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Empirical Evidence of Marketability Discounts 289
had to be able to withstand Securities and Exchange Commission [SEC], IRS or
judicial review, particularly in light of the subsequent public offering.”
The mean and median discounts for lack of marketability indicated by the
aggregate of Emory’s eight studies of transactions that occurred five months prior to
an IPO were 44 and 43 percent, respectively. For the most recent period studied,
November 1995 to April 1997, the mean discount was 43 percent and the median
discount was 42 percent (see Exhibit 8.9).
Exhibit 8.9 Summary of the Emory Studies
Period of Study Number of Transactions Mean Discount Median Discount
_________________________ _____________________ ______________ _______________
May 1997–December 2000
(a)
283 50% 52%
May 1997–December 2000
(b)
36 48% 44%
May 1997–March 2000
(c)
53 54% 54%
November 1995–April 1997 91 43% 42%
January 1994–June 1995 46 45% 45%
February 1992–July 1993 54 45% 44%
August 1990–January 1992 35 42% 40%
February 1989–July 1990 23 45% 40%
August 1987–January 1989 27 45% 45%
January 1985–June 1986 21 43% 43%
January 1980–June 1981 13 60% 66%
Combined Results
(d)
593 47% 48%

(a) The Expanded Study
(b) The Limited Study
(c) The Dot.Com Study
(d) To avoid double counting, transactions from the Dot.Com and Limited Study are included only as a part of
the Expanded Study
The following is a brief explanation of each study:
• January 1, 1980–June 20, 1981. Emory reviewed private placements of securities
taking place prior to initial public offerings. The difference between the price of
a security sold prior to the IPO and the offering price is the discount for lack of
marketability. Emory examined 97 prospectuses of securities offered in the
period from January 1, 1980, through June 30, 1981. Of the 97 IPOs, he chose
13 that involved “financially sound” companies and transactions that took place
no more than five months prior to the IPO. Emory found that the private place-
ments sold at a mean discount of 60 percent and a median of 66 percent.
• January 1985–June 1986. Emory analyzed 21 IPOs and the transactions taking
place immediately before the offerings. His analysis showed that the mean dis-
count of the securities before the offerings is 43 percent with a median of 43 per-
cent. Emory attributed the difference between the mean of this study (43 percent)
and the mean of a similar study he performed in 1980 (60 percent) to the fact
that the market for initial public offerings in 1986 was more active.
• August 1987–January 1989. Emory reviewed the prospectuses of 98 IPOs, of
which 27 met the study criteria of financial soundness, an IPO price greater than
$5, and transactions taking place five months before the offering. He found that
the mean discount of the securities sold before the initial public offering is 45
percent with a median of 45 percent.
• February 1989–July 1990. Emory’s analysis of transactions of 23 companies
showed that the mean discount for lack of marketability is 45 percent with a
median of 40 percent.
• August 1990– January 1992. Out of 35 transactions, Emory found that the mean
discount on the price of the securities was 42 percent with a median of 40 percent.

• February 1992– July 1993. Emory reviewed the transaction data of 54 compa-
nies selling securities in IPOs. He found that the average discount on the price of
the securities was 45 percent with a median of 44 percent. Consolidating the
results of the six studies that he has performed, he found that the mean discount
of the total 173 transactions to be 47 percent.
• January 1994–June 1995. Emory evaluated 46 IPO transactions. Both the mean
and median discounts on the purchase price of the securities before the IPO were
45 percent. The discounts ranged from 79 to 6 percent. Emory combined the
results of all seven studies and found that the mean discount for the 219 trans-
actions to date in all the studies was 45 percent and the median was 43 percent.
• November 1995–April 1997. Emory evaluated 91 transactions. The mean and
median discounts on these transactions were 43 and 42 percent, respectively. The
range of discount was 5 to 85 percent. The combined results of the 310 transac-
tions to date in all the Emory studies indicated a mean discount of 44 percent
and a median discount of 43 percent.
• May 1997–March 2000 (Dot.Com Companies). For the first time, Emory
included Dot.Com companies in his study, and evaluated 53 transactions. The
mean and median discounts on these transactions were 54 percent.
• May 1997–December 2000. Emory prepared two studies based on his review of
1,847 IPO prospectuses over this period. In his “limited” study, he analyzed 36
transactions and found a mean discount of 48 percent and a median discount of
44 percent. In his “expanded” study, he broadened his search and did not elimi-
nate companies on the basis of financial strength. The “expanded” study analyzed
283 transactions and found a mean discount of 50 percent and a median discount
of 52 percent. Over the entire 11 studies from 1980 to 2000, the 593 transactions
analyzed had a mean discount of 47 percent and a median discount of 48 percent.
Willamette Management Associates Studies
11
Willamette Management Associates has published the results of 18 studies (time
periods) that analyze IPO transactions that took place from 1975 to 1997. The

