal versus external cash flow. The results are set to different degrees of tolerance by manipulating specific variables to determine various levels of risk. Thus, sustainable growth acts as a telescope focused on the cash flow map. For example, if the model

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shows 90% of growth financed externally with historical leverage dangerously out of balance, the situation could get out of hand, and fast.

The sustainable growth rate is derived by setting up variables (X), including projected sales, assets, profit margin, dividend payout, and spontaneous liabilities and solving for (Y), the sustainable growth rate. Again, sustainable growth runs are singularly important for highly leveraged rapid-growth operations since their cash flows are often volatile and unpredictable. These units operate in an environment much riskier than any other period in a typical life cycle since unsystematic (company specific) risks are unique and difficult to analyze. Let's see what this really means.

The Industry Life Cycle

Start-Up Phase

Businesses just starting out face greater risk than any other type of business unless, of course, they are heavily endowed by the parent. Start-up requires initial asset investments in anticipation of sales. Enter collateral, corporate guarantees, and venture capital. No unsecured debt permitted.

Rapid Growth Phase

Following start-up, an operating unit usually enters phase 2. Achieving initial success, growth accelerates. However, small equity increments established by earnings (source of cash) are often trivial and cannot finance the insatiable appetite for new investments demanded by rapid growth operations. For that matter, creditors may not realize that further advances could easily represent down payments for accelerating credit demandsuntil the business implodes or, it is hoped, evolves to the mature stage of its life cycle.

Mature or Stable Growth Phase

The mature phase is one in which the growth rates for price, book value, earnings, and dividends are all approximately equal and are in line with the growth of gross national product or a broad range of stocks like the S&P Composite. Operating activities throw off more cash at higher levels of sales. The need for growth diminishes enough so that investing activities are reduced. Financing requirements are much lower now that the business generates more cash than it absorbs.

Decline Phase

Sales decline results in eroding profits, the cause being more competition or changes in consumer demand. Thus, operating cash flow falls short of working capital and capital expenditures, though reduced investment activities provide limited cash flow because plant capacity is lowered.

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Case Study

High Risk Inc., a young growth company, operates as a producer of cable for the computer industry. The business requests a $50 million loan for plant expansion. The expansion program is needed to raise operating leverage, reduce labor costs, improve production efficiency, and increase the gross profit margin. Management believes that improved manufacturing techniques will boost productivity and increase the net profit margin to 7%. Ratios were extracted from the new projections, including the net profit margin, dividend payout rate, assets to sales, and targeted growth rate. Projections include the plant expansion program related to the loan request (see Exhibit 52).

Exhibit 52.
High risk's ratios versus the industry.

Solving for the sustainable growth rate:

A = projected assets
d = dividend payout rate
g* = sustainable growth rate
L = maximum leverage allowable by the bankers
S = projected sales.

Thus, the business can sustain only a 4% sales growth rate without raising financial leverage above 150%, the ceiling placed by the bank. However,

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growth is pegged at 10%. If the company grows at a higher rate than the sustainable growth rate, the business's current leverage will increase beyond the ratio permitted. The next step for High Risk is to deal with three conditions that control leverage, discussed next.

Three Different Appoaches for L

The Debt/Equity Ratio

The sustainable growth model (g*) depicts a case in which a company is inundated with additional debt. If the sustainable growth rate(g*) falls below the targeted growth rate (T), excessive leverage will halt growth and might even sink the business. This is readily observable as follows:

1. The CFO sets L, the debt/equity ratio, at the maximum allowable level. The ratio may be set at the industry unsystematic risk maximum, a "bankruptcy" leverage, or simply at the lender's tolerance level. We saw this approach used on the previous page.

2. The CFO can set g* equal to the targeted growth rate T and solve for L to secure the debt/equity ratio in equilibrium with the firm's targeted growth rate. The question is, simply, if the firm continues its growth pattern, how high will leverage climb, assuming that the business raises no new equity? Formula: g* = P(1 D)(1 + L)/ [A/S P(1 D)(1 + L)]. LEVERAGE AT GROWTH Equilibrium (L*): Leverage will approach L* when the targeted growth rate (T) and the capital structure are in equilibrium. The model assumes an indefinite growth period.

3. Alternatively, the CFO might develop a forecast taking the debt/equity ratio in the last year of the forecast period and substituting it into the formula to determine the sustainable growth rate in the business's residual period.

High Risk's growth rate will seriously impact cash flow. Without adequate cash funneling in from sales, operating leverage will increase because of the debt raised to cover cash shortfalls. A high degree of both operating leverage and financial leverage spells trouble because of the high level of sales needed reach its breakeven.

Will the business have to revert to increased borrowings to substitute for differences between internal and external financing? Here, we are concerned with the effect that recessions have on a company's cash flow and financial condition. During a period of economic slowdown, sales may decrease enough to cause cash flow streams to run dry. Technological improvements, as with High Risk, also cause financial needs to jump. To keep up with competition in an ever-changing and high-pressure marketplace, companies must adapt quickly to the latest changes in machinery and

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equipment technologytechnology that can either improve production efficiency or bring the company down in a climate of do-or-die.

The "do" factor: This means that more money must be spent on new asset purchases, and there must be a corresponding increase in sales and internal cash flow to match the purchases of the assets. The "die" factor: Lenders, along with the firm's finance people, are well aware that without adequate cash inflows, default risk compounds dramatically.

Example Approach 2

Set g* equal to the targeted growth rate T and solve for L to obtain the debt/equity ratio in equilibrium with the borrower's targeted growth rate:

Solving for L, we obtain L = 4.84. Thus, leverage must increase to 484% for the sales growth rate and financial structure to fluctuate in equilibrium. Since the maximum allowable debt/equity was 150%, the deal, as presented, cannot be approved.

Approach 3 is redundant here and will not be explored.

Solving Sustainable Growth Problem

Techniques available to solve sustainable growth problems include issuing equity, improving asset management, reducing dividend payout, and increasing the profit margin. Profit pruning, including dissolving unprofitable divisions, is still another way to ease growing pains. Also, knowing when rapid growth ends and the mature phase starts will quickly end a sustainable growth problem. Once the business has entered the mature phase of its company life cycle, greater amounts of cash will be generated, risk decreased, and cash flows more predictable.

Issue Equity

This may be difficult to do in a small operation with limited access to the venture capital market. Most countries do not have active, developed equity markets. Also, new equity is expensive, dilutes ownership, and is likely to reduce earnings per share.

Improve the Capital/Output Ratio (Assets/Sales)

The asset-to-sales ratio is an important component of the sustainable growth model. It is positioned in the equation to represent the base (before profit

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retention) on which an appropriate and sustainable growth rate is calculated. If this rate exceeds a tolerable rate, we know that leverage will increase rapidly.

Capital output is crucial to cash flow because it examines the tier (of assets) needed to produce a given sales level. For example, in today's ultra-competitive environment, the left side of the balance sheet is managed aggressively to allow for sustainable growth. Just-in-time (JIT) inventory, as we saw in the section on cash flow, is but one example. Often, JIT inventory requires an expensive investment in technology. For example, JIT can require scanners at the point of sale that transmit information directly to the supplier, who then ships additionally items. This type of arrangement eliminates some cost of carrying inventory. Operations not leveraged to the hilt, with strong debt capacity and cash flow, are in a better position to finance sophisticated asset management systems.

However, High Risk is in no position to bargain and may need to make hard decisions to reduce debt levels. For example, the business may decide to contract out production assignments to other vendors to reduce raw materials and work-in-process inventorynot a sweet pill to digest, as this activity will reduce profit margins as well because goods will cost more to produce.

Increase Profit Margins

Improved profit margins reflect strategic, operating, and financing decisions, certainly on the divisional level. Strategies involve critically important decision areas, such as choice of product market areas in which the business or division conducts operations, whether to emphasize cost reduction or product differentiation, and whether to focus on selected product areas or seek to cover a broad range of potential buyers.

Reduce Dividend Payout

Increases in both dividends and debt-to-equity ratios are potentially alarming because dividends reduce cash flow. On the other hand, profit retention shows a commitment to reinvest in the business rather than satisfy the short-term satisfaction of equity investors through dividend distributions.

Profit Pruning

When a business spreads its resources across many products, it might not be able to compete effectively in all of them. It is better to sell off marginal operations and plow the proceeds back into the remaining businesses. Profitable pruning reduces sustainable growth in two ways: (1) It generates cash directly through the sale of marginal businesses, and (2) reduces actual sales growth by eliminating some sources of the growth. Profit pruning is also available for a single-product company. The business could prune out slow-paying customers or slow-turning inventory. This lessens sustainable growth problems in three ways: (1) It frees up cash that can be used to support new

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growth, (2) it increases asset turnover, and (3) it reduces sales. The strategy reduces sales because tightening credit terms and reducing inventory selection will drive away some customers.

High Risk's New Strategy

As we saw earlier, g* is equal to 4%; the company can grow at 4% without increasing leverage over 150%. However, High Risk is preparing for a 10% sales increase. Since the company is growing at a higher rate than the sustainable growth rate, the business's current debt-to-equity ratio exceeds the 150% maximum level set by the business's lenders. By setting the targeted growth rate at 10% and solving for L the lenders realize that a leverage of 484% equates with the business's 10% growth ratemuch too high.

High Risk Inc., like almost all firms, will use sales growth as a major component of long-run financial planning. However, in the search for more profit dollars, many managers fail to consider the growth rate that the company's financial structure can support. Financial planning establishes guidelines for changes in the business's financial structure. Thus, a sure understanding of this business's financial planning will help reduce credit risk by structuring a tighter deal.

The sustainable growth model depends on the major elements of the business's financial planning. High Risk's financial planning should include the following:

· An identification of the business's financial goals

· An analysis of the differences between these goals and the current financial status of the business

· A statement of the actions needed for the business to achieve its financial goals

The financial policies that the business must decide for its growth and profitability include the following:

· The degree of financial leverage the business chooses to employ

· The amount of cash the business thinks is necessary and appropriate to pay shareholders (dividend policy)

· The investment opportunities the business elects to take advantage of in the future

Financial plans are not the same for all firms. Economic assumptions, sales forecast, pro forma statements, asset requirements, and financial requirements are some common elements of the financial plan.

High Risk's sales will be influenced by several "cash flow" factors. The prevailing economic conditions at a given time affect separate industries differently. For example, automobiles and home construction contracts would be reduced during a recession, whereas food sales would not be affected as

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greatly. In analyzing the potential cash flows and credit risks of this business, the prevailing market conditions will need to be considered first. These are factors that will affect an industry as a whole. You can analyze an individual company by finding its market share compared with its industry.

The fact that a firm is an innovator and market leader will reflect market share. Innovative operations with aggressive R&D programs will often gain advantages over competitors. Confirmed orders are good indications of future sales and needed production capacities, but projecting sales is often difficult in emerging industries because the predictability horizon is very short.

While growth in leverage ratios also increase the sustainable growth rate, the composition of High Risk's debt is also very important. If this emerging company continuously uses short-term debt as a financing mechanism, the business will become overexposed to volatile and rising yield curves that may drastically increase cost of debt when refinancing/rollover of debt is required; overreliance on short-term debt reduces the company's financing flexibility.

Also, it may suggest that other creditors are skeptical of the company's future cash flows and may not want the credit exposure of extending long-term debt that may not be remunerated. However, what may be inferred here is management's confidence that liquidity can be sustained principally through profit retention, enabling them to search for the lowest cost of capital.

Asset quality should be reviewed with leverage ratios because higher-quality assets allow for increased leverage ratios. Regarding debt capacity, an analysis of High Risk's cash flow coverage ratios should be measured and trended over a period to decide whether the leveraged company is experiencing any current or near-term problems covering interest expense and satisfying debt payments.

Also, leveraged companies that continue to increase debt without raising equity capital may suggest questions about the business's viability if equity capital market investors have rejected any public offerings of stock. It may also suggest that the company is not exploring its various capital-raising alternatives, and overreliance on a single financing method may not provide the business with the least expensive cost of capital.

In High Risk, the business's lenders will likely advise the business to decrease its debt-to-equity ratio by injecting new equity. If the business declines, High Risk could reduce its operating leverage, inventory, and debt levels by hiring subcontractors, thus raising the sustainable growth rate to acceptable levels.

The business decided not to issue new equity, preserving ownership control. Instead, as agreed, subcontractors will produce and ship to High Risk's customers. Other considerations are the following (see Exhibit 53):

· Because the use of subcontractors will squeeze profit margins, sales will continue to grow at 10%. High Risk has agreed to absorb higher costs of production.

· Using subcontractors will lower inventory levels and reduce capital spending.

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Exhibit 53.
Revised srategy.

· High Risk consents to tight control of receivables.

· Dividends must be reduced.

· Leverage will not transcend the ceiling imposed by the business's lenders.

The previous condition was:

The sustainable growth rate is 11%. Thus, High Risk Inc. can grow at 11% a year over the foreseeable future without increasing leverage beyond 150%, the leverage ceiling. Since the business's 10% targeted growth rate is less than its 11% sustainable growth rate, leverage will fall below the maximum level permitted by the business's creditors. With improved asset management, a less aggressive dividend policy and even considering reduced profits, the sustainable growth rate actually increased. In other words, the business's cash flow problems were substantially eliminated and the strategic problem identified. Poor asset management proved to be the guilty party. With poor asset management, an aggressive dividend policy, and declining profits, the sustainable growth rate actually increased, causing the business to have cash flow problems.

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Chapter Five
References and Selected Readings

Books and Periodicals

Bierlen, R., and A. M. Featherstone. (1998). ''Fundamental q, cash flow, and investment: Evidence from farm panel data." Review of Economics and Statistics, 42735.

Dechow, P. M., et al. (1998). "The relation between earnings and cash flows." Journal of Accounting and Economics, 13368.

Emmanuel, C. B. (1988). "Cash flow reporting, Part 2: Importance of cash flow data in credit analysis." Journal of Commercial Bank Lending, 1628.

Gahlon, J. M., and R. L. Vigeland (1988). "Early warning signs of bankruptcy using cash flow analysis." Journal of Commercial Bank Lending, 415.
Establishes that seven cash flow variables and suggested ratios capture statistically significant differences between bankrupt and nonbankrupt firms, on average, as much as five years prior to bankruptcy. These ratios and variables are thus strong candidates for inclusion in the early warning systems that banks use for identifying potential credit problems.

Gentry, J. A., et al. (1990). "Profiles of cash flow components." Financial Analysts Journal, 4148.

Helfert, E. A. (1994). Techniques of financial analysis. Burr Ridge, Ill.: Irwin.

Kathuria, R., and D. C. Mueller. (1994). "Investment and cash flow: Asymmetric information or managerial discretion." Working paper. Department of Economics, University of Maryland, no. 3, 146.

Mills, R. (1998). "Strategic value analysis." Economic and Financial Computing, 15398.

Nordgren, R. K. (1986). "Understanding cash flow: A key step in financial analysis." Journal of Commercial Bank Lending, 217.

Schulman, E. M. (1988). "Two methods for a quick cash flow analysis." Journal of Commercial Bank Lending, 2936.

Shin, H.-H, and R. M. Stulz. (1996). "An analysis of divisional investment policies."

Other Periodicals

Benveniste, Lawrence M. (1999). "Comment: Gain-on-sale's 'problem': Too much information." American Banker, September 16, p. 19.

Charitou, Andreas. (1999). "Earnings, cash flows and security returns over long return intervals: Analysis and UK evidence." Journal of Business Finance and Accounting, 26(3/4), p. 283.

Farragher, Edward J. (1999). "Current capital investment practices." The Engineering Economist, 44(2), p. 137.

Felthan, Gerald A. (1999). "Residual earnings valuation with risk and stochastic interest rates." The Accounting Review, 74(2), p. 165.

Hartmann, Matthias H. (1999). "Theory and practice of technological corporate assessment." International Journal of Technology Management, 17(5), p. 504.

Penman, Stephen H. (1998). "A comparison of dividend, cash flow, and earnings approaches to equity valuation." Contemporary Accounting Research, 15(3), p. 343.

Smith, James E. (1998). "Evaluating income streams: A decision analysis approach." Management Science, 44(12), p. 1690.

Strauss, Mel. (1998). "Examining FAS 133." US Banker, 108(9), p. 68.

CD

Name

Size

Type

2.17 International Accounting Standard IAS 7
Cash Flow Statements
1KB
Internet Shortcut

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Chapter Six
Statistical Forecasting Methods and Modified Percentage of Sales

Yogi Berra, the famous baseball catcher, once said, "If you don't know where you're going, any road will take you there." The rules that made baseball the grand game that it is are as rigid as earth's orbit around the sun. However, try applying rules to a great pitch, and it just will not work; and, like the exploding curveball, financial forecasting rises above the steely rulebook of laws and statistics. It has become the hero on the mound; the brave new world. Forecasting is an art, and like great pitching, it is dynamic and somewhat unsettling and moves with the speed of the Discoverer. Yogi would suggest that great pitchers know the road to the mound"and it ain't a dirt trail either." There are few dirt roads and even fewer mediocre pitchers in the game of financial forecasting. Slow, easy lobs just will not make it in the new century.

Recently scientific forecasting and its family of techniques have won wide acceptance as planning and decision-making tools. To satisfy these diverse situations, computer-generated techniques such as regression, simulation, optimization, neural networks, data mining, and a host of varied time-series techniques and causal methods are now mainstream. This means all areas: sales planning, working capital management, marketing research, R&D, pricing, production planning and scheduling, financial planning, program planning, corporate bond ratings, and strategy formulation.

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The good old days when naive methods carried the day have gone the way of the dirt road. Yet, in the final analysis a financial forecast is simply a file. Beyond that, good judgment on your part, plus a bit more than basic knowledge, will metamorphose the document to life. Art, power, and skill deliver the game-winning strikeout. Still, though, the rules, the statistics, and the scientifically generated report define the play and will drive your argument home, and that is what board members like to hear.

This chapter focuses on statistical forecasting and modified percentage of sales methods. Simulations and neural forecasting are covered in chapters 7 and 8.

A "Statistics" Approach to Financial Forecasting

Statistical methods generally fall into two broad groups: causal models and time-series analysis. Causal models include both regression models and econometric models. Time-series analysis includes moving averages, Box-Jenkins methods, and exponential smoothing.

Forecasting techniques include qualitative and quantitative methods (see Exhibit 61). We stress scientific methods in the three chapters on forecasting, so we will focus on quantitative methods there.

Causal models assume that forecast variables exhibit a cause-effect relationship. For example, sales may be a function of market share, markup, promotion, competition, and economic sensitivities. The whole idea of casual models allows you to discover that relationship so that the future value of sales can be determined. Conversely, a causal model is more involved than time series but can be particularly more relevant to frame policy and decision making.

Causal (simple regression) is a special case of regression when you work with a single independent variable. In simple regression, as in multiple, you assume a linear association within historical data and allow models to estimate the relationship using the method of least squares. Simple regression is not limited to time-series relationship. Rather, it predicts connections between any two variables, determining the value of one variable (dependent) as a function of the second variable (independent). Thus, the logo causal model. Mathematically, the causal is written as Y = f(X). The value of Y is a function of the value of X. When this is assumed to be a straight-line relationship, you write it as Y = a + bX.

Time-Series, or Trend, Forecasting

Time series, on the other hand, predicts the future by expressing it as a function of the past, for example, Sales = f (time). We learn forecast modeling by activating Excel's functions that will draw either a line straight (trend func-

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Exhibit 61.
Flowchart of qualitative and quantitative forecasting techniques.

tion) or a curve (growth function) in such a way that it passes through "the middle" of your historical data. Not long ago, you likely would have shied away from time series because of the large numbers of calculations involved. Since spreadsheet applications began offering built-in trend functions, the use of linear and curve fit analysis has become standard.

Excel Example 1

[CD:\MODELS\EXCEL\CGREGBook]

Excel includes several array functions for performing linear (LINEST, TREND, FORECAST, SLOPE, and STEYX) and exponential (LOGEST and GROWTH) regression. These functions are entered as array formulas and produce array results. You can use each of these functions with one or several independent variables. The following example shows you how to

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Exhibit 62.
RegBook opening page.

develop simple trend and growth regressions. Open RegBook.xls located in the "Models" subdirectory of the CD and follow the instructions (see Exhibit 62).

Let us develop a straight-line regression first. Excel labels this function a trend. When you finish, you can generate a curve through your data. Excel labels this function "growth." The following instructions will enable you to complete this operation.

To develop a trend:

1. Select c3:c14 by dragging mouse.

2. Click on formula bar. In formula bar type =trend(.

3. With mouse drag b3:b14. Watch formula bar change. Type in comma.

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Exhibit 63.
RegBook solution.

4. With mouse drag a3:a14. Watch formula bar change. Type in ).

5. Create array and regression by pressing simultaneously keys Control Shift Enter.

Develop regression forecast as follows:

1. Select c15:c24 by dragging mouse.

2. Click on formula bar. In formula bar type. = trend(.

3. With mouse drag b3:b14. Watch formula bar change. Type in comma.

4. With mouse drag a3:a14. Watch formula bar change. Type in comma.

5. With mouse drag a15:a24. Watch formula bar change. Type in ).

6. Create array and regression by pressing simultaneously keys Control Shift Enter.

Your solution should look like Exhibit 63. [CD:MODELS\EXCEL\ C6REGBkSolutions] If so, congratulations. Now let's move to a much higher order time-series level, reviewing a powerful tool, Decisioneering's CB Predictor.

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Regression Using Decisioneering's CB Predictor¹

A growing list of top financial executives are convinced that Decisioneering's CB Predictor is one of the best time-series models in the literature. Go to [CD:Applications\Decisioneering\Customer]. The firm's client list includes most of the Fortune 500 along with major accounting, investment, and commercial banking firms.

CB Predictor breaks historical data into three components: trend, seasonality, and error. We will develop and optimize time-series forecasting using the model.

CB Predictor uses techniques of time-series and multiple linear regression categories. The Crystal Ball product uses simulation. Each technique and method has advantages and disadvantages for particular types of data, so forecast your data using several methods and then select the method that yields the best results. Time-series forecasting is a category of forecasting that assumes that the historical data is a combination of a pattern and some random error.

Its goal is to isolate the pattern from the error by understanding the pattern's trend and seasonality. You can then measure the error using a statistical measurement test both to describe how well a pattern reproduces historical data and to estimate how accurately it forecasts the data into the future. When you select different forecasting methods to try from the Methods Gallery, CB Predictor tries all of them. It then ranks them according to which method has the lowest error, depending on the error selected from the Advanced dialog box. The method with the lowest error is the best method.

Before using CB Predictor, you must create an Excel spreadsheet with your historical data not unlike the one we developed (see Exhibits 62 and 63). [CD:MODELS\EXCEL\C6ShampooSolution] Creating a spreadsheet for use with CB Predictor is easy. The spreadsheet needs to include only a descriptive title and, optionally, a date (or other time period, such as Q4-1997) column or row, either at the top or along the left side of your data. If you format your dates as Excel dates, CB Predictor's Intelligent Input can find the dates, extend them with the forecasted values, and use them as labels on charts. Historical data, spaced equal time periods apart, are in columns or rows adjacent to the date column or row. You can use CB Predictor to simultaneously forecast from 1 to 10,000 adjacent historical data series.

After you create your Excel spreadsheet with your historical data, forecasting data using CB Predictor follows a 10-step process:

1. Select a cell range with your historical data to forecast. That is A3:B42 (see Exhibit 64).

2. Specify your data.

¹ Reproduced with permission of Decisioneering and Dr. Carl Crosswhite, the man behind CB Predictor. This chapter could not have been developed at the present level without Dr. Crosswhite's innovative and brilliant work in two disciplines: statistical analysis and software engineering and tools. This author is deeply indebted to this gentleman.

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Exhibit 64.
Shampoo sales opening.

3. View a graph of your historical data to identify any seasonality or trend and to see summary statistics.

4. Identify your time periods and whether your data has seasonality and, if so, how long your season is.

5. Set whether you want to use multiple linear regression to forecast any variables.

6. Select the time-series forecast methods to try for each variable.

7. Enter the number of periods you want to forecast.

8. Select a confidence interval to calculate or display with your forecasted values.

9. Select the results you want.

10. Preview and run the forecast, creating your results.

CB Predictor leads you through these steps using the CB Predictor Wizard, but you can also go directly to any of these steps to change methods or select different options and reforecast data (see Exhibit 65).

Also, many of these steps might be done automatically by CB Predictor. For example, CB Predictor's Intelligent Input can find and select your data, its arrangement, and the data units. You can also skip many other steps if the settings are already what you want. For example, all the time-series forecast-

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Exhibit 6-5.
Shampoos data box.

ing methods are selected by default, and that is probably how most users will leave them. Now lets review all the reports (see Exhibits 6-6 through 6-9).

See glossary of forecasting terms and additional statistical definitions dealing with predictor models at the conclusion of this chapter.

Simple Moving Averages

Simple moving averages are initially calculated by starting with the leftmost period in the data and adding up the specified prices (open, high, low, close, mid-point, or average) for the chosen number of periods. This total is then divided by the number of periods set in the Parameters menu. The formula is:

where
n = number of bars
Pt= selected calculation price
Pt₋₁ = selected calculation price 1 period ago
Pt-n = selected calculation price n periods ago

The moving average has distilled the trend from the daily price fluctuations (see Exhibit 6-10).

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Exhibit 66.
Report for Shampoo Sales.

Exhibit 67.
Trend line best-fit graph.

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Exhibit 68.
Method errors.

Exponential Smoothing Averages

Since the development of exponential smoothing 50 years ago, the method has become a popular method of forecasting with finance people. Exponential smoothing requires only a few data points to produce predictions and is well suited for large numbers or items. Exponential smoothing smoothes past values of a time series in a decreasing (exponential) fashion. This is achieved by a formula embedded on a statistical model that derives exponentially decreasing weights associated with past observations, visualized in Exhibit 611.

Regression Curve Fitting:
The Exponential and Logarithmic Curve Fit

Background

In a nutshell, watch out. If your firm is undercapitalized, exponential growth will likely stress it. Conversely, logarithmic growth is akin to stronger bond ratings, less default risk, and stronger cash flows. Exponential

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Exhibit 69.
Methods table for shampoo sales.

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Exhibit 610.
NYSE and moving averages.

Exhibit 611.
Exponential smoothing.

growth models are appropriate when growth increases at an increasing rate. Exponential growth is characteristic of hot Internet operations. An exponential growth curve has an upward rate of growth at any point in time, resulting in staggering increases over longer periods of time as the increase is compounded exponentially.

Growth is vital to the well-being of a firm, but it is also a two-edged sword. You might be able to play around with shareholder value numbers working through various valuation models, but if your blinders are on to unimpetuous risk, there may be little value left in your firm to maximize. Aggressive firms often try to expand sales too quickly for their own good. This is particularly true among smaller companies deficient in financial planning expertise. As a result, they may ignore the old axiom that the faster one grows, the easier it is for cash flows to become cannibalized by investment cash

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drains. Small increments to equity via earnings pale when matched against the insatiable appetite for new assets required by rapid growth firms.

Exponential growth has been the focus of much discussion among researchers investigating food and raw material requirements. Some analysts argue for growth limits because finite space and resources bind exponential increases. Others argue that stabilizing social and market mechanisms slow or stop exponential growth. As for business, most valuation experts argue that exponential growth retreats in the face of competitive markets when output becomes saturated in the marketplace, forcing down internal rates of return.

Whatever one's position, exponential growth may take place for extended periods of time, and that is the danger. Popular models, notably Excel's trend-line functions, are powerful tools to track data and spin them off into ''lower risk"/"higher risk" curve fits.

Trend Lines and Curve Fit Correlations in Excel

Open [CD:MODELS\EXCEL\C6REGRESS\Statistics] and select C6:C15 (see Exhibit 612). After you have selected cells C8:C15:

1. Create a Chart using the Wizard.

2. Click on line. You will see square boxes on your line.

3. Select chart and add trend line. See Exhibit 613.

4. Click on Exponential.

5. Select Options. Check off display equation on chart and display R² value on chart.

To add a trend line to a data series, do the following:

1. Click the data series to which you want to add a trend line or moving average.

2. On the Chart menu, click on Add Trend line.

3. On the Type tab, click the type of regression trend line or moving average you want.

4. Under options, select R² and Formula. See Exhibit 614.

Exhibit 612.
Sales/inventory matrix.

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Exhibit 613.
Trend line.

The R² statistic in Excel tells you what percentage of variation in the dependent variable (Y) is "explained" by changes in the independent variable. It ranges from 1 (meaning that the variation in the independent variable perfectly explains the variation in the dependent variable or that the relation between the two variables is very strong) to 0 (meaning that there is no relationship between the variables). In general, the larger the R² value, the better changes in the independent variable explain variations in the dependent variable. Let's examine sales data. We can see whether the trend fits an exponential or logorithmetic curve (see Exhibit 615).

BoxJenkins

The BoxJenkins methodology, (1976) has emerged as a widespread statistical method for autoregressive or time-series analysis. There are several types of BoxJenkins models. These include (1) univariate models (modeling a time series as a condition of its past), (2) transfer function models (modeling a time series as a function of its past and the past of one or more independent series), and (3) multiple equation models (modeling more than one time series as a function of all other series in the equation). Transfer function models are a particular case of multiple-equation models, where there is a unidirectional relationship between the output series and each of the input series.

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Exhibit 614.
Curve fit statistics.

One model that offers vector BoxJenkins modeling is MTS. The package includes a menu-driven system to set up and run the program. MTS allows forecasters to retain control over model identification, estimation, and forecasting procedures or to allow the program builds in heuristic to develop the model for the analyst. Vector ARIMA modeling is multiple-equation modeling where each input series may have a causal relationship with every other input series and each series is to be forecast. MTS is AFS's software package designed to allow the modeler/forecasters to develop these multiple endogenous variable models. Contact autobox@icdc.com.

BoxJenkins methodology need not assume an initial pattern. It begins with a tentative pattern, and a model is fitted in such a way that the error will be minimized. It then provides explicit information as to whether the tentative pattern employed is the correct one. If this pattern is not correct, the method provides guidelines for finding the right one.

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Exhibit 615.
Exponential and logarithmic curve fit and correlations.

Thus, the BoxJenkins methodology provides enough information to tentatively identify the pattern that best describes the data, estimate the parameters involved by minimizing the sum of the squared errors, and provide for a diagnostic check of the residuals to determine whether the tentative pattern (model) is an adequate one.

Multiple Regression

Multiple regression has become one of the most puissant models in the domain of statistical financial analysis. The purpose of multiple regression is to predict a single variable from one or more independent variables. Multiple regression with many predictor variables is an extension of linear regression with two predictor variables. A linear transformation of the X variables is done so that the sum of squared deviations of the observed and predicted Y is a minimum. The computations are more complex, however, because the interrelationships among all the variables must be taken into account in the weights assigned to the variables. The interpretation of the results of a multiple regression analysis is also more complex for much the same reason.

Here we find a lead/lag relationship between the dependent variable and a leading (independent) variable that could be used in predicting. From a practical view, the approach of paired indices is useful providing causal information. For example, you employ multiple regression and estimate causal relationships in data. This approach complements time-series forecasting. But be careful: You can run into problems. For example, to predict sales you may decide that disposable income and television spots

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are two linking factors. However, future levels of that disposable income may prove not to be a viable link, nor can one be certain of the role that television advertising will play in the future (i.e., the "error factor" in the formula).

While a compelling relationship may appear between sales and disposable income/advertising, the association might yield limited value. Thus, forecasting issues are not necessarily resolved by identifying causeeffect relationships. Relationships between variables may change as as your firm moves through its economic environment, so causal forecasting is never used alone.

Multiple regression designates one variable as dependent (Y) and picks, via a stepwise operation, which variables are independent (X). You may elect to develop the regression apart from stepwise. For example, you may want to change one variable, measure another, and then analyze the data with one or more of the standard statistical tests.

The prediction of Y is accomplished by the following equation:

If there is only a single X variable, then the equation is Y = ß₀ + ß1x1, and the "multiple regression" analysis is the same as simple linear regression (ß0 is the Y intercept; ß₁ is the slope).

One of the most famous examples of multiple regression is Altman's Z score. Altman developed the Z (zeta) score to predict distress at a certain confidence level. His causal regression, developed from stepwise, found crucial critical variables that were highly correlated to financial distress: working capital, leverage, sales, earnings retention, and operating profits.

Altman's sample included 33 financially distressed manufacturing firms along with a control group of 33 healthy companies. From financial statements one period prior to bankruptcy, Altman extracted 22 financial ratios, of which 5 were found to contribute most to the prediction model. The discriminate function Z was computer derived as:

where
x₁ = working capital/total assets
x₂ = retained earnings/total assets
x₃ = EBIT/total assets
x₄ = market value of equity/book value of debt
x₅ = sales/total assets

Z > 2.99 is classified as healthy and remained continuing entities. The higher the Z score, the healthier the firm and the lower the probability of failure. Z < 1.81 is classified as financially distressed or bankrupt.

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By applying the previous discriminate function to data obtained two to five years before bankruptcy, Altman discovered that the model correctly classified 72% of the initial sample two years before failure. A trend analysis shows that all five observed ratios, x1 . . . x5, deteriorated as bankruptcy approached and that the most serious change in most of these ratios occurred among the third and second years before failure. Following is an example of the function Z:

Two researchers, Moses and Liao, have suggested that individual ratios included in the model may be highly correlated with each other. This is serious stuff. As we will see shortly, highly correlated independent variables (multicollinearity) pose a threat to the accuracy of regression and must be statistically resolved.²

Individual ratios included in the model may be highly correlated with each other. This causes three problems. First, the relationship between individual ratios and the dependent variable (failure status) may be distorted. Second, correlation between predictor ratios may differ in other samples making results developed on one sample applicable only to that specific sample. Third, individual coefficients are not meaningful so conclusions concerning the importance of any individual ratio in explaining failure are not possible, making the model difficult to interpret. In fact the standard approach may assign coefficients with signs that are counterintuitive.³

Though this may be so, we need to look beyond multicollinearity to conceptualize the numerous threads of brilliant financial logic that drives the regression (did the logic drive the regression or the regression, the logic?). Let's give Altman the benefit of the doubt. In any event, I call Altman's linkage the domino-multiplier syndrome. For example, take sales. Firms running high operating leverage are sensitive to revenue declines. Follow how the model tracks sales declines:

1. Abrupt and sharp sales declines drive down x₃ (EBIT/assets) due to the negative effects of operating leverage. Thus, x₅ and x₃ drop.

2. A drop in x₃ (EBIT/assets) knocks over a domino by driving down 1.4x₂ (retained earnings/assets) as losses flow through because fixed costs are not covered.

² Douglas Moses and Shu S. Liao, "On Developing Models for Failure Prediction," Journal of Commercial Bank Lending (March 1987).

³ IBID

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3. Retained earnings are a component of working capital (along with increases in long-term obligations and reductions in fixed assets). Thus, x₂ (retained earnings/total assets) links to x₁ (working capital/total assets).

4. What effect will our dominos have on x₄ (market value of equity/book value of debt)? Investors start dumping shares in panic selling, fearing that the firm's weak liquidity (caused by operating losses) makes it difficult or nearly impossible to reduce debt.

A second regression factor, low asset productivity, has also been shown to be significant. Firms bankrupt when assets such as inventory, receivables, and equipment go out of control. Distressed companies break the cardinal aphorism of basic planning: Keep assets at minimum levels consistent with maintaining strong sales and profits. We note that four out of five Z score (X) variables carry assets in the denominator. Zeta will fall below critical mass if asset management loses out as a key strategic event. This means that if you want to keep your firm out of the minor leagues, check assets, ensure that they operate at optimal efficiently, develop goods and services that produce healthy profits, and keep watch over the firm's equity base and capital structure.

Is Multiple Regression the Right Tool for Your Forecasts?

1. Is the relationship between the X variable and Y variables linear? If the relationship between X and Y variables is nonlinear, multiple regression may not be the method for the task at hand. In some cases, you may be able to transform one or more X variables to create a linear relationship. If so, fine. In chapter 8, we explore neural networking, which will resolve nonlinear data problems.

You may also be able to restrict your data to a limited range of X variables where the relationship is close to linear. Some programs can perform nonlinear regression with multiple independent variables.

2. Is the variability the same everywhere? Multiple regression assumes that data scattering from predictions has identical standard deviations for all values of independent variables. The assumption is violated if the scatter goes up (or down) as one of the X variables gets larger. The assumption that the standard deviation is the same everywhere is termed homoscedasticity.

3. Is multicollinearity a problem for your forecasts? Multicollinearity can cause regression results to end up in the old garbage-in, garbage-out bin. This is when two or more independent variables are highly related to one other. High correlation between independent variables creates computational problems, but you correct this by eliminating all but one of the highly correlated independent

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variables from the regression model. Crystal Ball will test degrees of correlation between independent variables, so do not worry.

Here is an example. Imagine you are running a multiple regression to extract the average collection period (the Y variable) from credit policy, credit terms, and collection phone calls. Now imagine that you have entered collection phone calls in hours and collection phone calls in minutes as two separate (X) variables. The two (X) variables measure exactly the same thing, the only difference is that the two variables have different time units. So you solve problems of multicollinearity by taking one of the variables out of the regression.

Simulation software makes it easy by testing how well each independent (X) variable can be predicted from the other (X) variables (ignoring the Y variable). However, in general there are three methods that you can employ to determine the degree of multicollinearity:

1. R² with other X variables: the fraction of all variance in one X variable that can be predicted from the other X variables.

2. Use the variance inflation factor (VIF): If the X variables contain no redundant information, you expect VIF to equal one. If the X variables are collinear (contain redundant information), then VIF will be greater than one. Multicollinearity increases the width of the confidence interval (which is proportional to the square root of variance) by a factor equal to the square root of VIF. If a variable has a VIF of 9, the confidence interval of that coefficient is three times wider than it would be were it not for multicollinearity.

3. Determine tolerance, which is the fraction of the total variance in one X variable that is not predicted by the other X variables.

Since all three measure multicollinearity the same way, take your pick between R² and VIF. Also, for each X variable, the corresponding VIF can be derived from R² by VIF = 1/(1 R²). And you easily calculate tolerance for each variable as 1.0 R². If R² and VIF are high for some X variables, then multicollinearity is a problem in your data.

What are the benchmarks? The usual threshold is that if any of the R² values are greater than 0.75 (so VIF is greater than 4.0), suspect that multicollinearity might be a problem and start thinking of throwing out a duplicating independent variable. If any of the R² values are greater than 0.90 (so VIF is greater than 10), then you should assume that multicollinearity is serious, and at this point do not think but act, discarding the duplicating variable.

Finally, remember that there are individual R² values for each X variable and the R²t correlating all the X's with the Y. The Y R² is the one that is really the summation but it means little until you tidy up the regression

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by adjusting the individual X variables to eliminate multicollinearity. You want the overall R² value to be high (good fit) and all the individual R² values to be low (little multicollinearity).

Econometric Forecasting (Econometric Models)

Econometric forecasting is an extension of regression analysis. As we saw, regression analysis assumes that each of the independent variables included in the equation is determined by outside factors. In economic or organizational relationships, however, such an assumption of independence is unrealistic. Often there is mutual independence among all variables in a forecasting equation, and regression analysis is incapable of dealing with such interdependence.

Econometric forecasting enables one to deal with such a situation. It expresses a more accurate relationship by developing a system of simultaneous equations. These, by their nature, are capable of dealing with interdependent variables.

For example, suppose that Sales = f(GNP, price, advertising). (This is the multiple regression form.) In econometric form, one might have the following:

1. Sales = f(disposal income, price, advertising)

2. Cost = f(raw materials, production, and inventory levels)

3. Selling expenses = f(advertising, transportation, and other selling expenses)

4. Price = cost + selling expenses

Now, instead of one relationship there are four. As with regression analysis, you need to do the following:

· Determine the functional form of each of the equations.

· Estimate in a simultaneous manner the values of their "parameters."

· Test for the statistical significance of the results and the validity of the assumptions involved.

The main advantage of this method of forecasting is that it provides the values of several of the interdependent variables within the model itself, thus eliminating the need to estimate them externally. It also provides useful explanatory information as to the type of relationships involved. The estimating of the equation parameters involves problems far more complex than those encountered in regression analysis. It is these problems that make the application of econometric forecasting both difficult and expensive. However, the advantages gained by the method may well compensate for the extra costs incurred.

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A "Sensitivities" Approach to Financial Forecasting

Modified Percentage of Sales

Relationships that held up in the past generally persist at least into the near term. Finding regularities in historical statements improve predictions of the future. If historical relationships were to change, however, your ability to predict would become less effective until you identified new relationships. Thus, you need to complement statistics with a forecasting method that more or less ties to financial statements.

This is the popular method known as modified percentage of sales. The rationale behind this method is based on the premise that the balance sheet is correlated to changes in sales. Whether a firm restructures or just grows normally, variations in revenue generally require asset/liabilities adjustments. The "sensitivity" approach to forecasting is an efficient method to develop strategic plans. In the process of developing a forecast, you will work with two important equations: the financial needs formula (F) and the projected percentage of sales externally financed formula (E):

where
F = cumulative financial
A = projected spontaneous assets
S = projected sales
DS = change in sales
DNFA = change in net fixed assets
L1 = spontaneous liabilities
P = projected profit margin (%)
D = dividend payout rate
R = debt maturities
T = targeted growth rate
L = leverage
g = sales growth rate

The F formula determines the external financing needs of the firm. If used in conjunction with the percentage-of-sales method, both techniques render the same answer. The formulas are easy to enter into the HP 19BII solver:

The E formula identifies the percentage of sales growth requiring external financing. The two equations are interconnected since both are derived from the popular IAS and FAS cash flow statement.

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For example, firms with high growth potential create shareholder value. That aphorism is as old as the hills. Yet a high growth firm running on high octane fixed assets can push the firm to the brink (see chapter 5).

Setting up the Percentage-of-Sales Method
[CD:\MODELS\EXCEL\C6BosProj]

On the left-hand side, or asset portion, of the balance sheet, current assets that vary proportionately with sales include cash, accounts receivable, prepaid expenses, and inventory. For example, if accounts receivable historically run 30% of sales and next year's sale are forecasted to be $100 million, accounts receivable will be projected at $30 million. Fixed assets are generally somewhat independent of sales.

On the right side, spontaneous liabilities, accounts payable and accruals move in tandem with sales. Liabilities independent of salesall the funded ones representing financing activitiesare excluded. Equity, including preferred and common, are financing activities and are not directly derived from variations in sales. Retained earnings is calculated by deducting the dividend payout from net profits. Before we go further, another important point to make is that you also need to identify and estimate noncritical variables (not included in this exercise). This is accomplished by extrapolating historical patterns or adjusting historical trends. Examples of noncritical variables include various prepaid assets and disposals.

Applying modified sales percentage method to Boston's 1998 financial statements, Exhibit 617 we see that the following accounts have been calculated as a percentage of 1999 sales and will be used as projection assumptions for the company's original five year strategic plan. Cash, receivables, inventory, fixed assets, accounts payable and accruals (see Exhibit 616).

Two outcomes occur as a result of applying modified percentage of sales: (1) projected liabilities and equity less than projected assets pro-

Exhibit 66.
Input screen projection assumptions.

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Exhibit 617.
Boston Widget Co. Inc.

duces financial needs (e.g., amount of additional funding required to obtain predicted sales), and (2) projected liabilities and equity greater than projected assets produce a cash surplus. You can see that Boston requires additional debt or equity funding to meet sales targets in each of the four years projected (see Exhibit 618).

Reintroducing the F and E equations, we can draw conclusions that go beyond the yields provided by a simple accounting projection (see Exhibit 619). Let's begin by first examining the F equation:

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Exhibit 6-18.
Boston Widget Co.

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Exhibit 6-19.
Deriving financial needs using The F and E equations.

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The results yield exactly the same financial needs as the projected financial statements.

We see the effect independent (X) variables have on Boston's (Y), that is, financial needs after adjustments. The first test involves changes in spontaneous asset levels. Currently, Boston's asset investments are projected at 49.2% of sales. If, for example, spontaneous assets levels decrease, the overall effect on financial needs, or F, will also decrease. Since inventory and accounts receivable usually make up 80% of current assets, it may be in your best interest to hold the line to minimum levels to maintain optimal levels of working capital. When current assets operate at optimal points, the cash cycles become smooth and clean.

The second sensitivity variable is spontaneous liabilities. If Boston's spontaneous liabilities increase from its current level of 14%, financial needs decrease. For example, by increasing accruals (a source of cash), financial needs will decrease as they approach or surpass assets levels. What would be the overall effect if sales decreased? It makes sense that reduced sales projections require less financing and result in reduced external support. The same theory holds true for the dividend rate. By lowering the dividend payout ratio, additional funds will be funneled back into the company (retained earnings). With additional internal funds available to support future needs, cash requirements lower along with unsystematic risk. Stakeholders relax a bit. Now let's look at E:

where
E = projected percentage of sales growth externally financed
G = growth rate

Thus, 23.4% percent of Boston's sales growth will be generated by external financing with 76.6% generated by internal cash flow (.234 × 35,213 = 8,244, the same answer as previously).

As the formula implies, the E equation determines how much sales growth requires external financing. If E reaches 95% in the projection period, only

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5% of sales growth will be internally financedan immediate storm signal, especially if base-year leverage is excessive.

Setting E to zero and solving for G, the sales growth rate will give you a fast reading on the quality and magnitude of cash flows. Say that E is set to zero and G falls somewhere in the first industry quartile. This means that you are not only strong but can be financed with internal cash flow as well. Another example: Let's assume that base-year leverage is high and you want to reduce leverage by internal financing levels set at 40%. Set the equation at 60% and solve for the capital output ratio required to make your strategy work. If embedded ratios (receivables, inventory, and fixed assets) are below industry or benchmarks, call a meeting of the department heads and read them the riot act. The F and E equations, Exhibit 619, reconcile to the financial statement in Exhibit 616 and 618.

We can now summarize, as shown in Table 64.

Glossary of Forecasting Terms

Double moving averageApplies the moving average technique twice, once to the last several periods of the original data and then to the resulting single moving average data. This method then uses both sets of smoothed data to project forward.

