Quantitative Business Valuation E-Book

Jay B. Abrams

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1067

Veröffentlichungsjahr: 2010

Beschreibung

Quantitative Business Valuation A Mathematical Approach for Today's Professionals Essential reading for the serious business appraiser, Quantitative Business Valuation, Second Edition is the definitive guide to quantitative measurements in the valuation process. No other book written on business valuation is as well researched, innovative, and bottom-line beneficial to you as a practitioner. Written by leading valuation and litigation economist Jay B. Abrams, this text is a rigorous and eye-opening treatment filled with applications for a wide variety of scenarios in the valuation of your privately held business. Substantially revised for greater clarity and logical flow, the Second Edition includes new coverage of: * Converting forecast net income to forecast cash flow * Damages in manufacturing firms * Regressing scaled y-variables as a way to control for heteroscedasticity * Mathematical derivation of the Price-to-Sales (PS) ratio * Monte Carlo Simulation (MCS) and Real Options (RO) Analysis * Venture capital and angel investor rates of return * Lost inventory and lost profits damage formulas in litigation Organized into seven sections, the first three parts of this book follow the chronological sequence of performing a discounted cash flow. The fourth part puts it all together, covering empirical testing of Abrams' valuation theory and measuring valuation uncertainty and error. Parts five to seven round it all out with discussion of litigation, valuing ESOPs and partnership buyouts, and probabilistic methods including valuing start-ups. The resulting work, solidly grounded in economic theory and including all necessary mathematics, integrates existing science into the valuation profession--and develops valuation formulas and models that you will find useful on a daily basis.

Leseprobe

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Library of Congress Cataloging-in-Publication Data:

Abrams, Jay B. Quantitative business valuation : a mathematical approach for today’s professionals / Jay B. Abrams. — 2nd ed. p. cm. Includes index. ISBN 978-0-470-39016-0 (cloth) 1. Business enterprises—Valuation—Mathematical models. I. Title. HF5681.V3A28 2010 657′.73—dc22 2009042697

To my father, Leonard Abrams, who taught me how to write. To my mother, Marilyn Abrams, who taught me mathematics. To my wife, Cindy, who believes in me. To my children, Yonatan, Binyamin, Miriam, Nechamah Leah, and Rivkah, who gave up countless Sundays with Abba (Dad) for this book.

To my great teachers, Mr. Ohshima and Christopher Hunt, who brought me to my power to make this happen. And finally, to R. K. Hiatt and Scott Deifik, who caught my mistakes and made significant contributions to the thought that permeates this book.

Introduction

Nature of the Book

This is an advanced book in the science and art of valuing privately held businesses. In order to read this book, you must already have read at least one introductory book such as Valuing a Business (Pratt, Reilly, and Schweihs, and subsequent). Without such a background, you will be lost.

I have written this book with the professional business appraiser as my primary intended audience, though I think this book is also appropriate for attorneys who are very experienced in valuation matters, investment bankers, venture capitalists, financial analysts, and MBA students.

Throughout this book, I generally write to you, the reader, as if you are sitting next to me and we are conversing. I am writing to you as my colleague with whom I share my thinking process. I prefer a conversational tone to a more formal one.

Uniqueness of This Book

This is a rigorous book, and it is not easy reading. However, the following unique attributes of this book make reading it worth the effort:

1. It emphasizes regression analysis of empirical data. Chapter 8, “Adjusting for Levels of Control and Marketability,”1 contains the first regression analysis of the data related to restricted stock discounts. Chapter 9 from the first edition was a sample fractional interest discount study containing a regression analysis of the Partnership Profiles database related to secondary limited partnership market trades. In both cases, we found very significant results. We now know much of what drives (a) restricted stock discounts and (b) discounts from net asset values of the publicly registered/privately traded limited partnerships. We moved the old Chapter 9 out of this book. It is our intention eventually to publish a workbook to accompany this book—probably when we produce the third edition. In the meantime, we intend to provide the old Chapter 9 on our website, www.abramsvaluation.com, under “Books,” “Quantitative Business Valuation.” You will also see much empirical work in Chapter 5, “Discount Rates as a Function of Log Size,” and Chapter 9, “Empirical Testing of Abrams’ Valuation Theory.”