premise of the studies was similar to that of the Emory studies; Willamette com-
pared the sale price of stock placed privately before an IPO to the price at IPO to
determine the discount for lack of marketability.
The Willamette studies, however, reviewed transactions that took place from 1
to 36 months before the initial public offering, whereas Emory analyzed transactions
up to five months prior to IPO. Emory used information provided in the company
prospectuses while Willamette used S-1 and S-18 registration statements which dis-
closed more information. Willamette also compared the price-earnings (P/E) multiple
of the security at the time of the private transaction to the P/E multiple at the IPO.
290 VALUATION DISCOUNTS AND PREMIUMS
11
Pratt, Shannon P., Business Valuation Discounts and Premiums (New York: John Wiley &
Sons, Inc., 2001), p. 84.
Willamette also made adjustments to reflect differences in market conditions
between the dates. To do this, Willamette used an Industry P/E multiple at the time
of offering and compared it to the Industry P/E multiple at the time of the private
transaction.
Exhibit 8.10 presents the results of the Willamette studies.
Exhibit 8.10 Lack of Marketability Discount
Willamette Management Associates Summary of Discounts for Private Transaction
P/E Multiples Compared to Public Offering
P/E Multiples Adjusted for Changes in Industry P/E Multiples
a
Period of Study Median Discount
1975–1978 52.5%
1979 62.7%
1980–1982 56.5%
1983 60.7%
1984 73.1%
1985 42.6%

1986 47.4%
1987 43.8%
1988 51.8%
1989 50.3%
1990 48.5%
1991 31.8%
1992 51.7%
1993 53.3%
1994 42.0%
1995 58.7%
1996 44.3%
1997 35.2%
a
Pratt, Shannon P., Business Valuation Discounts and Premiums (New York: John Wiley & Sons, Inc., 2001), p. 84.
Summary of the Emory and Willamette Initial Public Offering Studies
The range of discounts associated with both the Emory and Willamette IPO studies
is from a low of 32 percent to a high of 73 percent. The majority of the discounts
are in the range of 40 to 60 percent. As discussed later, critics of these studies are
concerned with the reliability of both the pre-IPO prices and the IPO prices.
Hitchner Study No. 1
James R. Hitchner, CPA/ABV, ASA, in Atlanta, performed an additional analysis on
the Emory study data. Emory reported average discounts for companies that had
transactions in their stock within five months prior to IPO. Hitchner analyzed and cal-
culated the discounts on transactions taking place in the fifth, fourth, and third
months, respectively, prior to the date of the IPO to see if the discounts were higher
for those companies that had transactions farthest from the IPO date. Hitchner also
analyzed the discounts on transactions taking place up to five, four, and three months,
respectively, prior to the date of the IPO. He also separately analyzed data on stock
options only.
Empirical Evidence of Marketability Discounts 291

292 VALUATION DISCOUNTS AND PREMIUMS
Discounts on transactions occurring between January 1980 and June 1995 were
broken into fifth-, fourth-, and third-month analyses up to and including each period.
• Fifth Month. The mean and median discounts on the 47 transactions taking
place in the fifth month prior to the IPOs were 54 and 50 percent, respectively.
For the 219 transactions that took place within five months prior to the IPOs,
the mean and median discounts were 45 and 43 percent, respectively.
• Fourth Month. The mean and median discounts on the 43 transactions that took
place in the fourth month prior to the IPOs were both 51 percent. For the 172
transactions that took place within four months prior to the IPOs, the mean and
median discounts were 43 and 42 percent, respectively.
• Third Month. The mean and median discounts on the 56 transactions taking
place in the third month prior to the initial public offerings were 43 and 42 per-
cent, respectively. For the 129 transactions that took place within three months
of the initial public offerings (i.e. transactions at one, two, and three months
prior to the initial public offerings), the mean and median discounts were 40 and
39 percent, respectively.
Discounts on transactions occurring between January 1994 and June 1995 also
were broken into fifth-, fourth-, and third-month analyses, at only that monthly period.
• Fifth Month. For the most recent Emory study period, January 1994 to June
1995, the mean and median discounts on the 10 transactions that took place in
the fifth month prior to the IPOs were 50 and 46 percent, respectively. The mean
and median discounts on the 46 transactions that took place within five months
prior to the IPOs were both 45 percent.
• Fourth Month. For the January 1994 to June 1995 study period, the mean and
median discounts on the 17 transactions that took place in the fourth month
prior to the IPOs were 48 and 50 percent, respectively. The mean and median
discounts on the 36 transactions that took place within four months prior to the
IPOs were 43 and 45 percent, respectively.
• Third Month. For the January 1994 to June 1995 study period, the mean and