Double exponential smoothingApplies SES twice, once to the original data and then to the resulting SES data. CB Predictor uses Holt's method for double exponential smoothing, which can use a different parameter for the second application of the SES equation. CB Predictor can automatically

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calculate the optimal smoothing constants, or you can manually define the smoothing constants.

Single exponential smoothing (SES)Weights all of the past data with exponentially decreasing weights going into the past. In other words, usually the more recent data have greater weight. This largely overcomes the limitations of moving averages or percentage change models. CB Predictor can automatically calculate the optimal smoothing constant, or you can manually define the smoothing constant.

Moving averagesEliminate randomness and smooth out a time series. This objective is achieved by averaging several data points together in such a way that positive and negative errors eventually cancel themselves out. The term moving average is used because, as each new observation in the series becomes available, the oldest observation is dropped and a new average computed. The result of calculating the moving average over a set of data points is a new series of numbers with little or no randomness. The ability of moving averages to eliminate randomness can be used in time-series analysis for two main purposes: to eliminate trend and to eliminate seasonality.

Exponential smoothing methodsDeveloped in the early 1950s, these have since become a particularly popular method of forecasting among businesspeople because they are easy to use, require very little computer time, and need only a few data points to produce future predictions. These smoothing methods are well suited for short-or immediate-term predictions of a large number of items. They are suitable for stationary data or when there is a slow growth or decline over time. The method of exponential smoothing is based on averaging (smoothing) past values of a time series in a decreasing (exponential) manner. In Excel, for example, exponential smoothing averages the smoothed value for the previous period with the actual data for the previous data point. This feature automatically includes all previous periods in the average. You can specify how much to weight the current period.

Definitions:
Statistical Forecasting

Mean and variants of each variableThis information can be useful in understanding the sampling distribution of the mean of each variable and can be used in constructing confidence intervals. The mean (average) is a measure of central tendency in a frequency distribution, usually calculated as the arithmetic mean. The arithmetic mean is equal to the sum of observations divided by the number of observations. The geometric mean represents the nth root of the product of a set of n numbers, will always be less than the arithmetic mean unless all numbers are equal and usually is used for averaging rates of change. The mode is a measure of central tendency equal to the most commonly occuring value in a distribution. It is generally applicable only to discrete data (e.g., integer values) because with continuous data (e.g., real numbers) it is highly unlikely that duplicate observations will occur. The median represents a measure of central tendency in a frequency

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distribution, is very resistant, and often is used in exploratory data analysis (EDA), equal to the value in the distribution that divides the distribution into two halves of equal numbers of observations (50th percentile). If there is an even number of observations in the distribution, then the median is equal to the mean of the two adjacent values

Standard deviation of each variableA measure of dispersion of a frequency distribution standardized to sample size.

R²A measure of the adequacy of the fit. It indicates the percentage of the total variations of the dependent variable explained by variations in the independent variables. R² varies from zero to one. If it is zero, it means that the regression equation does not explain the variations in the dependent variable. If it is one, it means that the regression fit is perfect and that any changes in the dependent variable are accounted for by changes in the independent variables. Such a relationship is deterministic, and forecasting will be perfect. Between these two extremes of zero and one, R² can serve as one indicator of how ''good" the regression equation is. However, an R² value of close to one does not necessarily indicate a good forecasting equation.

Correlation coefficientsThe correlation coefficients (or, alternatively, the simple correlation matrix, which is the aggregation of all correlation coefficients) show how all the independent variables are correlated between themselves and with the dependent variable. As a general rule, one does not want to include in a regression equation two or more independent variables that are highly correlated between themselves (i.e., more than 0.7), nor does one wish to include independent variables with low (i.e., less than .05) correlation with the dependent variable. The first case introduces multicollinearity, which is a computational problem causing the results to become unreliable. (It is like trying to divide 1 by .00000000001: The computer may not have enough significant digits to handle the division.) If there are two independent variables with a high correlation between them, no information is lost by removing one of them. Low correlations imply that there is no relationship between the dependent and the corresponding independent variables. Thus, if such an independent variable is included, it generally will add little in explaining variations in the dependent variable. Looking at the correlation matrix of all variables, one can immediately exclude those independent variables having a low correlation with the dependent variable and then add independent variables that do not have a high intercorrelation between them. This can be achieved by starting with the independent variable with the highest correlation with the dependent variable and then adding the independent variable with the next highest correlation with the dependent variable but with a low correlation with the previously included independent variable(s). (This information can be found by examining the correlation coefficients.) The correlation matrix allows one to exclude many variables (either high or low correlated), which makes the job of deciding on a final equation much easier.

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(b) Standard errorA term applied to various statistical measures (such as the mean) that gives the distribution within which that measure will fall when samples are drawn from any population or distribution. The standard error is dependent on the dispersion in the population and the size of the sample. The standard error for the arithmetic means is calculated as standard error = SD of population/SR of number of units in the sample.

Coefficient of determinationThis statistic indicates the percentage of the variability of the dependent variable that the regression equation explains. For example, an R² of 0.36 indicates that the regression equation accounts for 36% of the variability of the dependent variable. It corrects R² to account for the degrees of freedom in the data. In other words, the more data points you have, the more universal the regression equation is. However, if you only have the same number of data points as variables, the R² might appear deceivingly high. This statistic corrects for that. For example, the R² for one equation might be very high, indicating that the equation accounted for almost all the error in the data. However, this value might be inflated if the number of data points was insufficient to calculate a universal regression.

Sum of square deviationsThe least-squares technique for estimating regression coefficients minimizes this statistic, which measures the error not eliminated by the regression line. For any line drawn through a scatter plot of data, there are a number of different ways to determine which line fits the data best. One method is to calculate the SSE (sum of the squared errors) for each line. The lower the SSE, the better the fit of the line to the data.

F statisticTests the significance of the regression equation as measured by R². If this value is significant, it means that the regression equation does account for some of the variability of the dependent variable. The F test is similar to the t test except that it tests the simultaneous significance of the variables in the regression equation. It is a statistical means of checking the hypothesis that the overall relationship between the dependent variable and all the independent ones is statistically significant. As a general rule, if F > 5, it means that there is a statistically significant relationship. The F test is the first statistic to examine in regression analysis. If it is greater than 5, then one can continue with the other tests. If it is less than 5, one must examine alternative models. If the F test is significant, one can examine each of the I tests and the R². If the F test is > 5 and each of the I tests > 2, then one can decide whether the R² is satisfactory. If it is, the remaining task is to check the regression assumptions. If R² is not satisfactory, it implies that there are other important factors that influence the dependent variable and that have not been included in the regression equation. It may be possible to identify these factors and increase the value of R² to some acceptable level

t statisticA very important test, this statistic tests the significance of the relationship between the coefficients of the dependent variable and the

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individual independent variable in the presence of the other independent variables. If this value is significant, it means that the independent variable does contribute to the dependent variable.

Percentage variation explainedThe percentage variation explained indicates what percentage of the overall variation in the dependent variable each one of the independent variables explains. The higher the percentage, the more influential that variable. The sum of all percentage variations explained is R².

DurbinWatson test and homoscedasacityThere are four assumptions made in any application of regression: linearity, normality, independence of residuals, and constant variance. The first two are of little concern because they are almost always satisfied. For the last two, however, one must check to be sure that they are not violated.

BoxJenkinsTo create forecasts, you need to find a relationship between the variable being predicted, such as equity returns, and lagged values of predictive variables, such as dividend yield or earnings momentum. This ensures that forecasts are based solely on data available at the time the forecast is made, thereby avoiding the "look-ahead" bias. The autoregressive and moving average (ARMA) model, proposed by Box and Jenkins, predicts future values of a variable solely on the basis of its own past history. One of its sortcomings is that it ignores the role of other factors. ARMA models are often good at providing short-term forecasts but typically produce poor long-term forecasts

Significance testIn hypothesis testing, a test that provides a criterion (probability associated with a particular sample or observation) for determining whether a difference between that observation and an expected value can be attributed to chance. The null hypothesis is either accepted or rejected by comparing the calculated probability with a critical value (such as 0.05).

Chi-square testA nonparametric test for comparing the goodness of fit of a single sample distribution to a theoretical distribution or between any number of sample distributions. It is applicable only to nominal data in the form of frequencies in mutually exclusive categories and not to percentage data. There should also not be many categories with very low frequencies, and none with zero frequency, and if there are only two categories, both frequencies must be at least 5.

Chapter Six References and Selected Readings

Books

Addin Enbbu, et al. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, Calif.: Sage Publications.

Berry, W. D., and S. Feldman. (1985). Multiple regression in practice. Beverly Hills, Calif.: Sage Publications.

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Boyce, D. E., et al. (1974). Optimal subset selection: Multiple regression, interdependence, and optimal network algorithms. Berlin: Springer-Verlag.

Grimm; L. G., and P. R. Yamold. (1995). Reading and understanding multivariate statistics. Washington, D.C.: American Psychological Association.

Hardle, W., et al. (1988). Investigating smooth multiple regression by the method of average derivatives. Cambridge: Sloan School of Management, Massachusetts Institute of Technology.

Heward, J. H., and P. M. Steele. (1973). Business control through multiple regression analysis; a technique for the numerate manager. New York: John Wiley & Sons.

Launer, R. L., et al. (1982). Modern data analysis. New York: Academic Press.

Rothman, P. (1999). Nonlinear time series analysis of economic and financial data. Boston: Kluwer Academic Publishers.

Shorter, J. (1982). Correlation analysis of organic reactivity, with particular reference to multiple regression. Chichester: Research Studies Press.

Thomas, J. J. (1964). Notes on the theory of multiple regression analysis. Athens.

Wesolowsky, G. O. (1976). Multiple regression and analysis of variance: An introduction for computer users in management and economics. New York: John Wiley & Sons.

Periodicals

Anonymous. (1992). "Model behavior." Financial World, 161(11), 74.

Anonymous. (1997). "Information technology." Chartered Accountants Journal of New Zealand, 76(3), 75.

Anonymous. (1998). "Faster financial forecasting." Credit Management, 18.

Anonymous. (1998). "New software speeds up financial forecasting." Accountancy Ireland, 30(2), 28.

Baker, Al. (1992). "Financial forecasting at Atlantic Richfield Company." Journal of Business Forecasting Methods and Systems, 11(3), 9.

Balmat, Robert E, III. (1992). "Financial forecasting at Rockwell International's Defense Electronics." Journal of Business Forecasting Methods and Systems, 11(2), 3.

Benson, P. George, and Christopher B. Barry. (1982). "On the implications of specification uncertainty in forecasting." Decision Sciences, 13(1), 176.

Berglas, Anthony. (1999). "Spreadsheet errors: Risks and techniques." Management Accounting, 77(7), 46.

Brockhoff, Klaus. (1983). "Group processes for forecasting." European Journal of Operational Research, 13(2), 115.

Chopra, Vijay Kumar. (1996). "Improving financial forecasting: Combining data with intuition." Journal of Portfolio Management, 22(3), 97.

D'Attilio, David F. (1992). "Net working capital forecasting at Dupont." Journal of Business Forecasting Methods and Systems, 11(1), 11.

Fisher, Steven A. (1991). "Financial forecasting and the CPA." Journal of Business Forecasting Methods and Systems, 10(1), 7.

Fulford, James. (1996). "Financial forecasting software." Accountancy Ireland, 28(6), 30.

Funkhouser, G. Ray. (1984). "Using qualitative historical observations in predicting the future." Futures, 16(2), 173.

Hogan, Mike. (1995). "Financial forecasting for the rest of us." PC/Computing, 8(1), 108.

Lam, K. Chi. (1999). "Modelling financial decisions in construction firms." Construction Management and Economics, 17 (5), 589.

Martino, James P. (1993). "Financial forecasting at Teleport Communications Group." Journal of Business Forecasting Methods and Systems, 12(1), 7.

Murray, Peter. (1992). "Financial modelling." Australian Accountant, 62(2), 51.

Myhre, T. C. (1992). "Financial forecasting at Martin Marietta Energy Systems, Inc." Journal of Business Forecasting Methods and Systems, 11(1), 28.

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Singhvi, Suren S. (1991). "Polishing the controller's crystal ball: Financial forecasting tips." Corporate Controller, 3(6), 31.

Snyder, Donald. (1982). "Current approaches to time series forecasting." Business Forum, 7(2), 24.

Speight, Alan E. H. (1997). ("Financial forecasting for business and economics." International Journal of Forecasting, 13(2), 293.

Walkin, Lawrence. (1991). "Pro-Forma Plus: The financial forecasting model." CMA, 65(7), 28.

Wells, Martin T. (1997). "Financial forecasting for business and economics." Journal of the American Statistical Association, 92(439), 1227.

Select Internet Library

Statistical Software for Forecasting
Provides 20 statistical programs for those who are interested in using the computer to make more profitable forecasting business decisions. It includes such programs as multiple correlation and regression, time-series analysis and decomposition, trend projections, and exponential smoothing for forecasting. A Computer Assisted Investment Handbook, which also functions as the manual, lists and explains all the programs in detail. http://business.software-directory.com/cdprod1/swhrec/017/214.shtml."

Forecasting Links Author: Brian C. Monsell
Last Update: October 23, 1999, Business Forecasting Links to sites of interest to forecasters, including news, the International Institute of Forecasters, conferences, journals and books for forecasters, FAQs, and other forecasting sites. Maintained by Fred Collopy. http://www.cpcug.org/user/bmonsell/forecast.html.

Statistical Software on the Web. http://www.udel.edu/ASA/stats_software.html

Forecasting Bibliography and Links; Links to web sites on forecasting
International Association of Business Forecasters (IABF)
International Institute of Forecasters (IIF)
Forecasting e-mail discussion groups
Institute of Business Forecasting (IBF)
http://www.autobox.com/links.html.

California State University, Los Angeles, has an extensive collection of links to other sites on the Web related to the statistical packages used most often at the university.
http://artemis.calstatela.edu/stats/statlinks.htm

CD

Name
Size
Type

C6BosProj
102KB
Microsoft Excel Worksheet

C6REGBkSolution
32KB
Microsoft Excel Worksheet

C6REGBook
29KB
Microsoft Excel Worksheet

C6REGRESS
152KB
Microsoft Excel Worksheet

C6ShampooSolution
704KB
Microsoft Excel Worksheet

Forecasting Bibliography and Links
1KB
Internet Shortcut

Forecasting Links
1KB
Internet Shortcut

Statistical Software for Forecasting
1KB
Internet Shortcut

Statistical Software Links
1KB
Internet Shortcut

Statistical software on the web [21
1KB
Internet Shortcut

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Chapter Seven
How to Apply Monte Carlo Analysis to Financial Forecasting

This chapter and chapter 8 focus on simulation and neural networking, two new and powerful tools in finance, and goes far beyond traditional sensitivity analysis, creating spreadsheets that quantify real-world uncertainties. These topics are true money savers, as assumption variables having little impact on forecast variables need not be highly funded or for that matter, investigated.

This chapter will look at project and research investment analysis, Monte Carlo simulation, defining assumptions and identifying a distribution type, responding to problems with correlated assumptions, working with confidence levels, determining certainty levels for specific value ranges, determining the expected default frequency, understanding probability distributions, and using descriptive statistics tools.

A "Simulations" Approach to Financial Forecasting

Standard forecasting models rely on single sets of assumptions that usually lead to two outcomes: base case and worst case. But how unrealistic these scenarios are! If your sense of being were limited to two scenarios, your existence would compress to an ultramundane static plane. Thus, in finance, as in life, base case/worst case does not exist. Only real case

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doesexperiential and dynamic, that is, as you define real from experience, wisdom, and a lot of old-fashioned nitty-gritty causalities.

Static forecasting, base and worst cases, limits the variability of outcomes. This is important since variability not only is your moneymaker but also is crucial in strategic decision making. It's very difficult to know which of a series of strategic options the firm should pursue without being able to appreciate differences in both the range and the distribution shape of possible outcomes and the most likely result associated with each option. In the final analysis, simulation forecasting is kinetic; sensitivity models are immobile, models for old-fashioned decision makers.

A simulation is a computer-assisted extension of sensitivity forecasting (as an add-on to Excel). It gives the decision maker the ability to answer questions such as "Will we stay under budget if we build this facility?," "What are the chances this project will finish on time and in the money?," "What independent variable do I have to fix up before we get a go on the project?," ''Is multicollinearity a problem with my forecast?," and "How do we develop a convincing impact analysis?"

With the technique known as Monte Carlo simulation, an entire range of results and confidence levels are feasible for any given forecast run. The principle behind Monte Carlo simulation comprises real-world situations involving elements of uncertainty too complex to be solved with naive methods. It is a technique requiring a random number generator set in the program. Crystal Ball and @Risk are two popular programs that generate random numbers for assumption cells that you define. Using these random numbers, simulation programs compute the formulas in the forecast cells. This is a continuous process that recalculates each forecast formula over and over again.

France Telecom is a good example of how one firm built a powerful simulation model.¹ France Telecom, the French national telephone company, provides the network both for its own telephone operations and for the operations of recent competitors, such as Bouygues and Alcatel. Faced with heightened competition, the firm felt that it needed to better grasp market demand. Thus, the firm produced a spreadsheet model that worked with assumptions dealing with French regional market demand. This called for analyzing the number of calls, the distribution of the length of a call, and a host of other key independent variables.

By examining the distribution of these possible demands, France Telecom wanted to forecast the correlation of these factors on the profit margin, that is the Y, or dependent, variable. The firm invited a consulting company that specialized in operations research to work with them to amend their marketing model through optimization and simulation. Using Crystal Ball, assumptions were defined for all the variable model elements, including the number of calls and the distributions of call duration, and then defined the significant results, such as profit margins, as forecasts.

¹ Example courtesy of Decisioneering.

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France Telecom was also interested in adding linear programming optimization to the model so that, once the market demand was known, they would be able to project out and reorganize their network so as to minimize costs. For the linear programming element of the model, the consultants first wrote a small user macro that called Excel's Solver and requested that this macro be run at the end of each Crystal Ball simulation. Thus, France Telecom was able to simulate possible demand structures and to obtain in each case, through the linear programming optimization, the resulting profit.

France Telecom now has the capacity to optimize, in real time, its network structure to satisfy the market demand, an asset that was very useful in its budget-planning phase.

Hasbro is the nation's second-largest toy manufacturer. The firm uses simulation in investment analysis to help determine the profitability of new toy brands and lines. In one case, simulations were run to determine the probability of achieving a favorable outcome in a technology acquisition. After running the simulation, management decided that the new technology had only a 20% probability of success, thus allowing Hasbro to walk away before engaging in such a high-risk investment. Before using this powerful financial tool, Hasbro engaged in "eternal what-if scenarios," which required a huge number of manual calculations and still resulted in not much better than best/worst-case scenarios that at best achieved numbers somewhere in the middle. In a competitive environment such as the toy industry, where the product line is continually changing, sensitivity analysis is too simplistic in making the right decisions necessary for survival.

As a third example, Bankers Trust's Risk Management Advisory (RMA) group builds on its recognized strengths in risk measurement and management to help clients reshape their perception of the risks in their businesses and elevate their competitive positions by enhancing their risk management. Their clients span all industries and geographic sectors. RMA uses packages such as Crystal Ball to build customized financial and strategic models for their clients. While each of these models is unique, most contain stochastic processes and necessitate the incorporation of simulation.

Examples at Bankers include an asset valuation model for electric utilities, a cash-flow-at-risk model for a large corporation, and a hedging model for trading portfolios. Without the use of these products, RMA's financial models would require significant amounts of time to run. RMA provides customers with transparent quantitative methodologies and approaches to risk management as opposed to traditional "black box" solutions, as we referred to in our discussion on sensitivity forecasting in chapter 6.

Developing a simulation using Crystal Ball is not difficult. Let's start a tutorial using a simple spreadsheet: SampleSim.xls/Spread (see Tables 71 and 72). You are invited to open this spreadsheet which is in the "models" subdirectory of your CD. You are also invited to follow Decisioneering's demo, Fin_demo, by clicking this application file on the CD.

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Next pick (X) variables and define assumptions (Table 72). The assumption variables are Cost of goods sold (triangular distribution), Selling expenses, (uniform distribution) and Administration expenses (normal distribution). Next, define forecast by selecting the Y variable, net profit.

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Finally, run the simulation, set profits at 95% confidence and run the report. The report is displayed in Exhibit 71.

As you can see there is a world of difference between a simple spreadsheet presentation of Samplesim.xls and the identical spreadsheet developed through a simulation and report provided by Crystal Ball. Without simulation, cost of goods sold as a value driver will reveal only a single outcome, generally the most likely or average scenario. Spreadsheet risk analysis uses both a spreadsheet model and simulation to automatically analyze the effect of varying inputs on outputs of the modeled system. One type of spreadsheet simulation is Monte Carlo simulation, which randomly generates values for uncertain variables over and over to stimulate a model. How did Monte Carlo simulation get its name?

Monte Carlo simulation was named for Monte Carlo, Monaco, where the primary attractions are casinos containing games of chance. Games of chance, such as roulette wheels, dice, and slot machines, exhibit random behavior. The random behavior in games of chance is similar to how Monte Carlo simulation selects variable values at random to simulate a

Exhibit 71.
Piece of Cake Crystal Ball report.
Simulation started on 8/30/99 at 19:47:42
Simulation stopped on 8/30/99 at 19:47:56

(continues)

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Exhibit 7-1.
Continued.

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Exhibit 71.
Continued

model. When you roll a die, you know that either a 1, 2, 3, 4, 5, or 6 will come up, but you do not know which for any particular roll. It is the same with variables that have a known range of values but an uncertain value for any particular time or event (e.g., interest rates, staffing needs, stock prices, inventory, and phone calls per minute).

Following is a sampling of frequently asked questions that may be very helpful to readers not acquainted with simulations.

What do you do with uncertain variables in your spreadsheet?² For each uncertain variable (one that has a range of possible values), you define the possible values with a probability distribution. The type of distribution you select is based on the conditions surrounding that variable.

To add this sort of function to an Excel spreadsheet, you would need to know the equation that represents this distribution. With Crystal Ball 2000, these equations are automatically calculated for you. Crystal Ball 2000 can even fit a distribution to any historical data that you might have.

What happens during a simulation? A simulation calculates multiple scenarios of a model by repeatedly sampling values from the probability distributions

² These questions were extracted from Decisioneering's Crystal Ball Web site. The author wishes to thank Decisioneering for permission to extract these questions and answers from their site.

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for the uncertain variables and using those values for the cell. Crystal Ball 2000 simulations can consist of as many trials (or scenarios) as you wanthundreds or even thousandsin just a few seconds. During a single trial, Crystal Ball 2000 randomly selects a value from the defined possibilities (the range and shape of the distribution) for each uncertain variable and then recalculates the spreadsheet.

How do you analyze the results of a simulation? For every spreadsheet model, you have a set of important outputs, such as totals, net profits, or gross expenses, that you want to simulate and analyze. Crystal Ball 2000 lets you define those cells as forecasts. You can define as many forecasts as you need, and when you run a Monte Carlo simulation with Crystal Ball 2000, Crystal Ball 2000 remembers the values for each forecast for each trial. During the simulation, you can watch a histogram of the results, referred to as a Frequency Chart (see Exhibit 71) developed for each forecast. While the simulation runs, you can see how the forecasts stabilize toward a smooth frequency distribution. After hundreds or thousands of trials, you can view the statistics of the results (such as the mean forecast value) and the certainty of any outcome.

What is certainty? Certainty is the percent chance that a particular forecast value will fall within a specified range. For example, you can see the certainty of breaking even (results better than $0) by entering the $0 amount as the lower limit. In the case of "Piece of Cake" example, 1000 runs were made (Exhibit 71). A 95% confidence was set with net profit falling between 180.1 and 269.8. Therefore, the forecast results not only show you the different result values for each forecast, but also the probability of any value or, if you want, a particular confidence level. Other charts allow you to examine different facets of your model:

The Sensitivity Chart lets you analyze the contribution of the assumptions (the uncertain variables) to a forecast, showing you which assumptions have the greatest impact on that forecast. What factor is most responsible for the uncertainty surrounding your net profit? Which geological assumptions are most important when calculating oil reserves? Sensitivity analysis lets you focus on the variables that matter most. The Overlay Chart lets you display multiple forecasts on the same axis, even when the forecasts are from separate spreadsheet models. Which of six potential new projects has the highest expected return with the least variability (smallest range of values) surrounding the mean? With the Overlay Chart, you can compare and select the best alternatives.

The Trend Chart lets you stack forecasts so that you can examine trends and changes in a series.

How do your risks change over time? You need to assign a probability distribution to each uncertain element in the forecast. The distribution describes the possible values at 100% confidence the variable could take on, and, thus, it states the probability of each value occurring. The software randomly picks a value for each uncertain variable associated with an assigned probability distribution and will generate a set of financials (if this is what you want) based on values you selected. This creates one trial. Performing the last step many times produces a large number of trials.

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Case Study
International Drug Corporation,
Project Analysis under Uncertainty³

International Drug Corporation (IDC) is a research-focused pharmaceutical company. Pharmaceutical research has led to numerous advances in medical therapy. However, such research, by its nature, involves a tremendous amount of risk and uncertainty. Often 1,000 or more compounds are screened for each one that ultimately is nominated for development. On average, for every 10 compounds that reach development, only one gains FDA approval.

The "Digoxin Drug Project" spreadsheet models a business situation filled with uncertainty. IDC has completed preliminary development for a new drug, code named Digoxin, designed to correct back problems. While headquartered in Dallas, production facilities are located in Guayaquil, Ecuador. This revolutionary new product could be developed and tested in time for release next year if the FDA approves the product. Although the drug works well for some patients, the overall success rate is marginal, and IDC is uncertain whether the FDA will approve the product. With $30 million in debt and $25 million in equity, the project is capitalized with a debt to equity ratio of 120%.

An important aspect of pharmaceutical development is selecting the proper portfolio of compounds to developa portfolio that will provide the expected level of sales at the right level of cost and risk. Crystal Ball simulations are used to model the key risks and uncertainties for each individual project. In addition, Crystal Ball simulations are used to estimate total portfolio value and riska probability distribution of potential R&D spending and sales by year.

The CFO, Marcia Wilson, wanted the firm to perform simulations. She wants to determine whether to scrap the project or, alternatively, to proceed to the next step, which is to develop and market this exciting new drug. Few mistakes are allowed. The project is a multi-million-dollar risk. Marcia knows that simulation models such as Crystal Ball are powerful decision-support programs designed to take the mystery out of decisions like this.

The model gives Wilson the ability to answer questions such as "Will we stay under budget if we build this facility?," "What are the chances this project will finish on time?," "How likely are we to achieve this level of profitability?," and most important in this case, "What are the probabilities that the project will make money?," "Is the project feasible enough to attract three-year revolver financing?,'' and "What is the expected default (unsystematic risk) factor?"

As is the case with drug products, being the first or second to the market can have a significant impact on total sales realized. In certain high-potential

³ This case was derived using a Crystal Ball example.

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markets, there may be 10 or more competitors with drug products such as Dixogin in development. If the first round of analysis is successful, that is, if the product is viable from a profit perspective, simulations could be used to estimate the probability of being first or second to market. This information helps focus attention on the need to achieve key project milestones to ensure a reasonable level of certainty that a compound will be first to the market.

Departmental estimates were obtained and some of the terminology was reviewed. A project estimate is an "informed" assessment of the likely project cost or duration. Informed" means that department heads have an identified basis for the estimate. "Likely" does not mean certain the term focuses on the inherent uncertainty of the estimate: Every estimate is but one of many possible outcomes. Cost and duration measures are crucial and refer to the two major categories of estimates. The team, realizing that the project was unique, focused on management similarities rather than on the technical differences and found that they could generate valuable insights even though the product of the project is wholly different. They even got biopharmaceuticals experts from competing firms to exchange estimating insights.

A few questions came up at initial meetings. Someone on Marcia's team wanted to know whether there are many possible outcomes, and how can he tell the one most likely? The answer is to not pick just one outcome but identify the full range of possible outcomes. If the problem is single point estimates and A and B are equally likely, the information is factored in and the results, for example, might be a uniform distribution. In addition, single point estimates tend to become self-fulfilling prophecies. Indeed, both the Digoxin project manager and the person responsible for a critical X variable needed to know its range dimension. For the most part, the distribution configuration is not nearly as important as recognizing that there is a range of possible results. In the late 1950s, the U.S. Navy developed the Program Evaluation and Review Technique (PERT) using a beta distribution. In the absence of evidence to the contrary, the best approach generally is to assume a triangular distribution because a triangular distribution produces more conservative results than a beta.

Marcia brought up the issue dealing with time spent developing range estimates. Her experience has been that it takes less time by eliminating the posturing and gamesmanship that often accompany the estimating process. Competitors have put together teams that spent less than a day estimating a 3,000-hour projectan estimate that later proved highly accurate. The time spent on estimates is not a cost; rather, it is cheap insurance.

Spreadsheet models only approximate a real-world domain. When building the spreadsheet models, careful interpretation must be given to the problem in order to refine the models on a continuous basis until they reflect the real-world condition as closely as possible.

In summary, to perform a simulation, Wilson needed accurate information from department heads involved in the project. She wanted a probability distribution assigned to each uncertain element in the forecast. The distribution describes the possible values that the variable conceivably could take on and states the probability of each value occurring.

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The next step is to have the software randomly pick a value for each uncertain variable associated with an assigned probability distribution. The software will generate a set of financials based on the values selected. This creates one trial. Performing the last step many times produces a large number of trials. The output from a simulation is a table or a graph summarizing the results of many trials.

The group developed the "Digoxin Drug Project" spreadsheet in the context of a most likely scenario. Wilson required experts from different areas of production to submit reports along with projections and probability distributions. Information is included as follows (see Exhibit 72 and C7DIS-EASE file in the Excel subdirectory).

1. Defining Testing: The Uniform Distribution. For this variable, "testing costs," IDC felt that any value between $3.6 and $4.4 million has an equal chance of being the actual cost of testing. The budget will not allow costs over $4.4 million. Based on this information, the CFO selected the uniform distribution to describe the testing costs.

The uniform distribution describes a situation where all values between the minimum and maximum values are equally likely to occur, so this distribution best describes the cost of testing Digoxin Drug.

2. Defining Marketing Costs: The Triangular Distribution. IDC plans to spend a sizable amount marketing Digoxin Drug if the FDA approves it. They expect to hire a large sales force and kick off an extensive advertising campaign to educate the public about this exciting new product.

(text continues on page 188)

Exhibit 72.
Digoxin drug project income statement and distributions, Guayaquil, Ecuador.

(continues)

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Exhibit 72
Continued

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Exhibit 72
Continued

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Exhibit 72.
Continued

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Exhibit 72.
Continued

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Including sales commissions and advertising costs, IDC expects to spend between $14 and $17.6 million, most likely $16.0 million. IDC chooses the triangular distribution to describe marketing costs.

The triangular distribution describes a situation where you can estimate the minimum, maximum, and most likely values to occur.

3. Defining Patients Cured: The Binomial Distribution. Before the FDA will approve Digoxin Drug, IDC must conduct a controlled test on a sample of 100 patients for one year. The FDA has stipulated that they will approve Digoxin Drug if it completely corrects the back problems of 20 or more of these patients without any significant side effects. In other words, 20% or more of the patients tested must show corrected vision after taking Digoxin Drug for one year. IDC is very encouraged by their preliminary testing, which shows a success rate of around 20%.

For this variable, "Patients Cured," IDC knows only that their preliminary testing shows a cure rate of 50%. Will Digoxin Drug meet FDA standards? Marcia's staff picked the binomial distribution to describe the uncertainties because the binomial distribution describes success number (20) in a fixed number of trials (100).

4. Defining Market Penetration: The Normal Distribution. The marketing department estimates that IDC's eventual share of the total market for the product will be normally distributed around a mean value of 8% with a standard deviation of 0.80%. "Normally distributed" means that analysts expect to see the familiar bell-shaped curve with about 68% of all possible values for market penetration falling between one standard deviation below the mean value and one standard deviation above the mean value, or between 7.2% and 8.8%.

The low mean value of 8% is a conservative estimate that takes into account the side effects of the drug that were noted during preliminary testing. In addition, the marketing department estimates a minimum market share of 5%, given the interest shown in the product during preliminary testing.

Wilson wants to know the certainty of achieving a profit. With simulation technology, Wilson can easily answer this question. The final result: Digoxin can be (input your assumptions and see) certain of achieving a minimum profit. IDC is encouraged/discouraged by the forecast results. Wilson wants to know whether key assumptions together with distributions are correct. If assumptions and distributions are reasonable, the project will be accepted/dropped.

Exhibit 73 shows a Lognormal Distribution. The assumption name is identified: "Development Cost of Dioxin Drug . . ." The Gallery button provides numerous distribution choices. The Correlate button enables you to test correlations between assumption variables so to reduce the possibilty of redundency in the simulation.

Exhibit 73A illustrates a "constructed" custom distribution used if other distribution possibilities do not match your objectives. You are allowed the freedom to develop your own distribution to fit the data.

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Exhibit 7-3.
Development cost: An example of a lognormal distribution.

Exhibit 7-3A.
Growth Rate of Muscoloskeletal Injuries: An Example of a Custom Distribution

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Case Study
Hope Street Apartments

As vacancy rates began to drop in the Providence, Rhode Island, area, Malcolm Singer, a local contractor, saw an opportunity. Singer realized that the apartments market was growing rapidly. There had been little multifamily construction in Providence's affluent East Side area in over seven years. As a result, vacancy rates in existing apartments near Brown University were dropping rapidly, from 7% in 1995 to 5% in 1997 and down to less than 3% in late 1998.

Singer was determined to move fast. In a short time, he zeroed in on a "builders special" located on Hope Street near Brown. This location was excellent, and so he decided to refurbish and redesign an existing 216-unit "dilapidated" structure and make it "almost like new."

Singer took his plans and projections to ABC Bank, who offered to provide $3 million of permanent financing at 9% interest for a 12-year term with a balloon payment due at the end. The constant payment, including interest and principal, would be 10.23%. The bank stipulated that the building's operating cash flow should be adequate to cover debt service of $306,900 to the tune of at least a 98% probability. While Singer had provided an adequate personal net worth statement, the bank did not feel comfortable that external funds were available to supplement the project's expected cash flow coverage ratios. The following Excel income statement projection [C7HopeStOrg] in the Excel subdirectory, was included in the feasibility study developed by the bank⁴.

⁴ Shaded cells represent assumption variables; the forecast variable. Cash flow from operations is labeled on the spreadsheet.

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(continues)

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A Comparison of Different Distributions Applied to Vacancy Rate,
Sensitivity, and the Effect on the Hope Street Project's Cash Flow Coverage

The income statement was left unchanged from the original. The only changes made were the shape of the distribution. The following table has been set up to compare (1) certainty level (the probability that operating cash flow falls below debt service), (2) sensitivity by rank correlation, and (3) the run's statistics. The important message here is that the distribution selection you arrive at is as important as the underly ing assumptions that form the variable itself.

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Glossary of Distribution Terms

Triangular DistributionDescribes a situation where you know the minimum, maximum, and most likely values to occur. For example, we could describe the vacancy rate associated with the minimum, maximum, and most likely vacancy rate. Three conditions are required:

1. The minimum number of items is fixed.

2. The maximum number of items is fixed.

3. The most likely number of items falls between the minimum and the maximum values, forming a triangular-shaped distribution that shows that values near the minimum and maximum are less likely to occur than those near the most likely value.

Unlike the uniform distribution, in which all values between the limits are equally likely, the triangular distribution peaks at a central value.

Example

Analysis of Hope Street's property, showing that the vacancy rate will not fall below 13% or increase beyond 25%, with 15.4% the most likely.

The first step in selecting a probability distribution is to match your data with a distribution's conditions. Checking the triangular distribution:

Minimum vacancy rate is 13.0%.
Maximum vacancy rate is 25.0%.
The most likely vacancy rate is 15.4%, forming a triangle.

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Parameters: Lower limit a, central value c > a, upper limit b > c.
Domain: a £ X £ b.

Triangular Distribution for Type B UncertaintyOften all that is known about a process that contributes type B uncertainty is the maximum and minimum potential values and that central values are more likely to occur than extreme values. The uncertainty contribution from this process can be calculated from a triangular distribution.

Normal DistributionThis is a continuous probability distribution that is used to characterize a wide variety of types of data. It is a symmetric distribution, shaped like a bell, and is completely determined by its mean and standard deviation. The normal distribution is particularly important in statistics because of the tendency for sample means to follow the normal distribution (this is a result of the Central Limit Theorem).

Most classical statistics procedures, such as confidence intervals, rely on results from the normal distribution. The normal is also known as the Gaussian distribution, after its originator, Frederich Gauss. The normal distribution is the most important distribution in probability theory because it describes many natural phenomena, such as peoples' IQs or heights. Decision makers can use the normal distribution to describe uncertain variables, such as the inflation rate or the future price of gasoline. The three conditions underlying the normal distribution are as follows:

1. Some value of the uncertain variable is the most likely (the mean of the distribution).

2. The uncertain variable could as likely be above the mean as it could be below the mean (symmetrical about the mean).

3. The uncertain variable is more likely to be in the vicinity of the mean than far away. Approximately 68% are within 1 standard deviation on either side of the mean. The standard deviation is the average distance of a set of values from their mean.

Example

You feel that the mean vacancy rate on the Hope Street proposed project will be 15.4% with a standard deviation of 1.5%. This means that there is approximately a two-thirds probability that the vacancy rate will fall between 15.4% minus 1.5% and 15.4% plus 1.5%, or between 13.9% and 16.9%.

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The first step in selecting a probability distribution is to match your data with a distribution's conditions. Checking the normal distribution:

Parameters: Mean mu, standard deviation sigma > 0.
Domain: All real X.

Lognormal DistributionThe lognormal distribution is widely used in situations where values are positively skewed (most of the values occur near the minimum value), for example, in financial analysis for security valuation or in real estate for property valuation, such as the Hope project. Stock prices are usually positively skewed rather than normally (symmetrically) distributed. Stock prices exhibit this trend because they cannot fall below the lower limit of zero but may increase to any price without limit.

Conditions

Real estate prices illustrate positive skewness since property values cannot become negative, unless it poses an environmental hazard. The three conditions underlying the lognormal distribution are as follows:

1. The uncertain variable can increase without limits but cannot fall below zero.

2. The uncertain variable is positively skewed with most of the values near the lower limit.

3. The natural logarithm of the uncertain variable yields a normal distribution.

Example

You assume that the lowest value vacancy rate can drop to zero. On the other hand, the project could end up with a vacancy of 100%.

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Uniform DistributionA continuous probability distribution that is useful for characterizing data that range over an interval of values, each of which is equally likely. It is sometimes called the rectangular distribution because of its shape when plotted. The distribution is completely determined by the smallest possible value, a, and the largest possible value, b. For discrete data, there is a related discrete uniform distribution. The three conditions underlying uniform distribution are as follows:

1. The minimum value is fixed.

2. The maximum value is fixed.

3. All values between the minimum and maximum are equally likely to occur.

Examples of Distributions

The vacancy rate of at least 13% is expected but not more than 25%. All values between 13% and 25% are equally likely to occur.

The first step in selecting a probability distribution is to match your data with a distribution's condition. Checking the uniform distribution:

The minimum value is 13%; the value is 25%, and all values in between are equally possible. The conditions in this example match those of the uniform distribution.

Parameters: Lower limit a, Upper limit b > a.
Domain: a £ X £ b.

Extreme Value DistributionA distribution used for random variables that are constrained to be greater than or equal to 0. It is characterized by two parameters: mode and scale.

Parameters: mode a > 0, scale b > 0.
Domain: All real X.

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Other Distributions You May Deal with in Finance

Gamma DistributionA distribution used for continuous random variables that are constrained to be greater than or equal to 0. It is characterized by two parameters: shape and scale. The gamma distribution is often used to model data that are positively skewed.

The gamma distribution applies to a wide range of physical quantities and is similar to a host of other distributions: lognormal, exponential, Pascal, geometric, Erlang, Poisson, and chi-square. The gamma distribution can be thought of as the distribution of the amount of time until the rth occurrence of an event in a Poisson process. It is used in meteorological processes to represent pollutant concentrations and precipitation quantities and has other applications in economics, inventory, and insurance risk theories. The parameters for the gamma distribution are location, scale, and shape.

The three conditions underlying the gamma distribution are as follows:

1. The number of possible occurrences in any unit of measurement is not limited to a fixed number.

2. The occurrences are independent. The number of occurrences in one unit of measurement does not affect the number of occurrences in other units.

3. The average number of occurrences must remain the same from unit to unit.

The sum of any two gamma-distributed variables is a gamma variable. The product of any two normally distributed variables is a gamma variable.

Parameters: Shape a > 0, scale B > 0.
Domain: X > 0.

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Binomial Distribution

A distribution that gives the probability of observing X successes in a fixed number (n) of independent Bernoulli trials, p represents the probability of a success on a single trial.

For each trial, only two outcomes are possible. Trials are independent, and the first trial does not affect the second trial and so on. The probability of an event occurring remains the same from trial to trial.

Example

You want to describe the number of defective items in a total of 70 manufactured items, 2% of which were found to be defective during preliminary testing. There are only two possible outcomes: The manufactured items is either good or defective, and the trials are independent. The probability of a defective item is the same each time.

Parameters: Event probability 0 £ p £ 1.
Number of trials: n > 0.
Domain: X = 0,1 . . . n.

Negative Binomial DistributionA discrete probability distribution is useful for characterizing the time between Bernoulli trials. For example, suppose that machine parts are characterized as defective or nondefective and let the probability of a defective part equal p. If you begin testing a sample of parts to find a defective, then the number of parts that must be tested before you find k defective parts follows a negative binomial distribution. The geometric distribution is a special case of the negative binomial distribution, where k = 1. The negative binomial is sometimes called the Pascal distribution.

Parameters: Event probability: 0 £ p £ 1.
Number of successes: k (positive integer).
Domain: X = k, k+1, k + 2, . . .

Pareto DistributionThe Pareto distribution is widely used for the investigation of distributions associated with such empirical phenomena as city population sizes, the occurrence of natural resources, the size of companies, personal incomes, stock price fluctuations, and error clustering

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in communication circuits. This is a distribution used for random variables constrained to be greater than or equal to 0.

Parameters: Shape a > 0.
Domain: X < 1.
Mean: a/(a1) for a > 1.

Geometric DistributionA discrete probability is useful for characterizing the time between Bernoulli trials. For example, suppose that machine parts are characterized as defective or nondefective and let the probability of a defective part equal p. If you begin testing a sample of parts to find a defective, then the number of parts that must be tested before the first defective is found follows a geometric distribution.

The three conditions underlying the geometric distribution are as follows:

1. The number of trials is not fixed.

2. The trials continue until the first success.

3. The probability of success is the same from trial to trial.

Example⁵

If you are drilling for oil and want to describe the number of dry wells that you would drill before the next big ''gusher", you would use the geometric distribution. Assume that in the past you have hit oil about 10% of the time. The first step in selecting a probability distribution is to match your data with a distribution's conditions. Checking the geometric distribution:

1. The number of trials (dry wells) is not fixed.

2. You continue to drill wells until you hit the big "gusher."

3. The probability of success (10%) is the same each time you drill a well.

The geometric distribution has only one parameter: probability. In this example, the value for this parameter is .10, representing the 10% probability of discovering oil. You would enter this value as the parameter of the geometric distribution in Crystal Ball.

Parameters: Event probability 0 £ p £ 1.
Domain: X = 0,1,2, . . .

Poisson DistributionA distribution often used to express probabilities concerning the number of events per unit. For example, the number of computer malfunctions per year or the number of bubbles per square yard in a sheet of glass might follow a Poisson distribution. The distribution is fully characterized by its mean, usually expressed in terms of a rate.

⁵ Source: Decisioneering's Crystal Ball Manual and online help.

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The three conditions underlying the Poisson distribution are as follows:

1. The number of possible occurrences in any unit of measurement is not limited to a fixed number.

2. The occurrences are independent. The number of occurrences in one unit of measurement does not affect the number of occurrences in other units.

3. The average number of occurrences must remain the same from unit to unit.

Parameters; mean B > 0.
Domain: X = 0,1,2, . . .

Chapter Seven
References and Selected Readings

Books

Addin Enbu, et al. (1988). The dividend ratio model and small sample bias: A Monte Carlo study. Cambridge, Mass.: National Bureau of Economic Research.

Gourley, S. K., and Massachusetts Institute of Technology, Department of Aeronautics and Astronautics. (1979). Technological risk analysis/assessment.

Harris, R. F. (1975). Monte Carlo study of fatigue crack growth under random loading.

Kleijnen, J. P. C. (1974). Statistical techniques in simulation. New York: Marcel Dekker.

Lloyd, J. A. (1992). Numerical methods for Monte Carlo device simulation.

Mooney, C. Z. (1997). Monte Carlo simulation. Thousand Oaks, Calif.: Sage Publications.

Najafabadi, R. F., and Massachusetts Institute of Technology, Department of Nuclear Engineering. (1983). Monte Carlo simulation of structural and mechanical properties of crystal and bicrystal systems at finite temperature.

Rubinstein, R. Y. (1981). Simulation and the Monte Carlo method. New York: John Wiley & Sons.

Vose, D. (1996). Quantitative risk analysis: A guide to Monte Carlo simulation modelling. Chichester: John Wiley & Sons.

Yakowitz, S. J. (1977). Computational probability and simulation. Reading, Mass.: Addison-Wesley Advanced Book Program.

Periodicals

Anderson, Heather M. (1998). "Testing multiple equation systems for common nonlinear components." Journal of Econometrics 84(1).

Campbell, Terry. (1989). "Forecasting financial budgets with Monte Carlo simulation." Financial and Accounting Systems, 5(1), 28.

Clements, Michael P. (1999). "A Monte Carlo study of the forecasting performance of empirical SETAR models." Journal of Applied Econometrics, 14(2), 123.

Fellows, Richard. (1996). "Monte Carlo simulation of construction costs using subjective data: Comment." Construction Management and Economics, 14(5), 457.

