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is guaranteed and public minority shareholder rights are generally better
protected they are in private ¬rms. We therefore reduce this premium for
illiquidity from the premium in Mercer™s example of between 1 and 2%
(H18 and I18) to 0% (K18, L18) for the restricted stock. While it is possible
that the restricted stocks should have a positive premium for this factor,
they are nevertheless far more liquid than all of the private ¬rms in Mer-
cer™s examples. If we should increase K18 and L18 to, say, 1%, then we
should increase H18 and I18 to at least 2“3%, respectively, or probably
higher yet.
Relative to the private C corporation shares, the expected holding
period for the restricted stock is short and certain. We therefore reduce
the premium for holding period uncertainty from between 0 and 1% (H19
and I19) for Example 1 to 0 (K19, L19) for the restricted shares. As both



PART 3 Adjusting for Control and Marketability
278
T A B L E 7-19

QMDM Comparison of Restricted Stock Discount Rate versus Mercer Example 1


A B C D E F G H I J K L

5 Mercer Example Restricted Stock
1

6 Range of Range of
Returns Returns

7 Components of the Required Holding Period Return Lower Higher Lower Higher

8 Base equity discount rate (adjusted capital asset pricing model)
9 Current yield-to-maturity composite long term treasuries 6.7% 6.7% 6.7% 6.7%
10 Adjusted Ibbotson large stock premium 6.5%
11 applicable beta statistic 1
12 Beta adjusted large stock premium 6.5% 6.5% 6.5% 6.5%
13 Adjusted Ibbotson small stock premium 3.5% 3.5% 3.5% 3.5%
14 Base equity discount rate 16.7% 16.7% 16.7% 16.7%
17 Investment Speci¬c Risk Premiums

18 General illiquidity of the investment [1] 1.0% 2.0% 0.0% 0.0%
19 Uncertainties related to length of expected holding period [2] 0.0% 1.0% 0.0% 0.0%
20 Lack of expected interim cash ¬‚ows [3] 0.5% 1.0% 0.5% 1.0%
21 Small shareholder base [4] 0.0% 1.0% 0.0% 0.0%
22 Range of speci¬c risk premiums for the investment 1.5% 5.0% 0.5% 1.0%
24 Initial range of required returns 18.2% 21.7% 17.2% 17.7%
26 Concluded range of required holding period returns (rounded) 18.0% 22.0% 17.0% 18.0%


[1] The restricted stock should be much easier to sell than a minority stake in a private closely held C corporation, since public minority shareholder rights are generally better protected.
While it is possible that the restricted stocks should have a positive premium for this factor, they are nevertheless far more liquid than all of the private ¬rms in Mercer™s examples. If we
should increase K18 and L18 to 1%, then we should increase H18 and I18 to at least 2% to 3% or probably higher yet.
[2] Relative to the private shares, the expected holding period for the restricted stock is short and certain.
[3] We assume a non dividend paying restricted stock. The example also concerned a non dividend paying C corporation. We therefore assign the same risk premium for this factor.
[4] The restricted stock shares are shares of public corporations, which in general have large shareholder bases.




investments are expected to pay no dividends, there is no difference in
the premium for lack of expected interim cash ¬‚ows (Row 20), although
the latter experiences that lack of dividends for a far shorter and much
more certain time period, which could well justify a lower premium than
the former.
At this point I can digress to pose my objections to the ¬rst two
factors. General illiquidity of the investment is a very fuzzy term. It can mean
almost anything. There is no empirical measure of it. Therefore, it can be
almost anything that one wants it to be”which I admit has its advan-
tages in practical application, but it™s not good science. It is also unclear
where general illiquidity stops and uncertainties in the holding period
begin. Do they overlap? How does one prevent him- or herself from
double-counting them? That is a problem with loosely-de¬ned terms.
Returning to the main train of thought, the private, closely held C
corporation would have a much smaller shareholder base than the re-
stricted stock corporations. We therefore reduce the premium for a small
shareholder base from between 0 and 1% (H21 and I21) for Example 1 to
0 (K21, L21) for the restricted stock. The total speci¬c risk premium for



CHAPTER 7 Adjusting for Levels of Control and Marketability 279
the restricted stock comes to 0.5% (K22) to 1.0% (L22) versus the 1.5%
(H22) to 5% (I22) for the private shares. After adding the base equity
discount rates and rounding, we arrive at a concluded range of required
holding period returns of 18“22% and 17“18% (Row 26) for Mercer™s
Example 1 and the restricted stock, respectively.
Next we need to determine the expected growth rate in value of the
unrestricted marketable minority shares. Since there are no dividends, the
expected growth rate must be equal to the discount rate”by de¬nition.76
In this example the equity discount rate of the unrestricted marketable
shares or the ˜˜base equity discount rate™™ is 16.7%.
Let™s now calculate the QMDM discount on the restricted stock with
the following assumptions:

1. A midrange (of K26 and L26) required holding period return of
17.5%.
2. The 2.5-year average holding period.
3. The growth rate in value of 16.7%.