median discounts on the 11 transactions that took place in the third month prior
to the IPOs were 44 and 43 percent, respectively. For the 19 transactions that
took place within three months prior to the IPOs, the discounts were 39 and 38
percent, respectively.
Discounts on option transactions occurring between January 1980 and June
1995 were divided into fifth-, fourth-, and third-month analyses.
Most of the transactions included in the Emory study involved options. PHG
analyzed the discounts on option transactions that took place in the fifth, fourth,
and third months prior to the date of the initial public offerings.
• Fifth Month. The mean and median discounts on the 32 option transactions that
took place in the fifth month prior to the IPOs for the aggregate Emory studies
were 55 and 51 percent, respectively. The mean and median discounts on the 166
option transactions that took place within the five months prior to the IPOs were
44 and 43 percent, respectively.
• Fourth Month. The mean and median discounts on the 31 option transactions
that took place in the fourth month prior to the IPOs for the aggregated Emory
Empirical Evidence of Marketability Discounts 293
studies were 52 and 51 percent, respectively. The mean and median discounts on
the 134 option transactions that took place within four months prior to the IPOS
were 42 and 41 percent, respectively.
• Third Month. The mean and median discounts on the 45 option transactions
that took place in the third month prior to the IPOs for the aggregate Emory
studies were 41 and 40 percent, respectively. The mean and median discounts on
the 103 option transactions that took place within three months prior to the
IPOs were 39 and 37 percent, respectively.
Discounts on option transactions occurring between January 1994 and June
1995 also were divided into fifth-, fourth-, and third-month analyses.
For the Emory study period, January 1994 to June 1995, the mean and median
discounts on option transactions were 44 and 43 percent, respectively.
• Fifth Month. For the January 1994 to June 1995 study period, the mean and

median discounts on the eight option transactions that occurred in the fifth
month prior to the IPOs were 53 and 49 percent, respectively. The mean and
median discounts on the 33 option transactions that took place within five
months prior to the IPOs were 44 and 43 percent, respectively.
• Fourth Month. For the January 1994 to June 1995 study period, the mean and
median discounts on the 12 option transactions that occurred in the fourth
month prior to the IPOs were 47 and 48 percent, respectively. The mean and
median discounts on the 25 option transactions that took place within four
months prior to the IPOs were 42 and 38 percent, respectively.
• Third Month. For the January 1994 to June 1995 study period, the mean and
median discounts on the nine option transactions that took place three months
prior to the IPOs were both 43 percent. For the 13 option transactions that took
place within three months prior to the IPOs, the discounts were 37 and 33 per-
cent, respectively.
Hitchner Study No. 2
Hitchner performed a second analysis that was very similar to that performed by
John Emory in his studies. Hitchner reviewed the prospectuses of guideline compa-
nies from February 1995 to June 1996 in the consulting industry that had gone pub-
lic. This analysis focused on transactions that had taken place within the companies
prior to their IPOs. Hitchner found 23 transactions that had taken place among 14
companies within 15 months of their IPO.
The mean and median discounts on the 23 transactions that took place prior
(up to 15 months) to the initial public offerings were 51 and 52 percent, respectively.
• Fifth Month. The mean and median discounts on the transactions that took place
in the fifth month prior to the IPOs were 49 and 53 percent, respectively. The
mean and median discounts on the transactions that took place within five
months prior to the IPOs were 44 and 36 percent, respectively.
• Fourth Month. The mean and median discounts on the transactions that took
place in the fourth month prior to the IPOs were 56 and 57 percent, respectively.
The mean and median discounts on transactions that took place within four

