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Quali¬cations. Appendix: Tax Court™s Opinion for Discount for
Lack of Marketability. Introduction. The Court™s 10 Factors.
Application of the Court™s 10 Factors to the Valuation.


10. Empirical Testing of Abrams™ Valuation Theory
Introduction. Steps in the Valuation Process. Applying a Valuation
Model to the Steps. Table 10-1: Log Size for 1938“1986. Table 10-2:

Contents ix
Reconciliation to the IBA Database. Part 1: IBA P/CF Multiples.
Part 2: Log Size P/CF Multiples. Conclusion. Calculation of DLOM.
Table 10-4: Computation of the Delay-to-Sale Component“$25,000 Firm.
Table 10-5: Calculation of Transactions Costs. Table 10-6: Calculation of
DLOM. Table 10-6A“10-6F: Calculations of DLOM for Larger Firms.
Calculation of DLOM for Large Firms. Interpretation of the Error.

11. Measuring Valuation Uncertainty and Error
Introduction. Differences Between Uncertainty and Error. Sources of
Uncertainty and Error. Measuring Valuation Uncertainty. Table 11-1:
95% Con¬dence Intervals. Summary of Valuation Implications of
Statistical Uncertainty in the Discount Rate. Measuring the Effects of
Valuation Error. De¬ning Absolute and Relative Error. The Valuation
Model. Dollar Effects of Absolute Errors in Forecastng Year 1 Cash Flow.
Relative Effects of Absolute Errors in Forecasting Year 1 Cash Flow.
Absolute and Relative Effects of Relative Errors in Forecasting Year 1
Cash Flow. Absolute Errors in Forecasting Growth and the Discount
Rate. Table 11-5: Summary of Effects of Valuation Errors. Summary and


12. Valuing Startups
Issues Unique to Startups. Organization of the Chapter. First
Chicago Approach. Discounting Cash Flow Is Preferable to Net Income.
Capital Structure Changes. Venture Capital Rates of Return. Table 12-1:
Example of the First Chicago Approach. Advantages of the First Chicago
Approach. Discounts for Lack of Marketability and Control. Venture
Capital Valuation Approach. Venture Capital Rates of Return.
Summary of the VC Approach. Debt Restructuring Study. Backgound.
Key Events. Decision Trees and Spreadsheet Calculations. Table 12-3:
Statistical Calculation of FMV. Conclusion. Exponentially Declining
Sales Growth Model.

13. ESOPs: Measuring and Apportioning Dilution
Introduction. What Can Be Skipped. De¬nitions of Dilution. Dilution
to the ESOP (Type 1 Dilution). Dilution to the Selling Owner (Type 2
Dilution). De¬ning Terms. Table 13-1: Calculation of Lifetime ESOP
Costs. The Direct Approach. FMV Equations”All Dilution to the
ESOP (Type 1 Dilution; No Type 2 Dilution). Table 13-2, Sections 1 and
2: Post-transaction FMV with All Dilution to the ESOP. The Post-
transaction Value Is a Parabola. FMV Equations”All Dilution to the
Owner (Type 2 Dilution). Table 13-2, Section 3: FMV Calculations”All
Dilution to the Seller. Sharing the Dilution. Equation to Calculate Type 2
Dilution. Tables 13-3 and 13-3A: Adjusting Dilution to Desired Levels.
Table 13-3B: Summary of Dilution Tradeoffs. The Iterative Approach.
Iteration #1. Iteration #2. Iteration #3. Iteration #n. Summary.
Advantages of Results. Function of ESOP Loan. Common Sense Is
Required. To Whom Should the Dilution Belong? Appendix A:

Mathematical Appendix. Appendix B: Shorter Version of Chapter

14. Buyouts of Partners and Shareholders
Introduction. An Example of a Buyout. The Solution. Evaluating the

Glossary 475
Index 479

Contents xi
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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 1996). 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 appro-
priate for attorneys who are very experienced in valuation matters, in-
vestment bankers, venture capitalists, ¬nancial analysts, and MBA stu-

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 7,
adjusting for control and marketability, contains the ¬rst
regression analysis of the data related to restricted stock
discounts. Chapter 9, a sample fractional interest discount study,
contains a regression analysis of the Partnership Pro¬les
database related to secondary limited partnership market trades.
In both cases we found very signi¬cant 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. You will also see much
empirical work in Chapter 4, ˜˜Discount Rates as a Function of
Log Size,™™ and Chapter 11, ˜˜Empirical Testing of Abrams™
Valuation Theory.™™
2. It emphasizes quantitative skills. Chapter 2 focuses on using
regression analysis in business valuation. Chapter 3, ˜˜Annuity
Discount Factors and the Gordon Model,™™ is the most
comprehensive treatment of ADFs in print. For anyone wishing
to use the Mercer quantitative marketability discount model,


Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
Chapter 4 contains the ADF with constant growth not included
in the Mercer text. ADFs crop up in many valuation contexts. I
invented several new ADFs that appear in Chapter 3 that are
useful in many valuation contexts. Chapter 11 contains the ¬rst
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, uni¬ed approach to valuation that can
be empirically tested and whose principles work for the
valuation of billion-dollar ¬rms and ma and pa ¬rms alike.
While this book contains more mathematics”a worm™s eye
view, if you will”than other valuation texts, it also has more of
a bird™s eye view as well.

