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reliable. We have accurately re¬‚ected such information in this report;
however, we make no representation as to our sources™ accuracy or com-
pleteness and have accepted their information without further veri¬ca-
tion.
We have not made a physical visit to the properties. We assume that
the present owners would continue to maintain the character and integ-
rity of the property through any sale, reorganization, or diminution of
the owners™ participation or equity interest. We also assume there are no
present or future ˜˜skeletons in the closet,™™ e.g., environmental problems
with the property, litigation, and so on.
Our opinion of the fractional interest discount in this report is valid
only for the stated purpose and only for the effective dates of the ap-
praisal. It is our understanding that this opinion will be used for gift tax
purposes. The fractional interest discount shall not be used for other pur-
poses and cannot even be used for the same purposes and time frame for
different size member interests, as they could be misleading and danger-
ous. Though some similarities exist between the fractional interest dis-
count for this purpose and others, it would be incorrect to use the dis-
count as determined in our report for any other purposes. Speci¬c timing,
performance, and marketability issues that arise in evaluating the fair
market value of the properties and related ownership interests could
change the results. Accordingly, any such use of the fractional interest
discount as determined in this report for other purposes or effective dates
may be inaccurate and misleading, and no such use shall be made with-
out our written consent.
Our determination of the fractional interest discount does not rep-
resent investment advice of any kind to any person and does not consti-
tute a recommendation as to the purchase or sale of shares of the property
or related interests or regarding any other course of action.
Future services regarding the subject matter of this report, including,
but not limited to, testimony or attendance in court shall not be required
of Abrams Valuation Group unless previous arrangements have been
made in writing.
No part or all of the contents of this report shall be conveyed to the
public through advertising, public relations, news, sales, mail, direct



PART 3 Adjusting for Control and Marketability
348
transmittal, or other media without the prior written consent and ap-
proval of Abrams Valuation Group. This report may only be distributed
in its entirety to those directly involved with the purpose of this study.
All other users are to be considered unintended users.
This report may not be distributed in part, as only a thorough read-
ing of this report can accurately convey the logic contained within. Ex-
cerpts taken out of context can be dangerously misleading and are there-
fore forbidden without the written consent of Abrams Valuation Group.


APPRAISER™S QUALIFICATIONS
Jay B. Abrams, ASA, CPA, MBA, author and inventor, is a nationally
recognized valuation economist.
Mr. Abrams lectured at the June 1996 Toronto International Confer-
ence of the American Society of Appraisers, the organization from which
he holds the professional designation of Accredited Senior Appraiser
(ASA) in Business Valuation. He has lectured for the National Association
of Certi¬ed Valuation Analysts and the Anthony Robbins™ Financial Mas-
tery Seminar.
Mr. Abrams has provided services to clients representing a variety
of organizations from small entrepreneurs to Columbia Pictures, Dr. Pep-
per, Purex Corporation, and other Fortune 1000 ¬rms in the area of in-
tangibles, including goodwill, customer lists, licensing agreements, con-
tracts, and business enterprise and capital stock appraisals for numerous
purposes, including the following:
— Employee stock ownership plans (ESOPs).
— Estate planning, estate and gift taxes.
— Income taxes and charitable contributions.
— Mergers and acquisitions and sales.
— Divestitures.
— Warrants and stock options.
— Shareholder buy/sell agreements.
— Blocks of publicly traded securities.
— Private placements and public offerings.
— Restricted securities.
— Recapitalization and reorganizations.
— Debt and equity ¬nancing.
— Company dissolutions.
— Litigation settlement.
Additionally, Mr. Abrams has prepared and given expert testimony
in the capital stock and business enterprise valuation areas in various
courts of law.
Mr. Abrams™ valuation experience encompasses a wide array of in-
dustries and assignments, for mergers/acquisitions, sales and leaseback,
litigation support, leveraged buyouts, and stockholder agreements. Mr.
Abrams was Vice-President of Paci¬c Corporate Valuation, Inc. in charge
of the valuation practice, and he was a Project Manager at Arthur D. Little