2. It emphasizes quantitative skills. Chapter 3 focuses on using regression analysis in business valuation. Chapter 4, the official title of which is “Annuity Discount Factors and the Gordon Model” (and the unofficial title of which is “The Chapter that Would Not Die!”) is the most comprehensive treatment of ADFs in print. For anyone wishing to use the Mercer quantitative marketability discount model, Chapter 4 contains the ADF with constant growth not included in Mercer (1997).2 ADFs crop up in many valuation contexts. I invented several new ADFs that appear in Chapter 4 that are useful in many valuation contexts. Chapter 10 contains the first treatise on how much statistical uncertainty we have in our valuations and how value is affected when the appraiser makes various errors.

3. It emphasizes putting all the pieces of the puzzle together to present a comprehensive, unified approach to valuation that can be empirically tested and whose principles work for the valuation of billion-dollar firms and ma-and-pa firms alike. While this book contains more mathematics—a worm’s-eye view, if you will—than other valuation texts, we also refocus to the bird’s-eye view in this section.

Organization

There are seven parts to this book:

1. Forecasting Cash Flows (Chapters 1 through 4)

2. Calculating Discount Rates (Chapter 5 through 7)

3. Adjusting for Control and Marketability (i.e., valuation premiums and discounts) (Chapter 8)

4. Putting It All Together (Chapters 9 and 10)

5. Litigation (Chapters 11 and 12)

6. Valuing ESOPs and Buyouts of Partners and Shareholders (Chapters 13 through 15)

7. Probabilistic Valuation Methods (Chapters 16 through 18)

The first three parts of this book follow the chronological sequence of performing a discounted cash flow, although the regression analysis material in Chapter 3 applies to market methods as well.

The fourth part is empirically testing whether my methodology in the first three parts works (i.e., yields reasonable results). Additionally, we explore (1) confidence intervals around valuation estimates and (2) what happens to the valuation when appraisers make mistakes.

The reason for moving partnership and shareholder buyouts into Part VI, the ESOP section, is they share the common intellectual problem of post-transaction dilution. While the specific topic applications differ, the intellectual problem and process to solve it are similar.

The appraisal profession is still in the relatively early stages of using probabilistic valuation methods. However, it is a topic that is rapidly growing in importance. Hence we have added Chapters 17 and 18, Monte Carlo Simulation (MCS) and Real Options (RO) Analysis, to the book. Because valuing start-ups, which was Chapter 12 in the first edition, makes use of probabilistic valuation methods, it logically fits together with Chapters 17 and 18, which is why I moved it to Chapter 16 in the second edition.

I invited Dr. Johnathan Mun, author of Wiley books Modeling Risk and Real Options Analysis, in addition to many other books, to write Chapters 17 and 18. They are introductions to these two topics and to Dr. Mun’s software. We intend to cover practical examples of using MCS and RO in the workbook. Since that is likely to wait to accompany the third edition of this book, in the meantime look for it on our website somewhere between June 2010 to June 2011. I encourage readers who want to develop a deep understanding of each topic to buy Dr. Mun’s books and software, and watch for the workbook and updates on our website. It is simply impossible to cover these complex topics in one chapter each.

Differences in the Chapter Numbering

I added a new chapter as Chapter 2 in the second edition. That means that Chapters 2 through 7 in the first edition are now 3 through 8, respectively. I moved Chapters 8 and 9 from the first edition to our website—eventually to appear in the workbook. Thus, Chapters 10 and 11 from the first edition are now 9 and 10 in the second edition.

Part V, the “Litigation” section, which consists of Chapters 11 and 12 in the second edition, is entirely new. “Valuing Start-Ups” moved from Chapter 12 in the first edition to Chapter 16 in this edition, as it now fits in a new section of the book, “Probabilistic Valuation Methods.”

Chapter 13 has kept the same number in the second edition. Chapter 14 is new in the second edition. Chapter 14 in the first edition is now Chapter 15 in the second edition. Finally, Chapters 17 and 18 are new in the second edition.

The following two tables should help you reference between chapter numbers in the two editions. The first one is in chapter order number of the first edition, whereas the second one is in chapter order number of the second edition.

First EditionSecond Edition112334455667788—9—1091110121613131415

The missing chapters in the second edition sequence are new to the second edition: Chapters 2, 11, 12, 14, 17, and 18.