The calculation is as follows:

1
1.1672.5
DLOM 1 (FV PVF) 1 1.7%
1.1752.5

Assuming the correct discount is 30%, the QMDM is almost 95% too low!


Mercer™s Response
After reviewing Mr. Abrams™ response to my rebuttal of his criticism of
the QMDM, it is apparent that he and I continue to disagree over how
the QMDM is applied in practice. The average marketability discounts in
the 10 examples cited in my rebuttal of his criticism was 37%, and the
median discount was 30%, not 1.7%. Mr. Abrams™ mistake is in assuming
that the discount rate embedded in the pricing of a publicly traded stock
is the required return of restricted stock investors. The fact that the av-
erage restricted stock discount is 30% or so indicates that investors have
extracted a signi¬cant premium in return relative to the expected returns
of the counterpart publicly traded securities.
What may be true ˜˜by de¬nition™™ in a perpetuity calculation may
well not be true for shorter holding periods. The QMDM deals, not with
perpetuity calculations, but with investor assessments of expected cash
¬‚ows over ¬nite time horizons. And it makes explicit the assumptions
made about the relationship between the expected growth in value of
investments and the required returns of investors in those investments. I
maintain that the model does indeed provide an excellent tool for esti-
mating marketability discounts (from an estimated freely traded value)
for minority interests in closely held companies.



76. This is the discount rate applicable to marketable minority shares, not the higher discount rate
applicable to illiquid shares, i.e., the required holding period return.


PART 3 Adjusting for Control and Marketability
280
Conclusion
We have reviewed the professional and some of the academic literature
dealing with control premiums and DLOM. My opinion is that with our
current information set, we should use control premiums in the 21“28%
range. We developed this as being three to four times the value of the
voting rights premium adjusted to U.S. laws and for liquidity differences
between voting and nonvoting stock. This measure is consistent with the
median going private premium of 24.1% (Table 7-1, E21), although it is
preferable to make a clean separation of expected performance improve-
ments, which increase the ˜˜top line,™™ i.e., cash ¬‚ows, versus the pure
value of control, which is represented by a reduction in the discount rate.
We reviewed three quantitative models of DLOM: Mercer™s, Kas-
per™s, and Abrams™. The QMDM was unable to provide any meaningful
restricted stock discounts for the Management Planning, Inc. data, as dis-
counting modest risk premiums for two to three years provides little var-
iation in discount. Abrams™ non-company-speci¬c Black-Scholes options
pricing model performed worse at explaining restricted stock discounts
than the mean, while using BSOPM with ¬rm-speci¬c calculations of stan-
dard deviations was superior to the mean. While that makes Black“
Scholes a viable candidate for restricted stock studies, it is not a possible
model for valuing the delay-to-sale component of DLOM, and we must
use the regression of the MPI data.
We quanti¬ed component #2, monopsony power to the buyer, as 9%,
according to Schwert™s ¬ndings of a 12.2% greater premium in takeovers
when there are multiple buyers than when there is only one buyer.
Finally, we quanti¬ed transactions costs separately for the buyer and
the seller. The premise of fair market value is such that we ask, ˜˜What
would a hypothetical buyer be willing to pay for this interest,™™ which
means that we are presuming a ¬rst sale immediately. Buyers care about
their own transactions costs, but they do not care about sellers™ transac-
tions cost on the immediate transaction. However, buyers do care that in
10 years or so they become the sellers. They therefore care about all sub-
sequent sellers™ (and buyers™) transactions costs. We presented two dis-
count formulas”equations (7-9) and (7-9a), which are appropriate for
seller and buyer, respectively, to translate the pure discount that applies
to each transaction into a discount based on the present value of the
in¬nite continuum of periodic transactions.
In Table 7-14 we applied our DLOM model to a control interest in a
hypothetical private company. The result was a DLOM of 23.1%, which
is a reasonable result.
Of course, the economic components model is merely a model. It is
certainly imperfect, and it must be used with common sense. It is possible
to obtain strange or nonsensical results, and if the appraiser is asleep at
the wheel, he or she may not realize it. There is plenty of room for ad-
ditional research to improve our modeling and results. Nevertheless, in
my opinion this is the most realistic and comprehensive model to date
for calculating DLOM.