Franses, Philip Hans. (1998). "A model selection strategy for time series with increasing seasonal variation." International Journal of Forecasting, 14(3), 405.

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Gupta, Yash P., and Rajendra K. Gupta. (1984). "Forecasting of working-capital require-ments under capital constraints: A Monte Carlo simulation approach." Engineering Costs and Production Economics, 8(3), 223.

Kalff, H. (1982). "How to tackle the future." Marketing and Research Today, 10(1), 37.

Kim, Iae H. (1999). "Asymptotic and bootstrap prediction regions for vector autoregression." International Journal of Forecasting, 15(4), 393.

McCullough, B. D. (1996). "Consistent forecast intervals when the forecast-period exogenous variables are stochastic." Journal of Forecasting, 15(4), 293.

Ozcicek, Omer. (1999). "Lag length selection in vector autoregressive models: Symmetric and asymmetric lags." Applied Economics, 31(4), 517.

Pflaumer, Peter. (1988). "Confidence intervals for population projections based on Monte Carlo methods." International Journal of Forecasting, 4(1), 135.

Ridley, Dennis. (1997). "Antithetic lognormal/normal random variables." Computers and Industrial Engineering, 33(12), 149.

Ristroph, John H. (1990). "Monte Carlo modeling of the tracking signal for forecast errors in computer integrated manufacture." Computers and Industrial Engineering, 19(14), 67.

Select Internet Library

Decisioneering, Inc.
Decisioneering, Inc., is the leading provider of risk analysis software and desktop decision intelligence software tools. Products include Crystal Ball 2000, CB 2000 Pro, CB Turbo, and CB Predictor. Decisioneering has made a substantial contribution to this book. The firm's risk analysis software, the Crystal Ball line of analytic tools, helps individuals and organizations make more informed and lucrative decisions. More than 85% of the Fortune 500 rely on our risk analysis forecasting tools to manage risk, make optimal decisions, and increase shareholder value. http://www.decisioneering.com/index.html.

MATLAB's Simulink
Simulink is built on top of MATLAB. This system runs simulations either interactively, using Simulink's graphical interface, or systematically, by running sets of experiments in batch mode from the MATLAB command line. Users can then generate test vectors and analyze the results collectively, if desired. Simulink, Stateflow®, provides event-handling simulation and supervisory logic. http://www.mathworks.com/products/simulink/.

Palisade
Palisade is a well-known source for software and books for risk analysis, decision analysis, forecasting, optimization, and data analysis. Products include @Risk to manage all kinds of risk by adding Monte Carlo simulation to users' spreadsheet models. http://www.palisade.com/Default.htm.

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Chapter Eight
Neural Networks and Scientific Financial Management

Neural networks are more than just a more powerful substitute for statistical models of data. Neural networks are a new set of tools that provide a variety of data analysis capabilities. One main attribute of neural networks is that they are trained from the data, not preprogrammed like most software and expert systems. The network architecture is chosen based on either a priori knowledge about the problem or through trial and error, but the parameters of the system are learned through training based on the input data. The same network architecture can be used to solve a wide variety of problems (from image recognition to disease classification). Neural networks are typically trained first and then implemented using fixed parameters. Neural networks, however, can be used adaptively as well. They can be trained to an "average solution" and then be updated while in use to adapt to unique situations or changing conditions.

This new technology is now an international financial tool used in a wide variety of applications. These include financial markets predictions, forecasting demand in banking and manufacturing, corporate bond rating and credit grading, accounts receivable credit standards, inventory control, market classification, modeling manufacturing processes and resulting product quality, job cost estimating, fraud detection, and many others.

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What sets this methodology apart from just a year or two ago is that now it is easy to use. The output is extremely impressive in backing up cash flow valuation reports and serves as a powerful complement to simulation and optimization packages.

A neural network is an adaptable system that can learn relationships through the repeated presentation of data and is capable of generalizing to new, previously unseen data. Some networks are supervised, in that a human determines what the network should learn from the data. In this case, you give the network a set of inputs and corresponding desired outputs, and the network tries to learn the input-output relationship by adapting its free parameters. Other networks are unsupervised, in that the way they organize information is hard-coded into their architecture.

When it comes to data, developing reliable forecasting models in the dual arena of neural nets and fuzzy logic requires a winning collaboration between management and knowledge engineers. Even when fusion of working knowledge and abstract concepts are realized, the outcome is sometimes thwarted by a host of unpredictable dynamics congenital to business. Corporate objectives change, operating divisions are acquired and divested, and new products are marketed and existing ones phased out. Corporate decision makers and their model builders are also faced with the unprecedented acceleration of new applications in the financial sciences. Thus, it is no wonder that many CFOs push aside elaborate financial business and forecasting models in favor of the ubiquitous spreadsheet and the so-called spreadsheet add-in.

Taking aim at the problem dealing with "what is the right analysis to work this deal," you might train on the model itself. This is a real challenge and can easily mean looking beyond a statistical analysis of your data and/or variations of Bayesian probabilities. You may need to develop financial models that spontaneously and instinctively change their internal behavioral structure to accommodate changes in how X variables react to the outside world.

The adaptive model is, of course, one powerful and obvious solutiona model that changes its rules based on outside world developments. A compelling approach to constructing an adaptive model involves merging three interrelated technologies: fuzzy logic, neural networks, and genetic algorithms. Fuzzy logic preprocesses the data through a collection of fuzzy sets associated with each variable. The preprocessed data is then fed into a neural network for classification. A genetic algorithm creates and tests many candidate models by changing the network parameters until one is optimized. Of course, merging the models is a task far beyond the scope of this book. Let's look at two of these technologies, neural networks and genetic algorithms, one at a time.

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Neural Networks

Neural networks actualize time-series prediction by automating the process of discovering neural network parameters (i.e., weights). Genetic algorithms can be used to find the best neural network architectures (i.e., input variables, learning rates, and hidden processing elements) and grouping and determines input, or X, variables critical to the forecast.

When a data set channels into the neural net system, genetic algorithms can be used to search through different combinations of forecast variables to find critical ones while weeding out redundant or irrelevant variables. Simultaneously, the optimal neural network parameters are trained and evaluated by the neural training mechanism, called back-propagation.

Thus, neural networks work data automatically, determining appropriate structures of the systems. Neural models search out and work data by altering the states of networks formed by interconnecting enormous bits of elemental data. As we saw in chapter 1, these data interact with one another by exchanging signals, as neurons do in the body's nervous system.

As such, neural systems represent a quantum leap when working with financial time-series problems, as they use multivariate nonlinear analytics, estimating nonlinear relationships with data alone. They are proficient at recognizing patterns that come out of noisy, complex data. For example, neural networks learn the underlying mechanics of a time series or, in the case of trading applications, the market dynamics in ways that mimick the human brain.

Now compare this to statistical time-series models and most regression programs. Statistic models do not "discover." They are predetermined by equations, and if the equations or assumptions are incorrect, the results are flawed. A simple classical linear model for a time series uses building blocks much like the equation Ylinear = a₁ + a₂x, where the dependent variable, y, is a linear function of the regression coefficients, a₁ and a₂ (see chapter 6). Neural networks, conversely, attempt to model the same data with nonlinear functions that better capture the intricacies of financial forecasting.

Neural networks are often pictured as layers of functional nodes. Exhibit 81 shows a

Exhibit 81.
Multilayer perceptron network.

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typical three-layer multilayer perceptron (MLP) network, the most popular neural network architecture.

Layer 1 consists simply of the inputs, all of which are connected to a "hidden" layer 2. In the hidden layer, each node represents a different non-linear function of the inputs. Finally, in layer 3 a single node combines the outputs of the second layer to create the network output. The specific functional form in each layer must determined by pragmatic experimentation.

As we just saw, neural network models determine neural network weights. First, random values are assigned to all the weights. Second, a set of training data, consisting of multidimensional input vectors with corresponding output values, is submitted to the model. For each input pattern, the model output is compared to the known, correct output. Third, the weights are iteratively adjusted to reduce the mean squared error over all training sets.

However, the MLP is only one neural network topology. Others include time delay, continuous adaptive time, probabilistic, generalized regression, and self-organizing maps.

The iterative algorithm to adjust the weights is an application of the chain rule of calculus. Derivatives of the mean square error are computed, and adjustments are made using a gradient search method that propagates back down the network from layer 3 to layer 2. This learning method is commonly referred to as back-propagation.

While a neural network system can be set up from scratch, the availability of neural network software packages makes the process easier. These packages supply predefined neural network architectures, such as the MLP, and include algorithms to handle the delicate iterative computation of neural network weights. Prepackaging the software has become a vital issue particularly since neural networks have become an important tool for analyzing financial time series. A comprehensive model can craft and produce a first-rate time-series prediction whereby you can compare results to system such as CB Predictor. However, before we get involved with this, let's build a simple network.

Building a Simple Neural Network:
The T-C Problem

A Little Background

The T-C problem is a simple example of how a neural network can be used to set up a model to provide optical character recognition (OCR). The problem is one where a handwritten letter ("T" or "C") is scanned into a computer and the computer must determine what the letter is. The problem is slightly more complicated than it seems because the letter, when

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scanned in, may be rotated by 90, 180, or 270 degrees. Additionally, the letter may not have been scanned completely, or the person writing the letter may have sloppy handwriting.

The model is formulated by having the computer assign a vector to each handwritten letter based on where the markings are (see attached Excel spreadsheet for vector derivation, Exhibit 82). The computer then needs a means of mapping the vector to the correct letter. Now, unlike the traditional forecasting techniques that we saw in chapter 6 (causal models or time-series analysis), there is no defined model structure or equation that will map the scanned vector to the correct output. Simple solutions such as a "search-and-compare" algorithm consist of comparing the scanned-in data to the data for a "T" and ''C" and determine where an exact match is found. This type of solution, however, becomes extremely tedious and time consuming. It is simply not efficient. For example, what if the scanned-in letter does not exactly match an output vector because of sloppy handwriting or there was an error with the scanning process? A procedure could be written so that the output letter is selected on the basis of where the difference between the scanned vector and output vector is smallest. However, as the number of letters used in the OCR algorithm is increased and handwriting becomes sloppy, there is a substantial increase in computational time. How then should this problem be solved?

A more modern modeling technique, such as our neural network, can be easily employed to solve this problem. We need a data-driven model one that lets the data speak by finding a hidden structure in the data set.

The Problem

The T-C problem could be solved by training the neural network using only eight (8) input vectors (see attached excel spreadsheet (in the Excel subdirectory of your CD) C8T-CNeural workbook, Display worksheet entitled Exhibit 82 Setting up a Neural Network. The worksheet also appears below. The input vector assigns a value of 0.9 if there is a marking in the grid and a value of 0.1 if there is no marking in the grid. We then assign a value of 0.9 to the letter "T" and a value of 0.1 to the letter "C."

The neural network is then trained (this is an example of a neural network that contains three hidden nodes) and finds the hidden structure of the model (e.g., some mapping from the input vector to the output letter value). After training, any input vector can be processed quickly and efficiently by the neural network to produce the correct letter. The neural network also easily solves for the correct letter for sloppy handwriting. The neural network does not need to compare any vectors and so on. A neural network solution for this problem is much quicker and more efficient than the search-and-compare algorithm. This is illustrated in Exhibit 83.

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Exhibit 82.
Setting up a neural network.

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Exhibit 83.
Neural network layout.

Statistics and Neural Networks¹

A survey of relevant literature in this area shows that most researchers use the following methods to interpret their data: linear regression, multiple regression, logistic regression, decision trees, and artificial neural networks. The majority use logistic regression when the outcome variable is dichotomized.

Simple linear regression finds the best linear model to fit the data, using the mean squared error as the criteria that defines "best." Linear regression is optimal when the error is normally distributed and the variance of the error is a constant for all values of the inputthe error associated with different observations are independent. The model used in linear regression is

The goal of linear regression is to adjust the parameters ß such that the output is most similar to the desired output, Y.

An analytical solution to the parameters can be found using the regression equations. Another approach is to adjust the parameters in an adaptive manner. An adaptive system schematic diagram of a linear regressor is shown in Exhibit 84a (typically the offset or bias ß0 is ignored). The adaptive system methodology inputs the data to the system and computes a response. The response is compared to the desired response (the dependent variable). The parameters are adjusted to minimize the mean squared error.

¹ This important section was written by Neil R. Euliano of NeuroDimension, Inc. and donated with his kind permission along with the kind permission of NeuroDimension.

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Exhibit 84.
Statistical and neural network models.

In linear systems, the adaptive solution will be identical to the analytical solution. In nonlinear systems, however, often times there are not analytical solutions, so an adaptive approach must be taken.

Multiple regression simply extends the simple linear regression model to multiple independent variables. The same assumptions apply to multiple regression with the addition that the errors are assumed independent for any set of independent variables. The multiple regression equation is:

Exhibit 84b shows an adaptive system diagram of the multiple regression model. In general, linear regression models can use nonlinear functions of their inputs as independent variables, but they are still linear in the unknown parameters and are thus still linear models.

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When the dependent variable is binary or dichotomized, as is typical in outcome-related studies, linear regression suffers from three problems. First, the error terms are heteroskedastic, which means that the error variance is different with different values of the independent variables. Second, the error is not normally distributed since the dependent variable takes on only two values. Third, regression systems model a continuous output, thus giving results that may be greater than 1 or less than 0. The logistic regression model solves these problems by applying a nonlinear transformation to the linear regression model. The logistic regression model equation can be written as:

or

where p is the probability that event Y occurs, p(Y=l). This ratio of probabilities limits the output of the model to be between 0 and 1 and applies a logistic nonlinearity (S-shaped distribution) to the output. The main difference between the logistic regression and linear regression is the interpretation of the coefficients, ß. In standrad regression analysis, the parameters ß determine the relative importance of each input. In logistic regression, the coefficients represent the rate of change in the "log odds" as X changes. Using exp(ß) provides a good interpretation of the ß valuesthe "odds ratio" interpretation where a value greater than 1 indicates a correlation between the input and the positive outcome and a value less than 1 indicates a correlation with the negative outcome (Whitehead 1996). In adaptive systems, logistic regression involves simply applying a function to the output of the multiple regression system (see Exhibit 84c).

Neural networks are systems composed of multiple processing elements (PEs) that are interconnected and arranged in layers. Each PE sums its scaled inputs and applies a nonlinear function to this summation before outputting this value to other PEs. Exhibit 84d shows a schematic diagram of the multilayer perceptron (MLP). Notice that all three statistical methods can be easily implemented in a single PE, where the linear regression PE has a linear output function and the logistic regression PE has a sigmoid output function. All three of these methods can be easily implemented in an adaptive system simulator like NeuroSolutions.

The three statistical methods can only use linear combinations of scaled inputs. Although the logistic regression analysis extends linear regression to classification problems (where the dependent variable is

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Exhibit 85.
Classification and decision surfaces.

binary on/off), it will provide good results only if the data are linearly separablemeaning that the data can be separated by an N-dimensional hyperplane (where N is the number of inputs). Using regression with nonlinear functions of the input simply warps the input space, but the new input space must still be linearly separable. Many problems cannot be separated by a single hyperplane. Exhibit 85a shows an example of linearly separable problem with two inputs. Exhibit 85b shows an example of a problem that cannot be solved using a linear system. There is no single line that can be used to divide the input space and achieve correct classification. The neural network can solve this problem.

The most common neural network, the MLP, can be thought of as nonlinear combinations of many (logistic) regression PEs. It offers greater computational power than the regression models; in fact, an MLP is a universal approximator, meaning that it can approximate any function or relationship to any level of precision, given that it has enough PEs. Thus, it can solve problems that are not linearly separable. In general, since the MLP is a superset of the regression models, the MLP will always provide a solution that is at least as good and usually betterparticularly if the data are noisy or nonlinear, as is usually the case with real data. In addition, the MLP does not make any assumptions on the distribution or characteristics of the data.

Decision trees are different than the regression and neural network models. They are structures that determine the result on the basis of creating a series of questions with discrete answers. Based on the answer, the user progresses down different branches of the tree. The end of each branch, the leaf nodes, always indicates the category or classification result. Decision trees are created using a prescribed method of successively improving an arbitrary initial tree. Decision trees typically evaluate a single input at each branch of the tree, so their decision surface can be made up of only lines perpendicular to the axes of the input space. They can therefore separate classes only using multidimensional rectangular

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shapes. Exhibit 85c shows an example of a decision tree separation surface. Again, the neural network decision surface is potentially much more powerful. Another difficulty with decision trees (and other models that dichotomize their inputs) is that they suffer from the artificial discretization of their inputs into different classes. For example, the weight of the patient may be discretized into thin, normal, or heavy. Someone near the upper end of normal may be more similar to the heavy class than the normal class. Decision trees are restricted to discretized inputs, and thus the number of classes and the thresholds for each input are critical to their performance. In general, however, decision trees can classify nonlinearly separable patterns and thus are theoretically more powerful than the regression models.

In addition to the theoretical discussions of classification power, there are many relevant papers that compare the performance of neural networks to regression models and decision trees, including (but not limited to) Rosen (1997), Tucker (1998), Maeda (1997), and Hamilton (1997). Depending on the data, most authors report that the model performance is best with neural networks, then decision trees, and finally regression models. Of course, in some situations, a linear model is a good approximation, and in these cases most techniques will have the same performance.

Genetic Algorithms²

Genetic algorithms are general-purpose search algorithms based on the principles of evolution observed in nature. A genetic algorithm begins by creating a population of chromosomes. Each chromosome is made up of a collection of genes (the parameters to be optimized) and represents a complete solution to the problem at hand. The gene values are usually initialized to random values within user-specified boundaries.

Once the initial population has been created, each of its chromosomes is evaluated by a user-defined fitness function to determine the quality of the solution. This fitness function is problem specific and defines the genetic algorithms objective for the current problem.

Next, the genetic algorithm uses a selection operator to choose which chromosomes will have their information passed on to the next generation. The most common selection operator is "roulette selection." This selection operator is based on the evolutionary principle know as "survival of the fittest," whereby a chromosome's probability of getting selected is proportional to its fitness.

After two chromosomes have been selected, a crossover operator is applied (according to some user defined probability of crossover) to produce two new chromosomes. The most common crossover operator is

² The author wishes to thank Dan Wooten of NeuroDimensions for authoring this section.

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"one-point crossover." This crossover operator picks a random point within the chromosomes, then switches the genes of the two chromosomes at this point to produce two new offspring.

Following crossover, the genes of the new offspring undergo mutation according to a user-defined mutation probability. For binary genes, the most common mutation operator simply flips a bit from one type to another (i.e., 0 to 1 or 1 to 0).

The selection, crossover, and mutation operators are continuously applied until the new population is completely filled. The chromosomes in this new population are then evaluated, and the process is repeated again for multiple generations (starting with the selection operation) until some termination condition has been reached, such as population convergence, fitness convergence, or number of generations evolved.

For many problems, genetic algorithms can often find good solutions (near optimal) in around 100 generations. This can be many times faster than an exhaustive search. For example, a chromosome containing 32 binary genes would have 4,294,967,296 possible combinations (solutions) to evaluate when using an exhaustive search. If the same problem were to be solved with a genetic algorithm of population size 50, requiring 100 generations of evolution, the genetic algorithm would need to evaluate only 5,000 possible solutions.

Combining Genetic Algorithms with Neural Networks

There are four main ways that genetic algorithms can be used in conjunction with neural networks to enhance their performance. They can be used to choose the best inputs to the neural network, optimize the neural networks parameters (such as the learning rates, number of hidden layer processing elements, and so on), train the actual network weights (rather than using back-propagation), or choose/modify the neural network architecture. In each of these cases, the neural network error is the fitness used to rank the potential solutions.

Neural Architectures

While the MLP is the most common neural architecture, other architectures exist that may be more appropriate, depending on the task at hand. Radial basis function (RBF) networks and generalized regression neural networks (GRNN) provide excellent performance and fast training when using small data sets with small input dimensionality. Competitive networks implement an on-line version of K-means clustering. Self-organizing maps (SOMs) implement a unique clustering algorithm that maintains the relationships in the datainputs that are similar are

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mapped to locations in the output that are similar. In addition, SOMs can be used as a data representation or visualization tool, showing the relationships between various inputs.

Just as a neural network is a nonlinear extension of regression models, temporal neural networks provide a nonlinear extension of standard linear time-series analysis. Temporal neural networks provide much more powerful modeling than the linear models and can potentially produce much better results when extracting information or predicting temporal signals such as stock prices or exchange rates. These will be utilized in phase 2.

Real-World Financial Applications

1. Daiwa Securities and NEC Corp. applied neural network technology to the learning and recognition of stock price chart patterns for use in stock price forecasting. NEC had already developed neural network simulation software. Daiwa Computer Services Co., Ltd., an information-processing subsidiary of the Daiwa Securities Group, transferred the NEC system to its supercomputer and taught it to recognize the stock price chart patterns for 1,134 companies listed on the Tokyo Stock Exchange. DCS has since been using neural nets to forecast stock prices.

2. You can use neural nets to rate your firm's corporate bonds by assigning a label that reflects ability to repay coupon plus par and using S&P examples, ratings varying from AAA (very high probability of payment) to BBB (possibility of default in times of economic adversity) for investment-grade bonds.

The problem is that there is no hard-and-fast rule for determining unsystematic (company risk) since a vast spectrum of factors end up in the rating formula: sales, assets, liabilities, and other factors that are rather nebulous, such as willingness to repay debt. That is where neural training hits the mark, leaving regression far behind.

Some neural experts (e.g., Dutta) maintain the problems with the more aggressive domain (the class of problem domains such as the nonlinear that lack a domain model) such as bond ratings could be better solved by training a network using back-propagation than by trying to perform a statistical regression.

For that reason, regression is inappropriate because no matter how you try, the X, or independent, variables are not clear when applying the standard bond rating formulas to many firms. Conversely, experiments were conducted with networks having no hidden layers and networks with one hidden layer (with different numbers of nodes in the hidden layer). Bond ratings for 30 companies together with 10 financial variables were used as data in training the neural network using back-propagation. The network was then used to predict the ratings of 17 other issuers and consistently out-performed standard statistical regression techniques.

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3. Neural networks can be powerful forecasting tools in marketing. For years, advertising agencies and other companies have been trying to identify and sell to target, or specific, markets. For example, a company selling life insurance might send out an advertisement enclosed in a monthly credit card bill. The company would like to send out a small percentage of these advertisements to consumers and keep information on what type of person responds.

Once the company has data on who responded, it can then build a predictive model to analyze potentially good customers. Thus, a life insurance company may be able to save money by sending out advertisements to only a select one million credit card holders who are more likely to buy life insurance rather than to all credit card

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holders. Successful target marketing can save large companies hundreds of thousands of dollars each year.

4. A neural network can also be used to solve credit standards problems when applied to your accounts receivable portfolio where certain characteristics are known to exist (e.g., payment history, charge-off, credit bureau rating, industry characteristics, size of order, years in business, and so on), but the actual relationship is ''fuzzy." The neural network can aid in determining whether the credit will become delinquent, charged off, or paid off, but the exact relationship or model structure is unknown.

Typically, as a means to get around not knowing the exact structure of the model, some credit models assign scores or number values, depending on what each characteristic is; then, depending on the total score, the person's credit worthiness is determined.

A neural network can be used in this situation by first creating input vectors made up of the characteristics of the historical credit applicant and an output vector of how the applicant performed (e.g., delinquent, charged off, or paid off) using historical data. The model is trained with the historical data and used afterward to determine any new customer's credit worthiness. The neural network will provide output as to how the applicant should perform (e.g., delinquent, charged-off, or paid off), thus stating if a credit extension should be accepted. Table 81 depicts common neural models, descriptions, and uses.

Designing Neural Networks³

The neural network design and use life cycle is a complex dynamic process with many steps. However, careful consideration of the following steps can yield a vast improvement in neural network performance.⁴

The Neural Network design and use life cycle is a complex dynamic process with many steps. However, careful consideration of the following steps can yield a vast improvement in neural network performance.

· Understand the data. Neural networks cannot be used as black boxes, even in the best of circumstances. There is no substitute for a firm understanding of the data. Explore the data in as many ways as possible:

1. Try to understand the physical process that produced the data.

2. Plot the data: Plot the individual channels, as well as one channel against another.

³ Courtesy of NeuroDimension, Inc., 1800 N. Main Street, Suite D4, Gainesville, FL 32609.

⁴ Courtesy of NeuroDimension, Inc. Reprinted from online help with permission.

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3. Examine the statistics: Calculate the within channel mean and variance, as well as the between channel correlations.

4. Use digital signal processing (DSP) analysis techniques, such as the Fast Fourier Transform (FFT), to understand the data in the frequency domain.

· Transform the data so that it better represents "features" of the known physical process.

1. Transform the data to a more compact representation using universal techniques such as Principal Component Analysis (PCA) or Kohonen Self-Organizing Feature Maps (SOFM). Note that these techniques can also be implemented online at the first layer of a neural network.

2. Eliminate superfluous input channels. It is also possible to identify superfluous input channels after a network has been trained.

· Choose a desired input-output mapping. Decide what the neural network is to accomplish. In particular, what is to be the desired input-output relationship? Sometimes this can require laborious hand coding of the data.

· Choose a neural architecture. For regression, always start out with a linear network. For classification, always start out with a linear discriminant classifier. Even if these networks do not perform well, they provide a baseline comparison for other networks as you graduate in complexity. Also, a consideration here is whether an unsupervised network can perform the desired input-output mapping.

· Train the network. If possible, monitor the training with a subset of the training exemplars set aside as a cross-validation set. If the data set is too small to use cross-validation, then stop the training when the learning curve first starts to level off.

· Repeat the training. There is a high degree of variability in the performance of a network trained multiple times, but starting from different initial conditions. Therefore, the training should be repeated several times, varying the size of the network and/or the learning parameters. Among those networks that perform the best (on the cross-validation set, if available), choose the one with the smallest number of free weights.

· Perform sensitivity analysis. Sensitivity analysis measures the effect of small changes in the input channels on the output and is computed over the whole training set. It can be used to identify superfluous input channels. Eliminate those channels and repeat the training process.

· Test the network on new data. This is where you put the network to use. If you have carefully followed the previous steps, the network should generalize well to new data.

· Update the training. Occasionally, when enough new data is accumulated, include old test data in with the existing training set and repeat the entire training process.

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Developing a Neural Network within Excel

There are several commercial software packages available for the PC that provide the tools needed to model your data with a neural network. One of the market leaders is a program developed by NeuroDimension titled NeuroSolutions. This leading-edge software combines a modular, icon-based network design interface with an implementation of advanced learning procedures not found in other packages.

Neural networks have come of age because just about everyone works with spreadsheets, and especially Excel. Excel allows you to access the power of NeuroSolutions as a neural network environment while working within a familiar spreadsheet environment. Since the whole process is automated and works with popular spreadsheets, you do not need to know a lot about neural networks to gain the benefits they provide.

Let's review the minimum steps necessary to train a network, then we will work on a demo of NeuroDimension's Excel add-in product, NeuroSolutions for Excel, included in the CD. You may also download a demo at www.nd.com. or open the 30 day trial version (application) NS30FULL.EXE listed in the subdirectory [CD:applications\NeuroDimension]. Open the demo. Click on "run the NeuroSolution for Excel Demos." Select Demo 3, "Concept: Testing Regressors," "Application: Prediction of the S&P 500."

(text continues on page 227)

Exhibit 86.
S&P financial data.

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Exhibit 87.
Train MLP MSE.

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Exhibit 88.
Test MLP report.

Exhibit 89.
Test MLP input-output data.

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Exhibit 810.
NS variables.

Exhibit 811.
Train MLP report.

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Exhibits 86 through 811 are sample pages taken from this application and provided with permission by NeuroDimensions Inc.

First we develop a very simple model for predicting the S&P 500 one week in advance. Later, of course, you can build up more complex financial models once you tackle the basics. The models you develop will be no less compelling than the powerful ones we reviewed early on.

The inputs to the model consist of the one-year Treasury bill yield, the earnings per share and dividend per share for the S&P 500, and the current week's S&P 500. (see Exhibit 86) The desired output is the next week's S&P 500. (5th column in Exhibit 86) The data have been pretagged and are stored within the worksheet named "Financial Data." There are 507 weeks worth of data that cover approximately a 10-year period. We will use a simple MLP to model this data.

The data have been presampled such that the first 254 exemplars contain the data for weeks 1, 3, 5 . . . 505, 507 and the last 253 exemplars contain the data for weeks 2,4,6 . . . 504,506. The first 254 exemplars will be used for training and the last 253 exemplars for evaluating the trained network performance.

An MLP has been pretrained on these data and the training results are shown in the worksheet named "TrainMLP Report." (see Exhibit 811) Next, test the networks performance on the 253 weeks of data tagged as "Testing." Let's click on the Test Network button now to run the NeuroSolutions for Excel "Test" process. A dialog box will be displayed with the correct options preset such that the testing process will load the best weights (automatically saved during pretraining), run the testing data set through the network, and produce a report summarizing the network's regression performance. Examine the settings, then click on OK. NeuroSolutions for Excel is an Excel Add-in that integrates with any of the six levels of NeuroSolutions to provide a very powerful environment for manipulating your data, generating reports, and running batches of experiments.

Exhibits 87 through 811 are pages selected from NeuroSolutions for Excel Demo, "Prediction of the S&P 500" courtesy of NeuroDimensions Inc.

Because the "Report Type" of the "Test" process was set to "Regression," the resulting report contains a plot of the desired and actual network output in place of the confusion matrix. Furthermore, the "Percent Correct'' performance measure has been replaced by the correlation coefficient (see Exhibit 88 and Exhibit 89. In Exhibit 89 the correlation coefficient is its form of ~ and its value is .9952 for this run.) The other performance measures are the same as those computed for classification since they are useful in evaluating the performance of either type of problem. Since this a financial application, the true value of this model can be determined only by applying the model to a trading strategy and computing the profits over several time spans. This type of analysis can easily be done within Excel (see Exhibits 86 through 811).

⁵ Reprinted with permission NeuroDimensions, Inc.

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This demo⁵ has shown that NeuroSolutions for Excel can be used to model and test time-series data. To model the S&P500 data, we used a very simple MLP with only four inputs. Perhaps the results could have been improved by using more inputs, including more lags of the inputs that were used, or by using some form of time lagged recurrent network. The Gamma, Leaguer, and Time Delay are three forms of time-lagged recurrent networks included in the Consultants version of NeuroSolutions. You may choose to open the slide show, NDInfo V.

Chapter Eight References and Selected Readings

Books

Arbib, M. A., and S. I. Amari. (1989). Dynamic interactions in neural networks: Models and data. New York: Springer-Verlag.

Barndorff-Nielsen, O. E., et al. (1993). Networks and chaos: Statistical and probabilistic aspects. London: Chapman and Hall.

Beltratti, A., et al. (1996). Neural networks for economic and financial modelling. London: International Thomson Computer Press.

Cherkassky, V.S., et al. (1994). From statistics to neural networks: Theory and pattern recognition applications. Berlin: Springer-Verlag.

Dasarathy, B. V. (1993). Decision fusion. Los Alamitos, Calif.: IEEE Computer Society Press.

Deboeck, G. (1994). Trading on the edge: Neural, genetic, and fuzzy systems for chaotic financial markets. New York: John Wiley & Sons.

Deboeck, G., and T. Kohonen. (1998). Visual explorations in finance: With self-organizing maps. London: Springer.

Hey, A. J. G., and R. P. Feynman. (1999). Feynman and computation: Exploring the limits of computers. Reading, Mass.: Perseus Books.

Husmeier, D. (1999). Neural networks for conditional probability estimation: Forecasting beyond point predictions. London: Springer.

IEEE Computer Society, et al. (1995). Proceedings of the IEEE/IAFE 1995 Computational Intelligence for Financial Engineering (CIFEr), April 911, New York. Piscataway, N.J.: IEEE Service Center.

Jensen, F. V. (1996). An introduction to Bayesian networks. New York: Springer.

Kingdon, J. (1997). Intelligent systems and financial forecasting. London: Springer.

Lackes, R., et al. (1998). Neural networks basics and applications. Berlin: Springer-Verlag Electronic Media.
This CD-ROM provides an interactive introduction to neural nets and how to apply them. The learning program is easy to understand and use, and numerous multimedia and interactive components give it an almost gamelike feel. The learner is taken step by step from the basics to the use of neural networks for real projects, and the examples illustrate practical applications of neural networks in business management.

Lindblad, T., and J. M. Kinser. (1998). Image processing using pulse-coupled neural networks. London: Springer.

Neal, R. M. (1996). Bayesian learning for neural networks. New York: Springer.

Refenes, A. P. (1995). Neural networks in the capital markets. Chichester: John Wiley & Sons.

Saint-Dizier, P., and E. Viegas. (1995). Computational lexical semantics. Cambridge: Cambridge University Press.

Trippi, R. R., and J. K. Lee. (1996). Artificial intelligence in finance and investing: State-of-the-art technologies for securities selection and portfolio management. Burr Ridge, Ill: Irwin Professional Publishing.

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Trippi, R. R., and E. Turban. (1990). Investment management: Decision support and expert systems. New York: Van Nostrand Reinhold.

Trippi, R. R., and E. Turban. (1996). Neural networks in finance and investing: Using artificial intelligence to improve real-world performance. Chicago: Irwin Professional Publishing.

Von Altrock, C. (1997). Fuzzy logic and neurofuzzy applications in business and finance. Upper Saddle River, N.J.: Prentice Hall PTR.

Zirilli, J. S. (1997). Financial prediction using neural networks. London: International Thomson Computer Press.

Technical References

Aiken, M. (1995). "Forecasting T-bill rates with a neural network." Technical Analysis of Stocks and Commodities, 13(5), 85-88.

Aiken, M. (In press). "Artificial neural systems as a research paradigm for the study of group decision support systems." Group Decision and Negotiation.

Aiken, M., Jay Krosp, Chitti Govindarajulu, M. Vanjani, and Randy Sexton. (1995). "A neural network for predicting total industrial production." Journal of End User Computing, 7(2), 1923.

Aiken, M., J. Morrison, J. Paolillo, and L. Motiwalla. (1995). "Forecasting gross domestic product using a neural network." Decision Sciences Conference, November.

Fish, Kelly, James Barnes, and M. Aiken. (1995). "Artificial neural networks: A new methodology for industrial market segmentation." Industrial Marketing Management, 24(5).

Singleton, Tommie, Morris Stocks, and M. Aiken. (1995). "Using a group decision support system for financial decision making." SEDSI Conference, March.

Stocks, M., T. Singleton, and M. Aiken. (1995). "Bankruptcy prediction: Logistic analysis vs. an artifical neural network." 1995 Southwest Decision Sciences Institute Conference, March 14, Houston.

Stocks, Morris, T. Singleton, and M. Aiken. (1995). "Forecasting bankruptcies using a neural network." International Business Schools Computing Quarterly, 7(1), 3235.

Tan, P. (In prep.). "Automatic selection of neural network architectures via genetic algorithm." M.Sc. thesis.

Tan, P., G. Lim, K. Chua, F. Wong, and S. Neo. (1992). "A comparative study among neural networks, radial basis functions and regression models." Second International Conference on Automation, Robotics and Computer Vision, Singapore, September.

Wong, F. "Hybrid systems of neural network, fuzzy logic and genetic algorithms." In Advanced technology for trading, portfolio and risk management, ed. Guido Deboeck. Advanced Analytical Laboratory, Investment Department, World Bank.

Wong, F (1990). "NeuroForecasterA neural network for time series predictive analysis." Technical Report, National University of Singapore, May.

Wong, F. (1990). "Time series forecasting using backpropagation neural networks." Neurocomputing. Amsterdam: Elsevier.

Wong, F. (1990/91). "Time series forecasting using back propagation neural networks." Neurocomputing, 2, 147, 159.

Wong, F (1991). "FastProp: A selective training algorithm for fast error propagation." Proceedings of the International Joint Conference on Neural Networks, IJCNN, Singapore.

Wong, F. (1991). "An integrated neural network for financial time series analysis." Proceedings of the 24th Hawaii International Conference on System Sciences, January.

Wong, F. (1994). "NeuroFuzzy computing technology." NeuroVe$t Journal, MayJune, pp. 810.

Wong, F. (1994). "NeuroGenetic computing." NeuroVe$t Journal, JulyAugust.

Wong, F., and C. Tan. (1994). "Hybrid Neural, Genetic and Fuzzy Systems." In Trading on the Edge, ed. G. Deboeck. New York: John Wiley & Sons.

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Wong, F., and D. Lee. (1993). "A hybrid neural network for stock selection." Proceedings of the Second Annual International Conference on Artificial Intelligence Applications on Wall Street, April 1922, New York.

Wong, F., and P. Tan. (In press). "Neural networks and genetic algorithm for economic forecasting." In AI in Economics and Business Administration, ed. I. H. Daniels & Feelders.

Wong, F., P. Tan, and X. Zhang. (1992). "Neural networks, genetic algorithms and fuzzy logic for forecasting." Proceedings of the Third International Conference on Advanced Trading Technologies AI Applications on Wall Street and Worldwide, New York, July.

Wong, F., P. Wang, T. Goh, and B. K. Quek. (1992). "A fuzzy neural system for stock selection." Financial Analysts Journal, JanuaryFebruary.

Wong, F., and P. Tan. "Neural networks and genetic algorithm for economic forecasting." In AI in economics and business administration, ed. I. H. Daniels & Feelders.

Wong, F, and P. Wang. (1990/91). "A stock selection strategy using fuzzy neural networks." In Neurocomputing, vol. 2. Amsterdam: Elsevier.

Wong, F., and P. Z. Wang. (1991). "A fuzzy neural network approach for forex investment." International Fuzzy Engineering Symposium, November, Japan.

Wong F, P. Wang, and T. Goh. (1991). "Fuzzy neural systems for decision making." Proceedings of the International Joint Conference on Neural Networks, November, Singapore.

Zhang, X., and F. Wong. (1992). "A decision support neural network and its financial applications." Technical Report, Institute of Systems Science, National University of Singapore, June.

Technical References (General)

Kamijo, K., and T. Tanagawa. (1990). "Stock price pattern recognition: A recurrent neural network approach." Proceedings of the International Joint Conference on Neural Networks, San Diego, June.

Lapedes, A., and R. Farber. (1987). "How neural nets work." Advances in Neural Information Systems.

Parker, D. "Learning Logic." Report TR 47. Cambridge: MIT Center for Computational Research in Economics and Management Science.

Peters, E. (1992). Chaos and order in the capital markets. New York: John Wiley & Sons.

Peters, E. (1993). "Fractal structure in the capital markets." Financial Analysts Journal (May/June).

Peters, E. (1994). Fractal market analysis. New York: John Wiley & Sons. Holland, J. (1975). Adaptation in natural and artificial systems.

Rumelhart, D., G. Hinton, and R. Williams. (1986). Parallel distributed processing. Cambridge: MIT Press.

Trippi, R., and J. Lee. (1992). State-of-the-art portfolio selection: Using knowledge-based systems to enhance investment performance. Chicago: Probus.

Walter, J., H. Ritter, and K. Schulten. (1990). "Nonlinear prediction with self-organizing maps." Proceedings of the International Joint Conference on Neural Networks, San Diego, June.

Zimmermann, H. (1990). "Applications of the Boltzman machine in economics." In Methods of operations research, vol. 60/61, ed. Reider. 14th Symposium on Operations Research, Verlag Anton Hain.

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Select Internet Library

NeuroDimension, Inc.
This firm's original goal was to develop software tools that would improve their own efficiency and productivity. Since that time, NeuroDimension has assembled research innovators, software design engineers, and technicians encompassing an extended knowledge of the computer sciences. Neurodimension operates with strong ties with the world-renowned Computational Neural Engineering Lab at the University of Florida to enable the firm to bring state-of-the-art neural network technology to the marketplace. The company has customers in more than 40 countries around the world benefiting firsthand from this unique synergism. NeuroDimension has made a generous contribution to this book; its neural network software products are among the most powerful and flexible on the market today, yet their intuitive graphical user interfaces make them easy to use. The reason may be because their systems can operate in Excel. Readers are invited to download an evaluation copy. http://www.nd.com/company.htm.

Artificial Neural Networks and Computational Brain Theory Group
This interdisciplinary graduate and faculty discussion group at the University of Illinois at Urbana-Champaign addresses issues in neuroscience, cognitive science, and distributed artificial intelligence that concern the functional design of the nervous system and the construction of large-scale, biologically inspired artificial neural network systems. Visitors are always welcome. http.//anncbt.ai.uiuc.edu/.

The MathWorks
The MathWorks develops technical computing software for engineers and scientists in industry and education. The Fuzzy Logic Toolbox features a point-and-click interface that guides users through the steps of fuzzy design, from setup to diagnosis. It provides built-in support for the latest fuzzy logic methods, such as fuzzy clustering and adaptive neuro-fuzzy learning. The Toolbox's interactive graphics allows users to visualize and fine-tune system behavior. http://www.mathworks.com/products/fuzzylogic/.

Neural Networks and Fuzzy Systems
Welcome to the home page of the Research Group on Neural Networks and Fuzzy Systems at the Institute of Knowledge Processing and Language Engineering, Faculty of Computer Science, University of Magdeburg, Germany. http://fuzzy.cs.unimagdeburg.de/intro.html.

International Neural Network Society
The International (INNS), European (ENNS), and Japanese (JNNS) Neural Network Societies are associations of scientists, engineers, students, and others seeking to learn about and advance our understanding of the modeling of behavioral and brain processes and the application of neural modeling concepts to technological problems. http://cns-web.bu.edu/inns/.

University of Bristol, Faculty of Engineering
Neural network information, including conferences, societies, archives, journals, publishers, software, hardware, FAQs, mailing lists and newsgroups, and neural nets in industry http://www.fen.bris.ac.uk/engmaths/research/neural/sites.html.

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Applied Intelligence
The International Journal of Artificial Intelligence, Neural Networks, and Complex Problem-Solving Technologies. http://www.wkap.nl/kapis/CGI-BIN/WORLD/journalhome.htm?0924-669X.

IEEE Neural Network Council
Member societies, and contact information for NNC officers and various committees, publications of the IEEE NNC, books, videos, and journals of the IEEE NNC, including the latest journal table of contents, abstracts, and information for authors. Neural networks research, neural computing research programs and professional societies worldwide, information on IEEE NNC Regional Interest Groups, neural networks conferences, and up-to-date information on conferences and symposia with a neural network component. http://www.ewh.ieee.org/tc/nnc/.

CD

Name

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Type

ANNCBT Group Home Page

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Application Summaries

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Internet Shortcut

Applied Intelligence

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Internet Shortcut

C8ARNNeural

411 KB

Microsoft Excel Worksheet

C8Backup of SP500Trained

248KB

Microsoft Excel Worksheet

C8SP500Trained

246KB

Microsoft Excel Worksheet

C8T-CNeural

64KB

Microsoft Excel Worksheet

Complex Systems Virtual Library
Record Details

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Data Management Review

1KB

Internet Shortcut

DM Review Business Intelligence & Data Warehousing Enabling E-Business

1KB

Internet Shortcut

Download NeuroSolution

83KB

Microsoft Word Document

IEEE Neural Network Council Home Page

1KB

Internet Shortcut

Illiggal Home Page

1KB

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Integration with NeuroSolutions

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International Neural Network Society

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NDInfoV

5,701 . . .

WinZip File

Neural Network and Kernel Methods

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Neural Networks and Fuzzy Systmes

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NS for Excel Generated Report

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Products

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The MathWorksFuzzy Logic Toolbox

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USNews Putting evolution to work on
the assembly line [727-98]

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What is NN

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WizSoft SoftwareWizRule, WizWhy
Datamining, Database analizing

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Chapter Nine
Linear Programming, Optimization, and the CFO

Optimization has recently become one of the most important tools in shareholder value analysis. This is, in all honesty, "must-have" software for financial managers. Optimization may not be an easy process, but the value-added rewards are impressive: significant cost reductions, cycle time improvements, financial fine-tuning, and revenue opportunities. When strategic plans involve costly assets, financing charges, working capital limits, and marketing investments, there is small margin for error and certainly no room for ad hoc trial-and-error test-outs on those big financial problems. The name of the game is optimized resource allocation, that is, resources meticulously assigned (or combined) in the right amounts, at the right time, and in the right order.

Of course, situations may arise when optimization is inappropriate. Some problems may appear easy candidates for optimization but could just as readily be solved using differential calculus. Alternatively, seemingly commonplace problems can be immensely complex (e.g., the traveling salesperson problem). How do you plan the shortest route for a salesperson's trip, route airplanes for landings to minimize waiting costs, or find the optimal number of products to produce and sell for maximum profit?

The optimization (computer method) called for depends on the problem's structure. Many financial applications entail nonlinear functions, logical variables with many (if not tens of thousands) constraints linked to innumerable uncertainty. These problems are difficult to solve with the

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great majority of optimization software but are handled quite well by simulation/optimization software such as OptQuest for Crystal Ball, the MATLAB Optimization Toolbox, or Palisade's Risk Optimizer. We will cover all this later in the chapter.

On the other hand, if your decision variables are real (i.e., based on certainty conditions) and the objective variable and constraints are linear functions, linear programming will usually do a good job processing your data.

The Basics of Linear Programming

Linear programming is a procedure used to identify optimal maximum or minimum values subject to constraints. A few of today's linear programming and optimization models are robust and are able to solve problems containing thousands and even millions of variables without disproportionately tying up your computers. Any problem having decision variables and an objective function to be maximized or minimized is considered a linear programming and/or optimization problem. If the problem is bounded by constraints, it is called constrained optimization; otherwise, the term used is unconstrained optimization. A factory may be limited in size or able to produce only so much of a given product per day. Raw material may be in short supply, working capital sources limited, or work in process bottlenecked because of labor problems. Capital costs might be constrained by systematic and unsystematic risk factors. The question is, How do you combine these perhaps (thousands) of constrained variables in a way that produces maximum value within these set boundaries?

We maximize a linear expression of the form:

where

x₁ . . . xk = variables in the linear function
a₁ . . . ak = known coefficients

x variables are subject to constraints (restrictions) expressed by means linear inequalities. For that reason, we refer to these problems as linear programming problems. Linear programming and optimization models have three essential components: decision variables, objective function, and constraints. The first phase in the process is to define decision variables.