First EditionSecond Edition11NA22334455667788—9—1091110NA11NA121313NA1414151216NA17NA18

Similarities and Differences in the First and Second Editions

While the intellectual content of Chapter 1, “Cash Flow: A Mathematical Derivation,” is largely the same, I nevertheless made a substantial rewrite for better clarity and logical flow. In general, all chapters that were in the first edition have undergone intensive editing, even if there is no or little new material. Chapter 2, “Forecasting Cash Flow: Mathematics of the Payout Ratio,” is a new chapter that did not exist in the first edition. It should help the reader in converting forecast net income to forecast cash flow.

Chapter 3 (Chapter 2 in the first edition), “Using Regression Analysis,” is largely the same as in the first edition, with the important addition of regressing scaled y-variables (Price-to-Sales and Price-Earnings ratios) as a way to control for heteroscedasticity.

Chapter 4 (3 in the first edition), “Annuity Discount Factors and the Gordon Model,” is largely the same. However, there are two new sections added: (a) Mathematical Derivation of the PS Multiple;3 (b) The Bias in Annual (versus Monthly) Discounting Is Immaterial.

Chapter 5 (4 in the first edition) has the following new material: (a) Keeping in the Roaring Twenties and the Great Depression; (b) Ibbotson’s Opinion of Outliers and the Financial Crisis of 2008; (c) Is the Equity Premium Declining?; (d) Growth versus Value Stocks; and (e) The Wedge between Public and Private Firm Valuations [This section is extremely important, being a reconciliation between the Ibbotson total returns equation rd (dividend yield) + g (growth, i.e., capital gains) and the Gordon model.]; (f) Satisfying Revenue Ruling 59-60 is substantially different.

Chapters 6 and 7 (5 and 6, respectively, in the first edition), “Arithmetic versus Geometric Means” and “An Iterative Valuation Approach,” are largely the same.

Chapter 8 (7 in the first edition), “Adjusting for Levels of Control and Marketability,” is the largest chapter in the book and requires some explanation. Unlike other chapters, time pressure with the publishing schedule necessitated finishing the chapter before I would have preferred. This chapter could use another 3 to 6 months’ more research. Of course, by that time, it may well be large enough to become a book by itself. When I write the third edition of this book, it is likely either that Chapter 8 will become a book by itself, or that I will split it into two or more chapters.

Table 8.1A contains new data on the Mergerstat database. Chris Mercer extended the debate that we had in the first edition into a Business Valuation Review article, and I responded in kind. I have added my response to this chapter, which is covered in Tables 8.20, 8.21, 8.23, and 8.24. Table 8.22 shows summary statistics of Management Planning Inc.’s 2008 restricted stock study, and Tables 8.25 through 8.27 do the same with FMV Opinions’ 2008 restricted stock study.

In general, I cite and summarize new academic and professional articles and include those into our analysis. The analysis is more complex, the data conflict more, and conclusions are murkier in the second edition.

Chapters 9 and 10 (10 and 11 in the first edition), “Empirical Testing of Abrams’ Valuation Theory” and “Measuring Valuation Uncertainty and Error,” are largely the same. Chapters 11 and 12, “Demonstrating Expert Bias” and “Lost Inventory and Lost Profits Damage Formulas in Litigation,” are new to the second edition and comprise the litigation section.

The next three chapters comprise Part 6. Chapter 13, “ESOPs: Measuring and Apportioning Dilution,” is largely the same, while Chapter 14, “The Tradeoff in Selling to an ESOP versus an Outside Buyer,” is new. Chapter 15 (14 in the first edition), “Buyouts of Partners and Shareholders,” while covering the same topic, is completely different in the second edition. I use a different model for the effects of post-transaction dilution.

Chapter 16 (12 in the first edition), “Valuing Start-Ups,” has little change to the quantitative sections. However, there is some important new research on venture capital and angel investor rates of return. Chapters 17 and 18, “Monte Carlo Risk Simulation” and “Real Options,” are new.

How to Read This Book

Because this book is more difficult than most, I have done my best to try to provide more paths through it. Chapter 5 contains a shortcut version of the chapter at the end for those who want the bottom line without all the detail. In general, I have attempted to move most of the heaviest mathematics to appendices in order to leave the bodies of the chapters more readable. Where that was not optimal, I have given instructions on which material can be safely skipped.

How you read this book depends on your quantitative skills and how much time you have available. For the reader with strong quantitative skills and abundant time, the ideal path is to read the book in its exact order, as there is a logical sequence.