CHAPTER 9 Sample Appraisal Report 349
Valuation, Inc. He was a cofounder and president of Raycom, a radio
communications ¬rm, and prior to this was an auditor with Arthur An-
dersen & Company. Mr. Abrams received his MBA from the University
of Chicago in ¬nance and marketing, where he also pursued graduate
studies in economics.
Mr. Abrams invented and published the Abrams Table of Equity Pre-
mia and has published an article quantifying the discount for lack of
marketability. He invented several formulas for valuing leveraged ESOPs,
as well as the Abrams Table of Accounting Transposition Errors, used for
troubleshooting such errors. He also wrote software to automatically gen-
erate a table of potential sources of error.
Mr. Abrams™ writings include:
— Quantitative Business Valuation: A Mathematical Approach for Today™s
Professionals, McGraw-Hill, November 2000.
— ˜˜ESOPs: Measuring and Apportioning the Dilution,™™ Valuation,
June 1997.
— ˜˜Discount Rates as a Function of Log Size and Valuation Error
Measurement,™™ The Valuation Examiner, February/March, 1997.
— ˜˜An Iterative Valuation Approach,™™ Business Valuation Review,
March 1995.
— ˜˜A Breakthrough in Calculating Reliable Discount Rates,™™
Valuation, August, 1994.
— ˜˜Discount for Lack of Marketability: A Theoretical Model,™™
Business Valuation Review, September, 1994.
— ˜˜Cash Flow: A Mathematical Derivation,™™ Valuation, March 1994.
— ˜˜An Iterative Procedure To Value Leveraged ESOPs,™™ Valuation,
January 1993.
— ˜˜How to Quickly Find and Fix Accounting Transposition Errors,™™
The Practical Accountant, June 1992.
— Coauthor of ˜˜Valuation of Companies for ESOP Purposes,™™
Chapter 8 in Employee Stock Ownership Plans by Robert W. Smiley,
Jr. and Ronald J. Gilbert, Prentice Hall/Rosenfeld Launer
Publications, New York, 1989.
— ˜˜The Annuity Discount Factor: Generalization, Analysis of
Special Cases, and Relationship to the Gordon Model and Fixed-
Rate Loan Amortization,™™ unpublished.


BIBLIOGRAPHY
Mercer, Z. Christopher. 1997. Quantifying Marketability Discounts. Memphis, Tenn.: Pea-
body.
Pratt, Shannon P., Robert F. Reilly, and Robert P. Schweihs. 1996. Valuing a Business, 3d
ed. Burr Ridge, Ill.: McGraw-Hill.




PART 3 Adjusting for Control and Marketability
350
APPENDIX
Tax Court™s Opinion for Discount for Lack of
Marketability24



INTRODUCTION
The U.S. Tax Court outlined a list of 10 nonexclusive factors that in the
Court™s opinion affect discount for lack of marketability (DLOM). We ¬rst
present its list and then we comment on each item as to how we consid-
ered it in our analysis.



THE COURT™S TEN FACTORS
The Court™s 10 factors are:

1. The value of the subject corporation™s privately traded
securities vis-a-vis its publicly traded securities (or, if the
`
subject corporation does not have stock that is traded both
publicly and privately, the cost of a similar corporation™s public
and private stock). These are known as ˜˜Letter Stock™™ or
restricted securities, the restrictions arising from Section 144 of
the Securities Exchange Commission Rules.
2. An analysis of the subject corporation™s ¬nancial statements.
3. The corporation™s dividend-paying capacity, its history of
paying dividends, and the amount of its prior dividends.
4. The nature of the corporation, its history, its position in the
industry, and its economic outlook.
5. The corporation™s management.
6. The degree of control transferred with the block of stock to be
valued.
7. Any restriction on the transferability of the corporation™s stock.
8. The period of time for which an investor must hold the subject
stock to realize a suf¬cient pro¬t.
9. The corporation™s redemption policy.
10. The cost of effectuating a public offering of the stock to be
valued, e.g., legal, accounting, and underwriting fees25

The Court in general had the right idea. It created a list of criteria with
which to judge the difference in marketability between the source of the
valuation data and the asset to which we are applying the data.