Decision Variables

Each decision variable specifies the level of activity over which someone has control, such as production scheduling, capital investment allocations, and planning and budgeting. There should be enough decision variables

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to describe all possibilities associated with a financial or operational problem. For example, the management of Ace Cleaning is about to introduce a new detergent, but the company's management is undecided whether to bring out the new product now or next spring. The chief competitor of the firm is the widely known Dume, whose present product is inferior to Ace's. Dume also has a new product to introduce. If they both wait, Ace will come out a winner. If they both introduce their products now, Dume will gain since Ace cannot match Dume's current marketing capability. However, if Dume alone introduces now, Ace will be able to keep afloat this year because of its superior product and will likely outperform Dume next spring.

The decision to market the new product might logically be represented by a real (certainty) variable in the range of coordinates (0,1). Ace's management may want to know what marketing strategy should proceed first among four different strategies (A, B, C, D). The decision is represented by a discrete variable with possible values in (A, B, C, D). Because the decisionproceed or waitis so crucial to shareholder value, rather than look for easy (generic) solutions, Ace's management will take into account the shape, size, and form surrounding each decision variable. Decision variables take the form of real, integer, logical, choice, and set variables.

Real variables have lower and upper bounds and may take up any value in the range of the coordinates. Integer variables have a lower and upper bound and may take any integer (any member of the set of positive or negative whole numbers and zero) in the range. Logical variables may be either true or false. These variables may be represented by an integer variable with a lower bound of 0 (false) and an upper bound of 1 (true). Choice variables have a set of possible values (e.g., the bar codes of different products) and must take one of these values. These variables are often represented by an integer variable with a lower bound. Set variables have different sets as possible values (e.g., the set of products to store in a container) and must be one of these sets. These variables may be represented as choice variables, but their interactions with other variables are often more complex.

Objective Function

The objective function is a numeric benchmark associated with the problem, for example, maximize profits, minimize costs, or maximize shareholder value. The purpose of the decision maker is to select that course of action: Ai, which will maximize some measure of gain or minimize some measure of loss or cost (i.e., which will optimize some function), E, which measures the effectiveness of the various courses of action; that is, Ei = f(Ai). Objective functions are classified into two types: linear and nonlinear.

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Linear objective functions involve a linear combination of the decision variables (i.e., each decision variable is multiplied by a constant, and these values are added together). These are common for many cost functions:

Non-linear objective functions allow for any function of the decision variables, which covers a wider range of interactions and trade-offs that may occur in real-world finance:

For example, the objective of a firm might be to finance its short-term funding requirements so as to minimize net interest cost during the next 12 months. The interest payment on bank loans, commercial paper, and installment financing are measured and given. The objective function may call for borrowing "$X" from the bank and "$Y" in the commercial paper market. The next month, if the firm has a cash surplus after the payment of interest, the optimal solution may call for reductions of "$A'' in bank loans and the purchase of "$B" in government securities.

Constraints

Constraints are limitations or restrictions on the possible choices and combinations of decision variables (mentioned previously). Constraints describe the logical or physical conditions the decision variables must obey. Constraint functions may be linear or nonlinear.

Basic Deterministic Modeling

Deterministic linear programming or optimization models (all the previous examples are deterministic) contain no random variables and can produce only single-valued results, meaning that they actuate under the implicit assumption of certainty. While this procedure will usually lead to simplistic results, one way around the problem might be for you to run different values for select uncertainty variables and see how the output changes. However, sensitivity analysis might resolve small levels of uncertainty, but the extent and range of uncertainty conditions might be too significant for any well-reasoned amounts of (sensitivity) trials, not to mention on-line time. If things get that difficult, one way out might be to drop deterministic methods in favor of stochastic models; that is, the problem becomes a unification issue, or one of uncertainty/optimization integration. This will be the subject of the section "Stochastic Optimization Modeling."

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Setting up a Deterministic Linear Programming Exercise

Because constraints represent limited resources consumed by activities corresponding to decision variables, we write them as linear inequalities. Employing the "corner point theorem," we can determine an optimal solution(s) by locating a feasible region that contains our solutions. The corner point theorem says that if a maximum or minimum value exists, it will occur at a corner point of this feasible region. Let's see how this works as we seek to optimize Generic Bakery's profits.

Generic Bakery

Assume that we want to maximize profits on a given day (say, Sunday), our linear objective function. The problem becomes to select x₁, x₂ . . . xn in some combination so that the objective function, P, is maximized. Again, we want maximum profits, which are (graphically) mapped out by specific coordinates. Had there been no constraintshours in a day, the bakery's size, and dozens of other restrictionsour objectives might well be achieved by making x₁ . . . xn infinitely large. We could choose any point on the chart or even extend the point beyond the page, but clearly this is unrealistic.

Generic Bakery is subject to four linear inequalities (constraints). Linear inequalities are written as >, ³, <, or £, which occurs in place of the equals sign. Equals signs are associated with linear equations. We write the four constraints given in symbolic form:

x + y < 5

x + y > 4

x >0

y > 0

y > 0

The Basic Statement of the Bakery Problem

Next, identify decision variables. Again, each decision variable specifies the level of activity over which someone controls, for example, baking a particular cake for the Sunday crowd. The problem should include enough decision variables to describe all realistic strategies in search of a solution. Let's now select two decision variables: the number of cakes to bake on Sunday, x, and the number of bagels, y. A production plan calls for, essentially, choosing values for x and y. We could have easily defined variables in terms of the number of pounds of cakes and bagels rather than the count. There is usually more than one valid way to choose decision variables. Mathematically, this problem can be stated as:

Maximize P, subject to the constraints x + y < 5; 2x + y > 4; x > 0; y > 0

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Setting up the Linear Solution

Step 1
Rewrite Each of These Inequalities Isolating for y:

y < x + 5

y > 2x + 4

x > 0

Y > 0

Step 2
Graph All Four Constraints.

Inequality

Plot

First

Slope1 and y intercept 5

Second

Slope2 and y intercept 4

Third

Vertical line (y-axis)

Fourth

Horizontal line(x-axis)

The area that we want is below the blue line, above the orange line, to the right of the y-axis, and above the x-axis. The feasible region is outlined in black (see Exhibit 91).

Finally, we find the maximum value given a function we want to optimize. Assume that the function is P = 3x + 5y. Employing the corner point theorem to maximize the function and using the graph, the corner coordinates are (0,4), (0,5), (2,0), and (5,0). Inserting these four values in the objective function, we extract the largest value:

Coordinate

Function

Value

(0, 4)

0 + 5(4)

20

(0, 5)

0+ 5(5)

25

(2, 0)

3(2) +0

6

(5, 0)

3(5) + 0

15

We find maximum Sunday profits of $25 at coordinate (0, 5). Basic problems, such as that of the Generic Bakery, are easily solved by the Simplex method, an iterative system that locates successive basic-feasible solutions, testing them for optimality. Optimization is accomplished by moving from one corner of the feasible region to another, always improving the objective function until it can be amended no further, in which case the solution is optimal. The simplex method, in the old days, was the easiest and quickest method to optimize a problem. However, as business problems become more complex with a greater number of decision variables and constraints, the use of the simplex method is a thing of the past.

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Exhibit 91.
Graphical representation of feasible region.

Computer Optimization Models

Computer optimization models can be classified as (1) discrete, continuous, or mixed; (2) linear or nonlinear; and (3) deterministic or stochastic (see Table 91).

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There is no shortage of linear programming and optimization software packages. You can find them easily on the Web, and many are offered free. But be careful: While most of these models are fine for home or small-office use, many are limited to optimizing linear and deterministic problems (see Table 92).

(continues)

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Solver, Example 1
Using Solver to Determine the Optimal Stock Portfolio

Microsoft Excel Solver uses the generalized reduced gradient nonlinear optimization code developed by faculty at the University of Texas and Cleveland State University. Linear and integer problems use the simplex method (discussed earlier) and the branch-and-bound method.

Perfect Portfolio Ltd.

The Problem

You are a financial consultant specializing in retirement financial planning. Your function is to advise clients to follow conservative investment strategies, though many of your clients' financial objectives are unique. For the fixed-income portion of a typical portfolio, PPL employs yield to maturity. For equities, the firm typically utilizes a weighted average return rate that the S&P 500 compounded over the past 70 years.

Recently, a client brought you a list of securities that she had been followingMicrosoft, Intel, UAL, GM, JP Morgan, and so onand

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requested that you construct a portfolio positioned in terms of risk equal to the S&P 500. Your client could have easily purchased an S&P index fund, but she was biased to her "basket" alone.

First, you checked the betas of each stock in the client's portfolio. The portfolio's beta averaged 1.21, much too risky given her retirement objectives. However, the client's portfolio could be optimized by setting the objective function, equity returns, to maximize while fixing a constraint, portfolio stock beta, to one.

Betas can be obtained from stock research reports (Value Line) or calculated with knowledge of the covariance of security returns with the market and the variance of the market. This is achieved by use of the capital asset pricing model equation:

where

(Rj) = the required equity return investors demand for investing in the stock.

(Rm Rf) = the market risk premium or the difference between the returns on an S&P 500 index (Rm) and the risk-free rate (Rf).

(ßj) = the security's beta.

ßj = 1 means the security and the S&P index have identical volatility (returns should be identical);

ßj > 1 means the security's returns are more volatile than the S&P index (the security is more risky, and returns should be higher than the S&P index).

ßj < 1 means the security's returns are less volatile than the S&P index (the security is less risky, and returns should be lower than the S&P index).

Example

Assume that 20-year Treasury bonds currently yield 9%. The market returns 12% on a portfolio, while the historical long-term average yields on Treasury bonds are 3.1%. Beta estimate for Detroit Edison is .55. What is the return demanded by investors in Detroit Edison's stock?

However, one stock hardly represents a portfolio, and that is where the Solver comes in. You program Solver to generate a variance equal to a beta of one. Without the Solver optimizing the precise risk-reward space demanded by your client, her portfolio returns fall beneath the efficient frontier¹ (see Exhibit 92). By superimposing the client's indifference map on the efficient set of available portfolios, you determine the optimal (percentage) mix of securities in a "beta one" portfolio, thus maximizing the investor's utility.

¹ See chapter 2 for details on the efficient frontier.

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Exhibit 92.
Minimum variance set.

The Solution

Step 1
The Spreadsheet

[CD:MODELS\EXCEL\C9SoluJoeBk]

Set up the titles for each of the rows and columns (see Exhibit 93). Put these in an italic or a bold font to make them easier to find within the entire spreadsheet. It is also a good idea to highlight the cells that will contain the decision variables in a different color. These are the cells that will be altered by Solver. The decision cells are F10:F22, the weights of each security with respect to the total portfolio.

Next, insert the given values, the betas of each security, and respective yields.

Insert the known formulas. This will include not only the formulas for the resource utilization, weighted yields, and weighted betas, but also the formula for the target functions, portfolio dividend yield, equity return, and stock beta.

Allocate a cell for the target cell that you want to maximizeEquity Return, cell F25.

Allocate cells for constraints. Constraints are fundamental to Solver. A constraint specifies an upper or a lower limit, or an exact value that a calculated function of the decision variables must satisfy at any solution found by the Solver. The primary constraint, or the main decision cell, will be G25 = 1; that is, beta must equal 1. This type of constraint is of the form G25 = integer, where equity return is one of the decision variables. This specifies that the solution value for this cell must be an integer or whole number to within a small tolerance (also the precision setting).

The other constraints we set in Solver will prevent illogical solutions from occurring. You should plan constraints before calling up Solver:

· The basket of securities held must be greater than or equal to zero. ($F$10:$F22 >= 0); $ signifies an absolute reference.

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Exhibit 9-3.
Perfect Portfolio Ltd.

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Exhibit 94.
Solver parameters.

· The portfolio weights must total to 100%; that is, $F$23 = 1.

· Beta must equal 1; that is, $G25 = 1.

Now call up Excel's add-in, the Solver, by selecting Tools|Solver. The Solver dialog box consists of three main areas. The first area is the target cell and what we are attempting to do with that target (see Exhibit 94).

In our scenario, the Set Target Cell box will read $F25, corresponding to equity return. This can be entered directly or selected with the mouse. In this example, the Max radio button is selected because we are attempting to maximize equity return. The next area of the dialog box defines those cells that can change in the determination of the solution. This can be entered as a range of cells using the colon (:) operator or a comma-separated list of the cells. In our situation, the box will read $F$10:$F$22.

The last area of the dialog box deals with the constraints. To begin entering ''Subject to the Constraints:", click on Add. This presents a new dialog box. In this dialog box, the left box represents the formula being constrained, and the right box represents the limit. In the middle is an operator where you can define the type of constraint. Because the spreadsheet is organized as it is, it is very easy to enter these constraints using the mouse. To add each constraint, click first on the left box, then on the appropriate cell in the spreadsheet that contains the formula being constrained. Then click on the right box, followed by clicking on the cell in the spreadsheet that contains the limits of that formula. If necessary, change the operator. The constraints are

$F$10:$F22 > = 0
$F$23 = 1
$G25 = 1

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Exhibit 95.
Solver solution.

Finally, click on Solve. This will perform the calculations and change the values in the spreadsheet to show the results of the solution (see Exhibit 95). You are then presented with another dialog box asking whether you want the values to return to their original state or to leave them as is. Additionally, you can select which reports of the analysis you need to generate. Use the mouse to select any or all of the reports.

Solver optimizes the spreadsheet, and, in a manner of speaking, your client's custom-made securities portfolio is fixed on the efficient frontiernot too aggressive, not to conservative. Thus, the portfolio's risk profile exactly matches the S&P 500. The optimized spreadsheet has not been reproduced here but if you have worked out the optimization you can view the worksheet on your computer. Open C9SoluJoeSolution.

Solver creates three reports: Answer, Limits, and Sensitivity. We will review the reports in the next case. For now, let's use Solver to optimize an oil refinery's profits by allocating scarce resources.

Solver, Example 2
Optimization in Corporate Finance Allocation of Scarce Resources,
New Jersey Refining Inc.

New Jersey Refinery is located in northern New Jersey. The business is engaged in the following operations. Open C9mjr in the Excel subdirectory.

The Refining Process

Gasoline is produced from crude oil either by a distillation process alone or by a distillation process followed by a catalytic cracking process. Outputs of these processes are blended to obtain different grades of gasoline.

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The distillation process at a typical refinery separates gasoline from other parts of crude and places the crude oil under tremendous pressure until the gasoline vaporizes. The vapors are then collected and cooled in a condenser to produce distillate. New Jersey Refining buys its crude at $12 a barrel. The distillation tower uses five barrels of crude oil to produce one barrel of distillate and four barrels of other petroleum by-products. New Jersey Refining currently sells these other products for $12 a barrel.

The refinery's distillation tower can produce a daily output of up to 50,000 barrels of distillate at an operating cost of $4 per barrel. Some distillate will be blended into gasoline products; some will become "feedstock" for the Catalytic Cracker.

Catalytic Crackers

The catalytic cracking process utilizes high temperatures to break up "crack" heavy hydrocarbon compounds into lighter compounds. This process produces high-quality gasoline stock from the feedstock. New Jersey Refining catalytic cracker requires two barrels of feedstock to produce one barrel of gasoline stock and one barrel of petroleum by-products. These by-products currently sell for $20 a barrel. The catalytic cracker can produce up to 15,000 barrels of gasoline stock per day. The catalytic cracker has an operating cost of $5 per barrel output (see Exhibits 96 and 97).

The distillate produced by New Jersey Refining distillation tower has an octane rating of 84, while the gasoline stock from the catalytic cracker has an octane rating of 94. The New Jersey Refining gasoline refining process ends by blending distillate and cracker stock to form regular and premium gasoline, which have required octane ratings of at least 86 and 90, respectively. There is no volume or octane loss in blending; the variable cost of blending is negligible. New Jersey Refining sells its regular gasoline for $20 per barrel and its premium gasoline for $25 per barrel.

The final gasoline products are pumped from the New Jersey Refining Oil refinery in Louisiana via two small pipelines to several storage and distribution facilities in the eastern United States. One pipeline carries only regular gasoline, the other carries only premium gasoline. Each pipeline can handle up to 25,000 barrels a day.

Let's look at New Jersey Refining's initial spreadsheet setup (see Exhibit 98).

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Exhibit 96.
Flow chart for New Jersey Refining.

Exhibit 97.
Visual flow diagram using Analytica
(The New Jersey model is included in the CD).

Highlight cells that will contain decision variables in a different font size or color. These are the cells that will be altered by Solver in order to achieve an optimal solution. The decision cells are B7:B9Tower Capacity (bbl/day distillate, DistillateRegular bbls/day, DistillatePremium bbls/day). Allocate a cell for the target cell you want to maximizeProfits, cell D53.

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Exhibit 98.
New Jersey Refining, original condition.

Allocate cells for constraints. A constraint specifies an upper or a lower limit, or an exact value that a calculated function of the decision variables must satisfy at any solution found by the Solver.

Call up Solver by selecting Tools|Solver. The Solver dialog box consists of three main areas. The first area is the target cell and what we are attempting to do with that target (see Exhibits 99 and 910).

Set the target sell to Profits, $D$54. Next, select the Max radio button, maximize profits. The next area of the dialog boxBy Changing

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Exhibit 99.
Solver parameters, New Jersey Refining.

Exhibit 910.
Solver parameters, New Jersey Refining.

Cellsdefines those cells that change in determinating the solution. Enter "$B$7:$B$9" in this box, where:

$B$7 = tower capacity (bbl/day or distillate)
$B$8 = distillate (regular bbls/day)
$B$9 = distillate (premium bbls/day)

The last area of the dialog box deals with the constraints. To begin entering "Subject to the Constraints:", click on Add. This presents a new dialog box. In this dialog box, the left box represents the formula being constrained, and

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the right box represents the limit. In the middle is an operator where you can define the type of constraint. Because the spreadsheet is organized as it is, it is very easy to enter these constraints using the mouse. To add each constraint, click first on the left box, then on the appropriate cell in the spreadsheet that contains the formula being constrained. Then click on the right box, followed by clicking on the cell in the spreadsheet that contains the limits of that formula. If necessary, change the operator. Important constraints are explained as follows:

Constraint

Reference

$B$39< = 25000

Regular output (bbl/day) is restricted to less than or equal to 25,000.

$B$7< = 52000

Tower capacity (bbl/day or distillate) is limited to less than or equal to 52,000.

$B$7> = 49000

Tower capacity (bbl/day or distillate) is greater than or equal to 49,000.

$B$8< = 20000-$B$9

Due to capacity limits, regular distillate constraint must be less than or equal to 20,000 bbls/day (maximum capacity of both distillateregular and premium) less premium distillate.

$B$8> = 5000

Regular distillate production set at greater than or equal to 5,000 bbls/day.

$B9< = 12000

Distillatepremium bbls/day production less than 12,000.

$B$9> = 4000

Premium distillate production set at greater than or equal to 5,000 bbls/day.

$D$39< = 25000

Premium output (bbl/day) production limited to 25,000 or less.

Click on Solve. This will perform the calculations and change the values in the spreadsheet to show the results of the solution. You are then presented with another dialog box asking whether you want the values to return to their original state or leave them as is. Additionally, you can select which reports of the analysis you need to generate. Use the mouse to select any or all of the reports.

If you call for reports, Solver creates three reports: Answer, Limits, and Sensitivity. See C9NJRSolution.

Answer Report

The report lists the target cell and adjustable cells with their original and final values, constraints, and information about the constraints (see Exhibit 911). This report also includes information about the status of, and slack value for, each constraint. The status can be Binding, Not Binding, or Not Satisfied. The slack value is the difference between the solution value of the

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Exhibit 911.
Solver answer report, New Jersey refining optimization.

constraint cells and the number that appears on the right side of the constraint formula. A binding constraint is one for which the slack value is zero. A nonbinding constraint is a constraint that was satisfied with a nonzero slack value.

Limits Report

This report lists the target cell and the adjustable cells with their respective values, lower and upper limits, and target values (see Exhibit 912). This report is not generated for models that have integer constraints. The lower limit is the smallest value that the adjustable cell can take while holding all other adjustable cells fixed and still satisfying the constraints. The upper limit is the greatest value.

Sensitivity Report

This report provides information about how sensitive the solution is to small changes in the formula in the set (see Exhibit 913). This report has two sections: one for your variable cells and one for your constraints. The right column in each section provides the sensitivity information. Exhibit 914 shows the optimization completed report.

New Jersey Refinery is an example of how Solver provides a local optimal solution. Though the model deserves its well-known reputation, the fact

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Exhibit 912.
Solver limits report, New Jersey Refining optimization.

Exhibit 913.
Solver sensitivity report, New Jersey Refining.

remains that Solver is still a deterministic model, and deterministic models are often trapped in local optimal solutions. The results, "optimal refinery profits," are illusory since almost all business problems have nonlinear properties with manifest uncertainty (which commonly are present in the real world). For example, both the price of oil and the technical coefficients of oil production should be treated not as constants but as random variables. Even if only some parameters in a linear programming problem (such as the one we just examined) are random, the value of the objective function is also ran-

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Exhibit 914.
New Jersey Refining optimization completed.

dom. Thus, when linear programming is applied to these problems, special techniques must also be used, and they cannot be the same for all problems.

Management must be concerned with the variance as well as the expected value of refinery profits. The question becomes how to modify the problem to allow for New Jersey's aversion toward risk. We can allow for possible risk aversion by including in the objective function a term representing the variance of the refinery's profits. Unfortunately, if variance is introduced,

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the objective function becomes nonlinear in the decision variables, and the problem can no longer be solved by linear programming methods.

Again, the nonlinear solution component of deterministic models is able to obtain only a locally optimal solutiona solution whose quality may be substantially inferior to the quality of the solutions provided by a robust stochastic optimization model.

Stochastic models can handle nonlinear relationships that are specifiable by the kinds of equations and formulas that are used in mathematical programming formulations. Conversely, deterministic optimization does not apply to nonlinear problems other than those that can be expressed in ''classical" mathematical programming form. One of the most important issues deals with the ability of stochastic models such as OptQuest to solve a problem whose objective and constraining relationships can be captured only by means of a simulation, which, by definition, is beyond the capacity of any deterministic model to deal with. In addition, financial optimization in today's age of shareholder value should incorporate a combination of metaheuristic procedures from methods such as tabu search, neural networks, and scatter search. Only the best stochastic model is vigorous enough to blend these technologies.

Nonlinear components can create a solution space with many local optimal solutions that might be significantly inferior to the true optimal solution. Stochastic optimization can find global solutions for all types of objectives, especially complex objectives with many local, inferior solutions. This is important since global optimization finds the best solution from the set of all solutions. Local optimization (New Jersey Refining), on the other hand, finds the best solution from a set of solutions that are close to one another. In local optimization, the solution depends also on the starting point for the optimization. Global optimization will always find the same solution regardless of the starting point, but it takes a lot more computational power. Conversely, the refinery example found solutions that got trapped in the first remedy found, whether it happened to be a local or the true optimal solution. The problem with the Solver is that we just do not know.

Stochastic Optimization Modeling²

Stochastic programming is employed in energy and production planning, telecommunications, forest and fishery harvest management, engineering, and transportation, plus a much larger spectrum of financial applications, including financial modeling, asset-liability management, bond portfolio management, currency modeling, risk control, and probabilistic risk analysis.

Stochastically driven optimization models allow you to more realistically represent the flow of random variables. Consider an optimization

² This section was developed with the aid and support of many experts at Decisioneering. The author is greatly indebted to help and information supplied.

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problem whereby you try to maximize an objective function over a feasible region. Suppose that the problem is very large, containing tens of thousands of variables, so that it is unrealistic for you to run sensitivities. Obtaining these optimal values generally requires that you search in an iterative or ad hoc fashion. This entails running a simulation for an initial set of values, analyzing the results, changing more or more values, rerunning the simulation, and repeating this process until you find a satisfactory solution.

This process can be very tedious and time consuming even for small models, and it is far from clear how to adjust the variables from one simulation run to the next and so on. For example, a simulation run may contain only two decision variables. If each variable has 15 possible outcomes, trying each combination requires 225 simulation runs (152 alternatives). If each simulation takes only 1.7 seconds, then the entire process is completed using only two minutes of computer time.

However, suppose that you are running a problem containing five decision variables. Trying all combinations requires 769,000 simulations (155 alternatives), or five days of computer time. It is clearly possible that complete enumeration might take weeks, months, or even years to complete. This will not happen with well-designed stochastic models (e.g., Decisioneering's OptQuest). OptQuest employs combinations of metaheuristic procedures derived from systems like tabu search, neural networks, and scatter search. Let's examine how this works.

Neural networks and log file options are germane when calculations are tedious, time consuming, and expensive, like most of the problems we run up against in finance. How does the neural network procedure work? The log file records solutions generated during the search. The neural network searches for solutions before a new solution is transmitted. The search in the log file is justified only when evaluation of solutions is computationally not viable and expensive.

In this way, the network filters out inferior solutions. After a series of initial iterations, the trained network predicts the output of the function evaluator based on the values of the decision variables. Once the training is complete, the network evaluates new solutions and predicts the output of the function evaluator. If the prediction indicates that the solution is "likely" to be inferior to the best known, then the function evaluator does not evaluate the solution.

Tabu Search³

OptQuest also employs tabu search techniques. Tabu search is a very efficient heuristic (or learning) process designed for tackling complex combinatorial

³ Extracted from an article on the subject by M. Laguna and F. Glover, Colorado Business Review 61, no. 5 (September 1996).

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problems in business and other domains. For background, consider two important ways in which computers solve quantitative problems. The first deals with programming formulas that manage information (input data). The software works through the formulas and produces a solution. In the second method, software works through the problem and makes slight changes in the data, but now the operation cycles the data over and over again until the final result is processed or a termination criterion is met.

For example, if you wanted to estimate compound interest, the first method would produce the first run answer: simple interest. The second (repetitive) method calculates the interest for the first year and then uses this to calculate the interest for the second year and so on. In 99% of finance problems, the repetitive method serves as the only alternative. In fact, repetitive methods have the potential to assemble simple components to achieve remarkable levels of sophistication and complexity as we move toward optimizing real problems; a formula, as in the first example, may alternately become one of the pieces incorporated into a repetitive approach. Repetitive methods are commonly applied for the goals of finding the following:

· The best configuration of machines for production scheduling

· The best investment portfolio

· The best utilization of employees for workforce planning

· The best location of facilities for commercial distribution

· The best operating schedule for electrical power planning

· The best assignment of medical personnel in hospital administration

· The best setting of tolerances in manufacturing design

· The best set of treatment policies in waste management

· Many other business objectives

Tabu search has become a standard optimization process that is swiftly spreading to resource management, shareholder value-gap analysis, corporate planning and control, process design, logistics, and technology planning.

Optquest Case Study
Oil Field Development⁴

Oil companies need to assess new fields or prospects where very little hard data exists. Based on seismic data, exploration experts can estimate the probability distribution of the reserve size. With little actual data available, the discovery team wants to quantify and optimize the net present value (NPV) of the asset. You can simplify this analysis by representing the production profile by three phases:

⁴ Complements of OptQuest for Crystal Ball, version 1.0 manual, pp. 112115. Reproduced with permission.

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Phase

Description

Buildup

The period where you drill wells to gain enough production to fill the facilities.

Plateau

After reaching the desired production rate (plateau), the period when you continue production at that rate as long as the reservoir pressure is constant and until you produce a certain fraction of the reserves. In the early stages of development, you can only estimate this fraction, and production above a certain rate influences plateau duration.

Decline

The period when production rates, P, decline by the same proportion in each time step, leading to an exponential function: P(t) P(0) exp(C*t), where t is the time since the plateau phase began and c is some constant.

Exhibit 915 displays the original spreadsheet of Oil Field Development, C901 Field Development in the EXCEL Subdirectory. Our goal will be to maximize the Net Present Value of this project. A spreadsheet model for OptQuest is the same as a model for Crystal Ball with one exception: the OptQuest model has decision variables. After you define the assumptions, forecasts, and decision variables in Crystal Ball, you can begin the optimization process in OptQuest. Decision variables are the variables that you can control, such as we saw with the case, Perfect Portfolio Ltd. Recall, however, that case was developed around Deterministic software, Excel's Solver. Now we will employ a stochastic approach by first defining a decision variable as follows:

1. Select a cell or range of cells.

2. Select value cells only. You cannot define a decision on a formula, label, or blank cell.

3. Select Cell > Define Decision.

4. The Define Decision Variable dialog appears.

5. Complete the Define Decision Variable dialog.

6. Click on OK.

7. Repeat Steps 16 for each decision variable in your model. If you selected a range of cells, repeat steps 46 to define the decision variable for each cell.

With estimates only for the total Stock Tank Oil Initially In Place (STOIIP = reserve size) and percentage recovery amounts, the objective is to select a production rate, a facility size, and well numbers to maximize some financial measure. The oil company wants to optimize an NPV value, which they are 90% confident of achieving or exceeding.

A high plateau rate does not lose any reserves, but it does increase costs with extra wells and larger facilities. However, facility costs per unit decrease

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Exhibit 915
Oil field development original condition.

with a larger throughput, so choosing the largest allowed rate and selecting a facility and number of wells to match might be appropriate.

Start Optimization

We are now ready to start optimization. The first step of this process is selecting decision variables to optimize (Exhibit 916). The values of these decision variables will change with each simulation until OptQuest finds values

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Exhibit 916
Decision variable selection.

that yield the best objective. For some analyses, you might fix the values of certain decision variables and optimize the rest. OptQuest includes a wizard that leads you through the windows to complete for the optimization. The Decision Variable Selection window appears first, listing every decision variable defined in the Crystal Ball model. You select which decision variables to optimize. By default, all are selected. Optionally, change the lower and upper bounds for each decision variable. By default, OptQuest uses the limits you entered when you defined the decision variables. The tighter the bounds you specify, the fewer values OptQuest must search to find the optimal solution. However, this efficiency comes at the expense of missing the optimal solution if it lies outside the specified bounds. Readers interested in completing the next steps can visit Decisioneering's Internet site www.decisioneering.com.

Now let's look at few samples of the results (Exhibits 91 7 through 919)

The Maximize Objective NPV Mean column indicates that the highest NPV is 331,335. This result is optimized by drilling 16 wells with a plateau rate of 12.6 and facility size of 150. The Performance Graph window displays the trajectory of the search; that is, the rate at which the best objective value has changed during the course of the search. This is shown as a plot of the best objective values as a function of the number of trial solutions. As OptQuest runs, this window graphically displays the values listed in the Status And Solutions window.

Exhibit 95 reveals the Best, Average, Maximum solution and Standard Deviation. Included are NPV, Wells to drill, Plateau rate, and Facility size.

The simulation report (Exhibit 919) is the result of a set of Crystal Ball trials. OptQuest finds the best values by running multiple simulations for different sets of decision variable values.

(text continues on page 264)

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Exhibit 9-17.
Optimization is complete.

Exhibit 9-18.
Solution analysis.

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Exhibit 9-19.
Oil field development simulation report.

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The Optimization Log window displays details of the optimization and actual values of each decision variable, objective, and requirement for all the simulations run during the optimization, not just the best ones identified in the Status And Solutions window. Following is the first page of the log (see Exhibit 9-20.). The actual log in this example runs many pages.

Optimization File: UnNamed.opt
Total Number of Simulations: 123
Number of Trials per Simulation: 1000
Confidence Testing is Activated
Number of Simulations Run Maximum Number of Trials: 25
Number of Simulations Stopped by Precision Control: 0
Number of Simulations Stopped by Confidence Testing: 98
Neural Network Engaged after simulation: 40
Number of Simulations Avoided Due to Neural Network: 12
Population Size: 20

Simulation: 123

Values of Variables:
Wells to drill: 15
Plateau rate: 12.2628465868152
Facility size: 150

Objective: NPV: Mean: 327.224617756844

Simulation: 122

Values of Variables:
Wells to drill: 16
Plateau rate: 13.6524622879758
Facility size: 150

Objective: NPV: Mean: 325.642486973133

Simulation: 121

Values of Variables:

Wells to drill: 16
Plateau rate: 12.4949270283824
Facility size: 150

Exhibit 9-20.
Optimization statistics.

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Numeric Computation and Visualization Optimization Modeling

Matlab

MATLAB is a technical computing environment for high-performance numeric computational and visualization. This product integrates numeric analysis, matrix computation, signal processing, and graphics where problems and solutions are expressed just as they are written mathematically without traditional programming. The system is interactive, and its basic data elements consist of a matrix that does not require dimensioning. It enables the user to solve numeric problems in a much shorter time that writing a program in FORTRAN, BASIC, or C.

MATLAB also incorporates application-specific solutions called toolboxes. These toolboxes include comprehensive collections of MATLAB functions called M-files. These files extend the environment to solve certain classes of problems. Optimization techniques and problems are contained in MATLAB's Optimization Toolbox.

The Optimization Toolbox contains routines that implement the most widely used methods for performing minimization or maximization on general nonlinear functions. These routines may be used to solve complex design problems in order to improve cost, reliability, and performance in a wide range of applications.

This software is highly respected in the financial community and has extensive numeric capabilities and a fully extensible environment. The interactive nature of MATLAB allows optimization problems to be refined and adapted, providing the user with feedback and insight into a problem's "best" solution. Functions and constraints are formulated and then solved using the functions in the Optimization Toolbox (see Table 93). A variety of examples show in detail how to use the functions contained in the toolbox. These examples also compare how various algorithms perform when solving sample problems.

The Optimization Toolbox features a variety of nonlinear optimization routines that are designed to work with scalars, vectors, and matrices. The function to be optimized can be written as a MATLAB function or as an expression. Default optimization parameters are used extensively but can be changed through an optional parameter vector. Parameters can be passed directly to the functions, eliminating the need for global variables. Gradients are calculated automatically using an adaptive finite-difference method, unless they are supplied in a function. You can check supplied gradients against those calculated via finite differences. The toolbox also provides implementations of leading optimization algorithms:

· For unconstrained minimization: NelderMead simplex search method and BFGS quasi-Newton method

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· For constrained minimization, minimax, multiobjective, and semi-infinite optimization: variations of the sequential quadratic programming method

· For nonlinear least-squares problems: GaussNewton and LevenbergMarquardt methods

· For linear and quadratic programming and constrained linear least-squares problems: projection method

Graphically, an optimization problem can be visualized as trying to find the lowest (or highest) point in a complex, highly contoured landscape. The program's features include the following:

· Unconstrained nonlinear minimization

· Nonlinear least-squares and nonlinear data fitting

· Nonlinear equation solving

· Linear programming

· Quadratic programming

· Constrained nonlinear minimization

· Constrained linear least squares

· Minimax

· Multiobjective optimization

· Semi-infinite minimization

Chapter Nine References and Selected Readings

Books and Periodicals

Aliber, R. Z., and B. R. Bruce. (1991). Global portfolios: quantitative strategies for maximum performance. Homewood, Ill.: Business One Irwin.

Althoen, S. C., and R. J. Bumcrot. (1976). Matrix methods infinite mathematics: An introduction with applications to business and industry. New York: Norton.

Calman, R. F. (1968). Linear programming and cash management: CASH ALPHA. Cambridge: Mass., MIT Press.

Charnes, A., and W. W. Cooper. (1961). Management models and industrial applications of linear programming. New York: John Wiley & Sons.

Danø, S. (19631974). Linear programming in industry: Theory and applicationsan introduction. Vienna: Springer.

Dorfman, R. (1951). Application of linear programming to the theory of the firm, including an analysis of monopolistic firms by non-linear programming. Berkeley and Los Angeles: University of California Press.

Emmons, H., et al. (1989). Storm quantitative modeling for decision support. Oakland, Calif.: Holden-Day Inc. Quantitative modeling programs for business and engineering.

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Ferguson, R. O., and L. F. Sargent. (1958). Linear programming: Fundamentals and applications. New York: McGraw-Hill.

Garvin, W. W. (1960). Introduction to linear programming. New York: McGraw-Hill.

Heady, E. 0., and W. Candler. (1958). Linear programming methods. Ames: Iowa State College Press.

Ijiri, Y. (1993). Creative and innovative approaches to the science of management. Westport, Conn.: Quorum Books.

Koo, D. (1977). Elements of optimization, with applications in economics and business. New York: Springer-Verlag.

Kornbluth, J. S. H., and G. R. Salkin. (1987). The management of corporate financial assets: Applications of mathematical programming models. London: Academic Press.

Kwak, N. K. (1973). Mathematical programming with business applications. New York: McGraw-Hill.

Lapin, L. L. (1976). Quantitative methods for business decisions. New York: Harcourt Brace Jovanovich.

Levin, R. I., and R. P. Lamone. (1969). Linear programming for management decisions. Homewood, Ill.,: Richard D. Irwin.

Loomba, N. P. (1964). Linear programming: An introductory analysis. New York: McGraw-Hill.

Moore, P. G., and S. D. Hodges. (1970). Programming for optimal decisions: Selected readings in mathematical programming techniques for management problems. Harmondsworth: Penguin.

Myers, S. C. (1969). Linear programming for financial planning under uncertainty. Cambridge: MIT Press.

Naylor, T. H., et al. (1971). Introduction to linear programming: Methods and cases. Belmont, Calif.: Wadsworth.

Pogue, G. A., and R. N. Bussard. (1971). A linear programming model for short term finanicial planning under uncertainty. Cambridge: MIT Press.

Smith, D. (1973). Linear programming models in business. Stockport: Polytech Publishers.

Stockton, R. S. (1963). Introduction to linear programming. Boston: Allyn and Bacon.

Vajda, S. (1962). Readings in mathematical programming. New York: John Wiley & Sons.

Welem, U. P. Aggregate planning and control: A constrained non-linear programming approach. Göteborg: Bas.

Williams, N. (1967). Linear and non-linear programming in industry. London: Pitman.

Zenios, S. A. (1993). Financial optimization. Cambridge: Cambridge University Press.

Ziemba, W. T., and R. G. Vickson. (1975). Stochastic optimization models in finance. New York: Academic Press.

Periodicals

Brown, Kate, and Richard Norgaard. (1992). ''Modelling the telecommunication pricing decision." Decision Sciences, 23(3)673.

Cassou, Steven P. (1993). "Backward solving quarterly models with seasonal or annual shocks." Economic Modelling, 10(2)90.

Clarke, Peter. (1984). "Optimal solution? Try the linear programming way." Accountancy, 95(1096)119.

Clements, Dale W., and Richard A. Reid. (1994). "Analytical MS/OR tools applied to a plant closure." Interfaces, 24(2)1.

Crowder, Harlan, Ellis L. Johnson, and Manfred Padberg. (1983). "Solving large-scale zero-one linear programming problems." Operations Research, 31(5)803.

Deresky, Helen. (1981). "Analytical tools for increased productivity." Journal Of Systems Management, 32(7)28.

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Elimam, Abdelghani A. (1996). "The use of linear programming in disentangling the bankruptcies of al-Manakh stock market crash." Operations Research, 44(5)665.

Erenguc, S. Selcuk. (1985). "A non-dual approach to sensitivity analysisThe right-hand-side case." Decision Sciences, 16(2)223.

Griffith, Stephen W. (1999). "Optimization software helps earn highest possible profits." Wood Technology, 126 (3)16.

Holloway, Clark; John A. Pearce, II. (1982). "Computer assisted strategic planning." Long Range Planning, 15(4)56.

Ignizio, James P., and John H. Perlis. (1979). "Sequential linear goal programming: Implementation via MPSX." Computers and Operations Research, 6(3)141.

Kee, Robert. (1994). "Linear programming as a decision aid for downsizing." Journal of Managerial Issues, 6(2)241.

Kennedy, Kristin T. (1998). "Multiple sourcing alternatives using nearly optimal programming." Journal of Education for Business, 73(4)206.

Lee, Chau-Kwor. (1990). "Discriminant analysis using least absolute deviations." Decision Sciences, 21(1)86.

Matz, A. W. (1979/80). "Linear programmingThe model solution." Telecom World, 31(4)32.

Mesko, Ivan, and Tjasa Mesko. (1994). "Fractional piecewise linear optimization of the business process including investments." Decision Support Systems, 12(3)213.

Okorougo, Noel C. (1983). "Accountants, business decisions and mathematical programming techniques." CA Magazine, 116(6)75.

Ong, S. L.. (1985). "Microcomputer application for constrained nonlinear optimization program." Iie Solutions, 17(7)24.

Roche, Maurice J. 91998). "Linear-quadratic solution methods to non-linear stochastic models: A note." The Manchester School, 66(1)118.

Rychel, Dwight F. (1982). "A case history of financial and operational modeling in corporate planning." Computers and Industrial Engineering, 6(2)125.

Studt, Tim. (1994). "Optimization program speeds design of nonlinear systems: Nonlinear control design." Research and Development, 36(6)19.

Wiseman, Alex. 91998). "Operational research: A toolkit for effective decision-making." Management Accounting, 66(11)36.

Young, Martin R. (1998). "A minimax portfolio selection rule with linear programming solution." Management Science, 44(5)673.

Select Internet Library

Crystal Ball 2000 Professional's OptQuest technology provides an evolutionary step to this process by determining the optimal choice for a given business decision based upon multiple Crystal Ball simulations. OptQuest for Crystal Ball, the Crystal Ball Developer Kit and Crystal Ball Extenders are tools that vastly increase the power of Crystal Ball. http://www.decisioneering.com/cbpro/info.html.

Columbia University Computational Optimization Research Center
Researchers specialize in the design and implementation of state-of-the-art algorithms for the solution of large-scale optimization problems arising from a wide variety of industrial and commercial applications. http://corc.ieor.columbia.edu/.

University of Baltimore Business Center
Optimization with sensitivity analysis resources http://ubmail.ubalt.edu/~harsham/refop/Refop.htm.

The MathWorks
MATLAB Optimization Toolbox provides tools for general and large-scale optimization of nonlinear problems. Additional tools are provided for linear programming,

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quadratic programming, nonlinear least squares, and solving nonlinear equations. http://www.mathworks.com/products/optimization/.

Optimal Design Lab
Links Optimization Software; Altair; ANSYS; CPLEX Optimization, Inc.; the CWP Object-Oriented Optimization Library (COOOL); LMS Optimus, the MathWorks Web site (MATLAB, Opt ++, Vanderplaats Research and Development (GENESIS), VMCON2 (SQP implemented in FORTRAN)

Optimization Software Development
C++ programming information, documents/sources for C++ and OO, the Hilbert Class Library, Newmat09:, +++ matrix library, and SIMULINK Block Library.

Optimization Homepages, Global Optimization Homepage, the International Society for Structural and Multidisciplinary Optimization
List of useful optimization software, Michael Trick's Operations Research home page, NEOS Server, multidisciplinary optimization, Multidisciplinary Optimization Branch (MDOB) home page, OpsResearch.com (Operations Research Java Software).

Optimization Groups
Kenneth Holmström's Applied Opt. and Modeling (TOM) Group, Nick Sahinidis' Optimization Group, and RPI Design Optimization Lab.

Optimization Information
Linear and nonlinear programming FAQ. http://ode.engin.umich.edu/links.html.

Palisade Risk Optimizer combines advanced Genetic Algorithms of their product EvolverTM with the firm's simulation model:@Risk. http//www.palisade.com/html/risko.html

CD

Name

Size

Type

A Tutorial on Spreadsheet Optimization

1KB

Internet Shortcut

Bibliography for Optimization with
Sensitivity Analysis

1KB

Internet Shortcut

C9njr

48KB

Microsoft Excel Worksheet

C9NJRSolution

83KB

Microsoft Excel Worksheet

C9Oil Field Development

122KB

Microsoft Excel Worksheet

C9Oil Field DevelSolution

122KB

Microsoft Excel Worksheet

C9OilFieldSolReport

66KB

Microsoft Excel Worksheet

C9SolvjoeBk

61KB

Microsoft Excel Worksheet

Home Page of CORC

1KB

Internet Shortcut

Optimal Design Laboratory-Links

1KB

Internet Shortcut

OPTIMIZATION SOFTWARE-Crystal Ball
Pro-optimization software for
spreadsheets

1KB

Internet Shortcut

Stochastic Optimization with Learning

1KB

Internet Shortcut

The MathWorks-Optimization Toolbox

1 KB

Internet Shortcut

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Chapter Ten
Risk Analysis of the Corporate Entity and Operating Segments

Cost of capital involves two types of risk: systematic and unsystematic. Systematic risk is the risk of holding a market portfolio. Say that your firm's stock is one asset in an investor's portfolio. As the market moves, each individual asset comprising that portfolio is more or less affected. To the extent that your company's stock is affected by general market moves, the stock involves systematic risk. Specific risk is the risk that is unique to your firm, for example, the loss of a major contract, failure of an R&D effort, or the write-off of a large accounts receivable Unsystematic risk represents the component of an asset's volatility that is uncorrelated with general market moves.

Unsystematic and systematic risk are not restricted to assets traded on financial markets. For example, when an insurance company sells homeowners insurance in a particular region, the insurer faces systematic risk from such risks as hurricanes or earthquakes. Such risks can impact many homes simultaneously. The insurer also faces specific risk from risks such as fires or lightning strikes, which affect only individual homes. One of the benchmarks of stock market risk systematic risk is macroeconomic and industry risk.

The costs associated with both debt and equity financing are primarily a function of risk. Stakeholders require compensation in proportion to the risks they bear in financing. Additionally, the liquidity of the financing instrument (i.e., the relative ease of converting the instrument or assets underlying the instrument into cash) will also affect its cost. All else being equal, higher liquidity entails a lower cost of financing.

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Identifying Systematic Risk

The Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) and the more recent Arbitrage Pricing Theory help to estimate equity's required return (e.g., a firm's cost of equity capital). The CAPM is associated with systematic risk. Essentially, the required return demanded by shareholders is equal to a risk-free return plus an additional risk premium to compensate the investor for market risk.

The riskiness of an asset portfolio, be it stock or alternatively a "basket" of capital expansion projects, has direct implications for the required rate of return. Since investors generally hold portfolios of securities, it is reasonable to consider the riskiness of a security in terms of its contribution to the riskiness of the portfolio rather than in terms of its riskiness if held in isolation.