BIBLIOGRAPHY
Abrams, Jay B. 1994a. ˜˜Discount for Lack of Marketability: A Theoretical Model.™™ Business
Valuation Review (September): 132“39.


CHAPTER 7 Adjusting for Levels of Control and Marketability 281
” ”. 1994b. ˜˜A Breakthrough in Calculating Reliable Discount Rates.™™ Valuation (Au-

gust): 8“24.
Amihud, Y., and H. Mendelson. 1991. ˜˜Liquidity, Asset Prices, and Financial Policy.™™ Fi-
nancial Analysts Journal (November“December): 56“66.
Barca, F. 1995. ˜˜On Corporate Governance in Italy: Issues, Facts, and Agency.™™ Mimeo,
Bank of Italy.
Bergstrom, C., and K. Rydqvist. 1990. ˜˜Ownership of Equity in Dual-Class Firms.™™ Journal
of Banking and Finance 14:237“53.
Berkovitch, E., and M. P. Narayanan. 1993. ˜˜Motives for Takeovers: An Empirical Inves-
tigation. Journal of Financial and Quantitative Analysis 28:347“62.
Bolotsky, Michael J. 1991. ˜˜Adjustments for Differences in Ownership Rights, Liquidity,
Information Access, and Information Reliability: An Assessment of ˜Prevailing Wis-
dom™ versus the ˜Nath Hypothesis™.™™™ Business Valuation Review (September): 94“110.
” ”. 1995. ˜˜Is the ˜Levels of Value™ Concept Still Viable? Bolotsky™s Response.™™ Business

Valuation Education Sessions from the American Society of Appraisers Convention, June,
Denver, Col. 21“34.
Bradley, M., A. Desai, and E. H. Kim. 1988. ˜˜Synergistic Gains from Corporate Acquisi-
tions and Their Division between the Stockholders of Target and Acquiring Firms.™™
Journal of Financial Economics 39:3“40.
Chaffe, David B. H. 1993. ˜˜Option Pricing as a Proxy for Discount for Lack of Marketa-
bility in Private Company Valuations”A Working Paper.™™ Business Valuation Review
(December): 182“188.
Eckbo, B. E. 1983. ˜˜Horizontal Mergers, Collusion, and Stockholder Wealth.™™ Journal of
Financial Economics 11:241“74.
” ”. 1985. ˜˜Mergers and the Market Concentration Doctrine: Evidence from the Capital

Market.™™ Journal of Business 58:325“49.
” ”. 1992. ˜˜Mergers and the Value of Antitrust Deterrence.™™ Journal of Finance 47:1005“

30.
Einhorn, Hillel J., and Robin M. Hogarth. 1987. ˜˜Decision Making under Ambiguity.™™ In
Rational Choice, ed. Robin M. Hogarth and Melvin W. Reder. Chicago: University of
Chicago Press, pp. 41“66.
Ellsberg, D. 1961. ˜˜Risk, Ambiguity, and the Savage Axioms.™™ Quarterly Journal of Econom-
ics 75:643“69.
Franks, J. R., and Julian R. Harris. 1989. ˜˜Shareholder Wealth Effects of Corporate Take-
overs: The U.K. Experience 1955“1985.™™ Journal of Financial Economics 23:225“49.
Glass, Carla, and Mary M. McCarter. 1995. ˜˜The Foundations for Minority and Control
Position Adjustments.™™ Paper presented at American Society of Appraisers™ 14th
Annual Advanced Business Valuation Conference., November 3, Boston, Mass.
Grabowski, Roger, and David King. 1999. ˜˜New Evidence on Size Effects and Rates of
Return.™™ Business Valuation Review (September): 112“30.
Harris, Ellie G. 1994. ˜˜Why One Firm Is the Target and the Other the Bidder in Single-
Bidder, Synergistic Takeovers.™™ Journal of Business 67:263“80.
Horner, M. R. 1988. ˜˜The Value of the corporate voting right: Evidence from Switzerland.™™
Journal of Banking and Finance 12:69“83.
Ibbotson Associates. 1999. Stocks, Bonds, Bills, and In¬‚ation: 1999 Yearbook”Valuation Edi-
tion. Chicago: The Associates, p. 119.
Jankowske, Wayne C. 1991. ˜˜Valuing Minority Interests in Relation to Guideline Firms,™™
Business Valuation Review (December 1991): 139“43.
” ”. 1995. ˜˜Frameworks for Analysis of Control Premiums.™™ Business Valuation Review