months prior to the initial public offerings were 41 and 36 percent, respectively.
294 VALUATION DISCOUNTS AND PREMIUMS
• Third Month. The mean and median discounts on the transactions that took
place in the third month prior to the IPOs were both 31 percent. The mean and
median discounts on the transactions that took place within three months prior
to the IPOs were 31 and 35 percent, respectively. Exhibit 8.11 illustrates the
analysis of the guideline company transactions.
Exhibit 8.11 Analysis of Transactions Occurring In Guideline Companies
IPO Approx.
Guideline IPO Price Trans. Trans. Type of No.
Company Date ($) Date Price ($) Trans. Disc. of Mo.
_________ ______ ____ ________ _______ _________ _____ _______
Whittman Hart (1) 5/3/96 16 12/31/95 6.49 Option 59% 4
Carnegie Group (2) 12/4/95 8 3/1/95 *4.65 Option 42% 9
Cotelligent Group (3) 2/14/96 9 9/8/95 2.70 Option 70% 5
Data Processing Res. (4) 3/6/96 14 1/15/96 9.00 Option 36% 2
Data Processing Res. (5) 3/6/96 14 6/1/95 2.25 Option 84% 9
Data Processing Res. (6) 3/6/96 14 3/1/95 *2.25 Purchase 84% 12
Integrated Systems (7) 4/18/96 5 1/31/95 1.52 Option 70% 15
Integrated Systems (8) 4/18/96 5 11/17/95 3.33 Option 33% 5
Microware (9) 4/3/96 10 5/2/95 3.13 Option 69% 11
Registry, Inc. (10) 6/5/96 17 3/6/96 11.00 Option 35% 3
Registry, Inc. (11) 6/5/96 17 4/1/96 *11.00 Option 35% 2
Registry, Inc. (12) 6/5/96 17 5/1/96 *13.00 Option 24% 1
Ultradata (13) 2/16/96 10 7/31/95 6.00 Option 40% 7
Ultradata (14) 2/16/96 10 12/1/95 *7.25 Option 28% 3
Sykes (15) 4/30/96 18 12/31/95 8.67 Option 52% 4
APAC (16) 10/11/95 16 5/26/95 7.49 Option 53% 5
HCIA (17) 2/22/95 14 2/1/94 *10.50 Option 25% 13
HCIA (18) 2/22/95 14 4/1/94 *10.50 Option 25% 11

HCIA (19) 2/22/95 14 10/1/94 *10.50 Option 25% 5
Idx (20) 11/17/95 18 2/1/95 4.32 Option 76% 10
Mecon (21) 12/7/95 13 3/31/95 0.57 Option 96% 8
UUNet (22) 5/25/95 14 2/1/95 *6.00 Option 57% 4
UUNet (23) 5/25/95 14 1/1/95 *5.00 Option 64% 5
Discounts Mean Median
________ _____ _______
Overall 51% 52%
At Five Months 49% 53%
Five Months or Less 44% 36%
At Four Months 56% 57%
Four Months or Less 41% 36%
At Three Months 31% 31%
Three Months or Less 31% 35%
*Only month and year of transaction available. Assumed the first of the month because specific day was not
available.
Restricted Stock Studies
Additional support for the discount for lack of marketability can be found in the
study of purchases of restricted securities by investment companies.
Investment companies regularly purchase private placements of restricted secu-
rities. Restricted securities may be issued and sold by a publicly traded company
without prior registration with the Securities and Exchange Commission. These
securities typically cannot be resold for a minimum period of one year under the
SEC Rule 144 guidelines.
Because of the restriction on the marketability of the securities, the investment
companies purchase the securities at prices lower than the price of a registered secu-
rity of the same company. The difference between the two prices represents the dis-
count for the lack of marketability.
In the 1970s, the SEC required investment companies to make their transaction
records public. The availability of the records made it possible for analysts to directly