The CAPM Equation

CAPM divides the risk of holding risky assets into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As the market moves, each individual asset is more or less affected. To the extent that any asset is affected by such general market moves, that asset entails systematic risk. Specific risk is the risk that is unique to an individual asset. It represents the component of an asset's volatility that is uncorrelated with general market moves.

According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor's net exposure is just the systematic risk of the market portfolio. (See "Perfect Portfolio Ltd example in Chapter 9.)

CAPM was first introduced by William Sharp in 1964. It extended Modern Portfolio Theory to introduce the notions of systematic and specific risk. CAPM considers a simplified world where:

· There are no taxes or transaction costs.

· All investors have identical investment horizons.

· All investors have identical perceptions regarding the expected. Returns, volatilities, and correlations of available risky investments.

In such a simple world, Tobin's superefficient portfolio (see Exhibit 101) must be the market portfolio. All investors will hold the market

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Exhibit 101.
The security market line.

portfolio, leveraging or deleveraging it with positions in the risk-free asset. That is, in a competitive marketplace, risk premium investors require (Rj Rf) in direct proportion to beta (ß). This means that the investments that people make fall along a sloping line called the security market line (SML).

CAPM infers that the appropriate rate of return on a security is the sum of the rate available on a riskless investment plus a premium for risk actualized as a function of the investment's beta. For example, an investment with a beta of .5 will generate half the expected risk premium, while investments having a beta of 2 will produce twice the expected risk premium. In a two-investment world, the covariance of the returns that two securities generate is found. What we want to know is how two securities move with or against each other. If two securities move together, risk increases, as we realize quite quickly if we put two eggs in a basket and then drop the basket.

In the next section, "Corporate Analysis," we will develop a credit and bond rating working with an interactive computer model developed by the author.* The overall system is a linked matrix of 19 factors that combine to form a divisional risk grade (and bond rating). The model has a grading line of 1 to 10, whereby 1 is the best grade and 10 the worst. In certain cases, a grade of 10 will default the overall grade to an unacceptable 10.

In the section "Segment Analysis," the interactive model has been optimized to risk rate operating segments and/or divisions. The model incorporates S&P bond ratings into all the risk catagories from 1 through 10 and has been designed to be industry specific. However, S&P ratings are frequently updated and the one included are only examples. You can download updated ratings a subscription on basic from S&P or Moodys specific to your firm's operating segments and thus develop specific segment risk-rating worksheets for each of your operating divisions. The macros are included in the main model, and these can be easily adapted.

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Corporate Analysis

Introduction to Your Corporate Risk-Rating Interactive Model

Risk grading plays a leading role in the credit process of financial institutions. In this section, we will work through "rating" mirror imagethe corporate perspective. The interactive risk-rating system CorpRiskModel.xls is designed to credit "rate" your firm so that you know how credit stakeholdersthe suppliers of creditdecompose risk into its microcompoments. It is built across 10 points, from a triple A to a comparable D bond rating.

There are two major classifications of risk in any transaction. The first is risk associated with your firm as it looks at debt financing, and the second is risk associated with the structure of the deal that you plan to negotiate with credit suppliers, or the facility. Of the critical risk factors associated with a transaction, the firm is the obligor; that is, obligor risk is centered on factors dealing with your firm's operating cash flows, debt capacity, asset/liability quality, valuation concerns, financial reporting, management, industry, economic and country risk factors, guarantees, and collateral. The collateral your firm offers may change its, say, relatively high expected default factors into low expected loss factors that can make or break a deal. For example, if your firm's expected default factor is 2% (2% Probability of default without collateral), putting up collateral that passes the risk-rating requirements, depending on the liquidity of the collateral, could reduce potential losses to near zero.

Facility risks are adjusted for factors such as your company's borrowing purpose, tenor of the credit facility, documentation, and portfolio risk includes such factors as how easily the credit can be sold or syndicated to investors. Your corporate risk score, combined with the financial institution or investor' facility risk grade, forms the final risk grade.

The risk grade that is derived from this model will likely form the basis on which capital and loan provisions are calculated, developed, and assessed, allowing for the measurement of risk and reward standards via the debt stakeholder's risk-adjusted return on equity, return on assets, and other key firm ratios. These measurements serve as fundamental tools for pricing your deal as well as guides for resource allocation and active port-

*The corporate risk system was developed from an early prototype of a credit risk model I set up for a large international bank. The proprietary system that has since evolved at that bank has become a proficient tool to evaluate credit risk. Our corporate risk system works well, but in a somewhat restricted environment. That said, the interactive corporate model included in the CD would never have been possible without the expertise and experience of credit officials at that institution. The author is deeply grateful to these outstanding professionals.

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folio management and planning. By completing CorpRiskModel.xls, you will see how your financial institution, investment bank, or venture capitalist breaks the firm's complex credit fabric into its most elemental parts and recasts them later in compelling logic.

Thus, the principles underlying the risk rating process are ongoing and involve, among other factors, the following:

·Initiating and maintaining your firm's obligor risk and facility risk ratings on a continuous basis

·Reviewing your firm's credit ratings by the financial institution's credit policy and credit audit areas to test for accuracy, consistency, and timeliness

·Combining with traditional policy in setting the company's rates and/or fees commensurate with your firm's risk level

·Determining the degree of lending officer service and monitoring your credit required

The Structure of a Credit Risk-Grading System

Debt rating represents a current assessment of the creditworthiness of an obligor with respect to specific obligations. These ratings may take into consideration obligors such as guarantors, issurers, or lessees. Ratings supplied by S&P or Moodys are usually based on likelihood of default, capacity and willingness to repay interest and principle payment, nature and provisions of the debt, protection afforded by the obligation in event of failure, and creditor rights in a reorganization. Default probabilities, as a measure, have evolved into a science. KMV (www.kmv.com), a major player in measuring default risk, cites two critical ingredients to measure default probabilities: data and models. Models are the means by which data are transformed into expected default probabilities (EDF). Both default probabilities and bond rating are linked to credit grades as viewed in Table 101.

Risk definitions (Table 102) such as special mention, substandard assets, doubtful assets and loss assets are not left to financial institutions. Rather these definitions were issued by regulatory agencies including the Comptroller of the Currency, the Federal Deposit Insurance Corporation, the Federal Reserve Board and the Office of Thrift Supervision.

System Overview:
CorpRiskModel2

The model is a generic Industrial and Commercial Risk Grading worksheet set up for corporate use. In the next section, you will learn to use a divisional/operating segment model. CorpRiskModel2 located in the Risk

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Rating Subdirectory of the CD is a 10-point interactive system designed to provide maximum flexibility while maintaining ease of use. This is accomplished in several ways. The workbook is menu driven, complete with interactive dialog boxes. There is no need to memorize commands. Simply select options from menus, click tabs at the bottom of the worksheets, or respond to dialogs that pop up on the screen. The system follows your work and points out errors.

Each section within the Industrial and Commercial Risk Grading interacts with other sections. Simply record the risk grade below each component. Cumulative grades are in most cases determined by the program. Readers are encouraged to "experiment" with the model but because this model is a highly sophisticated tool you should not expect to be proficient except after many trials.

Begin by doing the following:

1. Open the Risk Grading Workbook: CorpRiskModel.xls in the Risk Rating subdirectory of the CD.

2. A dialog box will appear. You can enter your name, the date, financial institution, contact at financial institution, maximum exposure,

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a brief description of the facility you are requesting, and the previous credit grade. If guarantees or collateral support the credit, check the box labeled Guarantees? and/or Collateral? If guarantees or collateral are not checked, they disappear from the system.

3. Select Risk | Obligor Financial Measures | Worksheet from the main menu or page the worksheet over. Complete the corporation's primary risk measures labeled Module OneYour Firm's Primary Financial Measures.

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Part 1
The Firm's Risk Rating

Section 1
Your Firm's Financial Measures

(Worksheet: OPM1)

Exhibit 102 represents a sample page for reference. The model opens to S&P ratings linked to the manufacturing industry.

Exhibit 102A displays your firm's primary financial measures. These two pages are often most important in a risk rating system.

Included in Obligor financial measures, that are your firm's primary risk characteristics, are the following:

1. Operating cash flows

2. Debt capacity and financing flexibility

3. Asset quality

4. Valuation measures

5. Contingencies

6. Financial reporting

7. Management

Exhibit 102.
The opening risk-rating worksheet and S&P ratio comparatives.

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Exhibit 10-2A.
Your firm's primary financial measures.

(continues)

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Exhibit 10-2A.
Continued.

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Think about the following:

Earnings and Operating Cash Flow

1. Are margins solid compared to the industry?

2. Are your firm's earnings stable, growing, and of high quality?

3. Is cash flow magnitude sufficient to fund growth internally?

4. Is operating cash flow strong in relation to present and anticipated debt?

5. Is net cash flow from operations sufficient to cover most nondiscretionary outlays?

Debt Capacity and Financial Flexibility

1. Is leverage and coverage within the first quartile of your firm's industry peer group?

2. What are your company's alternative sources of debt and equity capital?

3. Does your firm have solid investment grade ratings?

4. Can your firm weather economic downturns?

5. Are debt maturities manageable?

6. Note: Since debt capacity is driven by cash flow, it would be unusual for debt capacity/financing flexibility to get a better grade than cash flow.

Balance Sheet Quality and Structure

1. Are assets solid and fairly valued?

2. Does the liability structure match the asset structure?

3. Do assets show concentration of location or use?

4. Are liquidity margins narrow?

Valuation

1. Is there a healthy spread between the the firm's asset values, that is, cash flow value (economic value) of assets (value of the corporate) and the market value of debt?

2. What is the spread between operating profit margin and the threshold margin? The threshold margin is the minimum profit margin required to increase shareholder value. See chapter 11.

3. Does your firm have hidden liabilities that may result in a significant erosion of shareholder value?

Contingencies

1. Are contingencies limited and easily controlled?

2. Is the potential impact on tangible new worth negligible?

3. Is the expected value of contingencies certain?

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Financial Reporting and Strategic/Business Plans

1. Is an audit regularly completed by a reputable corporation?

2. Are your financial reports promptly issued to financial institutions?

3. Are financial statements accurate and complete?

4. Is your business plan accurate and complete?

5. Have you completed a valuation appraisal report? An valuation appraisal template is included in chapter 11.

Management and Controls

1. Is management capable, now and for the foreseeable future?

2. Are strong operating and financial controls in place?

3. Does management have broad industry experience, good continuity, and depth?

4. Is management tried and tested?

Guidelines for Completing the Worksheet:
OFM1

First, examine each of the definitions corresponding to the columns (Grade, Bond Rating, and Expected Default Factor) and decide where your firm fits. Enter individual risk grades: Operating cash flows, debt capacity and financing flexibility, asset/liability quality, valuation measures, contingencies, and financial reporting and management (see Tables 103 and 104).

(Hint: You may want to unfreeze panes. Select Window, then click on Unfreeze Panes.)

Optional: Select Risk | Obligor Financial Measures | OFM Weights. Default numbers (or weights) provide a ''weighted" OFM cumulative grade. You can accept or change weights that impact cumulative grades more in line with your credit. In any case, weights pertaining to operating cash flows, debt capacity and financing flexibility, asset/liability quality, valuation measures, and management are not included in the boxes below. Table 105 a brief overview of the Obligor cumulative weighting system. This table is a sample cut-off. Readers may want to click in the formula cells to view the range of opportunities structured into the risk rating model. The following section illustrates how the weights work.

Using Weights to Determine the Firm's Cumulative Financial Risk Measures

Weights in the previous example (in columns) are set in default mode for illustration. However, you set the weights according to your perception of the importance that each column has with repect to the other columns. The program brings together the previous categories that you examined and arrives at cumulative grade for each category. Weights are subjective. You are the firm's credit "expert," anticipating what your firm thinks about the firm's risk. You are, thus, in the best position to program the weights that promote the primary risk cumulative grades.

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If your loan request is seasonal and you anticipate that the firm will look primarily to asset quality for repayment (with cash flow playing a minor role), you might weigh the cumulative grade (in column D) as, say, 2, 1, 7, 3.

Example 1: Assume that operating cash flow grade is 3, while debt capacity grade is 4. You feel that the default weights in column B (7 and 2) reflect the importance of cash flow to debt capacity since much of the firm's financing capacity is derived from cash flow. If weights are accepted, your firm's cumulative grade at this point is (7 * 3 + 2 * 4)/ (7 + 3) = 2.9.

Example 2: Assume that operating cash flow grade is 2, debt capacity grade is 3, and asset/liability quality grade is 4. You argue that the default weights in column C (5, 3, and 9) reflect the importance of operating cash flow and debt capacity to asset/liability. If weights are accepted, the cumulative grade is (5 * 2 + 3 * 3 + 9 *4)/(5 + 3 + 9) = 3.24.

Contingencies or Financial Reporting

These benchmarks are important to your firm. If unit grades fall below acceptable levels, the system assigns a cumulative Obligor grade equal to the grade assigned for that category. Contingencies or financial reporting grades of 5 or better usually have no impact on the cumulative grade; that is, contingencies and financial

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reporting will never help a cumulative grade, but bad contingencies or financial reporting will hurt it. The following two boxes contain examples:

The formula in the Contingencies box reads "If the category risk grade (cell N106) is worse than 5, let the cumulative risk grade default to the category Risk Grade. If the category Risk Grade is 5 or better, insert the cumulative risk grade into the Contingencies box." For example, in a worst-case scenario, if Contingencies were rated a 6, the cumulative grade would default to 6 (see Table 106).

The formula in the Financial Reporting box reads "If the category risk grade (cell P106) is worse than 5, let the cumulative risk grade default to 10. If the Category Risk Grade is 5 or better, insert the cumulative risk grade into the Financial Reporting box." For example, in a worst-case scenario, if Financial Reporting were rated a 6, the cumulative grade would default to 10:

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Note the Accept/Override row. You can decide on the weights and then protect them. Let's suppose that you allow one of your subordinates to complete the worksheet. Assume also that the worksheet accepted the default grade of 10 but your analyst felt that a 10 cumulative grade would be too harsh and entered a grade of 4 in the Accept/Override cell. The system will accept his or her decision, but a dialog will prompt for an explanation when data entry is verified:

Subjective Measures

Management depth is algorithmic (re: calculation of the cumulative grade). The default weighting, at 6 to 1, seems reasonable and sets management depth cumulative grade. Change the default weight if you disagree.

Example: The cumulative grade after you factor in financial reporting is 4. The management depth grade is 6. You feel that the default relationship (weight) of the cumulative grade to the management grade is 6 to 1. If you accept these weights, the cumulative grade is (6 * 4 + 1* 6)/ (6 + 1) = 4.3.

Module 1
Your Firm's Primary Financial Measures, Short Examples

1. Your firm has good cash flow, but debt capacity is somewhat strained, and financial flexibility may be limited. You believe that a 5 credit grade is justified.

2. The cumulative grade was carried as a 4 before contingencies. The company has significant contingent liabilities of an uncertain nature such that an unfavorable event likely will occur before loan maturity. A substantial erosion of tangible net worth is likely. The program dropped cumulative grade to 7. You agree.

3. The firm operates near break even or has losses, financial reporting is poor (i.e., rating of 6 or 7 without qualification by a local accounting corporation whose reputation is unknown, limited footnotes), and support is provided by soft comfort letter from German parent. The computer dropped the cumulative grade to 10. You let the grade stand.

4. Let's suppose that your firm is engaged in medical therapy and was formed by the merger of three entities, is highly leveraged with modest or negative tangible net worth, and operates in a dynamic and growing industry (health care) where it is a major player (number 1 or 2 in its market segments). As it consolidates its recent acquisitions, which creates economies of scale in terms of overhead and

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gives the entity a national presence, the company will generate sufficient profits and cash flow from volume increases (new patients) to offset lower prices dictated by managed care and pays back a recent term loan. The firm's revolver and subordinated debt will likely be refinanced. The company is publicly held and well regarded in the market, as is management, which you bet your last dollar is on the cutting edge. Suggest risk grade 4.

5. The firm has good profits and cash flow but limited financial flexibility because of high leverage. Stability of cash flows is helped by a contractual agreement with the former owner (a AAA credit). You believe that the terms go beyond the tenor that the firm will agree to. The facilities include an amortizing term loan and revolving credit with collateral (all assets) with a book value equal to outstanding at inception of the deal.

6. Let's suppose that you are proposing a 19-year lease transaction of a commercial jet with an exploding rate feature that is expected to be refinanced with 12 months by an equipment trust certificate. While there is no recourse to your firm, the plane is leased to one of the top two or three domestic carriers, giving you confidence in the cash flowgenerating ability of the aircraft under lease. You feel strongly that a grade of 3 is appropriate for operating cash flow.

Section 2
Industry, Macroeconomic, and Environmental Risk Included in This Section Are the Following:

1. Industry segment

2. Position within industry

3. Macroeconomic and environmental factor

4. Country transfer risk

Industry Overview:
An Analysis

You are an expert in your industry. Industry analysis is crucial. You need to consider the impact that industry risk and peer position have on Obligor financial measures. Following is an extract of the 1994 Federal Reserve Loan Examination Manual dealing with the nuts and bolts of an industry audit. Your financing sources know this. You should also be familiar with these guidelines.

Federal Reserve Audit Guidelines¹

·Attach an Standard Industrial Code (SIC) to every loan.

·Define industry groups.

¹ Source: Commercial Firm Examination Manual, Board of Governors, The Federal Reserve System, Division of Supervision and Regulation, December 1995.

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·Assign a credit risk rating to every loan.

·Distinguish between credit rating for firm versus credit rating for a loan transaction.

Stages of Industry Analysis, Level 2
Analyze Industry Fundamentals

·Prepare industry studies for loan officers and for credit committees.

·Evaluate credit risk exposure in relation to industry.

·Identify firms, by industry.

·Analyze individual firm credits, by industry.

·Perform comparative analysis of industries:

1. Analyze financial ratios.

2. Compare operating characteristics.

3. Understand financial and operating risks.

·Establish industry credit standards (loan structure, collateral cover-age, documentation requirements).

·Achieve functional independence but avoid isolation:

1. Remove responsibility for industry studies and analysis from the loan officers.

2. Organize industry analysis under chief economist or senior credit officer but preserve intelligence lines with lending personnel.

Stages of Industry Analysis, Level 3
Report Industry Concentrations

· Aggregate industry concentrations:

1. Use weighted average or percentiles of credit ratings aggregated by industry.

2. Analyze risk of portfolio by industry.

·Establish an Industry Credit Policy Committee:

1. Review industry studies.

2. Analyze concentrations in relation to capital or loans.

3. Set loan limits.

4. Use for strategic planning purposes.

5. Identify growth industries and problem industries.

Stages of Industry Analysis, Level 4
Quantify Industry Risk

·Develop industry risk ratings for industry analysis.

·Use an external model from an outside vendor.

·Develop an internal model.

·Use economic or industry data.

·Use financial or bond market data as indicators of industry risk.

·Compare industry risk ratings with the weighted average credit rat-ing of the firm's exposure by industry.

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· Run scenarios (commodity price changes, interest rate changes) to determine sensitivity of loan portfolio to outside shocks.

· Determine covariance of industries or interrelationships among industries.

Stages of Industry Analysis, Level 5
Incorporate Industry Analysis into the Loan Portfolio

· Diversify the loan portfolio to reduce industry risk and industry concentrations.

· Distinguish between decision to originate loan and the decision to retain it for the portfolio.

· Use loan sales to reduce concentrations in the portfolio.

· Sell loans to organized secondary markets.

· Use industry risk systems:

1. To influence loan pricing.

2. To develop risk-adjusted rates of return measures.

3. To assign capital or loan loss reserves.

4. To conceptualize the loan portfolio like a securities portfolio.

Working with the Matrix:
Industry and Economic/Environmental Factors/Country Risk

First, Click on the INDUS tab or select Risk I Industry & Economic Measures I Worksheet. Review risk-rating definitions. Evaluate other industry risk factors listed here:

1. Does your firm operate in a strong and growing industry?

2. Is your firm a significant factor in the industry or market?

3. Are legal or regulatory climates favorable?

4. Is industry cyclically minimal?

5. Is the industry vulnerable to sudden economic or technological change?

6. Is industry operating leverage modest?

7. Are labor problems minimal?

8. Is regulatory environment satisfactory?

9. Are long-term prospects favorable?

10. Does your firm rank in the first tier of the industry?

11. Is your firm's industry "focused," enjoying a meaningful market share?

12. Are performance ratios generally better than industry peers?

You Should Also Consider Other Industry Factors:

1. Cyclicality

2. Seasonality

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3. Regulatory Issues

4. Environmental Issues

5. Product Liability

6. Barriers to Entry

7. Technical Obsolescence

8. Commodity vs. Value Added

9. Manufacture vs. Service

10. Domestic reliance vs. International Sales Diversification

11. Government Contract Related Issues

12. Industry Life cycle

The system will calculate the "Correct" industry grade by combining your firm's industry grade with the firm's tier position. You simply enter a grade for the industry and a grade for your firm's industry tier position. The tier position listing is actually a quartile ranking. The first two grades, in the column titled Firm Rating, represents the top quartile, followed by the second, third, and fourth quartiles. For example, if you rate the industry 7 and industry position 5, the combined industry rating can be no better than 5. The firm's cumulative grade will default to the industry grade if the industry grade is worse than the firm's grade (see Exhibit 103).

Simply enter industry grade and industry position. The system takes these two numbers, completes the industry cumulative rating, and enters the rating on the Industry worksheet.

Exhibit 103.
Industry matrix.

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Risk-grading factors range from dynamism and strength, political and social climate always supportive of business and industry, and unquestioned creditor rights to possible unfavorable movements, unfavorable creditor rights or legal environment, unsupportive political and social climate, poor creditor rights or legal environment, and unacceptable risks.

Completing the Worksheet

The formula driving the macroeconomic and environmental factors cumulative grade is = IF[J106 > 6,J106,(7 * H107 + R7 * J106)/(7 + R7)].

In plain English, the formula states that macroeconomic and environmental factors grades 1 to 5 leave no impact on the cumulative grade. Grades 6 or worse will have a negative impact on the cumulative grade. In addition, weight the cumulative grade to macroeconomic and environmental factors grade 7 to 1, that is, 7 times as important.

Country/Transfer Risk:
An Analysis

Cross-Border Risks

1. What is country investment ranking?

2. What is the Interagency Country Exposure Review Committee (ICERC) rating?

3. Has the ICERC rating improved or deteriorated over the past six months?

4. What is the country's resource base in terms of natural resources, human resources, and financial resources?

5. What is the outlook for domestic political stability?

6. What is the quality of economic and financial management? Does the leadership have the political strength to implement decisions, particularly if they involve austerity measures?

7. What is the country's long-run development strategy?

8. Is industrial development based on efficiency or on support of prestige projects or the economic interests of politically powerful groups?

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9. Is economic growth financed largely by domestic revenues and savings or through foreign speculative investments?

10. Is inflation under control?

11. Are wage and price policies in line with productivity growth?

12. In looking at the outlook for the balance of payments, what is the prognosis of current account, capital account, and debt service account improvements?

13. How are capital account deficits financed? World firm or bilateral aid programs? Firm loans?

Federal Reserve Audit Guidelines:
Transfer (Country Risk)

Substandard

· A country is not complying with its external service obligations, as evidenced by arrears.

· The country is not in the process of adopting other suitable economic adjustment program.

· The country and its firm creditors have not negotiated a viable rescheduling and are unlikely to do so in the near future.

Value Impaired

· The country has not met rescheduling terms for over one year.

· The country shows no definite prospects for an orderly restoration of debt service in the near future.

Considerations

· Establish country exposure limits for credits.

· Establish limits for distribution of loans by type and maturity.

· Review concentrations of credit within countries.

· Review international loan portfolio management objectives and policies at least annually to determine whether they are compatible with changing market condition.

· Measure significant changes in country conditions and/or levels of exposure.

· Revised country limits in response to substantive changes in economic, political, and social conditions within particular countries.

· Reviewed country limits and updated at least annually.

· Prior to granting additional advances or commitments, check outstandings to appropriate country limits.

· Lending officers cognizant of specific country limitations.

· Clearly define procedures for exceeding country limits.

· Have a periodic foreign call program for countries.

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· Establish internal review system that determines that international risk assets outstanding and committed are within the firm's foreign exposure limits.

· Review country risk factors (economic, political, and social).

· Obtain a continuing review of current country data obtained from internal and external sources.

· Analyze of economic, political, social, and other factors affecting country risk.

· Establish a formal reporting system on country risk.

· Establish a country risk evaluation system recognizes exposure from country to country on the basis of legally binding guarantees, collateral, or reallocation by office of responsibility.

· Establish reporting system that provides exposure data quickly and in sufficient detail to assess particular risks.

The formula driving the country transfer risk cumulative grade is = IF(L106 > 5,L106,107).

If the category risk grade is worse than 5, then the cumulative risk grade defaults to the category risk grade; otherwise, the macroeconomic and environmental factors cumulative grade carries over.

It follows that the performance of a firm cannot be isolated from the economic climate of the industry, or macroeconomic and country risk factors in which the major portion of its activities occurs. For this reason, these risk categories are essential in the evaluation of an obligor firm. Table 107, a cut from the respective page, summarizes performance in terms of (1) component or category risk grade, (2) cumulative risk grade with respect to (1) industry segment, (2) position within the industry, (3) macroeconomic and environmental factors, and (4) country or transfer risk.

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Section 3
Guarantees

(Worksheet: GUAR3)

Guarantees: An Analysis A guarantee is a written contract, agreement, or undertaking involving three parties. The first party, the guarantor, agrees to see that the performance of the second party, the guarantee, is fulfilled according to the terms of the contract, agreement, or undertaking. The third party is the creditor, or the party to benefit by the performance. For example, Party B makes a loan through his firm. The firm desires a guarantor for this loan in case of default by B. B asks A to act a guarantor for his loan. A agrees and signs a guaranty agreement. A is the guarantor, B is the guarantee, and the firm is the creditor.

Note: For the purposes of a risk rating at Corporate, guarantees refer to third-party guarantees only; upstream guarantees of subsidiaries are not applicable, as are guarantees from principals.

The credit grade assigned to loans supported by third-party undertakings will lie somewhere between the firm rating and the guarantor rating. Unconditional guarantees of payment will have considerably more impact than will a nonguarantees such as a comfort letter or ''verbal assurance."

The Risk Grading Worksheet (GUAR3)

Important Reminder: If the guarantee is less than 100%, you may want to complete a risk-rating form or check the bond rating for the guarantor before initiating this worksheet (remember the bond rating will provide you with the expected default facto (EDF). Remember that if the loan is not supported by a guarantee, Excel removes the worksheet GUAR3.

For partial guarantees, GUAR3 generates a weighted risk rating. The weighted risk rating depends on prorate credit responsibility and the EDF for the obligor and guarantor (Table 108).

1. After you evaluate the guarantor (you may have to "guess" the risk rating from an implied bond rating or from another source), enter the guarantor's grade in the color-coded box: Enter Guarantor's Cumulative Grade. (Table 109)

2. The EDF obligor in basis points corresponds to the cumulative risk grade you determined thus far. You need to match the cumulative grade to the EDF and enter the EDF in the appropriate color coded box: Enter Expected Loss Factor Obligor in b.p. (Table 109)

3. Enter the Enter % Obligation: Obligator (Decimal) in the red coded box: Enter % Obligation: Obligator (Decimal). If, for example, the obligor is responsible for 98% of the obligation, 98% belongs to the obligor, and 2% belongs to the guarantor. (Table 109)

4. After completing a grading worksheet on the guarantor, enter the EDF in the correct red coded box: Enter Expected Default Factor Guarantor in b.p*. (Table 109)

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Table 10-8.
Classification of guarantor's risk-rating profile.

Table 10-9.
Derivation of new combined risk rating with guarantor.

5. Enter the % Obligation: Guarantor (Decimal) in the box: Enter % Obligation: Guarantor (Decimal). (Table 109)

6. The program calculates the EDF in basis points, 44.22 (gray box). (the last column in Table 109)

7. Match the EDF to the appropriate risk rating to generate a combined risk rating. Enter this risk rating in the color-coded box: Enter % Obligation: Guarantor (Decimal).

Guarantees: Short Examples

1. The Bank issued a $5 million unsecured term loan to Wilson and Smith to refinance long-term notes issued by Olive Baking Company in conjunction with Wilson and Smith's 1987 acquisition of Southern Type and Supply Company.

Wilson and Smith, which has been a wholly owned subsidiary of the Olive Baking Company since 1965, is a wholesale distributor of graphic art

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supplies, equipment, and chemicals to the printing industry. For year end 1993, Wilson and Smith contributed 47% of Olive's consolidated revenues and 22% of its net income. For the nine-month period ended 9/30/94, Wilson and Smith's sales increased 6.7% from the prior period to $98.9 million. The higher sales volume combined with consistent gross margins and continued control of operating expenses resulted in net income of $2.3 million compared to $1.4 million at 9/30/93. These trends are expected to continue given the company's emphasis on maintaining margins and improving profitability.

Olive Baking Company was incorporated in 1914 as a baking company specializing in single-portion pies, cakes, and cookies. Olive purchased Wilson and Smith in 1965 for diversification purposes. On a consolidated basis, total revenues and Net income for FY 1993 were $246 million and $9.5 million, respectively. For the nine-month interim ended 9/30/94, consolidated revenues were $204 million, and net income was $7.4 million, up 5% and 9%, respectively, when compared to the similar period during FY 1993.

While both companies have performed consistently, Olive Baking remains the stronger of the two companies, on both a balance sheet and a profit-and-loss basis. On a consolidated basis, the company displays strong interest coverage, adequate debt service capacity, and a satisfactory leverage position. In addition, the $5 million unsecured term loan to Wilson and Smith is guaranteed by Olive Baking Company. Historically, Olive has generated sufficient cash flow to meet current maturities and payments of dividends. Cash flow from operations coupled with short-term borrowings are used to fund capital expenditures. Suggested firm rating, 5; suggested parent rating, 4; suggested risk rating, 4.

2. Company operates near break-even or has losses, financial reporting is poor (i.e., rating of 6 or 7 without qualification by a local accounting corporation whose reputation is unknown, limited footnotes), and an unconditional guaranty is provided by a soft comfort letter from German parent. The computer dropped the cumulative grade to 10. However, the cumulative grade may improve when you evaluate guarantees.

Section 4
Loans Secured by Collateral

(Worksheet: COLL4)

Loans Secured by Collateral: Issues and Analysis

Collateral is defined as property pledged as security for the satisfaction of a debt or other obligation. The credit grade assigned to secured loans will depend on, among other things, the degree of coverage your firm offers its creditors, the economic life cycle of the collateral versus the term of the loan, possible constraints of liquidating the collateral, and of course, the bank's ability to skillfully and economically monitor and liquidate collateral. Evaluate the following:

1. What is its value compared to credit exposure?

2. What is its liquidity, or how quickly may its value be realized and with what certainty?

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3. Legal rights associated with the collateral?

Note: Collateral means tangible and intangible assets specifically pledged; it does not mean pledges of firms' stock or the pledge of stock of a subsidiary (domestic or foreign).

Federal Reserve Audit Guidelines:
Collateral (With Respect to the Bank's Position)

1. Is negotiable collateral held under joint custody?

2. Are receipts signed by the customer obtained and filed for released collateral?

3. Are securities and commodities valued and margin requirements reviewed at least monthly?

4. When the support rests on the cash surrender value of insurance policies, is a periodic accounting received from the insurance company and maintained with the policy?

5. Is a record maintained of entry to the collateral vault?

6. Are stock powers filed separately to bar negotiability and to deter abstraction of both the security and the negotiating instrument?

7. Are securities out for transfer, exchange, and so on controlled by prenumbered temporary vault-out tickets?

8. Has the bank instituted a system that

a. Ensures that security agreements are filed?

b. Ensures that collateral mortgages are properly recorded?

c. Ensures that title searches and property appraisals are performed in connection with collateral mortgages?

d. Ensures that insurance coverage (including loss payee clause) is in effect on property covered by collateral mortgages?

9. Are acknowledgments received for pledged deposits held at other banks?

10. Is an officer's approval necessary before collateral can be released or substituted?

11. Does the bank have an internal review system that

a. Reexamines collateral items for negotiability and proper assignment?

b. Checks values assigned to collateral when the loan is made and at frequent intervals thereafter?

c. Determines that items out on temporary vault-out tickets are authorized and have not been outstanding for an unreasonable length of time?

d. Determines that loan payments are promptly posted?

12. Are all notes assigned consecutive numbers and recorded on a note register or similar record? Do numbers on notes agree to those recorded on the register?

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13. Are collection notices handled by someone not connected with loan processing?

14. In mortgage warehouse financing, does the firm hold the original mortgage note, trust deed, or other critical document, releasing only against payment?

15. Have standards been set for determining percentage advance to be made against acceptable receivables?

16. Are acceptable receivables defined?

17. Has the bank established minimum requirements for verification of firm's accounts receivable and established minimum standards for documentation?

18. Have accounts receivable financing policies reviewed at least annually to determine whether they are compatible with changing market conditions?

19. Have loan statements, delinquent accounts, collection requests, and past due notices been checked to the trial balances that are used in reconciling subsidiary records of accounts receivable financing loans with general ledger accounts?

20. Have inquiries about accounts receivable financing loan balances been received and investigated?

21. Is the bank in receipt of documents supporting recorded credit adjustments to loan accounts or accrued interest receivable accounts? Have these documents been checked or tested subsequently?

22. Are terms, dates, weights, description of merchandise, and so on shown on invoices, shipping documents, delivery receipts, and bills of lading? Are these documents scrutinized for differences?

23. Were payments from customers scrutinized for differences in invoice dates, numbers, terms, and so on?

24. Do bank records show, on a timely basis, a first lien on the assigned receivables?

25. Do loans granted on the security of the receivables also have an assignment of the inventory?

26. Does the bank verify the firm's accounts receivable or require independent verification on a periodic basis?

27. Does the bank require the firm to provide aged accounts receivable schedules on a periodic basis?

Completing the Collateral Worksheet (COLL4)

At worse, collateral has no impact on the cumulative grade. Superior quality collateral will improve the cumulative grade by as many as four grade levels (see Exhibit 104).

Examples:
Collateral

1. Glantz and Blake Corporation is a manufacturer of high-capacity disk drives. The firm receives a $15 million line of credit secured by accounts receivable, inventory, and equipment. The company has suffered substan-

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Exhibit 104.
Collateral classification.

tial losses over the last three years because of price reductions from its major competitors. The company is leveraged 2.5 times. Because of losses, extreme competition in the industry, and its leverage position, an obligor rating of 8 is warranted.

The firm's line, secured by high-quality and diversified accounts receivable (major corporations), equipment, and (high tech) inventory is on a controlled basis. Advances are made based on 70% of eligible downstream receivables, 40% of foreign receivables, and 70% against the knock-down value of the equipment. Collections are controlled by lock box, and agings are received monthly with on-site audits at least three times a year. Turnover of receivables is 55 days. Due to advances being on a controlled basis, the quality of receivables a risk rating of 6 is warranted.

2. Subsidiary Securities is a regional broker/dealer that is a wholly owned subsidiary of Parent Mutual Life Insurance Company. Although Subsidiary Securities is a profitable, sound broker/dealer, the industry has shown signs of weakening. The firm receives a $10 million secured brokers line and a $5 million unsecured short-term line of credit.

Subsidiary is well capitalized and continues to maintain capital above SEC requirements. For the nine-month period ending 12/31/89, Subsidiary had excess net capital of $39 million. Net income for the nine-month period ending 12/31/94 totaled $11.7 million compared to $11.0 million in the prior period and $11.4 million for FYE 3/31/94. Revenues of $179 million are up 18% from the previous period.

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Parent Mutual has over $4 billion in assets and carries an A+ rating from Best signifying solid financial condition. Additionally, Parent Mutual has the capacity to provide additional financial resources, if necessary. The facilities are short term in nature, and although unsecured, our risk is minimized by the collateral that Subsidiary holds as a result of their strict margin requirements. Based on this, ratings are as follows:

Secured Line: Suggested Firm Rating

4

Suggested Risk Rating

3

Unsecured Line: Suggested Firm Rating

4

Suggested Risk Rating

4

3. Revolving credit to a U.S. subsidiary of a German company secured by borrowing base (75% receivables, 60% inventory). The bank relies on monthly borrowing base reports from the company. While the firm makes money, its financial flexibility is limited by modest debt capacity, and ultimate repayment lies in the ability of the German parent to provide financing. You suggest a 1 improvement in the grade.

4. Loan secured by marketable fixed-income securities where the firm is unprofitable on a GAAP basis and where the bulk of assets besides the securities portfolio consists of undeveloped land in a fast-growing area of the United States with a market value considered well in excess of book value.

Part 2
Facility Risk Rating

Section 1
Purpose
(Worksheet: PURPOS5)

Note: Facility risk rating should hold no surprises. Downgrades to the obligor risk rating will be the exception, not the rule. However, your firm might suffer a downgrade if the facility calls for unusual tenor, if documentation is weak, if the loan's marketability has deteriorated, or if the purpose of the loan is inappropriate. So, be cautious and as watchful as you were completing the obligor section, your creditor certainly will be. Following are criteria to evaluate the purpose of the facility (Exhibit 105).

Section 2
Documentation
(Worksheet: DOCUM6)

Example Unsecured loan to Latin American blue chip company to bridge capital markets transaction with repayment expected in 60 to 180 days. Financials are unaudited and provided from prospectus with information somewhat dated and incomplete. Documentation is satisfactory but lacks meaningful covenants. You decide 1 grade improvement is justified reflecting the short loan duration, (see Exhibit 106).

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Exhibit 105.
Facility grade, purpose of proposed facility.

Section 3
Tenor
(Worksheet: TENOR7)

Unusual Terms, Tenor, and Subordinated Position

From time to time and for various reasons, a bank may extend credit on terms or for a tenor that for a given firm subjects the firm to a greater level of risk than indicated by the obligor rating. The incremental risk should be reflected in a higher risk rating.

For example, an unsecured line of credit to a company with an obligor rating of 4 would not usually warrant a change in risk rating (the grade may actually improve in some cases with maturities under one year). However, a term loan of longer-than-usual tenor or with a bullet maturity or a weak loan agreement may warrant a 5 or worse credit risk rating.

Generally, term loans that amortize with equal installments up to three years leave the grade unchanged. Bullet and balloon term loans of the same tenor might be one grade worse, (see Exhibits 107 and 108).

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Exhibit 106.
Facility grade, documentation matrix.

Exhibit 107.
Facility grade, tenor matrix.

Section 4
Portfolio
(Worksheet: PORTFOLIO8)

The Summary Page

The summary page brings together the entire corporate risk-rating system on one page. The summary page includes (1) matrix of each risk component and respective cumulative grade, change in cummulative grade, and unit grade; (2) table with corporate grade, corporate/ facility grade, and previous grade attached; (3) corporation's financial measure cummulative grade weights; and (4) guarantor's matrix; chart displaying unit grades and cummulative grades, (see Exhibit 109).

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Exhibit 108.
Facility grade, portfolio matrix.

Corporate Segment Analysis

Systematic Risk:
Pure Play Approach

You will need to find the cost of equity for a division or private company when the stock is not publically traded and thus not observable. The cost of equity is often the largest cost-of-capital component.

The first step involves finding a benchmark publicly traded company that produces a homogeneous or similar product or service. That is how the name "pure play" came to be: In a sense they are "pure plays," competing in an identical line of business. The next step is to use the stock returns to detemine the beta of each pure play firm. Finally, use these market-determined betas to estimate the beta of your division.

Data on Comparative Publicly Traded Companies

In selecting corporations for comparative purposes, you should be careful to use only comparable companies. Although the only restrictive requirement as to comparable corporations specified in the statute is that their lines of business be the same or similar, it is obvious that consideration

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Exhibit 109.
Risk rating summary page.

must be given to other relevant factors in order to obtain the most valid comparison possible.

For illustration, a corporation having one or more issues of preferred stock, bonds, or debentures in addition to its common stock should not be considered directly comparable to one having only common stock outstanding. In like manner, a company with a declining business and decreasing markets is not comparable to one with a record of current progress and market expansion.

Once you have selected the right comparatives, compile a list of the firms. Derive the following median beta and standard deviation. Then select one or two ''true" benchmarks or the absolute best fit.

The pure play approach involves unlevering the homogeneous public firm's beta. This approach is very effective since unsystematic risk is "stripped away," leaving a beta benchmark of systematic risk. Next, gather research on the target firm's debt, equity, and tax rate. Finally, relever betas based on your division's capital structure and tax rate. The resulting beta

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approximates the business unit's beta if it, were publically traded. Inserting the new beta back into the CAPM yields the divisions cost of equity.

Examples of Pine Play Formulas

Example: Assume that your comparative public company's beta is 1.10, D/E of the comparative is .6, t = .35, and D/E of division is .3.

Insert this result back into the CAPM to arrive at the cost of equity.

Unsystematic Risk:
Divisional or Operating Segment Risk Rating

The cost of equity was handled by the pure play approach. Now we address the cost of debt for divisions and/or operating segments employing risk rating. Divisional, or operating segment, risk rating should be a key part of corporate strategy. The divisional risk rating (or grading) system, like the corporate system, is an interactive process based on a 10-point review. However, before we start, let's examine why the need for segmental information is important on two counts: corporate headquarters and from an investor's perspective:

· The size and relative importance of diversified companies presented many problems for your company's investors.

· Both size and uncertainty of future cash flows affected by industries and countries that a operating segment operates in.

· Different industries and different countries have various profit potentials, degrees and types of risk, and growth opportunities.

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· Different rates of return on investment and different capital needs are also likely to occur across the various segments of a business.

· Because of this diversification of operations, there is a demand for key segment information, especially systematic (macroeconomic) and unsystematic (divisional-specific) risk, turnover, and profits.

· Segmental data is typically provided for both geographical areas and lines of business.

· Segmental information allows you, the decision maker, to combine operating segment-specific information with external information with a more accurate assessment of both risk and potential for future growth.

You should examine business units with respect to the following:

· Default rate of its industry.

· Spread over the base (government rate). As a proxy to default risk.

· Hurdle rate of division (i.e., cost of capital). While for most diversi-fied companies such external yardsticks are not available, a com-prehensive risk-rating system can value the entity on a stand-alone-basis. Senior management and board of directors will usually ask for segment information to allow comparison of success of individ-ual segments with those of other companies.

· Problems are apparent, particularly with transfer pricing.

· Segment data may be important with employees, creditors, and host governments. For example, employees will also want information at the plant level, host governments at the individual country level, and creditors at the level of the individual subsidiary or legal entity.

Ruling of ISB, Analysis of Segmental Information: IAS 14; (1.1.83), requires a breakdown of segmental information meaning, analysis of trends, cost of investments, and obtaining information on international competitive mar-kets and producers. Your firm's creditor's will likely evaluate these points. They will at least consider them.

· The size and relative importance of diversified companies pre-sented many problems for the users of accounts.

· Financial executives are interested in the future cash flows they may obtain from investing in a operating segment and the risk or uncertainty of those cash flows.

· Both size and uncertainty of future cash flows are affected by indus-tries and countries that an operating segment operates in.

· Different industries and different countries have various profit potentials, degrees and types of risk, and growth opportunities.

Furthermore:

· Different rates of return on investment and different capital needs are also likely to occur across the various segments of a business.

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·Because of diversification of operations, there is a demand for key segment information, especially turnover and profits.

·Segmental data is typically provided for both geographical areas and lines of business.

·Segmental information allows financial executives to combine operating segment-specific information with external information with a more accurate assessment of both risk and potential for future growth.

·Compare segments to (1) benchmarks in other industries, (2) default rate of industry, (3) spread over the base (government rate), and (4) hurdle rate of division (i.e., cost of capital).

Problem: For most diversified companies, such external yardsticks are not available; thus, a risk rating is important. Also, segment data may be important with employees, creditors, and host governments. For example, employees will also want information at the plant level, host governments at the individual country level, and creditors at the level of the individual subsidiary or legal entity.

Valuations often involve multibusiness companies whose futures depend on successful management of the portfolio of business operations they are charged with. Segment multibusiness valuation is also useful for determining breakup value and assessing acquisition candidates. In general, the structure of a business unit analysis should be well planned and comprehensive. You should do the following:

1. Find "as is" discounted cash flow and compare this to current market value. The difference between the two represents the perceptions or value gap.¹

2. Try to close negative perceptions by internal improvements with increased operating margins, improved sales growth, and decreased working capital requirements and by selecting capital projects to achieve optimal results (and that means using real options).

3. Try to close negative perceptions by external improvements by shrinking the business or working out sell-offs, spin-offs, equity carve-outs, or acquisitions.

Valuing a multibusiness operating segment "as is" is the same as valuing a single business operating segment. Differences often exist in capital structure, cost of capital cash flows, and headquarters costs. Tom Copeland a partner of McKinsey & Co suggests²:

1. Break business units into its smallest components.

2. Try to allocate cash flows to business unit.

3. Select as many comparable companies as possible.

¹ Tom Copeland, Tim Koller, Jack Murrin, Valuation: Measuring and Managing the Value of Companies, John Wiley & Sons, Inc. 1994.

² IBID

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4. Use ratios (asset turnover ratios and so on) on comparable companies.

5. Use internal data and compare it with publicly available data on comparable operating units.

6. Perform business unit valuations.

7. Identify business unit cash flows.

8. Watch transfer pricing and taxation.

9. Allocate corporate overhead as accurately as possible.

10. Determine business unit tax rates and capital structure and cost of capital.

11. The capital structure of business unit should be consistent with comparable companies.

12. Develop bond ratings.

13. Debt-to-equity ratios vary from industry to industry.

14. Ensure that the capital structure reflects market rather than book values.

15. Pay close attention to the cost of equity. It is often the capital structure's largest component.

A Dynamic Business Unit (Divisional) Analysis

Open SegmentRiskModel2.s. The model follows the same pattern as the corporate risk-rating model.