(March): 3“10.
Johnson, Bruce A. 1999. ˜˜Quantitative Support for Discounts for Lack of Marketability.™™
Business Valuation Review (December 1999): 152“55.
Kasper, Larry, J. 1997. Business Valuations: Advanced Topics. Westport, Conn.: Quorum
Books.
Lang, L. H. P., R. Stulz, R. A. Walkling. 1991. ˜˜A Test of the Free Cash Flow Hypothesis:
The Case of Bidder Returns.™™ Journal of Financial Economics 29:315“36.
Lease, Ronald C., John J. McConnell, and Wayne H. Mikkelson. 1983. ˜˜The Market Value
of Control in Publicly-Traded Corporations.™™ Journal of Financial Economics 11.
Lerch, Mary Ann. 1991. ˜˜Quantitative Measures of Minority Interest Discounts.™™ Business
Valuation Review (March): 14“20.
” ”. 1997. ˜˜Yet Another Discount for Lack of Marketability Study.™™ Business Valuation

Review (June): 70“106.



PART 3 Adjusting for Control and Marketability
282
Levy, H. 1982. ˜˜Economic Evaluation of Voting Power of Common Stock.™™ Journal of Fi-
nance 38:79“93.
Maher, Maria, and Thomas Andersson. 1999. ˜˜Corporate Governance: Effects on Firm
Performance and Economic Growth.™™ Organization for Economic Co-operation and
Development. Downloadable from www.OECD.org.
Maquieira, Carlos P., William L. Megginson, and Lance Nail. 1998. ˜˜Wealth Creation ver-
sus Wealth Redistributions in Pure Stock-for-Stock Mergers.™™ Journal of Financial Ec-
onomics 48:3“33.
Megginson, William L. 1990. ˜˜Restricted Voting Stock, Acquisition Premiums, and the
Market Value of Corporate Control.™™ The Financial Review 25(May): 175“98.
Menyah, Kojo, and Krishna Paudyal. 1996. ˜˜The Determinants and Dynamics of Bid“Ask
Spreads on the London Stock Exchange.™™ Journal of Financial Research 19:377“94.
Mercer, Z. Christopher. 1990. ˜˜Do Public Company (Minority) Transactions Yield Con-
trolling Interest or Minority Interest Pricing Data?™™ Business Valuation Review (De-
cember): 123“26.
” ”. 1994. ˜˜Should ˜Marketability Discounts™ Be Applied to Controlling Interests of Pri-

vate Companies?™™ Business Valuation Review (June): 55“65.
” ”. Quantifying Marketability Discounts: Developing and Supporting Marketability Discounts

in the Appraisal of Closely Held Business Interests. Memphis, Tenn.: Peabody.
” ”. 1998. The 1999 Journal of Business Valuation: Proceedings of the Fourth Joint Business

Valuation Conference of The Canadian Institute of Chartered Business Valuators and the
American Society of Appraisers, September 24 and 25, Montreal, Que., Canada.
” ”. 1999. ˜˜Theoretical Determinants of Value in the Context of ˜Levels of Value.™ ™™

Presentation to the American Society of Appraisers, August 23. Memphis: Tenn.:
Mercer Capital. [See especially slides 17“28 and 46a“46d.]
” ”. 2000. ˜˜Revisiting, the Quantitative Marketability Discount Model.™™ Valuation Strat-

egies (March“April).
Much, Paul J., and Timothy J. Fagan. 2000. ˜˜The Value of Voting Rights.™™ In Financial
Valuation: Business and Business Interests, ed. James H. Zukin. 2000 Update with Cu-
mulative Index prepared by Richard C. May and Loren B. Garruto. New York: War-
ren, Gorham & Lamont/RIA Group, pp. U9B-1“U9B-7.
Nath, Eric. 1990. Control Premiums and Minority Interest Discounts in Private Compa-
nies.™™ Business Valuation Review (June): 39“46.
” ”. 1994. ˜˜A Tale of Two Markets.™™ Business Valuation Review (September): 107“12.