determine the lack of marketability discount on securities purchased by investment
companies and use it as a comparison for the discount on a closely held interest.
Revenue Ruling 77-287
The ruling also discusses a study undertaken by the SEC, published in 1971 and
covering the period from January 1, 1966, through June 30, 1969.
12
The SEC ana-
lyzed the purchases, sales, and holdings of restricted securities held by financial insti-
tutions that disclosed the valuation of their holdings. The average discount was
about 26 percent for all companies.
In Accounting Release No. 113, the SEC acknowledged discounts for restricted
securities.
Restricted securities are often purchased at a discount, frequently substan-
tial, from the market price of outstanding unrestricted securities of the
same class. This reflects the fact that securities which cannot be readily sold
in the public market place are less valuable than securities which can be
sold, and also the fact that by the direct sale of restricted securities, sellers
avoid the expense, time and public disclosure which registration entails.
Empirical Evidence of Marketability Discounts 295
The IRS, in Revenue Ruling 77-287, dealt with the issue of valuing
restricted stocks. It was issued “to provide information and guidance
to taxpayers, Internal Revenue Service personnel, and others concerned
with the valuation, for Federal tax purposes, of securities that cannot
be immediately resold because they are restricted from resale pursuant
to Federal securities laws.”
ValTip
12
Securities and Exchange Commission, “Discounts Involved in Purchases of Common Stock
(1966–1969),” Institutional Investor Study Report of the Securities and Exchange
Commission (Washington, DC: U.S. Government Printing Office, March 10, 1971),

Document No. 92-64, Part 5, pp. 2444–2456.
296 VALUATION DISCOUNTS AND PREMIUMS
Securities and Exchange Institutional Investor Studies. Securities and
Exchange Commission, “Discounts Involved in Purchases of Common Stock
(1966–1969),” Institutional Investor Study Report of the Securities and Exchange
Commission (Washington, DC: U.S. Government Printing Office, March 10, 1971),
Document No. 92-64, Part 5, pp. 2444–2456.
Period of Study
_________________
Mean Discount of 25.8 percent 1966–1969
The Securities and Exchange Commission reviewed purchases of restricted
securities by investment companies for the period January 1, 1966 through June
30, 1969. This study was published in March 1971. It compared the prices at
which the transactions of restricted securities were made to the prices of publicly
traded stocks from the same companies. The study included letter stocks traded on
the New York and American Stock Exchange as well as the over-the-counter (OTC)
markets. The mean discount for lack of marketability of the letter stocks was 25.8
percent.
The study analyzed discounts both by trading market as well as by sales of the
company. Of the OTC nonreporting companies, 56 percent had discounts over 30
percent; 34 percent of the companies had discounts over 40 percent. For companies
with sales between $1 million and $5 million, 54 percent had discounts over 30 per-
cent; 34 percent of the companies had discounts over 40 percent.
Other Restricted Stock Studies. Several additional studies since the 1971
Institutional Investor Study have measured the DLOM using similar comparisons
between restricted securities and their publicly traded counterparts. The results of
these studies have generally averaged between 30 and 35 percent. Many of these
studies were conducted during the period when securities were restricted for two
years. The more important studies and their results are summarized in Exhibit 8.12.
Hall and Polacek. Hall, Lance S., and Polacek, Timothy G., “Strategies for

Obtaining the Largest Valuation Discounts,” Estate Planning (January/February
1994), pp. 38– 44.
Period of Study
_________________
Mean Discount of 23 percent
1979– 1992
The authors discuss relevant factors for determining the taxable value of an
estate. These factors include the criteria outlined by relevant IRS Revenue Rulings
as well as the court-allowed discounts for minority interest and lack of marketabil-
ity. The authors define the purpose for the discounts, evaluate historical trends in
court-allowed discounts, and review several methods for determining the appropri-
ate discount for each situation.
The minority interest discount and the lack of marketability discount are sepa-
rate and distinguishable from each other. The study identifies them as “based upon
independent financial principles and analyses.”
Silber. Silber, William L., “Discounts of Restricted Stock: The Impact of
Illiquidity on Stock Prices,” Financial Analysts Journal (July–August 1991), pp.
60– 64.
Period of Study
_________________
Mean Discount of 33.75 percent
1981–1988
Silber developed a model that describes the relationship of the discount to
restricted securities and the factors that affect the discount.
Using data provided by the Securities Data Corporation, the author analyzed
reported transactions of restricted stock sales from 1981 to 1988.
Of the 310 private placements of common stock of public companies, Silber
chose 69 transactions that carried no “warrants or special provisions.” “For each of
these 69 companies, we recorded the date of the private placement, the price per
share of the restricted stock and the closing price (or the average of the bid and offer