Because most professionals do not have abundant time, I want to suggest another path geared for the maximum benefit from the least investment in time. The heart of the book is “Discount Rates as a Function of Log Size” and “Adjusting for Levels of Control and Marketability,” Chapters 5 and 8, respectively. I recommend the time-pressed reader follow this order:

1. Chapter 4—the following sections: from the beginning through the section titled “A Brief Summary”; “Periodic Perpetuity Factors: Perpetuities for Periodic Cash Flows”; and “Relationship of the Gordon Model Multiple to the Price/Earnings and Price/Sales Ratios.”

2. Chapter 5 (the log size model for calculating discount rates)

3. Chapter 8 (“Adjusting for Levels of Control and Marketability”)

4. Chapter 9 (this empirically tests Chapters 5 and 9, the heart of the book)

After these chapters, you can read the remainder of the book in any order, though it is best to read each part of the book in order and, better yet, to read the entire book in order.

This book has well over 100 tables, many of them being two or three pages long. To facilitate your reading, you can go to my company’s Web site, www.abramsvaluation.com, click under “Publications” (on the left), then “Books,” then “Quantitative Business Valuation,” and then look for the file download for the QBV tables in PDF format. Then print out the tables and have them handy as you read the book. Otherwise, you will spend an inordinate amount of time flipping pages back and forth.

My Thanks to You

I thank you for investing your valuable time and money to understand my work. I sincerely hope you will greatly benefit from it.

References

Mercer, Z. Christopher. 1997. Quantifying Marketability Discounts: Developing and Supporting Marketability Discounts in the Appraisal of Closely Held Business Interests. Memphis, TN: Peabody.

Pratt, Shannon P., Robert F. Reilly, and Robert P. Schweihs. 1996. Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 3rd ed. New York: McGraw-Hill.

1 Chapter 7 in the first edition of the book.

2 It is possible that he included this in a later edition, but I have not verified that.

3 The first edition had a mathematical derivation of the Price-to-Earnings (PE) ratio. Now these two topics are combined in one section.

Acknowledgments

I gratefully acknowledge help beyond the call of duty from my parents, Leonard and Marilyn Abrams. Professionally, R. K. Hiatt was my internal editor for the first edition of this book, and Scott Deifik is for the second edition. Without their help, this book would have suffered greatly. They also contributed important insights throughout the book.

Robert Reilly edited the first edition manuscript cover-to-cover. I thank Robert very much for the huge time commitment for someone else’s book. Larry Kasper gave me a surprise detailed edit of the first eight chapters. I benefited much from his input and thank him profusely.

Chris Mercer also read much of the book and gave me many corrections and very useful feedback. I thank Chris very much for his valuable time, of which he gave me much.

Michael Bolotsky and Eric Nath were very helpful to me in editing my summary of their work.

I thank Hal Curtiss, Roy Meyers, and Ezra Angrist of Management Planning, Inc. for providing me with their restricted stock data. I also thank Kyle Vataha and Lance Hall of FMV Opinions, Inc. for providing me with theirs.

I also thank Bob Jones of Jones, retired from Roach & Caringella for providing me with private fractional interest sales of real estate.

Chaim Borevitz, our vice president, provided important help. Mark Shayne provided me with dozens of insightful comments. Professor William Megginson gave me considerable feedback on Chapter 8. I thank him for his wisdom, patience, and good humor. His colleague, Professor Lance Nail, also was very helpful to me.

I also appreciate the following people who gave me good feedback on individual chapters (or their predecessor articles): Don Wisehart, Betsy Cotter, Robert Wietzke, Abdul Walji, Jim Plummer, Mike Annin, Ed Murray, Greg Gilbert, Jared Kaplan, Esq., John Kober, Esq., Robert Gross, Raymond Miles, and Steven Stamp.

I thank the following people who provided me with useful information that appears in the book: John Watson, Jr., Esq., David Boatwright, Esq., Douglas Obenshain, and Gordon Gregory.

I thank the following people, who reviewed the first edition of this book: Shannon Pratt, Robert Reilly, Jay Fishman, Larry Kasper, Bob Grossman, Terry Isom, Herb Spiro, Don Shannon, Chris Mercer, Dave Bishop, Jim Rigby, and Kent Osborne.

Many people have helped make this book a reality. You all have my profound gratitude. In fact, there have been so many that it is almost impossible to remember every single person, and I apologize to anyone who should be in this acknowledgment section whom I forgot. Please forgive me.