24. Bernard Mandelbaum, et al. v. Commissioner, TCM, CCH Dec. 50, 687(M), 1995-254.
25. See Estate of Gilford v. Commissioner [Dec. 43,622], 88 T.C. 38, 60 (1987); Northern Trust Co. v.
Commissioner [Dec. 43,261], 87 T.C. 349, 383-389 (1986); see also Rev. Rul. 77287, 1977-2 C.B.
319 (valuation of restricted securities).




CHAPTER 9 Sample Appraisal Report 351
APPLICATION OF THE COURT™S 10 FACTORS TO
THE VALUATION
In this section we will address the factors in the Tax Court™s opinion and
demonstrate how we have incorporated those factors into our analysis of
the discount for lack of marketability (DLOM), which, combined with the
discount for lack of control (DLOC), forms the fractional interest discount.
The following analysis applies regardless of the form of the subject entity,
whether it is a common stock interest in a corporation, Limited or General
Partnership interest, LLC interest, etc. We use the terms the entity and the
subject interest to maintain generality.

1. We estimate the letter stock discount in the delay-to-sale
component of the economic components approach. We do this
either by a regression analysis or a Black“Scholes put option
calculation, depending on the availability of data.
2. Our analysis of the entity™s ¬nancial statements is incorporated
into the calculation of DLOM in the calculation of transactions
costs, expected growth rates, the discount rate, and the delay-
to-sale component of the economic components approach.
3. We incorporate the dividends (distributions) into the analysis
in the Partnership Pro¬les (PP) approach. This is the single
most important factor in the regression model. Dividends or
distributions are also incorporated indirectly into the
calculation of DLOM through their effect on the growth rate
and, therefore, the transactions costs.
4. The nature of the entity and its history, industry position,
composition of assets, and economic outlook are factors that
are very signi¬cant in the valuation of the underlying assets.
The comments to item 2 apply here as well.
5. Management can be signi¬cant in determining the fractional
interest discount because of two factors: its dividend policy,
which is already considered in 3, and more importantly, its
potential for making decisions that favor one group of owners
over another or withholding bad news from any ownership
group. Owners of private interests generally have more
in¬‚uence with their management than the LPs in the
Partnership Pro¬les database would with theirs. We consider
this factor in the adjustment for increased in¬‚uence in
Partnership Pro¬les approach.
6. The degree of control of the block of stock is, strangely enough,
signi¬cant in calculating DLOM. The reason why that appears
strange is that the degree of control has its own discount”the
DLOC”for lack of control. Why then does the degree of
control in¬‚uence the DLOM? The reason is found in the above-
mentioned book, Chapter 7 in Quantitative Business Valuation: A
Mathematical Approach for Today™s Professionals. We calculate
control premiums and discount for lack of control by looking
at control premiums paid for marketable minority interests in
the stock market. But control matters less in publicly held ¬rms



PART 3 Adjusting for Control and Marketability
352
than in privately held ¬rms because the former generally have
both current cash ¬‚ow in the form of dividends and instant
marketability in the ability to cash out in three days.
Furthermore, management of publicly held ¬rms are generally
managing to maximize the per-share values of the minority
shareholders. With privately held ¬rms, control shareholders
often divert wealth from minority shareholders (similarly
general partners in LPs and managing members in LLCs can
divert wealth from limited partners and other members). It is
rare to see dividends in closely held corporations, and there is
generally no ability to cash out. Therefore, there is an
interactive effect in being both a minority shareholder (or LP/
minority interest member) and owning an interest in a private
¬rm. The whole is worse than the sum of the two parts. As in
5 above, we have considered this in the adjustment for
increased in¬‚uence in the Partnership Pro¬les approach.
The marketability of private interests is limited, since there is
7.
no formal market for such interests. We consider this limitation
in the economic components approach in the following ways:
(a) in the calculation of the delay-to-sale component; and (b) in
accounting for the buyer™s monopsony power (component 2).
In the Partnership Pro¬les approach, we implicitly considered
the lack of marketability in selecting the discount for lack of
public registration.
We incorporate time horizons into the delay-to-sale component
8.
in the economic components approach and the adjustment for
lack of public registration in the Partnership Pro¬les approach.
We also incorporate time horizons in another fashion in the
selection of the variable j”the average years between sales”in
the economic components approach.
The entity™s redemption policy is relevant in determining one™s
9.
ability to cash out of an investment. The subject entity does not
provide a redemption option.
The cost of undergoing an initial public offering is about 15“
10.
18% for a small ¬rm. There is a possibility that an IPO might
lower the discount by making the subject interest more
marketable. However, the cost of the IPO and the subsequent
regulatory administrative costs would be prohibitive in the
case, and we don™t need to account for the IPO possibility here.