” ”. 1997. ˜˜How Public Guideline Companies Represent Control Value for a Private

Company.™™ Business Valuation Review (December): 167“71.
Phillips, John R., and Neill Freeman. 1995. ˜˜Do Privately-Held Controlling Interests Sell
for Less?™™ Business Valuation Review (September): 102“13.
Pratt, Shannon P. 1998. Cost of Capital: Estimations and Applications. New York: John Wiley
& Sons.
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.
Roach, George P. 1998. ˜˜Control Premiums and Strategic Mergers.™™ Business Valuation Re-
view (December): 42“49.
Roll, Richard. 1986. ˜˜The Hubris Hypothesis of Corporate Takeovers.™™ Journal of Business
59:197“216.
Rydqvst, K. 1987. ˜˜Empirical Investigation of the Voting Premium.™™ Northwestern Uni-
versity. Working Paper No. 35.
Schilt, James H. 1996. ˜˜Discounts for Minority Interests.™™ Business Valuation Review (De-
cember): 161.
Schwert, G. William. 1996. ˜˜Markup Pricing in Mergers and Acquisitions.™™ Journal of Fi-
nancial Economics 41:153“92.
Simpson, David W. 1991. ˜˜Minority Interest and Marketability Discounts: A Perspective.™™
Business Valuation Review (March): 7“13.
Stern, Joel. 1993. ˜˜A Discussion of Mergers and Acquisitions.™™ Midland Corporate Finance
Journal (Summer) [cited in Jankowske 1995].
Stillman, R. 1983. ˜˜Examining Antitrust Policy Towards Horizontal Mergers.™™ Journal of
Financial Economics 11:225“40.
Stoll, H. R., 1978a. ˜˜The Supply of Dealer Services in Securities Markets.™™ Journal of Finance
33:1133“51.
” ”. 1978b. ˜˜The Pricing of Security Dealer Services: An Empirical Study of NASDAQ

Stocks.™™ Journal of Finance 33:1153“72.



CHAPTER 7 Adjusting for Levels of Control and Marketability 283
Tversky, Amos, and Daniel Kahneman. 1987. ˜˜Rational Choice and the Framing of Deci-
sions.™™ In Rational Choice, ed. Robin M. Hogarth and Melvin W. Reder. Chicago:
University of Chicago Press, pp. 67“94.
Vander Linder, Eric. 1998. ˜˜Cost of Capital Derived from Ibbotson Data Equals Minority
Value?™™ Business Valuation Review (December): 123“27.
Zingales, L. 1994. ˜˜The Value of the Voting Right: A Study of the Milan Stock Exchange.
Review of Financial Studies 7:125“48.
Zukin, James H., ed. 1998. Financial Valuation: Businesses and Business Interests. 1998 Update
with Cumulative Index prepared by Martin D. Hanan and Ray A. Sheeler. New
York: Warren, Gorham & Lamont/RIA Group, p. U9A-12.




MATHEMATICAL APPENDIX
DEVELOPING THE DISCOUNT FORMULAS
Initially we assume the current business owner will operate the business
for 10 years, sell it, and pay transaction costs of z.77 The next owner will
run the business another 10 years, sell it, and pay transaction costs. We
assume this pattern occurs ad in¬nitum. Of course, there will be variations
from the sale every 10 years”some will sell after 1 year, others after 30
years. In the meantime, in the absence of prior knowledge, we assume
every 10 years to be a reasonable estimate of the average of what will
occur.



NPV of Cash Flows with Periodic Transaction
Costs Removed
The net present value (NPV) of cash ¬‚ows to the existing business owner
with periodic transaction costs removed is the full amount of the ¬rst 10
years™ cash ¬‚ows, plus (1 z) times the next 10 years™ cash ¬‚ows, where
z)2 times the next 10 years™
z is the periodic transaction cost, plus (1
cash ¬‚ows, etc. We will denote the NPV net of transaction costs, i.e., with
transaction costs removed from the stream of cash ¬‚ows, as NPVTC .

g)9
(1 g) (1
1
NPVTC
r)0.5 r)1.5 r)9.5
(1 (1 (1
g)10 g)19
(1 (1
(1 z)
r)10.5 r)19.5
(1 (1
g)20 g)29
(1 (1
2
(1 z) (A7-1)
r)20.5 r)29.5
(1 (1

Multiplying each term in equation (A7-1) by (1 g)/(1 r), we get:



77. As explained in the body of the chapter, z is an incremental transaction cost. For example,
when we value a small fractional ownership in a privately owned business, often our
preliminary value is on a marketable minority basis. In this case z would be the difference
in transaction cost (expressed as a percentage) between selling a private business interest
and selling publicly traded stock through a stockbroker.




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