Chapter Ten References and Selected Readings

Books

R. A. Crowell. (1967). Earnings expectations, security valuation, and the cost of equity capital.

Duvigneau, J. C., and R. N. Prasad. (1984). Guidelines for calculating financial and economic rates of return for DFC projects. Washington, D.C.: World Bank.

Eisenbeis, R. A. (1978). Problems in applying discriminant analysis in credit scoring models. Washington, D.C.: Board of Governors of the Federal Reserve System.

Fortune, P. (1995). Debt capacity, tax exemption, and the municipal cost of capital: A reassessment of the new view. Boston: Federal Reserve Bank of Boston.

Hawkins, D. F., et al. (1983). Rating industrial bonds. Morristown, N.J.: Financial Executives Research Foundation.

Hutchison, G. S. (1971). The strategy of corporate financing. New York: Presidents Publishing House.

Moon, C.-G., et al. (1991). Municipal bond rating analysis: Sample selectivity and simultaneous equations bias. Piscataway, N.J.: Center for Urban Policy Research, Rutgers the State University.

Portney, P. R., and J. P. Weyant. (1999). Discounting and intergenerational equity. Washington, D.C.: Resources for the Future.

Riahi-Belkaoui, A. (1983). Industrial bonds and the rating process. Westport, Conn.: Quorum Books.

Stulz, R. M., and National Bureau of Economic Research. (1999). Globalization of equity markets and the cost of capital. Cambridge, Mass.: National Bureau of Economic Research.

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Thomas, L. C., and Institute of Mathematics and Its Applications. (1992). Credit scoring and credit control: Based on the proceedings of a conference on credit scoring and credit control, organized by the Institute of Mathematics and its applications and held at the University of Edinburg in August 1989. Oxford: Oxford Universtiy Press.

Twentieth Century Fund, Task Force on Municipal Bond Credit Ratings, and J. E. Petersen. (1974). The rating game: Report. New York: Twentieth Century Fund.

Periodicals

Asarnow, Elliot. (1994/95). "Measuring the hidden risks in corporate loans." Commercial Lending Review, 10(1), 24.

Fons, Jerome S. (1994). "Using default rates to model the term structure of credit risk." Financial Analysts Journal, 50(5), 25.

Hoffman, Thomas. (1999). "Neural nets spot credit risks." Computerworld, 33(30), 38.

Hyndman, Carl. (1994/95). "Are bank regulators ready for credit scoring of commercial loans?" Commercial Lending Review, 10(1), 92.

Hyndman, Carl R. (1996/97). "Internal models for measuring credit risks: Their impact on capital needs." Commercial Lending Review, 12(1), 58.

Laitinen, Erkki K. (1999). "Predicting a corporate credit analyst's risk estimate by logistic and linear models." International Review of Financial Analysis, 8(2), 97.

Lee, Peter. (1993). "Citi rates options on credit risk." Euromoney, June, p. 6.

Marshall, Jeffrey. (1999). "Credit risk ratings examined." USBanker, 109(3), 12.

Pedrosa, Monica. (1998). "Systematic risk in corporate bond credit spreads." Journal of Fixed Income, 8(3), 7.

Raiti, Lisa. (1993). "Rating enhanced derivative products companies." Financial Regulation Report, March, p. 5.

Treacy, William F. (1998). "Credit risk rating at large U.S. banks." Federal Reserve Bulletin, 84(11), 89.

Whiteman, Louis. (1998). "Small banks say one-on-one beats credit scoring models." American Banker, October 8, p. 13.

Zhai, Huaming. (1999). "Stochastic modelling and prediction of contractor default risk." Construction Management and Economics, 17(5), 563.

Select Internet Library

The Alcar Group Inc.
System Solutions: Debt Rater Plus combines market information with data analysis tools to give users the ability to estimate S&P debt ratings and how they might change under different financing and operating strategies. Users are also able to price loans and estimate the cost of debt for a company or division. Operating either as a stand-alone service or as a menu option with Alcar's software solution, the package allows users to estimate S&P bond ratings on the basis of common financial and industry inputs. http://www.alcar.net/index.html.

The Alcar Group Inc.
System Solutions: APT!Cost of Capital Calculator APT! helps users estimate the cost of capital. It combines a cost-of-capitalrelated database of over 6,000 companies with data analysis tools to provide users with a comprehensive approach to cost of capital estimation, peer group performance measurement, and capital structure analysis. The Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory estimate the cost of equity from the database and correct the anomalies associated

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with CAPM. The software provides users the ability to estimate the cost of debt by using cost-of-debt estimates for public companies in the database. The system can use readily available accounting and industry information to estimate S&P debt ratings and the cost of debt and can determine how they might change under different financing and operating strategies. APT! allows users to judge individual company, peer group, or industry performance by analyzing stock market returns over the previous quarter, year, and five years. It helps users identify appropriate capital structures by identifying industry and peer group average capital structures and predicting how bond ratings might change with capital structure. http://www.alcar.net/index.html.

CD

Name

Size

Type

CorpRiskModel2

634KB

Microsoft Excel Worksheet

Ratio98

249KB

Microsoft Excel Worksheet

SegmentRiskModel2

356KB

Microsoft Excel Worksheet

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Chapter Eleven
A Primer on Shareholder Value

The essence of strategy formulation is to organize the combined disciplines of risk and valuation and to guide the corporation into a new and better future. The key to effective strategic planning, then, has to deal with two relevant dimensions: (1) responding to changes in the external environment and (2) creatively deploying internal resources to improve the competitive position of the firm.¹ The lack of alertness to changes dealing with measuring and implementing economic, competitive, technological and financial factors can become extremely detrimental for sustained growth and profitability. The key to success is to be able to quantify these factors and integrate them into corporate and shareholder valuation, strategic planning, and formulation. Most important, a technical planning process must be responsive to individual talents and capabilities that reside within the corporation.

Thus, the exponential growth of analytics interfacing with modern-day disciplinessimulation, stochastic optimization, and visual modeling, to name a fewhas dramatically shifted the corporate culture and promises to raise individual capabilities to new heights.

Indeed, as I have inferred throughout this book, valuations are blueprints for long-term planning; short-term "chaotic" events, such as today's stock price, have a random component and are often only loosely tied to intrinsic value. And to think that not long ago, we looked stock price up in the Wall Street Journal, multiplied it by the number of shares outstanding, and sent the number to the bossa corporate lamb going to slaughter.

Management may be under significant pressure to deliver earnings to stockholders whether or not these short-term numbers support it. To make

¹ Aroldo C. Hax, professor of management, Sloan School of Management, MIT.

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matters worse, elasticity between earnings and stock prices has never been more pronounced. Some companies are playing an earnings game simply to jump the stock price. Only later does the truth surface, and by then, investors have shifted interest. With so much executive compensation tied to options, the power of the so-called positive spin (on stock prices) has never been more widespread. A common tactic for the less forthright is to publicize one set of results in a quarterly news release but then file a different, usually less positive, earnings report with regulators weeks later. Another maneuver from those managers incapable of delivering on the promise of long-term maximization of shareholder value is vagueness. News releases boast blockbuster results, leaving investors unsure about what contributed to the big gainsuntil quarterly statements are filed.²

We leave chaos to the markets and return to intrinsic valuations that relate to the natural harmonic structure of the firm, its growth potential, and, on a technical note, the measure of its value drivers. Technology and financial management are sides of the same coin.

Methods

Most of us recognize that corporate value is a function of the firm's future cash flow potential and the risks (threats) of those future cash flows. It is these perceived risks or threats that help define the discounting factor used to measure cash flows in present value terms. Cash flow depends on the industry and the economic outlook for the business' products, current and future competition, sustainable competitive advantage, projected changes in demand, and the business' capacity to grow in light of its past financial and operational performance. Risk factors include the business' financial condition (the threat to profitability and cash flows, the magnitude of financial and operational leverage, and ability to pay debt), management's ability to sustain operations and profitability, market and industry trends and outlook, competitive forces, the economic environment, legal and regulatory issues, and contingent liabilities.

Indeed, shareholder value is about data, and plenty of it. Cash flow forecasts and risk assessment require more than in-depth research and good old-fashioned intuition and creativity; it calls for a special kind of due diligenceone that employs technology, structure, and purpose. It means actualizing value drivers with all the tools: from neural network and visual modeling on up. However, remember that no software replaces sound financial judgment or experienceit is not the wand but the magician.

With few exceptions, we no longer question whether math and statistics have any bottom-line impact on measuring performance. The fact remains that data gathering in areas such as productivity, consumer value,

² Reported in the New York Times, December 21, 1999.

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and business and financial performance are no longer viewed so much as extraneous overload. Rather, it has become a question of what data are being mined, what technology is capturing that mining, and what valuation model brings this all together. The scientific method is as much a part of valuation as it is in NASA exploration designs.

Yes, I suppose that traditional methods are indispensable to a complete story, but composite weighting (of valuation methods) has shifted away from earnings-based measures to discounted cash flow, fortified by a quantitative value driver analysis. Let's examine the different valuation methods in use todaysome good, some not so good.

Valuation Methods

Book Values Reflect the Past

Book values, based on accounting numbers, reflect historical costs yielding only a vague approximation of real economic value. Moreover, book values are affected by decisions made by management regarding depreciation and amortization rates, the capitalization or expensing of certain costs, and perceived asset impairment. These choices, and more, are made by management in order to present the firm in the most favorable light. Say that a firm purchases a truck and after depreciating it over a period of time records it with a zero book value. If the truck is sold, chances are that the company will receive greater than zero for the truck as long as the truck can still operate. Thus, there is often little relationship between book and market values. Book value also ignores price fluctuations of real assets, such as real estate or timberland, as well as intangibles, such as goodwill, trademarks, franchise licenses, and patents, which can be strong cash providers.

Transaction Multiples

The fair market value of public companies are determined every day through the decisions made by many buyers and sellers of their publicly traded securities. These minority interest values can easily be determined and can be adjusted for control premiums. Since there are generally several public companies that are similar to any given private company, the fair market value of comparable companies can generally be compared to private companies.

Comparable public companies often are different in size and performance to a target private company; it is generally necessary to compare a comparable company's fair market value to some performance measure, such as revenue, cash flow, or assets. This comparison generally results in a multiple that can then be applied to the same performance measure of the private company to derive the fair market value of the private company.

A firm whose equity has recently been sold in a market priced transaction often provides a fairly good measure of minority interest value. If

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the company is similar to a private company, performance indicators of the recently sold firm can be compared to the private company to estimate a ''pro forma" market value along with an added premium for control.

The problem with transactions multiples is often the difficulty of locating comparable companies. Even firms listed in identical standard industrial code (SIC) classifications operate with opposing product lines or are diversified to some degree or other that can easily distort the picture. PricewaterhouseCoopers suggests that the value of using transaction multiples is only as good as the comparability of the companies from which the analysis is based. The higher the degree of correlation between the operations in the peer group and our company, the more accurate the analysis. Some of the more significant attributes used to determine comparability include the following:³

1. Type of product produced

2. Market segment to which the product is sold

3. Geographic area of operation

4. Positioning in marketplace

5. Influence of buyers/suppliers

6. Growth, historical and projected

7. Profitability

8. Leverage and liquidity

9. Diversification

Once the peer group has been identified, the companies should be adjusted to allow for comparability. Some of the more important adjustments include the following:⁴

· Extraordinary and nonrecurring items inventory policy: FIFO versus LIFO

· Revenue recognition policy

· Nonoperating assets

· Excess marketable securities and cash

· Contingent liabilities

· Pension and other postemployment benefits funding and expense policy

Price/Earnings

The price-to-earnings (P/E) ratio takes the stock price and divides it by the last four quarters' worth of earnings. For example, if a firm was trading at $10 a share, and $1.00 in trailing earnings per share, P/E is 15X:

³ PricewaterhouseCoopers Business Acquisitions and Leveraged Buyouts: Solutions for Business a 1993 publication for distribution to clients.

⁴ Ibid.

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$15 share price/$1.00 training EPS = 15 P/E

What must be remembered when using a P/E ratio is that a market "price" for a stock is based on expectations of the future performance, whereas earnings are a historical record of where the firm has been and how it performed. There are many permutations of P/Es using forecasted or trailing 12-month earnings. Another difficulty arises when using comparable P/Es for valuation purposes; a particular market sector may be temporarily mispriced by overly optimistic or pessimistic investors thus skewing your valuation estimates accordingly.

Firms may report low earnings yet produce impressive values because they are involved in research and product development or are recent entrants in high-growth industries. For valuation purposes, you can also consider the average industry P/E ratio to benchmark as long as the comparatives are homogeneous. Remember that earnings can be legally manipulated by changing accounting practices or manipulated to distort the truth. Earnings also disregard risk. Here is a case in point:⁵ I.D.T., a telecommunications services provider in Hackensack, New Jersey, put out a news release on October 14 "boosting"⁶ about its "record" fourth-quarter revenues and those for the full year ended July 31, 1999. The stock rose 3.6% on the news. When I.D.T. filed its SEC report on November 4, several of the company's expenses were greater than they had been in the earnings news release. As a result, the company reported a much greater loss. While the company's news release said that it lost 15 cents a share in the fourth quarter, the SEC filings indicated a loss of 18 cents a share.

The firm said that an error was found in figures supplied by a subsidiary and was not intentional. Everyone can make a mistake, of course, but investors suspect that some errors may not be inadvertent. Accordingly, the SEC's accounting watchdog countered by suggesting (in the article) that investors should be far more skeptical about news releases. Corporate earnings releases have become such a good source of misinformation that SEC researchers use them to identify companies that may be playing accounting games.

Price/Sales

The price-to-sales ratio takes the current market capitalization of a company and divides it by the last 12 months of trailing revenues. The market capitalization is the current market value of a company, arrived at by multiplying the current share price times the shares outstanding. This is the current price at which the market is valuing the company.

⁵ Reported in the New York Times, December 20,1999.

⁶New York Times reporter's word.

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Liquidation Valuation Approach

Management's decision to divest a business unit can often be quantified by the spreads between cash flow and liquidation value. Hax and Majluf are proponents of the market value/liquidation value ratio.⁷ They suggest that business units may destroy value if the discounted value of cash flow reaches a critically low mass and the corporate resources they tie up could be better served elsewhere. Business units of this sort are "cash traps" involving a permanent negative cash flow that diminishes the contribution of other businesses having positive cash flows. Under such conditions, divestiture might be the most logical choice.

Liquidation is preceded by asset appraisalstangible and intangibleincluding real estate, machinery and equipment, and inventory, trademarks, patents, customer lists, proprietary systems, and customer contracts. Normally, there are at least three liquidation values:

1. Orderly liquidation value is the amount that the assets will generate if disposed of in the normal course of business, net of any liabilities. Disposals of equipment, in the normal course of events, are a good example of orderly liquidation value.

2. Not-so-orderly liquidation based on auction is associated with a forced sale of company assets (and expenses) at auction prices based on liquidation value.

3. Replacement value (or cost approach) represents the amount that it would cost a potential buyer (ongoing business) to duplicate the firm's assets at current market prices.

Valuation Based on Dividends

This method suggests that the value of equity is driven by dividends. Before the introduction of the Capital Asset Pricing Model and certainly well before the age of Amazon.com, the dividend valuation method, known as the Gordon Dividend Growth Model, was used extensively. This particular method applies to companies whose earnings and dividends are expected to increase each year. Although expected growth rates vary from company to company, dividend growth, in general, is expected to continue in the foreseeable future at about the same rate as that of the nominal gross national product. On this basis, it is expected that the average or "normal" company will grow at a rate of 4% to 6% a year, rising if the inflation rate increases.

By using the dividend growth model of estimating future dividends, the current stock value can also be determined. By finding the expected future cash flow stream of dividends, the present value of each dividend payment, and then the sum these present values, the value of the stock is

⁷ Ibid.

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deciphered. Thus, the intrinsic value of the stock is equal to the present value of the expected future dividends.

A few aspects of the dividend method require special consideration. First, for the stock to have a meaningful price, the required rate of return must be greater than the dividend growth rate. If they are equal, the stock price becomes infinite. If the firm's required rate of return falls below the dividend growth rate, shareholder value is negative. Both results are nonsense. Second, it is important to restate the assumptions underlying the dividend model because the model is derived under the assumption that the growth rate in dividends is constant into perpetuity.

The first difficulty that this model of valuation produces is in determining the future growth ratenot an easy task. Then it must be assumed that this rate will be sustained forever. No company maintains a constant growth rate forever, especially if its current growth rate is high.

Finally, do dividends increase annual returns? It may appear from the model that the annual return rises when dividends increase, but life is not all that simple. An increase in dividends draws cash from investments, compelling management to raise funds through external sources to make the same investments. These decisions affect the financial leverage of the firm and thus the weighted average cost of capital that in turn serves as the discount rate to the growth model. As a firm moves further from its optimal debt equity balance, additional firm risk is introduced and must be paid for through higher returns to the providers of capital.

Discounted Cash Flow Approach (Going Concern)

Discounted cash flow is a valuation method that isolates the projected cash flow of a company available to service debt and provide a return to equity. The net present value of free cash flow to capital is computed over a projected period based on the perceived risk of achieving the cash flow. An important point to remember is that free cash flow to equity must be discounted at the cost of equity and that free cash flow to the firm must be discounted at the weighted average cost of capital. The numerator and the denominator must be measuring the same thing in order for the correct answer to be achieved.

Discounted cash flow (DCF) valuation, the most frequently used, provides a "going concern" valuethe value driven by a company's future economic strength. The firm's value is determined by adding the present value of future cash flows for a specific forecast horizon (projection period) plus the present value of cash flow beyond the forecast horizon (residual or terminal value). Because so much of the firm valuation is contained in the residual or terminal value, this is seen by some as an inherent problem in a DCF calculation.

Thus, shareholder value is determined by discounting the cash flow streams by the weighted average cost of capital assigned to it, adding

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unrealized and/or nonoperating asset values net of the expected value of contingencies, and then subtracting the market value of debt. There are a number of cash flow valuation benchmarks; including the following.

Cash Flow (EBITDA) and Noncash Charges

This is a common measure of value and defined as earnings before interest, taxes, depreciation, and amortization (EBITDA). Why look at earnings before interest, taxes, depreciation, and amortization? Interest income and expense, as well as taxes, are disregarded because cash flow quality, magnitude, and trends tend to focus on operations. Taxes are a function of deferred and current taxes along with tax codes and are disposed to distortions and volatility. For example, a firm might enjoy a low rate one year but in the next taxes could increase substantially or earnings distorted by the sudden appearance of deferred tax credit.

Preparation

The Building Blocks of Valuation

In calculating value using shareholder value analysis, we are looking to determine value by estimating the following three "building blocks" of value:

1. Cash flow from operations

2. Long-term horizon

3. Risk and time value of money

Cash Flow from Operations

By concentrating on forecasting the company's operating cash flow, we are able to make a distinction between the operating and the financing decisions of the firm. Once cash flow is estimated, we can then take risk into account discounting those cash flows by the cost of capital (more on cost of capital later). The definition of cash flow is:

Sales
Operating Expenses
Depreciation Expense
Taxes on Operating Profit
   Operating Profit (after tax)
+ Depreciation Expense
 Fixed Capital Investment
 Incremental Working Capital Investment
   = Operating Cash Flow

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The estimation of cash flow involves the employment of forecast techniques that try to include the best possible information. When estimating company cash flow, it is not practical to estimate discrete cash flow to infinity for a going concern. Thus, a simplifying assumption must be made to estimate the value of cash flow generated after a discrete time horizon (or "forecast period"). Instead of considering value equal to the present value of a single stream of cash flow, think of it as the sum of the present value of cash flow from a discrete forecast horizon plus the present value of a "residual" value estimate. This presents us with the necessity of having to both develop an estimate of how long we forecast discrete cash flow for a company (i.e., forecast horizon) and make a simplifying assumption regarding the value of cash flow generated after the end of the forecast horizon (i.e., the residual value).

Choosing the Length of the Forecast Horizon

The length of the forecast horizon is not simply a "convenient" period of time in which management feels comfortable in estimating financial performance (i.e., the typical long-range planning period is three years) but a period that is based in the economics of the company and industry. As a result, we will refer to this time horizon as a company's value growth duration (VGD). As will be demonstrated shortly in the section on value driver analysis, the VGD is as an important measure as any of the key value drivers (e.g., sales growth or operating margin).

As Michael E. Porter has emphasized, in a competitive market with free entry, firms cannot earn returns substantially greater than the cost of capital (hurdle rate) for long because that would encourage other firms to enter and drive down prices and thus returns.⁸ Normal accounting profits will be just enough to pay for the cost of capital and to compensate the owners for any unique inputs to production (e.g., management expertise) that they provide.

On the road to superprofits are barriers to entry, such as patents, economies of scale, research costs, product differentiation, and preferential access to scarce resources. Thus, the main assumption regarding the length of the forecast period is that it should be equal to the period that management expects the rate of return on its new investments to exceed the required rate of return (cost of capital) for the company or investment.

When estimating the appropriate VGD, management should consider the industry dynamics that will affect the firm's competitive position.⁹ The following is a short list of potential factors that can affect that position and the relevant effect on its VGD (we will discuss a technique referred to as

⁸ Michael E. Porter, Competitive Strategies, Techniques for Analyzing Industries and Competitors (New York: The Free Press, 1980).

⁹ Porter provides a detailed methodology to estimate a company's competitive position. See ibid.

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market signals analysis later to estimate what the stock market is estimating a company's specific VGD to be):

Existence of

Effect on VGD

Proprietary technologies

Lengthen

Patented products

Lengthen

Limited product life cycle

Shorten

Established brands

Lengthen

Extensive distribution channels

Lengthen

Industry-wide price competition

Shorten

Residual Value

Residual value represents the value of cash flow reasonably expected to extend beyond the forecast horizon. This value, also known as the terminal value, is calculated by multiplying the cash flow at the end of the forecast horizon (the first day of the residual period is the last day of the forecast horizon) by a multiple. Selected multiples commonly use the median multiple of total invested capital to EBITDA of the firm or comparable companies. The selected multiple may be discounted to reflect the company's performance or size characteristics relative to comparable companies. This is quite similar to dividing the cash flow by the weighted average cost of capital and including a growth factor.

Once the discrete forecast horizon cash flow is estimated, a simplifying assumption can be made regarding the cash flow generated after the forecast period. As was previously stated, the investment rate of return for new investments made during the VGD is greater than the cost of capital and thus will contribute to positive net present value (NPV). Thus, after the forecast period, the average rate of return on new investments will equal the cost of capital. Understand that this is not necessarily a no-growth state; rather, the implication is that any post-forecast-period growth is not expected to increase shareholder value since the rate of return on these new investments equals the discount rate (i.e., cost of capital). In any way of speaking, this is the same as a no-growth state. People think of growth in revenue terms; we are not saying or implying anything about revenues in the r = WACC VGD termination.

Incorporated in our discounted cash flow analysis, we will use the last forecast year's taxable operating profit (after-tax) as a proxy for continuing cash flow. The assumptions supporting the use of operating profit (after-tax) as the perpetuity cash flow instead of operating cash flow is as follows:

1. In growing capital-intensive firms, capital expenditures in any given year will be greater than depreciation expense.

2. Incremental fixed capital investment (the amount above depreciation expense necessary for new growth) and incremental work-

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ing capital investment have already been determined to return only the cost of capital and thus would not have any effect on the NPV of the firm if included. Thus, they are excluded to simplify the calculation.

The perpetuity method of calculating residual value is recommended in most cases, as it provides a methodology consistent with the shareholder value approach applied during the discrete forecast period. Of course, there may be cases in which a more aggressive assumption regarding the value impact from new investments is appropriate. Variations of the perpetuity method can be made to accommodate these alternate situations.

Market Signals Analysis

In order to estimate what the specific VGD should be for a given company (instead of speaking in relative terms), it is useful to gain insight into what the stock market is estimating the length of the horizon to be. Using market signals analysis, we can gain that insight. Having a reasonable handle on a company's forecasted cash flow and risk (i.e., cost of capital), we can "solve" for the known stock price. If our discrete period cash flow forecast is earning rates of returns above the cost of capital, we know that our estimate of value will increase by extending the forecast horizon. This, in essence, delays the time when the residual value assumptions (new investments earning only the cost of capital) will kick in.

This method obviously requires a publicly traded company for which to compare estimated value to stock market value. Privately held companies (or divisions of public companies) can estimate their VGDs by performing similar analysis on publicly traded peer companies.

Value Driver Structure

When estimating shareholder value, it may be helpful for you to think about the three "building blocks" of value (i.e., cash flow, time horizon, and risk) in terms of what Alfred Rappaport refers to as value drivers.¹⁰ Reducing an unnecessarily detailed discounted cash flow analysis to a set of observable value drivers accomplishes two objectives. First, it simplifies the analysis without cutting any corners with regard to the estimation of the key determinants of value. Second, it allows for an understanding of the key aspects of a business most responsible for value creation (or value impact). This second point is important. Knowing what value driver(s) has the biggest impact on the business' value gives management a basis to formulate strategy to maximize the value of the firm. The seven observable value drivers are the following:

¹⁰ Alfred Rappaport, Creating Shareholder Value: The New Standard for Business Performance (New York: The Free Press, 1986).

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Sales growth rate
Operating profit margin
Incremental working capital investment
Incremental fixed capital investment
Cash tax rate
Cost of capital
Value growth duration

Value Drivers and Scientific Financial Management

Spreadsheets alone do not provide you with enough detail to pull together a full blown valuation. Consider the following discourse on traditional spreadsheets versus modeling.¹¹

Traditionally, spreadsheet analysis tries to capture uncertainty in one of three ways: Point estimates, Range estimates, and What-if scenarios or classical worst, base and optimistic cases. Point estimates are when you use what you think are the most likely values (technically referred to as the mode) for the uncertain variables. These estimates are the easiest, but can return very misleading results. For example, try crossing a river with an average depth of three feet. Or, if it takes you an average of 25 minutes to get to the airport, leave 25 minutes before your flight takes off. You will miss your plane 50% of the time.

Range estimates typically calculate three scenarios: the best case, the worst case, and the most likely case. These types of estimates can show you the range of outcomes but not the probability of any of these outcomes. What-if scenarios are usually based on the range estimates and are limited by calculating only those scenario combinations that you can think of. What is the worst case? What if sales are best case but expenses are worst case? What if sales are average but expenses are best case? What if sales are average, expenses are average, but sales for the next month are flat? As you can see, this form of analysis is extremely time consuming and results in lots of data, but it still does not give you the probability of achieving different outcomes. If you use only spreadsheets to hold datasales data, inventory data, account data, and so onthen you do not have a model. Even if you have formulas that total or subtotal the data, you might not have a model. For analyzing data, you can use a time-series program.

A model is a spreadsheet that has taken the leap from being a data organizer to an analysis tool. A model represents a process with combinations of data, formulas, and functions. As you add cells that help you bet-

¹¹ Reprinted with permission Decisioneering (www.decisioneering.com).

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ter understand and analyze your data, your data spreadsheet becomes a spreadsheet model.

The Drivers

Substantiating Your Assumptions with the Scientific Method

Sales Growth Rate

Revenue growth is often the most crucial value driver of all. How can you tell? Try a value driver test.

A Value Driver Test

First, run a "rough draft" valuation, the main purpose being to determine value driver sensitivities.

Open the impotance of each value driver (assumption variable) to shareholder value (the forecast variable). During a simulation, Crystal Ball ranks the drivers according to their importance to shareholder value.

The Sensitivity Chart displays these ranking, as a bar chart, indicating which assumptions are the most important or least important ones in your model.

The assumption with the highest sensitivity ranking can be considered the most important one in the model. You certainly will want to research this assumption further to lower its uncertainty and thus its effect on the target cell.

The assumption with the lowest sensitivity ranking is the least important one in the model. If a value driver shows a low value, you might be able to hold back costly research or ignore it completely.

After running sensitivities analysis, go back and start up the valuation assumption, once againbut now you have the proper focus. Run a time series.

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Time-Series or Trend Forecasting

The objectives are to generate the right regression and to be ready to explain any errors or anomalies that appear in revenue forecast. Time-series anomalies are calculated by subtracting the forecast value for the actual value: Error = Forecast Revenue Trend Revenue.

Time-series forecasting assumes that the historical data are a combination of a pattern and some random error. There are two risks in extrapolation that we might call mathematical and practical. In both cases, there is no sharp division between safe interpolation and dangerous extrapolation. Rather, there is a continually increasing danger of misinterpretation as revenues get further from their central value. Normally, prediction intervals get larger as revenues move further along in the forecast period.

In situations where sales really drive value, the time-series methods should not be ad hoc, which means do not guess. Since sales is usually the most important value driver, a much better approach to generate a time series is with Decisioneering's CB Predictor. The model breaks historical data into three componentstrend, seasonality, and errorwhile the Method Gallery provides the best choice (see Exhibit 111).

The parameters for time-series forecasting methods are set automatically in CB Predictor (see Exhibit 111). The model automatically finds optimal parameters, unless you override this optimization by selecting to use User Defined parameters. As Exhibit 112 shows, there are four possibilities out of many contenders. However, in this case, the double moving average method was optimal. The criteria for optimal parameters included (1) root mean squared error (RMSE) which is an absolute error measure that squares the deviations to keep the positive and negative deviations from cancelling each other out (and tends to exaggerate large errors, which can help when comparing methods); (2) mean absolute deviation (MAD), an error statistic that average distance between each pair of actual and fitted data points, (3) mean absolute percentage error (MAPE) a relative error measure that uses absolute values to keep the positive and negative errors from cancelling each other out and uses relative errors to let you compare forecast accuracy between time-series models; (4) Durbin-Watson tests for autocorrelation of one time lag. Autocorrelation describes a relationship or correlation between values of the same data series at different time periods, while lag defines the offset when comparing a data series with itself. For autocorrelation, this refers to the offset of data that you choose when correlating a data series with itself); (5) Theil's Statistic which measures the root mean square error in relative terms. If Theil's Statistic is equal to 0 then the estimated forecasting model is a perfect fit; if Theil's Statistic is equal to 1, the predictive performance of the forecasting model is as bad as it could possibly be. A double moving average would be the best choice to time-series sales.

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Exhibit 111.
Textile time-series: Setting up the time-series with CB Predictor

Exhibit 112.
Methods table for shampoo sales.

Multiple Regression

Use multiple regression to predict sales from one or more independent variables. You may want to use multiple regression to determine how sensitive sales are to macroeconomic factors. For example, a textile manufacturer is interested in the effect that textile imports have on the firm's sales. Using CB Predictor, we can see the data generated in Table 111 and [CD:MODELS\EXCEL\CllRegressImports\OrigResults]

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Table 11-1.
Time-series original data for textile regression example.

Simulation

Without simulation, revenue changes (your first and usually most important value driver) will reveal only a single outcome, generally the most likely or average scenario. You define the possible values for revenues over the projection horizon with a probability distribution. The type of distribution that you select is based on the conditions surrounding that variable or series of variables that combine to form your assumption (see the hotel design problem that we look at shortly). To add this sort of function to an Excel spreadsheet, you would need to know the equation that represents the firm's revenue distribution. With Crystal Ball 2000, these equations are automatically calculated for you since the product can even fit a distribution to any historical data that you might have. Let's run a simulation on sales product by the textile manufacture's sales produced by the previous example.

Certainty is the percentage chance that a particular forecast value would fall within a specified range. In the previous chart, you can see the certainty associated with fiscal 2000 sales falling between 153 and 170 at 95% confidence. Of the 1,000 trials that were run, certainty of sales falling below 140 is zero. Forecast results display result values for each forecast and the probability of any value. Exhibit 115 represents a simulation run for the year 2000. The Gensis for the simulation is Exhibit 116, and includes input data: starting sales, growth rate, and standard deviation.

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Optimization

As we saw in chapter 9, optimization is a process that finds a best, or optimal, solution for your model. Here, our thoughts are directed to revenue, the value driver. Not all spreadsheet models require optimization; however, the technique is important when you actually control the variables

Exhibit 113.
The results: Textile regression.
(Report worksheet of C11 RegressImports Workbook)

(continues)

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Exhibit 11-3.
Continued.

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affecting sales (e.g., advertising, production limits, or distribution channels) and you want a maximum or minimum goal that relies on those variables.

Remember that optimization programs for spreadsheets, such as Solver, are good at finding the best combination of values that maximize or minimize a goal. However, these programs are not set up to handle uncertainty, as they get lost in all the permutations of possible values and changing solutions if your valuation model introduces uncertainty.

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Exhibit 114.
C11 Sales Projection worksheet.

Suppose that you own several hotels and were considering remodeling one.¹² You want to find the best combinations of rates and room sizes to maximize the revenue value driver (Exhibits 116 and 117). This is a straightforward optimization problem: maximize sales. Of course, you have to be careful. Just because sales reach high levels does not necessarily mean that you have maximized profits. Operating leverage is the determining factorairlines with their breakeven load factor and hotels with their breakeven occupancy rate. You begin to set up your model but then realize that several key factors associated with market segmentation. Deluxe rooms and suites (Platinum) attract a business and high-income clientele, and midpriced high-end (Gold) and standard (Standard) attract family and other customers. Each market segmentation has its own price/demand elasticity:

Room Type

Elasticity

Standard

3

Gold

1

Platinum

2

For example, a 1% decrease in the price of a standard room increases the number of rooms sold by 3%. Similarly, a 1% increase in the price will decrease the number of rooms sold by 3%. The price/elasticity are uncertain assumption variables. Standard optimization programs cannot handle

¹² The hotel pricing optimization problem was developed by Decisioneering and reproduced with their permission.

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Exhibit 115.
Quarterly sales projection, Textile Company Inc. simulation results.

these stochastic variables. Traditionally, you would have had to guess the values for these uncertain factors and hope for the best. Using simulation alone, you could run multiple simulations for price/demand elasticity and compare the results to total hotel revenue. However, did you try every possible combination of inputs? Of course, the answer is no.

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Exhibit 116.
Hotel pricing problem and options.

The fact remains that you likely will need optimization if the revenue (value) driver is significant to value and the firm is empowered with high operating leverage. Capital may be at risk as the hotel tries to work out its remodeling strategies. To figure out its remodeling the hotel utilized OptQuest by Decisioneering:

Total number of simulations: 557
Number of trials per simulation: 100
Confidence testing is activated
Number of simulations run maximum number of trials: 93
Number of simulations stopped by precision control: 0
Number of simulations stopped by confidence testing: 464
Neural network engaged after simulation: 40
Number of simulations avoided due to neural network: 165
Population size: 20

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Exhibit 117.
Hotel design problem: Optimization is complete.

Exhibit 118 displays the completed optimization solution generated by OptQuest for Crystal Ball 2000. The software displayed the results of the best simulations in the solutions area of this window. The first best simulation is always either the suggested values used in your spreadsheet, if those values satisfy the constraints imposed, or the first constraint-feasible solution that OptQuest generates. As you can see (Exhibit 118) each time OptQuest identifies a better solution during the optimization, it adds a new line showing the new objective value and the values of the decision variables. Thus, the optimal price choices between standard, gold and platinum prices under the room demand constraint (located in the exhibit's third column) maximizes the mean of total revenue.

The simulations verify that the probability of demand exceeding capacity is slightly under 20%.

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Exhibit 11-8.
Hotel design problem: Optimization is complete.

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Exhibit 118.
Forecast: Total room demand (cont'd)

Value Driver:
Operating Profit Margin

The operating profit margin is composed mostly of variable and fixed components associated with cost of sales, R&D, selling expenses plus general and administration expenses.

Based on the level of sales projected for a specified time period, production standards and the resources necessary to meet production criteria can be established. Production requirements are physical unit estimates of output; resources used to manufacture the borrower's product(s) are measured in terms of units of input. Price projections for units of input are necessary so that a monetary value can be consolidated into the forecast. As a result, management has a good idea of what the expenditure requirements are for production. Thus, the gross profit or gross margin can be calculated (sales less the cost of goods sold). Consider:

1. Direct materials: Part of a firm's finished product. How stable is supply and price in the projection period?

2. Direct labor: Costs physically traced to the product's creation. What will be the company's status in terms of unions, contract expiration dates, and labor relations history?

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3. Manufacturing overhead: All costs of manufacturing with the exception of direct material and direct labor costs. Are the costs associated with operating the facility enough to reach sales goals?

4. Changes in automation, substitution of capital for labor, and technology and its effect on costs.

5. Plant capacity: Is it physically possible with the resources at hand to meet excepted production requirements?

6. Operating leverage: A high degree of operating leverage implies a relatively small change in sales and will result in a larger than proportionate change in net operating income. The ratio of variable costs to fixed costs will determine the degree of operating leverage.

Operating leverage can be defined more precisely in terms of the way a given change in sales volume affects net operating income. To measure the effect on profitability of a change in volume, we calculate the degree of operating leverage, or the ratio of the percentage change in operating income to the percentage change in units sold or in total revenues.

Value Driver:
Incremental Working Capital Investment

Incremental Working Capital Investment

The incremental working capital investment required for operations is defined as the increase in total current assets (excluding any marketable securities and other current assets not necessary to support operations) minus the increase in total current liabilities (excluding debt due and other nonoperating obligations).

When calculating operating cash flow, the reason that incremental working capital investment excludes the increase in marketable securities, current portion of long-term debt, and notes payable is that those items are financing issues and are not part of the cash required for operations.

Following is the rationale for excluding each of these items:

1. Marketable securities are not investments required for operations; rather, the increase in these investments is the result of a cash surplus generated by operations.

2. The current portion of long-term debt and notes payable represents sources of financing rather than a direct investment in working capital to support the operations of the firm. Excluding these items from working capital is essential in order to evaluate investment decisions independent of financing decisions.

Value Driver:
Incremental Fixed Capital Investment

As we saw in chapter 3, the option pricing model and its ability to value capital allocation choices, thus assisting financial managers' real-world

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decision making, is no longer the province of commodity futures traders or something embedded in a fixed-income security. Options are the next logical step from sensitivity and scenario analysis, decision trees, and expected probabilities with regard to NPV and internal rate of return analysis.

The techniques presented in chapter 3 allow the financial manager to properly assign and value the capital expenditure decision, whether it is the probability of success regarding proper capital allocation or the valuing of an option as it applies to project continuance or abandonment. The market value of a project can be seen as the combination of the standard NPV measurement plus the option of contracting or expanding the project in response to the market acceptance.

From the standpoint of the value driver itself, the incremental fixed capital investment represents the portion of total capital expenditures necessary to support incremental sales. Thus, this value driver is defined as the capital expenditures in excess of depreciation expense (and net capitalized interest). Assumed here is that depreciation expense is assumed to approximate the cost of replacing equipment to maintain existing capacity. Net capitalized interest is excluded, as it is part of the financing decision, not the investment decision.

Depreciation expense, which is based on historical costs, may understate the cost of replacing existing equipment when that cost has increased because of inflation and regulatory forces (i.e., environmental controls). However, the F ratio does account for higher replacement costs because they are captured in the estimate of (total) fixed capital investment.

Value Driver:
Cash Tax Rate

As we look to discount forecasted (after-tax) operating cash flows, we must estimate a cash tax on operating profit instead of simply applying an effective tax rate to earnings before tax (EBT). Tax on operating profit represents the portion of total income taxes that is applicable to operating profit only. Tax on operating profit is the total taxes on taxable operating profit for a fiscal year that either have been paid by installments or are payable within 12 months.

Tax on operating profit is likely to be different than the actual amount payable to the taxing authority because the actual amount payable will include taxes on nonoperating items. Consider the following reconciliation between the current tax provision and tax on operating profit:

   Current provision for income taxes
  Tax on nonoperating profit
 + Interest tax shield
   Tax on operating profit

Note that for an interest-paying company, the cash tax on operating profit will be greater than the current tax provision by an amount equal to t*i (less tax on nonoperating profit), where T is the marginal tax rate and I is the firm's interest expense.

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Value Driver:
Cost of Capital

Risk and the time value of money are embedded into the cost of capital. The cost of capital or discount rate should be an average of the company's cost of debt (on an after-tax basis) and cost of equity weighted at a market-based capital structure. The target debt-to-equity ratio used in the weighting should mirror the anticipated, or target, capital structure, as that is the mix of capital that will fund the forecasted cash flows. A detailed discussion on estimating this important measure is available in appendix two of this chapter. Appendices that follow deal with valuation models appraisal reports and valuation optimization and output.

From Valuation Analytics to Application in Practice

Understanding the analytics driving valuation decisions arms management with a powerful tool. Now, for the first time, management has the requisite knowledge to enable it to determine the future value embedded in planned actions. The debate around what to do is honed dramatically by this newfound ability to estimate the value impact. This empowers management to make sound strategic decisions, to chart a positive value-creating course.

Our focus will shift from the analytics to practice. The final chapter, Chapter 12, introduces how these innovative concepts can lead to the actions that create the value management seeks. Translating analytic rigor embedded in scientific financial management into application in practice represents the synergy of the art and science of strategic management. Therefore, it is important to end the book with albeit a brief perspective into how leadership teams take their new knowledge into the competitive battle. These tools and frameworks operate at several levels. First, they set the total corporate portfolio context, summarizing the potential value impact of all the actions to be taken across the full set of businesses. It is a test of whether the strategies are robust enough to deliver sufficient value, and the effort can turn to implementation planning, or whether the result falls short. In that case, the strategy development cycle must be revisited. Second, the same analytics can translate the total result into strategic goals for the component businesses. Each business team can understand directly how its actions will contribute to the total and how it important is the effective execution of its strategies. Next, the tools work in setting strategic direction, and in monitoring its execution. This latter activity is becoming increasingly central to successful value creation. Perhaps at one time, long, long ago, strategies could be devised, then set in action, to be reviewed or updated on an attenuated cycle. Of course, this is no longer true. Competitive forces intrude with frequency, customer needs evolve rapidly, in short, strategies must be tightly monitored. An insightful set implementation metrics, directly connected to the robust valuation analytics, must be in place to allow rapid adjustments to the forces of change.

Thus, we enter the next stage of our journey to high, sustained value creation. Understanding how to leverage these powerful value driver modelsand analytics in practice allows management to convert potential value into value realized. This represents the destination on the journey begun in chapter 1.

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Appendix One to Chapter 11
Mort Glantz Associates, Valuation Appraisal Outline¹

I. Purpose of the valuation report

A. Taxes; estate tax purposes

1. Address factors enumerated in Revenue Ruling 5060

B. ESOP

1. Department of Labor Regulations

C. Lawsuit

1. Issues raised in relevant case law precedents

If the standard of value is derived from a statute or regulation, the exact source of the governing standard of value needs to be referenced. For example, we need to include the eight factors listed in Revenue Ruling 5960. If the valuation is for gift or estate taxes, an ESOP, or some other tax-related matter.

D. Strategic Planning

1. Maximize shareholder value

2. Understand the mechanics of wealth creation

3. Identify and sell off unprofitable business units

i. Liquidation versus cash flow value

4. Purchase business

While the outline looks long, the introduction is brief and may cover any or all of half a dozen key points in summary form.

E. Respond to offer to buy business

II. Scope and content of the valuation report

A. Audience

1. Prospective parties at interest and their beneficiaries

i. Internal use by officers and directors

a. Description of the company may be unnecessary or may allude only to certain salient points that directly affect the valuation.

b. If audience is financially sophisticated, we can assume some knowledge of finance and accounting.

The scope and organization of the appraisal report must be tailored to the purpose of the valuation. Formats or variations will differ, depending on purpose.

¹ This outline was complied from many sources and used over the years to help clients develop valuations, quite successfully so. You may want to refine the appraisal to suit our goals. I wish I could thank the one or ones who came up with the prototype but I can't.

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2. Representatives of any regulatory authorities involved

3. Judge and jury if there is existing or potential litigation

III. Organization

A. Introduction

1. Description of the assignment

i. Who was retained by whom to do the appraisal

The scope and content of valuation report can vary considerably, depending on the size and complexity of the firm and the use or uses to which the report will be put.

a. Appraiser's statement of qualifications

b. Reviewer's judgments: For example, have I adequately and convincingly supported the use of each discount rate, capitalization rate, and multiple used in the valuation? Is the conclusion consistent with the economic, industry, and financial statement analysis presented? Is the analysis and conclusion consistent with the stated purpose of the appraisal and standard of value, including any statutory, regulatory, or other legal requirements?

ii. Definition of the property being valued

iii. Effective date of the appraisal

iv. Purpose of the valuation

2. Summary description of the company

i. For the reader's convenience, it is useful to include in the introduction a brief statement of Robinson Textiles' business and location, some idea of its size, and possibly one or two salient or unique aspects of the company.

3. Capitalization and ownership

i. Class or classes of stock and the distribution of ownership

4. Applicable standard of value (if appropriate)

i. Internal Revenue Service Ruling 5960 outlines the valuation of closely held stocks and includes the following:

a. Nature of business and history of enterprise

b. Economic outlook and outlook of the specific industry

c. Book value and financial condition

d. Earning capacity

e. Dividend-paying capacity

f. Intangibles, including goodwill

g. Stock sales and size of the block to be valued

h. Market price of publicly traded stock in same or similar lines of business

ii. Statutes governing dissolution or dissenting stockholder actions (if any)

a. Statement to that effect or summary statement of interpretation of the case law from a financial analysis point of view

Generalized list of the sources of information used. The degree of detail that is appropriate depends on the purpose and audience.

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5. Sources of information used in the appraisal

i. List of financial statements and supporting schedules that were examined, including the years studied for each statement

a. Statement as to accountant's opinion

ii. Corporate tax returns (if appropriate)

iii. Internally prepared budgets for the next 6 to 12 months

iv. Facilities visited

v. Equipment list and depreciation schedule (if appropriate)

vi. Inventory lists and receivables aging (if appropriate)

vii. Stockholders' list as of December 31, 1993

viii. Schedule of total owners' compensation (if appropriate)

ix. Copies of leases

x. Articles of incorporation and by-laws

xi. Industry information and periodicals

xii. Information on comparative publicly traded companies from S&P Corporation records and SEC 10-Ks; various brokers reports on these companies

6. Valuation approach and conclusion

i. Broad criterion or criteria used in reaching the valuation conclusion

ii. Brief statement of the conclusion

B. Description of the company

1. Background

2. Physical facilities

3. Product and/or services

4. Distribution channels

5. Sources of supply

This section should be descriptive and analytical, allowing one to understand the firm and make qualitative judgements on the positive and negative aspects of the company that bear on its value.