Thanks go to John De Remegis at John Wiley & Sons for his commitment to this book, and my editor, Judy Howarth, for her pleasant helpfulness.

I thank Dr. Johnathan Mun for graciously providing Chapters 17 and 18 of this book. He is a great scholar in our profession.

Finally, I thank my wife, Cindy, for holding down the fort on endless Sundays while I was working on this book.

The majority of these acknowledgments apply to the first edition.

PART I

Forecasting Cash Flow

Introduction

Part I of this book focuses on forecasting cash flows, the initial step in the valuation process. In order to forecast cash flows, it is important to:

Precisely define the components of cash flow.Develop statistical tools to aid in forecasting cash flows.Analyze different types of annuities, which are structured series of cash flows.

Chapter 1: Cash Flow: A Mathematical Derivation

In Chapter , we mathematically derive the cash flow statement as the result of creating and manipulating a series of accounting equations and identities. This may provide the appraiser with a much greater depth of understanding of how cash flows derive from and relate to the balance sheet and income statement. It may help eliminate errors made by appraisers who perform discounted cash flow analysis using shortcut or even incorrect definitions of cash flow.

Chapter 2: Forecasting Cash Flow: Mathematics of the Payout Ratio

This chapter has extremely important practical use as a shortcut method of converting forecast net income to forecast cash flows based on a mathematical formula in the chapter. The formula measures the ratio of future capital expenditures to historical depreciation and then adds in the effect of sales growth on net working capital. It can save the valuation practitioner much time compared with the long method and alternatively can be a sanity check on the long method.

Chapter 3: Using Regression Analysis

In Chapter , we demonstrate in detail:

How appraisers can use regression analysis to forecast sales and expenses, the latter being by far the more important use of regression.When and why the common practice of not using more than five years of historical data to prevent using stale data may be wrong.How to use regression analysis in the market approach valuation methods. While this is not related to forecasting sales and expenses, it fits in with our other discussions about using regression analysis.

When using publicly traded guideline companies of widely varying sizes, ordinary least squares (OLS) regression will usually fail, as statistical error is generally proportional to the market value (size) of the guideline company. However, there are simple transformations the appraiser can make to the data that will (1) enable him or her to minimize the negative impact of differences in size and (2) still preserve the very important benefit we derive from the variation in size of the publicly traded guideline companies, as we discuss in the chapter. The final result is valuations that are more reliable, realistic, and objective.

Most electronic spreadsheets provide a least squares regression that is adequate for most appraisal needs. I am familiar with the regression tools in both Microsoft Excel and Lotus 123. Excel does a better job of presentation and offers much more comprehensive statistical feedback. Lotus 123 has one significant advantage: It can provide multiple regression analysis for a virtually unlimited number of variables, while Excel is limited to 16 independent variables. However, Lotus has lost most of its market share and is no longer widely in use.

Chapter 4: Annuity Discount Factors and the Gordon Model

In Chapter , we discuss annuity discount factors (ADFs). Historically, ADFs have not been used much in business valuation. Thus, they have had relatively little importance. Their importance is growing, however, for several reasons. They can be used in:

Calculating the present value of annuities, including those with constant growth. This application has become far more important since the Mercer “quantitative marketability discount model” requires an ADF with growth.Valuing intellectual property, which typically has a finite life.Valuing periodic expenses such as moving expenses, losses from lawsuits, and so on.Calculating the present value of periodic capital expenditures with growth (e.g., What is the PV of keeping one airplane of a certain class in service perpetually?).Calculating loan payments.Calculating loan principal amortization.Calculating the present value of a loan. This is important in calculating the cash equivalency selling price of a business, as seller financing typically takes place at less-than-market rates.The present value of a loan is also important in ESOP valuations.

An important addition to Chapter in the second edition is developing a mathematical formula for the price-to-sales (PS) ratio. Combined with the formula we already developed for the PE ratio in the first edition, these two formulas provide important theoretical guidance as to which independent variables to consider in a market approach method, thereby reducing the probability of obtaining spurious results through data mining.

Among my colleagues in the office, I unofficially titled Chapter , “The Chapter that Would Not Die!!!” I edited and rewrote this chapter close to 40 times striving for perfection, the elusive and unattainable goal. It was quite a task to decide what belongs in the body of the chapter and what should be relegated to the appendix. My goal was to maximize readability by keeping the most practical formulas in the chapter and moving the least useful and most mathematical work to the appendix.