I have tried to provide paths through this book to make it easier to follow.
Chapters 4 and 13 both contain a shortcut version of the chapter at the
end for those who want the bottom line without all the detail. In general,
I have moved 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
How to 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. The ¬rst three parts to this book
follow the chronological sequence of performing a valuation: (1) forecast
cash ¬‚ows, (2) discount to present value, and (3) adjust for control and
marketability. The fourth part is a bird™s eye view in order to test empir-
ically whether my methodology works. Additionally, we explore (1) con-
¬dence intervals around valuation estimates and (2) what happens to the
valuation when appraisers make mistakes. Part 5, on special topics, is the
place for everything else. Each of parts of the book has an introduction
preceding it that will preview the upcoming material in greater depth
than we cover here.
Because most professionals do not have abundant time, I want to
suggest another path geared for the maximum bene¬t from the least in-
vestment in time. The heart of the book is Chapters 4 and 7, on log size
and on adjusting for control and marketability, respectively. I recommend
the time-pressed reader follow this order:
1. Chapter 7 (discounts for lack of control and lack of
2. Chapter 8 (this is an application of Chapter 7”a sample
restricted stock report)
3. Chapter 9 (this is an application of Chapter 7”a sample
fractional ownership interest discount report)

4. Chapter 4 (the log size model for calculating discount rates)
5. Chapter 3”the following sections: from the beginning through
the section titled ˜˜A Brief Summary™™; ˜˜Periodic Perpetuity
Factors: Perpetuities for Periodic Cash Flows™™; and
˜˜Relationship of Gordon Model Multiple to the Price/Earnings
Ratio.™™ Some readers may want to read this chapter after
Chapter 7, though it will be somewhat helpful, but de¬nitely
not necessary, to have read Chapter 3 before 4 and 7.
6. Chapter 10 (this empirically tests Chapters 4 and 7, the heart of
the book)
7. Chapter 2 (some readers may want to start with Chapter 2 ¬rst,
as the material on using regression analysis may help reading
all of the other chapters).
After these chapters, you can read the remainder of the book in any
order, though it is best to read Chapter 14 immediately after Chapter 13.
This book has close to 125 tables, many of them being two or three
pages long. To facilitate your reading, it will help you to copy tables
whose commentary in the text is extensive and sit with the separate tables
next to you. Otherwise, you will spend an inordinate amount of time
¬‚ipping pages back and forth. Note: readers with low blood pressure may
wish to ignore that advice.

Mercer, Z. Christopher. 1997. Quantifying Marketability Discounts: Developing and Supporting
Marketability Discounts in the Appraisal of Closely Held Business Interests. Memphis,
Tenn.: Peabody.
Pratt, Shannon P., Robert F. Reilly, and Robert P. Schweihs. 1996. Valuing a Business:
The Analysis and Appraisal of Closely Held Companies, 3d ed. New York: McGraw-Hill.

Introduction xv
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I gratefully acknowledge help beyond the call of duty from my parents,
Leonard and Marilyn Abrams. Professionally, R. K. Hiatt has been the
ideal internal editor. Without his help, this book would have suffered
greatly. He also contributed important insights throughout the book.
Robert Reilly edited the original 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 ¬rst eight chapters.
I bene¬ted much from his input and thank him profusely.
Chris Mercer also read much or all 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 Rob Oliver and Roy Meyers of Management Planning, Inc.
for providing me with their restricted stock data. I also thank Bob Jones
of Jones, Roach & Caringella for providing me with private fractional
interest sales of real estate.
Chaim Borevitz provided important help on Chapters 8 and 9. Mark
Shayne provided me with dozens of insightful comments. Professor Wil-
liam Megginson gave me considerable feedback on Chapter 7. 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 Mur-
ray, Greg Gilbert, Jared Kaplan, Esq., Robert Gross, Raymond Miles, and
Steven Stamp.
I thank the following people who provided me with useful infor-
mation that appears in the book: John Watson, Jr., Esq., David Boatwright,
Esq., Douglas Obenshain, and Gordon Gregory.
I thank the following people who reviewed this book for McGraw-
Hill: Shannon Pratt, Robert Reilly, Jay Fishman, Larry Kasper, Bob Gross-
man, Terry Isom, Herb Spiro, Don Shannon, Chris Mercer, Dave Bishop,
Jim Rigby, and Kent Osborne.



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