6. Labor/capital intensive; operating leverage

7. Management

8. Capitalization and ownership

9. Seasonality (if any)

C. Industry data

1. Size of firm relative to competitors

2. Specialized segments of the market the firm serves

3. Competitive strengths and weaknesses

4. Technology and production

5. Regulation

Industry growth rate may be measured using any indicator relevant to the industry, including revenues, units shipped or produced, and assets. Appropriate benchmarks include real GNP growth, PCE (consumer spending), and S&P 500 growth.

6. Industry phase

i. Mature phase: Product technology well established, markets saturated, and long-term growth in line with general economy. Companies compete for market share on price basis

ii. Price-to-earnings ratio is down; thus, the equity market is less attractive to the company. Generally reduced need for financing.

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7. Cyclicality

i. Should be compared to a benchmark such as real GNP growth and should consider both industry specific cycles and economic cycles

8. Entry barriers

i. Economies of scale and other cost advantages, capital requirements, intensity, product differentiation, access to distribution channels, and regulations

9. Cost Structure

i. Labor cost, material cost, capital intensity, economies of scale, technological advantages/disadvantages, and operating leverage

D. Economic data

1. Aspects of economic conditions that may have a bearing on the firm's prospects

i. Identify clearly macroeconomic variables that affect the firms sales and gross profit margin

E. Financial Analysis

1. Analysis of the latest fiscal year

i. Income statement, balance sheet, cash flow, and ratios

ii. Industry comparatives

2. Projection analysis

i. Most likely projections; ratio, cash flow, financial needs, and debt capacity analysis will show the firm has financial resources available and is viable

ii. Conservative (worst-case) projection highlights

Most likely projections should be supported by simulations set at 200 trials and a 95% certainty level.

a. Sales growth and gross margin pegged to historical five-year lows; average collection and holding periods set at historical five-year highs

b. Analysis reinforces firm's viability given worst-case scenario Analysis reinforces firm's viability given worst-case scenario

F. Valuation analysis

1. Approaches

i. Price: Revenues multiples

ii. Capitalization of five-year average earnings

iii. Capitalization of projected earnings

iv. Market capitalization: Book capitalization multiples

v. Price earnings and price book

vi. Transaction multiple approach

vii. Liquidation value

viii. Dividend model

ix. Cash flow (while we will construct a weighted average, discounted free cash flow model will carry a substantial weight)

The length of the forecast horizon is not simply a convenient period on time in estimating financial performance but a period based on the economics of the company and its industry.

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x. The forecast horizon

a. Points we need to discuss to determine this extremely important valuation determinant

b. Proprietary technologies

c. Limited product life cycle

d. Distribution channels

e. Industry-wide price competition

2. Residual value

i. Once the discrete forecast horizon cash flows have been estimated, we can make a simplifying assumption regarding the cash flow generated after the forecast period.

3. Cost of capital

i. Textiles had a beta last year of 1.16.

ii. We need to discuss the cost of debt, applying the cost of debt to the firm's tax rate.

4. Value driver analysis

i. Sales growth rate

ii. Incremental working capital investment

iii. Incremental fixed capital investment

iv. Cash tax rate

v. Cost of capital

5. Relative impact of key variables on shareholder value

6. Analysis of valuation ratios

a. Threshold margin versus operating profit margin

b. Threshold spread profit margin

The threshold margin is a single-period measure of the minimum operating profit margin that is necessary to create shareholder value.

G. Simulations: ''Proving the valuation is right on target"

1. Define assumptions

i. Understanding and working with value drivers

ii. Selecting the right distribution to fit data

a. Fitting distributions to data

iii. Correlations between independent variables and/or between independent variable (s) and the forecast variable

a. Responding to problems with correlated assumptions

2. Define forecast

i. Determining the certainty level

a. Finding the probability that valuation falls within specific ranges

3. Developing a sensitivity check and working with sensitivity charts

4. Creating reports

H. Strategic planning: Optimizing the company's value

1. Setting up and optimizing the linear programming model (OptQuest)

i. Defining decision variables and selecting decision variables to optimize

ii. Specifying constraints (value drivers) limitations

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iii. Selecting the forecast objective: Maximize shareholder value by linear programming changes to value drivers

iv. Perform sensitivity analysis

I. Conclusion

1. Summary of the valuation appraisal and recommendations

Valuation Appraisals and Business Plans
Select Internet Library and SBA Source Contacts

1. Small Business Administration (SBA), The Business Plan: Road Map To Success, 9/97. The SBA provides a very through outline for a business plan you can easily download. This source is highly recommended. Use this model as a guide when developing the business plan for your business. http://www.sbaonline.sba.gov/starting/businessplan.html.

2. The Business Plan Road Map To Success, 9/97, a tutorial and self-paced activity for downloading or viewing as text version. The plan includes a case study "Someplace Fitness Center, March 1995" This through outline was prepared with the assistance of The Center For Technology And Small Business Development Central Missouri State University. http://153.91.1.141/sbdc/centsbdc/BUSPLAN.HTM

3. Howard University Small Business Development Center developed a business plan entitled " Discover what to put in a business plan" http://www.ntia.doc.gov/opadhome/mtdpweb/busplano.htm

4. Using Your Computer to Create A Winning Business plan was developed by Thomas Carroll which can be downloaded http://www.planmaker.com/about-bp.html

5. A business plan is included in the October 1997Sixth Edition Lansing Community College Small Business Development Center Counseling, Training, Research, and Advocacy for Michigan's small Business. U.S. Small Business Administration Small Business Development Center (SBA/SBDC) http://www.nemonline.org/bus plan/

U.S. Small Business Administration

Besides developing valuation appraisals and business plans for clients, financial consultants may want to consider an excellent information resources list compiled by the U.S. Small Business Administration (SBA).1 The SBA offers an extensive selection of information on most business management topics, from how to start a business to development of business plans (see above) to exporting your products. This information is

¹ Source US Small Business Administration

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listed in "Resource Directory for Small Business Management." This can be obtained at any SBA office. On behalf of your clients, you may want to recommend the following free services:

1. Service Corps of Retired Executives (SCORE), a national organization sponsored by SBA of over 13,000 volunteer business executives who provide free counseling, workshops and seminars to prospective and existing small business people.

2. Small Business Development Centers (SBDCs) sponsored by the SBA in partnership with state and local governments, the educational community and the private sector. They provide assistance, counseling and training to prospective and existing business people.

3. Business Information Centers (BICs), offers state-of-the-art technology, informational resources and on-site counseling for start-up and expanding businesses to create business, marketing and other plans, do research, and receive expert training and assistance.

Many publications on business management and other related topics, some examined in this book are available from the Government Printing Office (GPO). GPO bookstores are located in 24 major cities and listed in the Yellow Pages under the "bookstore" heading. You or your clients can request a "Subject Bibliography" by writing to Government Printing Office, Superintendent of Documents, Washington, DC 20402-9328. Many federal agencies offer publications of interest to small businesses. There is a nominal fee for some, but most are free. Below is a selected list of government agencies that provide publications and other services targeted to small businesses. To get their publications, contract the regional offices listed in the telephone directory or write to the addresses below:

·Consumer Information Center (CIC), P.O. Box 100, Pueblo, CO 81002. The CIC offers a consumer information catalog of federal publications.

·Consumer Product Safety Commission (CPSC), Publications Request, Washington, DC 20207. The CPSC offers guidelines for product safety requirements.

·U.S. Department of Agriculture (USDA), 12th Street and Independence Avenue, SW, Washington, DC 20250. The USDA offers publications on selling to the USDA. Publications and programs on entrepreneurship are also available through county extension offices nationwide.

·U.S. Department of Commerce (DOC, Office of Business Liaison, 14th Street and Constitution Avenue, NW, Room 5898C, Washington, DC 20230. DOC's Business Assistance Center provides listings of business opportunities available in the federal government. This service also will refer businesses to different programs and services in the DOC and other federal agencies.

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·U.S. Department of Treasury, Internal Revenue Service (IRS), P.O. Box 258, Richmond, VA 2326. The IRS offers information on tax requirements for small businesses.

·U.S. Environmental Protection Agency (EPA), Small Business Ombudsman (2131, Room 3423M, 401 M Street, S.W., Washington, DC 20460; 1-800-368-5888. The EPA offers more than 100 publications designed to help small businesses understand how they can comply with EPA regulations.

·U.S. Food and Drug Administration (FDA), FDA Center for Food Safety and Applied Nutrition, 200 C Street, SW, Washington, DC 20204. The FDA offers information on packaging and labeling requirements for food and food-related products.

For More Information a librarian at the SBA can help both you or your clients locate the specific information you need in reference books. Most libraries have a variety of directories, indexes and encyclopedias that cover many business topics. They also have other resources, such as trade association information. Trade associations provide a valuable network of resources to their members through publications and services such as newsletters, conferences and seminars.

Business and professional magazines provide information that is more current than that found in books and textbooks. There are a number of indexes to help you find specific articles in periodicals. In addition to books and magazines, many libraries offer free workshops, lend skill-building tapes and have catalogues and brochures describing continuing education opportunities.

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Appendix Two to Chapter 11
Ace Textile Production Corp.:
Valuation, Simulation, and Optimization
(A Case Study for Valuation Consultants and Appraisers)¹

Ace Textile's valuation was developed using the Excel spreadsheet model accompanying a highly rated book: Valuation: Measuring and Managing the Value of Companies, (2nd ed.), by Copeland, Koller, and Murrin (New York: John Wiley & Sons). While accompanying extracts are included as exhibits to this case, the valuation model itself and discussion of it has been excluded. However, you can purchase it from John Wiley & Sons at a nominal cost. The threshold spread and threshold margin,² along with simulations using Decisioneering's Crystal Ball, supplement the basic valuations. In order to obtain relatively uncomplicated solutions to this case, we used Excel's Solver to maximize operating profit (that turned out to be the most important value driver) by limiting business risk associated with operating leverage. Recall that Solver provides a local optimal solution since the model is deterministic. Stochastically driven optimization models discussed in chapter 9 would have provided more realistic solutions. Also, the case was recast to meet generic requirements to hide the real company. Thus, the Capital Asset Pricing Model (CAPM) furnished the risk/reward framework. The use of CAPM was less than optimal; in the financial literature, the theory is quite sound, but in practice the whole idea of divisional betas is not very practical. We will discuss this further when the problem comes up. The workbook for this case is C11 AceExcel Hard Copy located in the Excel subdirectory in the CD.

During the course of this discussion, we cover the following:

1. Forecasts of free cash flows during a 10-year explicit forecast period

2. Continuing value calculations for cash flows beyond the explicit forecast period

¹ Refer to appendix 1.

² Developed by Alfred Rappaport in Creating Shareholder Value (New York: The Free Press, 1986).

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3. Computation of the weighted average cost of capital utilizing the "pure play" approach

4. Maximizing operating margin by eliminating product lines, changing the contribution of product segments to consolidated operating margin, while constraining asset volitility associated with operating leverage

5. Optimization reports provided by Solver

6. Simulation reports provided by Crystal Ball delineating value driver impact on shareholder value

7. Determining probabilities that the shareholder value falls below zero

8. The threshold margin as a tool to measure the effectiveness of management strategy to add to or destroy shareholder value

9. Free cash flow, economic profit, and invested capital

The Company

Ace Textiles was founded in 1955. The company produces a number of diversified products in five operating segments. Ace's production and sales are divided into the operating segments: Shown in Table 11A1.

Ace hired a consulting firm to provide operating guidance and a valuation appraiser to map valuations. The team recommended that management improve the existing business with more efficient production methods such as reducing excessive variable labor costs and increasing operating leverage. In short, operating segments will be reexamined, and some may be sold off.

Table 11A-1.
Operating segments and operating leverage.

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The team will provide a discounted cash flow valuation and run simulations and optimizations that concentrate on (1) determining the operating segments the business should highlight (decision variables), (2) maximizing the combined operating margin and with it a pivotal link to shareholder value (objective variable), and (3) defining the major constraint in this business, that is, the volatility component linked to operating leverage. The restriction on operating variability is an important component to valuation because the firm's existing funded debt is sustained by low rates (low risk). If operating leverage (and asset volatility) were to increase beyond a measured tolerance acceptable to the lenders, the firm would be forced to bring in high-cost equity.

Summary

On balance, the firm's business risk is far lower than the industry average. Low business risk is associated with the firm's low fixed production costs (i.e., low operating leverage). However, this has had a negative effect on operating margins. If the firm were to augment operating leverage, margins would almost certainly rise, but so too would business and financial risk. While the firm is willing to alter the distribution of its product line mix, management is not quite sure how to accomplish this. That is why the consultants were brought in.

The Valuation Process:
The Valuation Summary

The explicit forecast period was 10 years (19952004), and the terminal value commenced at the beginning of year 2005. Table 11A1 and Orig Valuation Worksheet shows the results. First, management explicitly forecasted free cash flows from 1995 to 2004. Present value was $4,738. Next, the firm estimated the present value of free cash flows from the year 2005 and beyond. This continuing value was worth $5,005. The total, $9,743, represents operating value. To this total nonoperating assets and the firm's excess pension assets were added in. The result (i.e., the value of the firm) is $9,941. From this total, the market value of debt ($4,500), retirement-related liability ($500), and preferred stock ($333) were deducted, resulting in equity value of $4,608.

Economic profit calculation of value yields the same results as the free cash flow method. Management discounted back to present value economic profit in the years 19952004 and subtracted from this total continuing value to arrive at the present value of economic profit ($294.9). Adding invested capital at the beginning of the projection period, $9,661, yielded operating value of $9,743, which, as you can see by examining Exhibit 11A1 is equal to the flow method.

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Exhibit 11A-1.
Ace Textile Production Corp.

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The forecast assumptions were developed under uncertainty conditions. Assumption variables include revenue growth, cost of goods sold/revenues, selling, general and administration expenses/revenues, accounts receivable and inventory, capital expenditures and cost of capital. The distributions include triangular, uniform and lognormal (see Exhibit 11A2).

The Income Statement Value Drivers⁴

Revenue

Revenue growth was held constant in order to disguise the real company and to test value driver sensitivities. Quantitative methods, reviewed in this and other chapters, would naturally be called into play with sales following a cyclical pattern. In addition, macroeconomic factors (ignored here along with exogenous sensitivities) are normally a crucial element in determining sales growth. Other external factors affecting each of the firm's operating segment revenue include but are not limited to industry demand, industry supply, competitor pricing policy, competitor advertising policy, cotton and other raw material cost and availability, fashion and technology, foreign textiles competition, substitutes, supply conditions, barriers of entry into industry, historical patterns, and customer order backlogs.

Controllable factors driving Ace Textile's revenue, such as decisions and policies set by management, are important components in any sales projection. These include but are not restricted to product pricing, advertising, production policy, finished goods inventory policy, credit policy, and R. & D.

Cost of Goods Sold

This variable was also held constant to conceal the actual company and again to evaluate value driver importance. In reality, the consulting firm scrutinized and questioned the following factors:

1. Direct materials.

2. Direct laborcosts physically traced to each operating segment's product line.

3. The firm's status with unions, contract expiration dates, and labor relations history.

4. Manufacturing overhead, that is, all manufacturing costs with the exception of direct material and direct labor costs.

5. Changes in automation, substitution of capital for labor, and technology and its effect on costs (operating leverage).

6. Plant capacity (the valuation appraisers questioned whether it was physically possible with the resources on hand to meet production requirements; again the issue of operating leverage kept coming up).

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⁴ Value drivers discussed here are represented in their qualitative dress only. That said, value driver (qualitative) aspects represented the "heart and mind" of the appropriate quantitative models from real options to optimization, discussed in chapters 3, 7 and 9.

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Exhibit 11A-2.
Ace Textile Production

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Exhibit 11A2.
Continued.

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7. Production department procedures and controls (actually the valuation appraisers determined that shareholder value suffered because management lacked an adept production master plan).

8. Domestic distribution. By rearranging Ace's distribution pattern and making appropriate shifts in production and warehousing loads, it might be possible without any change in facilities to increase company profits. The largest component in this improvement package could come from reduced materials and warehousing costs, direct labor saving, and plant overhead. If cost of goods sold emerged as the most critical of value drivers, production and warehousing loads would warrant significant strategic changes. On balance, several labor-intensive operating segments could be phased out, reduced, or strengthened.

The appraisers and management integrated real options analysis into the cost of-goods-sold analysis and this critical variable's link to equity value, considering three options: shutdown, the option to expand, and most important, the operating scale option since the firm has the flexibility to expand or scale down operations.

For simulation runs, we assume that the appraisers projected 4.9% sales growth in 1995 and for the remainder of the projection horizon. The triangular distribution was reduced to a tight fit, 4.7% to 5.3%, with 4.9% set as most likely. Cost of goods sold along with selling (general and administration) were built around constricted triangular and uniform distributions, respectively. Even under a tight distribution fit assumption, cost of goods sold turned out to be the most important value driver. Before adjustments, operating margin measured 6% over the long term.

Of all the expense items, operating costs are usually the easiest to control by means of a ''low-fat" corporate diet. The key to properly limiting operating costs would be to cut the "fat" without inhibiting the infrastructure of the organization. In other words, firms such as Ace Textile should not "down-size" to the point where operations become so inefficient that profits suffer (see Exhibit 11A3 and the Orig Financial Worksheet).

Balance Sheet Drivers

Accounts Receivable

The firm's accounts receivable policy is closely tied to inventory since the two link up as components of the cash conversion cycle and together represent the largest component of working capital (we see the importance of working capital to the calculation of the threshold margin).

The volume of credit sales and the average collection period determine the level of accounts receivable for this firm. The average collection

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Exhibit 11A3.
Income Statement and retained earnings for Ace Textile Production Corp 1992Perpetuity.

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period is molded by both economic conditions and controllable factors, the most important being credit policy variables. Bad debt expense, usually tied to historical experience plus expected customer portfolio "quality," reflects the direction that write-offs take along with reserves that have been built into the operating budget.

Most important, the consultants pointed out that management would benefit greatly from the latest data mining and data visualization tools to help them track credit risk and to formulate a more optimal credit policy. Specifically, software featuring the latest utilities and analytical tools, including data mining algorithms, regression analysis, clustering, and decision tables, will provide management with a far more intuitive analysis of credit data.

Inventory

Inventory management is of vital importance as part of the firm's overall cash flow cycle. For example, computerized economic order quantity is one of the most widely used mathematical models in working capital management and has general applicability beyond inventory such as cash management. The firm does not use computerized inventory system in spite of the fact that the Web is full of excellent EOQ models available for trial download.

The consultants recommended that the firm discard its manual system in favor of computer optimization, which will help management control overbuying and misdirected buying, so that raw materials purchased adhere to production schedules.

The inventory turnover is held constant for valuation purposes so that results remain conservative and focus can be leveled at the the critical factor affecting this business: the degree of operating leverage, an attribute driving the cost of goods variable.

To summarize:

1. Because inventory is on a manual system, there is no standard cost system or cutting registers available to calculate real cost. By maintaining this outdated system, tracking and balancing inventories is nearly impossible.

2. Overbuying and misdirected buying have generated substantial inventory in two of the five operating segments.

3. Raw material purchases should conform more strictly to production schedules. This is hard to track since the company does not have a breakdown of inventory by season readily available.

4. The firm will invest in dedicated inventory data mining and neural network systems.

Ace's income statement Exhibit 11A3 and the balance sheet forecast Exhibit 11A4 should be mutually consistent lest the valuation lose credibility. Consistency between the income statement and the balance sheet is

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usually measured by the turnover ratios connecting accounts receivable to revenues and inventory to cost of goods sold. In Exhibit 11A6 the two ratios were held constant at 16.4% and 25% (unfortunately to keep the results relatively simple).

A common forecasting error is the failure to adequately tie capital requirements to sales growth. When this happens, the turnover ratio increases rapidly, implying that sales is supported with inadequate capitaleither that, or else the company is becoming inordinately efficient in its capital utilization. The result is that the company will be overvalued because cash outflows for capital investment are underestimated. Ace's capital expenditures were held to .5% of revenue, consistent with the firm's low operating leverage. Later, in the optimization runs this will change.

We calculate free cash flow (Exhibit 11A5 and the FCF & ECProf Worksheet) starting with earnings before income and taxes (EBIT) net of taxes on EBIT to arrive at net operating profit less amoritization and taxes (NOPLAT). Adding back depreciation yields gross cash flow. Gross investments are deducted from this total to arrive at free cash flow. Exhibits 11A5 through 11A7 are printouts from the AceExcelHardCopy.xls file in the Models sub-directory of the CD. You can view these worksheets in the workbook.

Weighted Average Cost of Capital

To be consistent with the free cash flow approach to valuation, the cost of capital must

1. Comprise the cost of all sources of capital, debt, quasi-equity and equity because free cash flow embodies the residual cash available to all providers of capital.

2. Be computed after tax since free cash flow is stated after tax.

3. Employ market rates, not book, for each financing element.

A number of steps are involved in developing Ace Textiles's cost of capital:

1. Establish target market value for capital structure.

2. Make sure that future financing levels are evaluated carefully since this could be different from current or past levels.

3. Estimate the current market value capital structure of the company.

4. Review capital structure of comparable companies.

5. Review management's approach to financing this business.

6. Estimate cost of nonequity financing.

Cost of debt also incorporates leases, interest, bond coupons, short-term debt, and leases. However, non-interest-bearing liability, such as accounts payable, are excluded from debt costs in order to steer clear of dissimilarities and facilitate the valuation process. Indeed, non-interest-bearing liabilities have cost-of-capital characteristics like other forms of debt, but this

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Exhibit 11A4.
Ace Textile Production Corp.

(table continued on next page)

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(table continued from previous page)

Exhibit 11A4.
Continued

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Exhibit 11A5.
Ace Textile Production Corp. free cash flow and economic profit for 1992Perpetuity.

(table continued on next page)

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(table continued from previous page)

Exhibit 11A5.
Continued.

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Exhibit 11A6.
Ace Textile Production Corp. operating ratios.

(table continued on next page)

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(table continued from previous page)

Exhibit 11A6.
Continued.

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Exhibit 11A7.
Continued

(table continued on next page)

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(table continued from previous page)

Exhibit 11A7.
Continued

(table continued on next page)

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(table continued from previous page)

Exhibit 11A-7.
Continued.

(table continued on next page)

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(table continued from previous page)

Exhibit 11A-7.
Continued.

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cost is implied in the price paid for goods and thus is recorded in operating costs and free cash flows.

To be sure, capital costs for this firm were not easy to pin down, as Ace is not publicly traded. To overcome this obstacle, the consultants employed the pure play approach (discussed in Chapter 10). Recall that pure play estimates capital costs of operating units or private firms whereby stock prices are not directly observable.

Employing this process, first Ace's beta is unlevered, meaning the firm's unsystematic risk is effectively ''stripped away," leaving a beta benchmark bound to systematic risk (and systematic risk only). Next, a carefully selected, publicly traded homogeneous firm's debt, equity, and tax rate are plugged into a formula (Chapter 10). Finally, betas are relevered (in still another formula) based on either each operating segment's or the firm's capital structure and tax rate. The concluding beta approximates Ace's beta on a proforma basis, as if it also were publicly traded. Thus, the cost of equity capital assimilates both macroeconomic (systematic) and company-specific (unsystematic) risk. Inserting the new beta back into the CAPM yields the cost of equity (see Table 11A2 and Orig Cost Cap Worksheet).

As depicted in chapter 11, the cost of capital, or discount rate should be an average of the company's cost of debt (on an after-tax basis) and cost of equity weighted at a market-based capital structure (Table 11A3).

Next, we evaluate cost of debt. In a real-world setting, and with a higher-risk firm, managers might have worked out a credit scoring or bond rating for each operating unit along with the firm's. Book value debt must always be converted to market value (see Table 11A4).

Length of the Projection Period

The length of the projection period depended on the line of this business and company operations. By the end of the projection period, set at 10

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Table 11A-3.
Cost of capital calculation.

Table 11A-4.
Capitalization weights.

years, operations are assumed to be at a mature and sustainable operating level so that a residual value can be easily estimated. "Growth" phenomena such as rapid revenue expansion, surges in operating margins, or unsettled working capital accounts should be behind the company. Five, 7-or 10-year projections are usual for companies projecting normal sales growth and profitability margins. Management and their valuation appraisers assumed that Ace will earn returns exceeding the cost of capital during the explicit forecast period but that the company's rate of return on new invested capital equals the cost of capital in the residual period. Extending the forecast period leads to an increase in value, attributable to

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the increase in rate-of-return assumptions. The important point to remember is that the forecast period should be long enough to allow the business to achieve a state of operations by the end of the period.

Residual (Terminal) Value

The residual value of a firm is attributable to the period after the forecast period, which was assumed at the beginning of year 11. This component of valuation estimates the future value of the company at the end of the projection period, $9,845, and discounts that value to the present, $5,005. The value of the company at the end of the projection period represented a significant portion of the firm's value. Terminal value depends on the underlying assumptions and the length of the projection period in addition to the specifics of the business. Projection periods that are short place more emphasis on residual value. The methods of estimating residual value included (i.e., the real firm, not the one disguised here) liquidation value, book value, steady-state EBIT capitalization, and market multiple techniques. Management and their consultants determined that steady-state income capitalization was the most appropriate residual value determinant. Steady state assumes the following:

1. Net investment in fixed assets are zero, and capital expenditures equal disposals.

2. Net working capital requirements are zero, and sources of working capital equal uses of working capital.

3. The firm earns constant margins, maintains a constant capital turnover, and thus earns a constant return on invested capital.

4. All new investments earn a constant return.

Gross Cash Flow, Gross Investment, and Free Cash Flow

Ace's gross cash flow represents the total cash flow thrown off by the company, or the internal cash provided for reinvestment. Gross cash flow includes net operating profit less amortization and taxes and depreciation. Gross cash flow internally finances gross investment. Gross investment includes working capital, capital expenditures, and net increases in other assets (nonoperating items are excluded from the calculation). Thus, the final result, free cash flow, represents the difference between gross cash flow and gross investment.

Change in Working Capital

Only operating working capital should be included. Nonoperating assets, excess marketable securities, and interest-bearing liabilities (short-term debt and the current portion of long-term debt) are excluded because they are produced externally as financing activities and do not represent internally gen-

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Table 11A-5.
Summary.

erated flows. Working capital changes equals changes in current assets (excluding marketable securities) net of changes in current liabilities (excluding all funded debt, including the current portion of long-term debt).

NOPLAT

Net operating profit less adjusted taxes (NOPLAT) represents the after-tax operating profits of the company after adjusting the taxes to a cash basis. Exhibit 118 and the Invested Capital Worksheet shows the calculation of the firm's NOPLAT and a reconciliation of NOPLAT to Ace's accounting net income.

Setting Up Optimization Runs

Optimization Engine

The CAPM was employed to maximize operating margin constrained by volatility. We assume a bit of editorial license by substituting operating margin for expected portfolio returns.⁵ The firm's asset portfolio is subject to risk, and this is related to the interaction between fixed and variable costs (e.g., operating leverage unique to each product segment; note again That cost of goods sold has been established as the key value driver). Certainly, a disasterous cost-of-goods policy would indeed impact on asset risk and escalate finance distress probabilities. (See Exhibit 11A9, The Base Case Optimization Employing the CAPM.)

In a more factual setting, it is better to assess each operating segment's cash flow and then run discounted cash flow valuations on both a stand-alone (segment) and a combined or consolidated basis. However, this entails breaking down each unit into its smallest component and allocating cash flows accordingly, assessing differences in capital structure, cost of

⁵ The Ace Textile optimization model was derived and modified from an Excel template to illustrate how a stock portfolio is optimized.

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Exhibit 11A-8.
Ace Textile Corp. NOPLAT, NOPLAT reconciliation and invested capital for 1992Perpetuity.

(table continued on next page)

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(table continued from previous page)

Exhibit 11A8.
Continued.

capital, and headquarters cost. The analysis required to accomplish a more authentic result is somewhat beyond the dimensions we allow in the case.

The CAPM permits the criteria for asset expansion decisions under uncertainty to be set out comprehensively and succinctly. With modifications, the CAPM meets the criterion allowing for capital budgeting analysis. The market constants remain the same. The risk-measuring variable, beta, traditionally fixed to individual firms, holds for operating segments as well: Systematic risk is systematic risk. Drawn from the financial literature, conditions that must hold if any project is deemed acceptable can be stated as shown in Exhibit 11A10.

Consider the following: The expected return on the new project for ABC Inc. must exceed the pure rate of interest plus the market risk premium adjusted by the project's beta, the measure of the individual project's systematic risk.⁶

The criterion in graphical terms is to accept projects that plot above the security market line and to reject all those that plot below the market line. Managers seek to find any number of projects, such as W and Y, with returns in excess of the levels required by the risk-return market equilibrium relationship. When such projects are added to the firm's operations, the expected return on the firm's common stock (at its previous existing price) will be higher than required by the market line.

From this, we extrapolate to measure product lines (after optimization). Will the new product line mix preserve or destroy shareholder value?

First, set up the optimization run (Exhibits 11A11 and 11A12):

Objective: Maximize combined operating margin. Set target cell to D16. Decision variables: Eliminate product lines and/or change contribution to operating margin by changing cells D9:D13. Subject to the constraints: Variance limit (cell F16) = 8%, no product line can be negative, Cells D9:D13 > 0 and total investment (cells D9:D13) = 100.

⁶ See chapter 10.

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Exhibit 11A9.
BASE CASE project optimization" The CAPM approach.

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Exhibit 11A10.
Project betas: A criterion to either accept or reject projects.

The results suggest that based on assumptions set in this example, the firm will optimize operating margins with volatility constrained at no more than 8% requires the following changes:

1. Product Line Kappa Management is scaled down to 1% of the business from 22%.

2. Product Line Epsilon expands slightly to 21%.

3. Product Line Sigma jumps to 53% up considerably from its previous level of 10%.

4. Product Line Omega Increases to 25% from 10%.

5. Product Line Lambda is divested altogether.

Then, test optimization (and the resulting valuation) utilizing Rapapport's threshold margin.

Ace Textile's Threshold Margin⁷

Quoting the author of the threshold margin:

The threshold margin represents the minimum operating profit margin a business needs to attain in any period in order to maintain shareholder value in that period. Threshold margin is a new type of "break-even analysis," a value-oriented economic break-even analysis. Stated in yet another way, threshold margin represents the operating profit margin level at which the business will earn exactly its minimum acceptable rate of return, that is, its cost of capital.

⁷ The case will only provide Rappaport's threshold/margin structure that was developed in Excel. For a complete examination of this important valuation concept, the reader is referred to Rappaport's excellent and groundbreaking text.

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Exhibit 11A-11.
Project optimization: Use the CAPM approach outlined above.

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Exhibit 11A12.
Microsoft Excel 9.0 answer report worksheet:

Exhibit 11A13.
Threshold margin formulas.

Instructing operating managers to invest in strategies that earn more than the cost of capital is not enough. To bridge valuation concepts of modem finance theory with the needs of corporate decision-makers, what is needed is an easily understood, operationally meaningful concept that enables managers to assess the value creation potential of alternative strategies. The threshold margin concept is particularly suited to facilitate this linkage because the operating profit margin has widespread acceptance from both security analysts and corporate management as an essential ratio for assessing operating profitability and efficiency. The threshold margin can be used to evaluate the past performance of a business so that management can establish performance targets for the future.⁸

Exhibits 11A13 and 11A14 depict the calculation of the threshold margin.

(text continues on page 380)

⁸ Ibid.

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Exhibit 11A-14.
Threshold margin calculation.

(table continued on next page)

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(table continued from previous page)

Exhibit 11A-14.
Continued

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The business has been optimally structured with shareholder value preserved. The measure of value added is the spread between the operating margin and threshold margin (Exhibit 11A15).

Finally, the summary (Exhibit 11A16) reveals that the optimal variance boundary allied with capital costs falls between 5.0% and 8.0%. The cost of capital under these conditions is expected to be 8.1% versus 12% of the variance boundary were to exceed 8.0%. Ideally, the relationship between capital expenditures and revenues falls out at 2.1% indicating that increasing operating leverage ''just enough" will optimize shareholder value. Increasing operating leverage too fast is a value destroying strategy.

This analysis would have been difficult to perform without simulation which was utilized early on to test and structure the firm's operating and financing strategy (Exhibit 11A17). Exhibits 11A15 and 11A16 are in the Optimization Worksheet and you can view Exhibit 11A17 in the Orig. Sim Worksheet.

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Exhibit 11A-15.
The new business optimized.

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Exhibit 11A16.
Summary

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Exhibit 11A17.
Ace Textile Production Corp.
the Crystal Ball simulation reportBase case.

(continues)

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Exhibit 11A17.
Continued

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Exhibit 11A17.
Continued

(continues)

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Exhibit 11A17.
Continued.

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Appendix Three to Chapter 11
The Alcar Group Inc1
http://www.alcar.net/index.html

The valuation output for Sample Corporation, Strategic Plan 19992003 included in this appendix represents state of the art valuation. Alcar has generously provided their demonstration software included in the Alcar subdirectory of the CD. It may be a good idea to view this application before reviewing Sample Corporation output. For nearly two decades, Alcar has been providing financial software and services worldwide. Client base includes many of the Fortune 500 and top financial institutions. Provides a standardized framework within which to perform strategic financial planning; flexibility to customize the system to specific business structure and planning requirements; enhanced portfolio management capabilities with consolidation of existing businesses and potential acquisitions; a system that uses value-based metrics integration with current or future general ledger and database systems. Before you read over these exhibits, you may want to view the Alcar demo, "Alcar" on the CD to facilitate data input and enhance reporting.

Key Features

· Historical and forecasted financial statement generation

·Consolidation of any business unit structure and M&A deal structure

·Valuation Analysis for strategic planning and M&A analysis

·Funding Options to manage optimal capital structure/funding surpluses and deficits

·Sensitivity Analysis to determine impact of changes in assumptions and key value drivers

·Scenario Manager to generate unlimited scenarios

·Analyze to drill down from report output to easily identify underlying assumptions and input errors

·Report Customization

·Translation to and from any currency

¹ Reproduced with permission The Alcar Group Inc.

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Chapter Eleven References and Selected Readings

Books

Bierman, H. (1999). Corporate financial strategy and decision making to increase shareholder value. New Hope, Pa.: Frank J. Fabozzi Associates.

Black, A. P. (1998). In search of shareholder value: Managing the drivers of performance. London: FT Pitman Publishing.

Booz Allen & Hamilton Inc. (1983). Creating shareholder value: A new mission for executive compensation: A study of corporate performance, the market-valuation process, and executive pay trends in U.S. industry. New York: Booz Allen & Hamilton Inc.

Clarke, C. J. (1993). Shareholder value: Key to corporate development. Oxford: Pergamon Press.

Cleland, A. S., and A. V. Bruno. (1996). The market value process: Bridging customer and shareholder value. San Francisco: Jossey-Bass.

Fruhan, W. E. (1979). Financial strategy: Studies in the creation, transfer, and destruction of shareholder value. Homewood, Ill.: Richard D. Irwin.

Gill, R. S. (1998). Shareholder value in the multi-business corporation : strategy and nature of diversification as indicators of performance.

Knight, J. A. (1998). Value based management: Developing a systematic approach to creating shareholder value. New York: McGraw-Hill.

McTaggart, J. M., et al. (1994). The value imperative: Managing for superior shareholder returns. New York: The Free Press.

Montgomery, C. A., and M. E. Porter. (1991). Strategy: Seeking and securing competitive advantage. Boston: Harvard Business School Press.

Rappaport, A. (1986). Creating shareholder value: The new standard for business performance. New York: The Free Press.

Rappaport, A. (1998). Creating shareholder value: A guide for managers and investors. New York: The Free Press.

Rotemberg, J., et al. (1989). Shareholder value maximization and product market competition. Cambridge: Sloan School of Management, Massachusetts Institute of Technology.

Seely, M. (1984). The guide to maximizing shareholder value: Financial, managerial, and marketing techniques that pathfinding managements are using to raise the price of their stock. New York: Investor Access Press.

Srivastava, R. K., et al. (1997). Market-based assets and shareholder value: A framework for analysis. Cambridge, Mass.: Marketing Science Institute.

Periodicals

Anonymous. (1994). ''Value is in the eye of the beholder." Management Accounting, 72(2)55.

Barney, L. Dwayne, Jr. (1997). "Uncertainty and the comparative dynamics of stock price." International Review of Economics and Finance, 6(4)405.

Boer, F. Peter. (1994). "Linking R&D to growth and shareholder value." Research Technology Management, 37(3)16.

Hamel, Gary. (1998). "Strategy innovation and the quest for value. "Sloan Management Review, 39(2)7.

Kopcke, Richard W. (1997). "Are stocks overvalued?" New England Economic Review, September/October, 21.

Mentzer, John T. (1999). "The impact of forecasting on return on shareholders's value." Journal of Business Forecasting Methods and Systems, 18(3)8.

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Piercy, Nigel F. (1998). "Facing the challenges of a new era in market-based strategic management." Management Accounting, 76(5)18.

Weigel, John R. (1999). "An integrative financial statement approach to the strategy value chain." Journal of Financial Statement Analysis, 4(2)41.

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Page 399

Chapter Twelve
The Value-Growth Link¹

by Thomas L. Doorely III

Clearly, high performance, that is, superior value creation, is the core goal of the enterprise. Our research confirms that a well-crafted, effectively executed growth strategy is the superior route to that goal. Companies that grow outperform their slow growth counterparts by a wide margin. Thus, if value/performance is the goal, then growth must be the path.²

To underscore this conclusion, we have worked with the World Economic Forum (WEF) for the past five years to identify the top performing companies, globally. (The most recent such list is contained in the WEF publication, WorldLink³). Beginning with a list of 25,000 companies, we identify the top 200 in terms of the three measures of success for which cross-company, and cross-geography data is available, namely, growth (over three years to indicate sustainability) of:

·Revenues (real, corrected for inflation and currency)an indicator of the creation of value for customers

·Job Creationan indicator of employee opportunity creation and job satisfaction

·Investor Returns (total return to shareholders)an indicator of investor confidence

Taken together the three metrics define a set of high-performance companies, models of behavior in the search for enterprise success.

¹ This material is based on the research and methodology contained in Mr. Doorley's book, Value-Creating Growth: How to Lift Your Company to the Next Level of Performance, (coauthored with John Donovan, San Francisco: Jossey-Bass, 1999)

² This assumes, as discussed in Chapter 5, a sound capital structure, and no sustainable growth problems. Recall that rapid growth, fueled by high operating leverage (business risk), misguided management and a heavy debt overload (financial risk) can prove fatal if anticipated growth fizzled.

³ "What the Winners Can Teach Us," Thomas L. Doorley, III, WorldLink, January/February, 2000, pg. 127138.

Page 400

The results these companies generate represent high performance, indeed! Against the total database of 25,000, here's how the top 200 perform:

TOP 200

Full Database

Revenue growth

41 %/yr.

3%/yr.

Job creation

20%/yr.

2%/yr.

Shareholder return

57%/yr.

6%/yr.

In each case the top 200 companies outperform the typical company by 10 to 13 times. This is spectacular performance.

Thus, our first message to those wishing to achieve high performance is:

·Growth is the superior strategy; it drives high levels of performance.

Spectacular Growth/Spectacular Performance:
A Global Phenomenon

As the "new economy" brings nations together, that is, intensifies the momentum already present for increasingly a one-global market economy, many value drivers jump across cultural barriers. The value-growth link is one such phenomenon. This relationship transcends local economies. Thus, the lessons developed in the preceding chapters apply widely in the Americas, Europe, and Asia/Pacific. They are not localized curiosities. Here are the facts underlying this bold assertion.

The following Figure, 121, demonstrates the strength of the value-growth relationship for a set of nearly 4,000 North American companies. For every company-size category, as revenue growth increases, investor value grows apace. (In this case the measure of investor returns is growth over five years of market capitalization.) For example, for the smallest-size company, less than $US 100 million, returns for those who grow revenues at 5 percent per year or less, is 3 percent per year. Returns become positive when revenue growth increases by five points (+4 percent per year), and continues to rise as revenue growth increases, until it reaches an attractive level of 16 percent per year at a revenue growth of 15 percent plus. Double-digit revenue growth, for example, in excess of 10 percent per year, represents a point of demarcation. That is, investor returns exceed 10 percent per year when revenue growth passes this mark. Generally speaking, a 10 percent per year return represents a reasonable return expectation for the equity investor during periods of low inflation. Thus, this level of revenue growth (double-digit) also should become the basic target for those companies focused on breaking out of the low performance category. In short, as management gathers its team to consider appropriate goals for performance across a three to five year planning horizon, the dialogue must begin with a discussion of how to reach or beat the double-digit revenue growth target. All else flows from this fundamental starting point.

Page 401

Exhibit 121.
The Revenue growth-value growth link, North America.

An object lesson is instructive here. I am working with the management team of a large process industry company from the midwestern region of the United States. Toward the end of 1999 the team was complaining about the low rate of growth of their share price. While the average company for the S&P 500 group had seen its share price increase at about 20 percent per year, they were mired in a 35 percent growth trough, not nearly enough in their view. The explanations varied from being too remote from the money center of New York to analysts not taking time to understand the hard work they had done. In fact, as I pointed out, they were getting what they deserved. The rate of revenue growth was a drab 23 percent. As Figure 121 depicts, in a revenue size category of $US 110 billion, they were squarely in the low value growth zone. For a low revenue growth rate, they received a correspondingly low growth of their share price. Understanding these facts, the team has turned from complaining to rebuilding its capability to grow. It is the correct orientation.

But, as noted, these value-growth relationships are not a peculiarity of the capital markets or other exogenous characteristics peculiar to North America. They are ubiquitous as Figure 122 demonstrates. The data is drawn from a group of 350 Australian companies (all public companies larger that $A 20 million). The figure has a slightly different appearance from its North American counterpart due to the lack of enough companies (Australia's economy is about 5 to 6 percent the size of North America's

Page 402

Exhibit 122.
The Revenue growth-value growth link, Australia.

economy) to populate the full set of cells in the matrix, thus for statistical validity the 4 × 4 version becomes a 3 × 3. Nonetheless, the pattern pertains. For each company-size category, the growth of market value rises with the growth of revenues.

As we scan a variety of developed economies, we observe the same behavior with variations on the basic theme. For example, Asia/Pacific companies tend to survive longer periods of low performance. In America the benchmark follows the "grow or go" construct very sharply, while in Europe the differences in the extremes are muted. That is, in North America the "winners" outscore the "losers'' by wide margins, for example, three or four to one, as growth moves from less than 5 percent per year to 15 percent plus (companies of $US 10 billion or more). For the Euro region the variance runs about half that level.

Two other features of this data are instructive. First, while the steady increase in market value with growth might have been anticipated (although its broad validity is dramatic), the increase in the growth of market cap, at a constant level of growth surprises most. Sight along any row in either Figure 121 or 122. As company size increases, value growth increases as well. The explanation lies in most investors' perspectives on company size. The underlying conclusion: smaller companies are more volatile, thus riskier. Unfortunately, the data support this assertion. Companies under $US 100 million have much higher failure rates. Further, the

Page 403

single most important determinant of a company's cost of capital is its size. As revenues increase, the cost of capital declines if unsystematic risk poses no concern. In essence smaller companies with higher risks must generate higher returns.

Second, if we isolate the fastest growing companies, we again observe the concern investors have for scale. If Figure 121 were recast, breaking the revenue growth rates into three categories (below 30%/yr.; 3060%/yr.; 60%+/yr.) the increasing return pattern pertains for companies above $US 1 billion, and companies between $US 100 million and $1 billion, and $US 1 billion to $US 10 billion. However, for the companies whose annual revenues fall under $US 100 million, the trend reverses. Companies in this category, if they grow at 60%/year plus, face average returns at one-half the level achieved by those growing at 3060%/yr. This is the only growth/size category where this condition occurs. This may seem surprising since young, fast growing companies are the most sought after by the investor. The value driver underscoring the reduced returns relates directly to concerns about sustainability, especially worries around whether or not the company has the infrastructure in place to meet the intensity of extremely high rates of growth. Thus, if they can sustain it, valuations soar. However, small missteps lead to major value degradations.

Finally, these data represent broad-based patterns applicable across geographies as demonstrated above, but also across industry sectors. This is not merely the influence of a high technology boom. For example the largest company/highest growth category for the North American companies does include technology stars such as Dell Computer and Cisco Systems, but also more traditional economy companies like WalMart, Enron, and Citigroup. The Australian list includes less than 15 percent of the high growth/high return companies from technology sectors. In fact the fastest growing, highest value-creating Australian companies are Austrim and Futuris, which provide components to customers in basic industries.

Thus, the inescapable conclusion and our second message is:

· Growth represents the most consistent value driver.

Value-Creation Everywhere That Matters

Our work demonstrates the vitality of fast growing organizations across every dimension. For example, most companies perform annual surveys of employee satisfaction. Hewlett-Packard calls its survey the Employee Satisfaction Survey, Corning's survey is the Climate Survey, and Deloitte and Touche conducts the annual survey of performance on nine categories of HR (Human Resource) standards. Given the critical importance of the high talent, knowledgable worker at these and peer companies, it makes

Page 404

sense to monitor how employees feel. Across many such organizations we track the change in employee satisfaction and find a direct relationship to the enterprise's rate of revenue growth. This result shines through in spite of a common complaint about pressure, intensity, and stress attendant to rapidly-growing organizations. In spite of these concerns, they report high and rising levels of satisfaction.

Exploring this apparent dichotomy, we find numerous programs embedded in company practice to assist the employee. They all work to find ways to make the lives of their people satisfying. They are careful to reward outstanding performers. However, few contend that satisfaction would stay high if growth declined sharply. Sustaining high growth is such a challenge that management has to operate on a meritocracy. Putting a lesser-qualified individual into a key slot would compromise performance. Thus, these organizations tend to exhibit low levels of office politics. Further, the excitement that comes from winning in the marketplace is palpable. Growth tells the organization it is winning. Winning generates excitement and energy.