CHAPTER 9 Sample Appraisal Report 353
PART FOUR


Putting It All Together




Part 4 of this book consists of Chapters 10 and 11. Chapter 10 empirically
tests the log size and economic components models by reconciling price
to cash ¬‚ow (P/CF) multiples calculated using these models with P/CF
multiples for groups of ¬rms of different sizes in the Institute of Business
Appraisers™ (IBA) database. The results provide weak support for the two
models, but missing data make it impossible to provide strong support.
There is simply too much data we need that does not exist in the IBA
database or any other one of which I am aware.
In Chapter 11 we look at two issues. In the ¬rst half of the chapter
we calculate 95% con¬dence intervals around our valuation estimate us-
ing the log size model (both for all 72 years of New York Stock Exchange
data and for the past 60 years), assuming we forecast cash ¬‚ows and
adjust for control and marketability perfectly. The importance of this is
to understand how much statistical uncertainty there is in our valuation
estimates.
The second half of Chapter 11 is concerned with measuring the val-
uation errors that arise from errors in forecasting cash ¬‚ow and growth
rates and calculating discount rates. We look at the effects of both relative
and absolute errors and show how the majority of these errors affect the
valuation of large ¬rms more than small ¬rms.
Whereas Part 3 of this book consists of practical, hands-on, ˜˜how-
to™™ chapters, Part 4 does not. It can be skipped by the time-pressed reader.
Nevertheless, for one who wants to be well educated and familiar with
important theoretical and empirical issues in valuation, these chapters are
important.




355




Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
CHAPTER 10


Empirical Testing of Abrams™
Valuation Theory1




INTRODUCTION
Steps in the Valuation Process
Applying a Valuation Model to the Steps
TABLE 10-1: LOG SIZE FOR 1938“1986
TABLE 10-2: 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
CONCLUSION




1. I offer my profound thanks to Mr. Raymond Miles for his considerable help. Without his vitally
important research, this article would be impossible. Also, Professor Haim Mendelson of
Stanford University provided extremely helpful comments.




357




Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
INTRODUCTION
Many appraisers have long believed that when small businesses sell, they
are priced very differently than large businesses and that the rules gov-
erning their valuation are totally different. I, too, held this opinion at one
time, but this chapter is evidence”though not proof”that it is not true.
A skeptic could level the charge that the log size discount rate equa-
tion is based on a mathematical relationship that exists between returns
and size of New York Stock Exchange (NYSE) ¬rms, but it may not apply
to the universe of small and medium privately held ¬rms. Additionally,
the calculations of the transactions costs component of the discount for
lack of marketability (DLOM) is based on interviews, then quanti¬ed in
an equation and extrapolated downwards for small ¬rms. Thus, it™s nice
in theory, but does it really work in practice?
The purpose of this chapter is to subject the log size and economic
components models to empirical testing to see whether they do a good
job of explaining real world transactions of smaller businesses. Our pri-
mary data comes from an article published by Raymond Miles (Miles
1992) (˜˜the article™™) about the relationship of size to price earnings (PE)
multiples in the Institute of Business Appraisers™ (IBA) database.


Steps in the Valuation Process
Using a simple discounted cash ¬‚ow model as the valuation paradigm,
valuation consists of four steps:
Forecast cash ¬‚ows.
1.
Discount to net present value.

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