Customers love their fast-growth partners as well. Our research demonstrates that the fast growers are more innovative. They bring out new products at one and a half to two times the rate of slow-growth suppliers. Further, their new product cycle times are two-thirds the norm. Customers love innovation. Thus, the growers are seen to create value for them. This translates directly into higher customer retention rates that in turn yield higher levels of profitability. Our analysis of client profitability across our own firm, as well as other service firms, confirms the link between the longevity of the client relationship and the profitability of that client; the longer the relationship, the more profitable the client. The value created for clients/customers in turn drives value for the innovative, that is, fast-growing company.

Thus, the third message for companies aspiring to high levels of performance is:

· High-growth companies are healthy, vital enterprises

· They create value everywhere that matters.

Growth-Value:
Cautionary Tales

Over the long term, as our analysis demonstrates, growth creates value. However, at any time in the life cycle of a business (or a strategic business unit (SBU) within a larger corporate portfolio of businesses) growth may not be the indicated strategy. There are at least four times when growth will not pay off:

· When the commitment to growth does not match the level of opportunity. For example, when a new product is launched into very favorable demand conditions, yet the innovator does not pro-

Page 405

Exhibit 123.
Growth-Return Trade-off.

vide sufficient resources to capture the market. Untapped value becomes the prize of the fast follower.

·When the Valuable Formula is not well designed, allowing a competitor to trump the card of the first mover.

·If the enterprise is not prepared for growth. An early spurt of growth is not sustained.

·When debt levels are too high to support growth and the firm resists equity infusions.

A quantitative display across a set of business units in a company's portfolio can be used to focus attention on whether the time is right for growth for a specific SBU. Figure 123 represents such a figure. The vertical axis portrays investment intention (or actual investment if the figure displays current momentum, not future plans) for the SBUs versus the level of return on the horizontal. The return is a calculation, like Economic Value Added (EVA), of the businesses' return level relative to the cost of capital. If the SBU returns its capital charge or more, it lies to the right of the mid-point, if not, it falls to the left. Each of the quadrants of the matrix is labeled to depict what will happen, in shareholder value terms, at a given rate of investment. For example, Q1 is the Destroy Value cell. In essence, if returns are not above the cost of capital, why should a rationale investor invest? It is asking for investment of capital that will not generate an attractive, or minimal yield.

Page 406

Q2 and Q3 represent subtle messages. In Q2 as investment is withdrawn from the business, it begins to release value (the capital can be redeployed productively elsewhere). While not sustainable over the long term, it is the appropriate short-term path. Businesses static in Q3 represent a typical mistake. The business has cleared its capital cost hurdle, but is not growing. These sorts of businesses show favorable results but are conceding the future to more aggressive players. Of course, Q4 is the quadrant to which all businesses should aspire. Maximum value creation occurs here.

While Q4 is the destination, not all SBUs are located there. In such cases, the dashed line on the figure depicts the normative path for an SBU starting in Q1. So, a poorly performing SBU should first correct the "over-investment" problem, yielding people and cash to better-positioned business opportunities. As it does so, its momentum moves down toward Q2. Its next step is to find its missing elements and correct them. That is, redesign its Valuable Formula to make it more compelling to customers or strengthen the weak links in its infrastructure, its capability to drive growth. As it accomplishes these tasks it moves further right, gradually crossing the cost of capital benchmark migrating into Q3. Once the SBU's leaders have confidence that the recent actions represent effective solutions to the problems, it is time to reallocate growth investment to the SBU and drive its performance into Q4.

In practice, of course, this migration does not occur without a significant effort. In fact, rarely will an SBU leader volunteer to concede resources. It is in the nature of a business leader to have faith that improved performance will occur any quarter. Thus, this figure should be utilized at a portfolio level. It should cause corporate leaders to raise questions, challenge assumptions, and reallocate growth investment. The display can serve as an effective tool in the search to maximize value creation. Along with the displays and tools discussed next, it plays a more central role in setting strategic direction than it does in monitoring its execution.

Metrics for Success:
Guiding Implementation

Growth clearly drives value creation. However, a proper balance must be struck in order to find the strategically appropriate rate of growth. If growth is too slow, the full market demand is not met, opening up the opportunity for a fast following competitor to come to the fore, to gather a portion of the value otherwise available for the innovator. If growth is too fast, the company may not have sufficient growth capability to sustain momentum. Starbucks avoided an error of the first type in the early 1990s. Just as it was beginning to broaden its base of coffee bars from its origin in Seattle, it was approached by a Japanese partner to build a similar franchise in Japan and Asia Pacific. Wisely, Starbucks's management declined in order to take their Valuable Formula down the West Coast, then across

Page 407

North America. They recognized trying to do an Asian expansion simultaneously would strain the resources of the leadership team, compromising long-term value creation. It was a wise decision. Starbucks's success in North America is legendary, and in 1998, with greater scale and enhanced depth and maturity of the leadership team, they have revisited their global expansion.

Purposely slowing down may seem counterintuitive, but it saved the fault tolerant computer company, Sequent. In the period 199496 Sequent was incredibly successful at competing for and winning contracts for their systems. However, they found themselves struggling to meet delivery and "go-live" dates. Rather than taking the risk of degrading their admirable image, they took nearly nine months to slow down and build lacking infrastructure. Then they returned to their high growth ways to maintain their status as industry leader.

Of course striking the optimal growth rate balance requires intuition, a feel for the market, and a deep understanding of your company's strengths and weaknesses. But here are some implementation guidelines:

Company/SBU Stage

Revenue Growth/Employee Growth

Create stage

2.22.5

Early Exploit stage

1.31.5

Late Exploit stage

1.71.8

We use this ratio, growth of revenues to growth of employees, as a guide. Early on (Create stage) the business model allows for substantial improvement of productivity. Employees are high on the learning curve. Thus, growing revenues at more than double the employee rate signals a rapid gain of understanding. As the model matures, productivity gains level off. In the second stage, revenues grow only slightly faster than employees, representing minor gains in a well-defined business model. Finally, the late Exploit stage allows for the advantages of scale. The scale effect causes productivity to rise once more, revenues growing about 70 percent faster than the employee count.

Because we find graphical displays especially helpful to our clients, generally capturing a great deal of varied data and generating a dramatic visual conclusion, we have developed Figure 124 as the overarching implementation matrix. It is designed to be an effective matrix for monitoring strategy execution and business unit performance, with the goal of maximizing value creation.

The display is grounded in two premises. The first premise is that a high-performing enterprise must deliver both growth and productivity. Without a growth focus, as Figures 121 and 122 demonstrate, inferior value creation results. However, adding ever increasing levels of resources in the pursuit of growth will not create value. One of the great lessons of

Page 408

Exhibit 124.
Performance Matrix: Value-Creating Growth.

the downsizing era of the 1980s through the mid-1990s is the need to utilize all resources productively. Thus any useful implementation monitoring methodology must encompass both factors. These two elements then become the columns in the matrix.

The second premise is the role of targets. All businesses set goals or targets, which if achieved, represent the desired high-performance level. But, by their nature, goals are lagging indicators. A business must also set in place leading indicators, milestones, and goals that will define progress toward the ultimate. These two factors become the rows in Figure 124, rounding out the types of metrics required to guide the implementation of the business or enterprise strategy.

Each cell of the matrix must be constructed effectively in order to serve as a helpful implementation guide. Cell #1 (productivity/goals) is the segment of the matrix most comfortable for most management teams. Thus, for example, in the goal cell management records a CFROI (cash flow return on investment) target it believes is achievable by the business and yields an appropriate level of value creation. While an overall target number satisfices for corporate reporting, it should be broken into its components to influence SBU and field management behavior. Thus, CFROI can be fanned out into those elements (what we term a waterfalldata

Page 409

cascading to more detail and to lower organizational levels) within control of successive levels of management, for example, an inventory turnover target for a manufacturing facility or a sales per person target for the regional sales organization.

While a valuable guide, nonetheless these indicators lag input. Thus, the next step is to convert cell #1 targets into the leading indicators of cell #2. In a simple sense any target that is meaningful for the relevant manager can be reset as a leading indicator by setting goals around rates of change. Thus, if inventory turnover needs improvement, a commitment to a regular improvement allows progress to be monitored. But other types of leading indicators work here as well. For example, a good indicator of improving productivity within a sales force is the level of unplanned turnover. Experienced professionals build strong relationships with key customers, driving high customer retention rates, thus improving profitability.

The growth side of this matrix, cells #3 and #4, represent less familiar territory for most management teams. For some time now (the unsavory legacy of the 1980s to the mid-1990s drive for productivity) most established companies have optimized management processes around tight control of resources. Growth is a new goal, and one with which too many teams struggle. Cell #3 then becomes a breakthrough. It serves to lift the sights of management to a longer and different horizon. Simply setting, and committing to, a specific growth target sets the team on a very different trajectory.

By reference to the evidence of Figures 121 and 122 above, the overall corporate goal for cell #3 must be a revenue growth rate of 1015 percent per year or higher. Lower levels assign the enterprise to a mediocre level of value creation. The next task requires allocating to each SBU a target that, in total, aggregates to the corporate target. Of course, consistent with Figure 123, some should have high growth targets, while others should shrink.

Cell #4 translates these goals (lagging indicators) into their leading indicator counterparts. For growth also there are a rich set of metrics available. For example, customer retention presages higher sales levels. Monitoring and setting targets for higher customer loyalty rates (or the inverse, lower customer defections) will precede higher rates of growth.

Once the four cells are rounded out they become the implementation-monitoring matrix. This is analogous to the Balanced Scorecard.⁴ In fact we recommend that the various elements of this display be coded to capture what behavior they intend to drive. Thus the elements should be identified according to whether or not they will impact growth or productivity, and are goal-oriented (lagging) metrics or are the leading indicator counterparts.

⁴ A Balanced Scorecard provides management with ways to track and evaluate implementation of business strategy.

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A client of ours, a global services company, uses these two figures to focus debate during the strategy development process, then to focus attention during the implementation stages. They prepare a version of Figure 123 that is historical. It plots for the SBUs how they have performed over the planning cycle, in this case, three years. This retrospective look (which is updated on a regular basis to monitor progress) portrays a stark picture of those SBUs that have gathered resources, but have not produced a positive CFROI. The CEO refers to the portrayal as "good constructive criticism" since it is fact-based and objective. The second iteration is a forward-looking projection. Now, the debate becomes more speculative. At issue is how the negative patterns of the past can be or will be reversed, or the positive momentum sustained. From the information on the figures come a discussion of customers, competitors, shifts in technology, and other factors central to the health of the businesses and the total enterprise. The conclusions are a reallocating of the available growth investment, and a re-plotting of the path of progress over the ensuing three years. This will allow the company to project a rough forecast of the expected value creation these investments, and this momentum should yield.

Armed with this broad strategy, the CEO then turns the attention of the SBU leaders to the development of Figure 124. The goal levels for cells #1 and #3 are drawn from the results of the Figure 123 debate. The first task, then, is to translate total corporate productivity and growth goals into SBU specific targets; then, of course to build the leading indicators into the program. Leading indicators are critical since no leadership team can hold its breath, wait three years, and ask did we make it? Once defined this CEO monitors the leading indicators on a quarterly basis formally, and informally whenever a key element changes. The metrics vary by type of business, especially by growth cycle stage. Thus, a very early Create stage business has many of its metrics designed to measure input. Before results become apparent, the challenge is to gauge whether the resources are being invested at the programmed rate. At the midpoint of an Exploit stage business, the more classic measures of rates of change can be utilized. Importantly, the CEO leads the quarterly meetings. She believes she has much to contribute, but her leadership also signals the importance of these implementation metrics. Incidentally, since growth via new products is a key to sustaining high growth, she is also the company's "chief growth officer," that is, she chairs the innovation task force as well.

A Vision:
The Desired State

An intense desire for high performance lies at the heart of the enterprise. Since we can demonstrate that growth drives such high performance, and yields such high levels of value creation, then it must become the under-

Page 411

lying principle for the management processes of the goal-driven company. To reap the rewards, growth promises management must lead with:

· An unyielding commitment to growth as the superior route to value creation

· Well-designed and executed Valuable Formulas, the strategic platforms for long-term growth

· The capability to sustain growth beyond the success of a hot product or the energy created by an especially charismatic leadership team

To embed these three elements of a growth system deep into and throughout the entire organization requires a set of implementation tools and frameworks such as described in this chapter and throughout the course of this book. Armed with them, and following their direction, the enterprise can reach and sustain the high level of value creation it deserves.

Page 413

Index

Page numbers of tables, exhibits, etc. are in italics

A

Abandonment options, 6065, 63, 64

Accounting, 313

cash flow, 117118

Accounts payable, 122

Accounts receivable, 121

Accounts receivable risk, 10

Accruals and taxes payable, 122

Ace Textile Production Corp

background, 34748

balance sheet value drivers, 354371, 355, 358367, 368, 369, 371

forecast assumptions, 352353

income statement value drivers, 351, 354, 355

net operating profit less adjusted taxes (NOPLAT), 371, 372373

operating segments and everage, 348

optimization runs, 371375, 374, 375, 376, 377

threshold margin, 375, 377, 378379, 380, 381, 382, 383386

valuation summary, 34951, 350

Acquisitions, 31

Adaptable models, 208

Adaptive system schematic diagram, 213, 214

ADS (neural network consulting firm), 11

Advanced cash flow, 117

Advanced visualization, 9

Advertising, 220

Aircraft, 62

The Alcar Group Inc., Appendix 3 to chapter 11, 387, 388396

Alcar software, 11, 87

Alcatel (telephone company), 174

Altman's Z score, 155, 156, 157

Amazon.com, 316

American options, 32, 55, 59, 60

Amortization, 128, 318

of bond premiums, 127

Amortization rates, 313

Analysis of cash flow, 123127

Analytica, visual financial models, 88, 90115

Anomalies, 9

Antimatter, 21

Appraisers, valuation, 347

Arbitrage Pricing Theory, 272

ARMA (autoregressive and moving average) models, 170

Artificial intelligence, 2, 9

Asset appraisals, 316

Asset divestitures, 121

Assets/sales ratio, 133134

Astronomy, 21

At the money options, 32

Auction, not-so-orderly liquidation based on, 316

Audit guidelines (Federal Reserve), 287289

collateral, 297300, 299

transfer (country risk), 292297, 293, 295

Austrim, 403

Autocorrelation, 324

Axon, 11

B

Back-propagation, neural networks, 209, 210

Backlogs, 126

Balance sheet value drivers, Ace Textile, 354371, 355, 358367, 368, 369, 371

Balanced Scorecard, 409

Bankers Trust, Risk Management Advisory (RMA) group, 175

Bar charts, 323

Barns and Mobile Publishing Corp. example, Black-Scholes model, 3339, 38, 39

Bayesian probabilities, 208

Beef cattle industry, 22

Begin or forgo investment options, real options, 67

Bell-shaped curves, 21 steep, 25

Benchmarking, 94, 127, 158

Berra, Yogi, 139

Best case, 322

BFGS quasi-Newton method, 265

BICs. See Business Information Centers (BICs), Small Business Administration (SBA)

Bifurcation diagram, 7

Binomial distribution, 202

Binomial model, real options, 5860

Black Holes and Baby Universes (Hawking), 6

Black-Scholes model, 31, 3340, 41

Barns and Mobile Publishing Corp. example, 3339, 38, 39

BMW Bank GmbH of Germany, 12, 13

BMW dealers, 12

Bond premiums, 127

Bond Rater software, 11

Bond rating compared to credit grade, 276

Bond ratings, 11, 20, 219

Book values, 313

Bouygues (telephone company), 174

Box-Jenkins methods, 140, 141, 152154, 170

Buffet, Warren, 117

Business cycles, 23, 24

Business failures, 20

Business Information Centers (BICs), Small Business Administration (SBA), 345

Business Plan Road Map to Success, Small Business Administration (SBA), 344

Business plans, 344

Business and professional magazines, 345

Business risk. See Risk analysis

Butterfly effect, 7, 8, 21, 22

C

Calculations of options values, Appendix A, 4149

Calculus, chain rule of, 210

Calls, options, 3132, 31, 37, 55

Capital Asset Pricing Model (CAPM), 5, 27273, 316, 347, 368, 371

Capital budgeting schedule, 125

Capital cost, 321, 322, 338, 403

Capital expenditures, 55, 56

Capital intensity, 20

Capital investments, 55

Capital markets, 4

Capital-intensive projects, 62

Capital/output ratio (assets/sales), 133134

Capitalization of costs, 313

Carroll, Thomas, ''Using Your Computer to Create a Winning Business Plan," 344

Case studies

Dix Guage Corporation, 6879

High Risk Inc., 131137, 131, 137

Hope Street Apartments, 190197, 190197

International Drug corporation (IDC) "Digoxin Drug Project," 181189, 183187, 189

Oil Field Development, OptQuest, 25864

Cash, 128

Cash conversion cycle, 124

Cash cow, 22

Cash flow, 117138, 312

accounting, 117118

advanced, 117

analysis, 123128

divisional, 117

EBITDA and noncash charges, 318, 320

from operations, 318

gross operating cash flow (GOCF), 119, 123124

IAS 7, 118

in-depth cash flow, 118119

return on investment (CFROI), 408, 410

and shareholder value, 118, 127

statement, 119123, 120

and sustainable growth problems, 129137

Cash tax rate, 322, 337

Cash traps, 316

Casinos, 177

Causal models, 140, 141, 211

CB Predictor software, 144146, 145, 146, 210, 324, 325

Center for Technology and Small Business Development, Central Missouri State University, "Someplace Fitness Center, March 1995," 344

Central Missouri State University, Center for Technology and Small Business Development, 344

CEO. See Chief executive officer

CFROI. See Cash flow, return on investment

Chain rule of calculus, 210

Chaos theory, 2, 3, 48

day-to-day business events, 21

definition, 4

grand design, 8

harmonic structure, 5, 8

initial departure point, 5

Document

Page 414

and portfolio risk management, 21

sensitive dependence of initial conditions, 78

Chi-square test, 170

Chief executive officer (CEO), 410

Choice variables, 235

CIC. See Consumer Information Center

Cisco Systems, 403

Citigroup, 403

Classification power, 217

Climate Survey, Corning, 403

Coefficient of determination, 169

Collateral, 274

Federal Reserve audit guidelines, 297300, 299

Collection periods, 124

Compensation, executive, 312

Competition, 20

Competitive positioning, 94, 311, 319, 338

Comptroller of the Currency, 275

Computer optimization models, 23956 See also Linear programming

Computers, office, 85

Consolidated equity value, 117

Constrained optimization, 234

Constraints, linear programming, 236

Constructive criticism, 410

Consultants

financial, 94

in neural networks, 1112

valuation, 347

Consumer Information Center (CIC), 345

Consumer Product Safety Commission (CPSC), 345

Consumer value, 312

Contingent claim contracts, 31

Continuing education, 346

Contractual options, real options, 66

Copeland, Koller, and Murrin, Valuation: Measuring and Managing the Value of Companies, 347

Copeland, Tom, 307

Corning, Climate Survey, 403

Corporate bonds, 219 See also Bond ratings

Corporate buyout, 86

Corporate finance, 4

Corporate restructuring, 94

Corporate risk analysis, 273303

risk ratings, 11

risk system, 274

risk-rating interactive model, 274275

Corporate valuation analysis, 85

CorpRiskModel2, 275277

Correlation, 21

of Antimatter Beef Company with Matter Poultry Corp., 2729, 27, 29

definition, 26

and portfolio theory, 40

Correlation coefficients, 168

Cost approach, 316

Cost of capital, 321, 322, 338, 403

Country risk (transfer), Federal Reserve audit guidelines, 292297, 293, 295

Covariance, 2629, 26, 27, 29

Covariance (systematic) risk, 20

Cox-Rubinstein binomial model, 5860, 59

CPSC. See Consumer Product Safety Commission

Credit bureaus, 12

Credit card holder risk classification, 12

Credit card industry, 26, 220221

Credit grade compared to bond rating, 276

Credit grades, poor, 275, 277

Credit ratings, 11

Credit risk model, 274

Cross-company data, 399

Cross-geography data, 399

Crosswhite, Carl, 144

Crystal Ball software, 26, 77, 144, 174, 323, 326, 347

OptQuest, 234, 25758, 333

Piece of Cake Company, 175180, 176179

Customer retention, 404, 409

Cyclical businesses, 26

D

Daily share prices and reactive interdependence, 8

Daiwa Computer Services Co., Ltd., 219

Daiwa Securities, 219

Data mining, 2, 8, 910, 312

Databases, 9

DCF. See Discounted cash flow

Debt, 126127

long-term, 126

Debt financing, 274

Debt structures, 86

Debt/equity ratio, 132133, 338

Decision making, and options, 30

Decision trees, 213, 216217, 216

Decision variables, linear programming, 23435

Decisioneering software, 87, 347

CB Predictor, 144146, 145, 146, 324

OptQuest, 234, 25758, 25864, 332

Default, and options, 31

Default probabilities, 275

Default (unsystematic) risk, 20

Deferred taxes, 125

Dell Computer, 403

Deloitte and Touche, HR (Human Resource) standards, 403

Delta in options, 45

Dependent variables, 9

Depreciation, 124, 128, 313, 318, 337

Derivative assets, 31

Deterministic linear programming, 236, 239, 239 See also Linear programming

Digital signal processing (DSP), 222

"Digoxin Drug Project" case study, International Drug corporation (IDC), 181189, 183186, 189

Dirty data, 9

Discounted cash flow (DCF) approach (going concern), 317318

"Discover what to put in a business plan," Howard University Small Business Development Center, 344

Distribution terms glossary, 197204

Distributions

normal, 24

See also Probability distributions

Diversification, 5, 20, 21

definition, 22

portfolio management, 272

Dividend based valuation, 316317

Dividend payout, 134

Dividend valuation method, 316

Dividends, 124, 127

Divisional accounting checklist, 127128

Divisional betas, 347

Divisional cash flow, 117

Divisional (dynamic business unit) analysis, 308

Divisional or operating segment risk rating, 305308

Dix Guage Corporation case study, 6879

Doorley, Thomas L., III and John Donovan, Value-Creating Growth: How to Lift Your Company to the Next Level of Performance, 399

Double exponential smoothing, 166167

Double moving average, 166

Downside protection, 66

Downsizing, 408

DSP See Digital signal processing

Durbin-Watson tests, 324

and homoscedasacity, 170

Dynamic business unit (divisional) analysis, 308

Dynamic systems, 4

E

E formula, 160

E-commerce start-up, on-line demonstration, 112113, 112

Earning before tax (EBT), 337

Earnings, 312, 315

Earnings before interest, taxes, depreciation, and amortization (EBITDA), 318

Earnings trends, 123

Earthquakes, 271

EBITDA. See Earnings before interest, taxes, depreciation, and amortization

EBT. See Earning before tax

Econometric forecasting, 159

Econometric models, 140, 141

Economic cycle risk/hedge strategies, 22

Economic function, 20

Economic value added (EVA), 405

Economics, 4

EDA. See Exploratory data analysis

EDF See Expected default probabilities

Einstein, Albert, 21, 39

Elasticity, 57, 58, 312

Electronic transfers, 92

Employee satisfaction, 403404

Employee Satisfaction Survey, Hewlett-Packard, 403

Energy prices, 20

Enron, 403

Environmental factors, 20, 311

Environmental Protection Agency (EPA), 346

Environmental protection laws, 62

EPA. See Environmental Protection Agency

Equity, 127

Equity value, 86, 316

Euliano, Neil R., 213

European options, 3233, 59

Ex ante returns, 23, 24

Excel, 38, 41, 80, 94, 95, 129

neural networks, 223228, 223226

Solver, 175, 347

spreadsheets, 223, 326, 347

statistical forecasting, 141143, 142, 143

Executive compensation, 312

Expanding operations option, real options, 6566

Expected cash flows, real options, 61

Expected default probabilities (EDF), 274, 275

Expiration date, options, 32

Exploratory data analysis (EDA), 168

Exponential and logarithmic curve fit, 148151

Exponential smoothing, 140, 141

Exponential smoothing averages, 148, 150

Exponential smoothing methods, 167

External environment, 311

Extracting patterns, 2

Extreme value distribution, 200201

F

F formula, 160

F ratio, 337

F statistic, 169

Facility risk rating, 300303, 301303

Facility risks, 274

Fair market value, 313

FASB 95 cash flow statements, 55

Fast Fourier Transform (FFT), 222

FDA. See Food and Drug Administration

Federal Deposit Insurance Corporation, 275

Federal Reserve audit guidelines, 287289

collateral, 297300, 299

transfer (country risk), 292297, 293, 295

Federal Reserve Board, 275

Feigenbaum's fractal, 7

FFT. See Fast Fourier Transform

FIFO-to-LIFO changes, 128, 314

Finalization, 2

Finance theory, 19

Financial analysis, versus option analysis, 31

Financial consultants, 94

Financial forecasting, simulations approach, 173180

Document

Page 415

Financial options. See Options; Real options

Financial policy variables, 121

Financial revolution, 2, 19

Financial symmetry, 3

Financing activities, debt, 126127

Firm's risk rating, 278287, 278280, 283285

Fixed-asset turnover, 126

Flexibility, real options, 57

Food and Drug Administration (FDA), 181, 346

Forecast assumptions, Ace Textile, 352353

Forecast horizon, 317, 319, 31920

Forecasting future events, 9 See also Statistical forecasting

Forecasting terms glossary, 166170

Fortune 500, 387

Forward-looking projection, 410

Fractals, 4, 67, 8

Feigenbaum's, 7

See also Multifractals

France Telecom, 174175

Franchise licenses, 313

Free parameters, 208

Future event forecasting, 9

Futuris, 403

Fuzzy logic, 2, 7, 1213

and neural networks, 208

G

Gains and losses, 128

Games of chance, 177

Gamma, time lagged recurrent network, 228

Gamma distribution, 201

Gamma in options, 45, 45, 46

Gauss, Frederich, 198

Gauss-Newton method, 267

Gaussian distribution, 198199

Generalized regression neural networks (GRNN), 218

Generic Bakery example, optimization models, 23738, 239

Genesis, 2, 3

Genetic algorithms, and neural networks, 208, 209, 217221

Geometric distribution, 203

Geometric mean, 167

German BMW Bank GmbH, 12, 13

Global market economy, 400403, 401, 402

Global optimization, 256

Glossary of distribution terms, 197204

Glossary of forecasting terms, 166170

Goals, 408

GOCF. See Gross operating cash flow

Going concern, 317318

Goodwill, 128, 313

Gordon Dividend Growth Model, 316

Government Printing Office (GPO), "Subject Bibliography," 345

GPO. See Government Printing Office

Grand design, chaos theory, 8

GRNN. See Generalized regression neural networks

Gross margin, 126, 335

Gross operating cash flow (GOCF), 119, 123124

Growth, 129

implementation for, 406410, 408

long-term, 411

and performance, 399, 400403, 401, 402

and value drivers, 403

Sec also Sustainable growth problems

Growth cycle stages, 407, 410

H

Harmonic structure, chaos theory, 5

Hasbro, 175

Hawking, Stephen, Black Holes and Baby Universes, 6

Hax, Arnoldo C., 311

Hedging

in the Black-Scholes formula, 33, 41

negatively correlated risks, 22

and options, 31

Heteroskedastic, 215

Hewlett-Packard, Employee Satisfaction Survey, 403

Hierarchies of models, 93, 115

High Risk Inc., case studies, 131137, 131, 137

Ho, Andrew, 4

Homoscedasticity, 157

Hope Street Apartments case study, 190197, 190197

Howard University Small Business Development Center, "Discover what to put in a business plan," 344

HR (Human Resource) standards, Deloitte and Touche, 403

Human brain, 1011, 12, 209

Hurricanes, 271

I

IAS 7, cash flow, 118

ICERC rating. See Interagency Country Exposure Review Committee (ICERC) rating

If-then patterns, 9, 10

Impact analysis, 174

Implied binomial trees, real options, 5860, 59

Imprudent exponential growth, 129

In the money options, 32

In-depth cash flow, 118119

Income statement, 128

Income statement value drivers, Ace Textile, 351, 354, 355

Incremental fixed capital investment, 322, 336337, 337

Incremental working capital investment, 322, 336

Independent variables, 9

Indifference curves, 23

Individual talents and capabilities, 311

Industry characteristics, 20

Industry and economic/environmental factors/country risk matrix, 289292, 290

Industry life cycles, 20, 130

Industry risk, 271

Inflation, 20, 337

Influence arcs, 98102

Influence diagrams, 89, 95105

Inform Software GmbH of Germany, 12, 13

Information influence, 98

Initial departure point, chaos theory, 5

Innovation, 404

Input-output technology, static versus dynamic, 58

Intangible assets, 128, 313, 316

Integer variables, 235

Intelligent Arrays, visual financial models, 93, 94, 115

Interactive corporate model, 274

Interagency Country Exposure Review Committee (ECERC) rating, 291

Interest, 318

Interest rates, 20

real options, 61

Internal rate of return, 5657

Internal resources, 311

Internal Revenue Service (IRS), 346

International Drug corporation (IDC), "Digoxin Drug Project" case study, 181189, 183187, 189

Internet, 85

on-line demonstration: e-commerce start-up, 112113, 112

Intrinsic valuations, 312

Intrinsic value options, 32

Inventory, 122, 124

work-in-process, 126

Inventory salability, 128

Investment activities, 119, 125126

Investment analysis, 4

Investment bankers, 31

Investment cost, real options, 61

Investment project cash flows and joint ventures, 121, 126

Investor returns, 399400

IRS. See Internal Revenue Service

Issue equity, 133

J

JIT inventory. See Just-in-time (JIT) inventory

Job creation, 399400

Joint ventures, 121, 126

Just-in-time (JIT) inventory, 134

K

K-means clustering, 218

Knowledge engineers, 208

Kohonen self-organizing feature maps (SOFMs), 222

L

Labeling requirements, 346

Lagging indicators, 408, 409

Lansing Community College Small Business Development Center, 344

Late payments, 124

Leadership team, 411

Leading indicators, 408, 409, 410

Leaguer, time lagged recurrent network, 228

Learning options, real options, 6667

Lease financing, 10

Leases, 62

Levenberg-Marquardt method, 267

Liabilities and equity, 128

Liao, Shu S., 156

Libraries, 346

LIFO-to-FIFO changes, 128, 314

Linear association, 26, 140

Linear models, 7, 85, 86, 209

Linear objective functions, 236

Linear programming, 175, 233270

constraints, 236

decision variables, 23435

deterministic linear programming, 236, 239, 239

objective function, 23636

optimization, 23334

optimization models, 23656

See also Optimization theory

Liquidation valuation approach, 316

Liquidity of financing instrument, 271

Local optimization, 256

Log file options, 257

Logical variables, 235

Logistic regression, 213

Lognormal distribution, 199

Long-term debt, 126127, 336

Long-term growth, 411

Long-term planning, 2, 311

Long-term trends, stock market, 6

Lorenz, Edward, 7, 8

Lotus 1-2-3, 94

Lumina Decision Systems, visual financial models, 88, 93, 96

M

M&A activities, 31

McKinsey & Company, 307

Macroeconomic conditions, 5, 20, 21, 271

Magazines, business and professional, 345

Maintenance requirements, 62

Management, 208, 311, 313

and vision, 410411

Management tools, 3

Mandelbrot, Benoit, 4

Mandelbrot set, 4, 4

Market options, 58

Market signals analysis, 321

Market trends, 21

Market values, 313

Marketable securities, 336

Marketing, 20

target, 220221

Markowitz's efficient frontier, 23

Mathematica software, 87

Mathematical formulas, 10

MATLAB software, 36, 46, 87, 234

Optimization Toolbox, 26567, 266

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Page 416

Mean

calculations for Antimatter Beef Company, 2426, 24

calculations for Matter Poultry Corp., 26, 26

Mean Absolute deviation (MAD), 324

Mean absolute percentage error (MAPE), 325

Mean and variants of each variable, 167168

Measurement units, 91

Median, 167168

Mergers, 31

Meritocracy, 404

Method Gallery, 324

Method of least squares, 140

Microeconomic factors, 20

Milestones, 408

Minimum variance set, 23, 23

Mining, 62

MIT, Sloan School of Management, 311

MLP network. See Multilayer perceptron (MLP) network

Mode, 167

Models, 322323 See also Visual financial models

Modified percentage of sales (sensitivities approach), statistical forecasting, 160166, 161164, 166

Module node. See Nodes

Monte Carlo simulations, 24, 69, 70, 77, 173206

glossary of distribution terms, 197204

Hope Street Apartments case study, 190197, 190197

International Drug corporation (IDC) "Digoxin Drug Project" case study, 181189, 183187, 189

Moodys, 273, 275

Mort Glantz Associates Valuation Appraisal Outline, Appendix 1 to chapter 11, 339374

Moses, Douglas, 156

Most likely case, 322

Moving averages, 140, 141, 167

Multiattribute decision analysis, 88

Multicollinearity, 158, 159, 174

Multidimensional visualization, 10

Multifractals, 19 See also Fractals

Multilayer perceptron (MLP) network, 209210, 209, 214, 215, 216, 220, 227

Multiple regression, 325, 326

Multivalued logic, 12

N

NASA, 90, 313

NEC Corporation, 219

Negative binomial distribution, 202

Negatively correlated risks, hedging, 22

Nelder-Mead simplex search method, 265

Net cash provided by operating activities, 125

Net fixed assets, 125

Net income, 124

Net operating cash flow, 123

Net operating profit less adjusted taxes (NOPLAT), Ace Textile, 371, 372373

Net present value, 56, 57

Net-present-value (NPV) method, 6365, 320321, 337

Neural architectures, 218219

Neural networks, 2, 7, 1012, 207232, 257, 312

back-propagation, 209, 210

background, 207210

developing within Excel, 223228, 223226

and genetic algorithms, 217221

neural architectures, 218219

real-world financial applications, 219221, 220

multilayer perceptron (MLP) network, 209210, 209, 214, 215, 216, 220, 227

Multiple regression, 325, 326

Multivalued logic, 12

N

NASA, 90, 313

NEC Corporation, 219

Negative binomial distribution, 202

Negatively correlated risks, hedging, 22

Nelder-Mead simplex search method, 265

Net cash provided by operating activities, 125

Net fixed assets, 125

Net income, 124

Net operating cash flow, 123

Net operating profit less adjusted taxes (NOPLAT), Ace Textile, 371, 372373

Net present value, 56, 57

Net-present-value (NPV) method, 6365, 320321, 337

Neural architectures, 218219

Neural networks, 2, 7, 1012, 207232, 257, 312

back-propagation, 209210

background, 207210

developing within Excel, 223228, 223226

and genetic algorithms, 217221

neural architectures, 218219

real-world financial applications, 219221, 220

multilayer perceptron (MLP) network, 209210, 209, 214, 215, 216, 220, 227

principal component analysis (PCA), 220, 222

radial basis function (RBF) networks, 218, 220

S&P 500, 223226, 227228

self-organizing feature maps (SOFMs), 220, 222

self-organizing maps (SOMs), 10, 210, 218219, 220

and statistics, 213217, 214, 216

the T-C problem, 210213, 212, 213

time lagged recurrent networks, 228

NeuroDimension, Inc., 213, 217, 223, 227

NeuroSolutions, 223, 228

New Jersey Refining Inc. example, optimization models, 24756, 24855

Nikkei index options, 32

Nodes, 9798, 209

Nonlinear financial models, 79, 85

Nonlinear objective functions, 236

Nonlinear systems, 6, 209

Normal distribution, 24, 198199

Not-so-orderly liquidation based on auction, 316

NPV method. See Net-present-value (NPV) method

Numa Financial Systems, 46

Numeric computation and visualization, optimization models, 26567, 266

Numeric Computation and Visualization Software, 46

O

Objective function, linear programming, 23636

Obligor, 274, 275

OCR. See Optical character recognition

Office computers, 85

Office of Thrift Supervision, 275

Oil Field Development OptQuest case study, 25864

On-line demonstration, e-commerce start-up, 112113, 112

Operating cash sources, 122, 124

Operating cash uses, 121122, 124

Operating leverage, 336

Operating leverage risk, 66

Operating profit, 320

Operating profit margin, 322, 335336

Operating scale options, real options, 65

Operating segments and leverage, Ace Textile, 348

Optical character recognition (OCR), 210, 211

Optimal portfolio, 23

Optimization

and shareholder value, 233

as value driver, 32735, 332, 333, 334335

Optimization models, 23656 See also Linear programming

Optimization runs, Ace Textile, 371375, 374, 375, 376, 377

Optimization theory, 19 See also Linear programming

Optimization Toolbox, MATLAB, 26567, 266

Option analysis, versus financial analysis, 31

Option grantor, 32

Option seller, 32

Option writer, 32

Option-pricing models, 37

Cox-Rubinstein binomial model, 5860, 59

Options, 3039, 312

Barns and Mobile Publishing Corp. example, 3339, 38, 39

Black-Scholes model, 31, 3340, 41

calculations of options values, 4149

calls, 3132, 31

and default, 31

definitions, 31, 45

differences between financial options and real options, 61

and hedging, 31

puts, 31, 31, 3233

uses and importance of, 3031

See also Real options

OptQuest

Crystal Ball, 234, 25758, 332, 333

Decisioneering, 332

Oil Field Development, 25864

Orderly liquidation value, 316

Out of the money options, 32

P

Packaging requirements, 346

Palisade, Risk Optimizer, 234

Pareto distribution, 202203

Partial truths, 12

Particle physics, 6

Patents, 313

Payables balances, 124

Payback period, 57

PCA. See Principal component analysis

Pearson's r, 28

Peer review, 88

Percentage variation explained, 170

Perfect Portfolio Ltd. example, optimization models, 24247, 24447, 272

Performance, 312313

and growth, 399, 400403, 401, 402

PEs. See Processing elements

Pharmaceutical research, 181189

Physics, 4

Piece of Cake Company, Crystal Ball software, 175 180, 176179

Pipelines, 62

Point estimates, 322

Poisson distribution, 203204

Poor credit grades, 275, 277

Porter, Michael E., 319

Portfolio management, 20, 2130, 338

Antimatter Beef Company, 2224

diversification, 272

Matter Poultry Corp., 22, 24, 2630

optimal portfolio, 23

and risk analysis, 271

stress-testing, 19

theory of, 23, 26, 36, 40, 272

Poultry industry, 22

PP&E. See Property, plant, equipment

Predictability of systems, 6

Price-to-earnings (P/E) ratio, 314315

Price-to-sales ratio, 315

Pricewaterhouse Coopers, 314

Principal component analysis (PCA), 220, 222

Private companies, 313, 314

"Pro forma" market, 314

Probability distributions, 19

for Antimatter Beef Company and Matter Poultry Corp., 2324, 24, 30, 30

Processing elements (PEs), 215, 216

Productivity, 312

Professional magazines, 346

Profit margins, 134

Profit pruning, 134135

Program Evaluation and Review Technique (PERT), U.S. Navy, 182

Project cash flows, 121, 126

Project financing, 121

Projection period, 317

Property, plant, equipment (PP&E), 119120, 128

Public companies, 313, 321

Pure play approach, systematic risk, 303305, 304

Puts, options, 31, 31, 3233, 37

Q

Quadratic equation, 23

Qualitative methods, statistical forecasting, 140, 141

Quantitative methods, 21, 89

statistical forecasting, 140, 141

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Page 417

Quarterly statements, 312

Quasi-American options, 32

R

R&D stages, 58

Radial basis function (RBF) networks, 218, 220

Random events, 2, 3

Random movement in the stock market, 5

Range estimates, 322

Rappaport, Alfred, 321, 375

RBF networks. See Radial basis function (RBF) networks

Reactivation, 62

Reactive interdependence of daily share prices, 8

Real options, 40, 5583, 126

abandonment options, 6065

begin or forgo investment options, 67

binomial model, 5860

contractual options, 66

definition, 5556

differences between financial options and real options, 61

Dix Guage Corporation case study, 6879

expanding operations option, 6566

flexibility, 57

implied binomial trees, 5860, 59

information required and not required, 60

learning options, 6667

operating scale options, 65

sequencing or compound options, 67

shutdown options, 65

switching options, 66

versus traditional methods, 5758

See also Options

Real variables, 235

Real-world financial applications, 219221, 220

Receivables, 128

Recessions, 20, 26

Recognizance, 2

Regression

logistic, 213

multiple, 154159, 213, 214, 214

simple, 140

using Decisioneering's CB Predictor, 144146, 145, 146

Regression curve fitting, 148151

Regression models, 140, 141, 209

Regulations, 20, 337

Regulatory agencies, 275

Replacement value, 316

Reserves, 124

Residual value, 317, 319, 32021

"Resource Directory for Small Business Management," Small Business Administration (SBA), 344345

Revenue changes, 326

Revenue growth, 399400

Rho in options, 45

Risk analysis, 271310, 349

corporate risk-rating interactive model, 273303

dynamic business unit (divisional) analysis, 308

segment analysis, 303308

specific risk, 271, 272

systematic risk, 271273

unsystematic risk, 271

See also Risk management

Risk factors, 312

Risk grading, 274

Risk management

assessment methods, 22

basic tools of, 1954

systematic (covariance) risk, 20

unsystematic (default) risk, 20

Risk Management Advisory (RMA) group, Bankers Trust, 175

Risk Optimizer, Palisade, 234

@Risk software, 174

Root mean squared error (RMSE), 324

See also Risk analysis

S

S&P 500, 223226, 227228, 273, 275, 401

Sales growth rate, 322, 323

Sales/net fixed assets ratio, 126

SBA. See Small Business Administration

SBDCs. See Small Business Development Centers (SBDCs), Small Business Administration (SBA)

SBUs. See Strategic business units

Scientific financial management, 338

definition, 34

overview of book, 1318

and value drivers, 322323

Scientific method, 323

Scientific research, 4

SCORE. See Service Corps of Retired Executives (SCORE), Small Business Administration (SBA)

SEC report, 315

Security market line (SML), 273

Segment analysis, risk analysis, 303308

Seidler, Lee, 117

Self-organizing feature maps (SOFMs), 220, 222

Self-organizing maps (SOMs), 10, 210, 218219, 220

Sensitive dependence of initial conditions, chaos theory, 78

Sensitivities approach (modified percentage of sales), statistical forecasting, 160166, 161164, 166

Sensitivity charts, 323

Sensitivity models, 173, 174, 236

Sequencing or compound options, real options, 67

Sequent, 407

Sequential quadratic programming method, 267

Service Corps of Retired Executives (SCORE), Small Business Administration (SBA), 345

SES. See Single exponential smoothing

Set variables, 235

Shareholder returns, 399400

Shareholder value, 3, 55, 80, 94

and cash flow, 118, 127

from valuation analytics to application in practice, 338

and optimization, 233

preparation, 318322

valuation methods, 311320

value drivers, 321338

Sharp, William, 272

Shelters from losses, 22

Short-term events, 2, 311

Shutdown options, real options, 65

SID. See Standard Industrial Code

Sigma. See Standard deviation

Significance level (reliability), 9

Significance test, 170

Simple moving averages, 146148, 147, 148

Simple regression, 140

Simulation, 2, 9, 24

of Antimatter Beef and Matter Poultry, 24, 25, 2930, 29, 30

and value drivers, 326, 331, 332

Simulation software, 38, 158

Sine qua non arrays, 7

Single events, 2

Single exponential smoothing (SES), 167

Sloan School of Management, MIT, 311

Small Business Administration (SBA), 344346

Business Information Centers (BICs), 345

Business Plan Road Map to Success, 344

"Resource Directory for Small Business Management," 344345

Service Corps of Retired Executives (SCORE), 345

Small Business Development Centers (SBDCs), 345

Small Business Development Centers (SBDCs), Small Business Administration (SBA), 345

SML. See Security market line

Software, 85

Alcar, 11, 87

Bond Rater, 11

CB Predictor, 144146, 145, 146, 210, 325

Decisioneering, 87, 25758, 347

fixed financial programs, 9

Inform Software GmbH of Germany, 12, 13

Lotus 12-3, 94

Mathematica, 87

MATLAB, 36, 46, 87, 234, 26567, 266

for neural networks, 210, 219

Numeric Computation and Visualization Software, 46

optimization packages, 233, 234, 240242

OptQuest, 234, 25758, 25864, 332, 333

@Risk, 174

Risk Optimizer, 234

simulation, 38, 158

Solver, 175, 329

stochastic optimization, 9

Value Planner, 11

for visual financial models, 88, 93

WizWhy, 10

See also Crystal Ball software; Excel software

Solver, Excel, 175, 329, 347

"Someplace Fitness Center, March 1995," Center for Technology and Small Business Development, Central Missouri State University, 344

SOMs. See Self-organizing maps

Space program, 90

Specific risk, 271, 272

Speculators, 31

Spreadsheets, 85, 86, 9293

and Analytica, 115

and documentation, 94

Excel, 223

and neural networks, 208

traditional, 322

and visual models, 9495, 95, 322

Square root of the variance, 24

Standard deviation of each variable, 168

Standard deviation (sigma), 21, 23

calculations for Antimatter Beef Company, 2426, 24

calculations for Matter Poultry Corp., 26, 26

Standard error, 169

Standard error of the mean, 26

Standard Industrial Code (SIC), 287, 314

Starbucks, 406407

Statistical forecasting, 139172

Box-Jenkins, 152154

casual models, 140, 141

econometric forecasting, 159

Excel example, 141143, 142, 143

exponential and logarithmic curve fit, 148151

exponential smoothing averages, 148, 150

glossary of forecasting terms, 166170

modified percentage of sales (sensitivities approach), 160166, 161164, 166

multiple regression, 154159

qualitative methods, 140, 141

quantitative methods, 140, 141

regression curve fitting, 148151

regression using Decisioneering's CB Predictor, 144146, 145, 146

simple moving averages, 146148, 147, 148

time-series analysis, 140, 141

time-series or trend forecasting, 140143

trend lines and curve fit correlations in Excel, 151152, 151, 152, 153, 154

See also Forecasting future events

Statistics, 39

and neural networks, 213217, 214, 216

Stochastic optimization models, 25657

Stochastic optimization software, 9

Stock analysts, 8