prices) for the company’s publicly traded shares on the placement date.”
Silber compared the securities based on several characteristics, including the
“percentage discount on the restricted stock, dollar size of the offering and number
of restricted shares as a percentage of all common stock.” He also looked at “the
earnings of the firm during the previous fiscal year, total revenues during the previ-
ous fiscal year and market capitalization prior to the private placement.” Analysis
of these transactions showed an average price discount of 33.75 percent. The dis-
counts ranged from 84 percent to a premium (negative discount) in one case of 12.7
percent. Further segregation of the data into discounts less than and greater than 35
percent indicates that “firms with higher revenues, earnings and market capitaliza-
tions are associated with lower discounts.”
Empirical Evidence of Marketability Discounts 297
Exhibit 8.12 Summary of Studies of Restricted Securities Transactions
Discount for
Study Period of Study Lack of Marketability
_____ _____________ __________________
Securities Exchange Commission 1966 – 1969 26%
Hall and Polacek 1979 – 1992 23%
Silber 1981 – 1988 33.75%
Stryker and Pittock 1978 – 1982 45%
Maher 1969 – 1973 35%
Gelman 1968 – 1970 33%
Moroney 1969 – 1973
a
35.6%
Trout 1968 – 1972 33.45%
Arneson Opinion
b
50% or greater
Willamette 1981 – 1984 31.2%

Management Planning, Inc. 1980 – 1995 28%
FMV Opinions, Inc. 1980 – 1997 22%
Johnson Study 1991 – 1995 20%
Columbia Financial Advisors Inc. 1996 – 1997 21%
Columbia Financial Advisors Inc.
c
1997 – 1998 13%
a
Moroney did not state the exact time period of his study of restricted stocks, but it is within this time frame.
b
The author used the 35 percent mean discount of the Maher study as a base discount. He then supports a higher
discount based upon his analysis of the SEC letter stock study and other SEC studies.
c
The effect of the SEC Rule 144 change from a two-year waiting period to a one-year waiting period.
298 VALUATION DISCOUNTS AND PREMIUMS
Using the relationships that he found in his analysis, Silber developed a statis-
tical model that described the discount as a function of the:
• Credit-worthiness of the issuing company
• Marketability of the shares
• Cash flow
• Special (value-added) concessions to the investor
Silber defined the measurable “proxies” for each of the factors. Earnings and
revenues were used to measure creditworthiness. The amount of restricted shares
issued as a percent of total shares outstanding was used to measure marketability.
Special provisions such as “guarantees of representation on the company’s board”
or “a customer relationship between investors and issuer,” also were included in the
model.
Using the least squares statistical model, Silber defined the relationships among
the factors. His results indicate that:
• “The size of the price penalty [discount] varies with firm and issue character-

istics.”
• The size of the block of restricted securities issued affects the size of the discount
more than the amount of revenues of the company.
• As the amount of restricted securities issues increases, those securities become
less liquid and the issuer will have to sell them at a greater discount.
Silber concludes: “The results indicated that marketing a large block of illiq-
uid securities requires significant prior concessions, even with firms with substan-
tial creditworthiness. Liquidity clearly has a significant impact on the cost of equity
capital.”
Stryker and Pittock. Stryker, Charles, and Pittock, William F., “Revenue
Ruling 77-287 Revisited,” SRC Quarterly Reports (Spring 1983), pp. 1– 3.
Period of Study
_________________
Median Discount of 45 percent
1978–1982
In the manner of the SEC study on letter stock, Standard Research Consultants
analyzed 28 restricted stock purchases that occurred from October 1978 through
June 1982. Comparing the value of restricted stocks to public stocks issued by the
same company, they found the median discount at which the restricted stocks sold
to be 45 percent.
According to the authors:
To be eligible for inclusion in our study, the private placement had to
involve the common stock (or the common stock with purchase war-
rants) of a United States corporation and had to occur as an arm’s-length
transaction between unrelated parties which did not affect control of the
corporation. In addition, the corporation could not be in a state of bank-
ruptcy; nor could it be a financial, insurance, or real estate company.
Empirical Evidence of Marketability Discounts 299
Other criteria included the fact that the placement price could not be less than
a dollar per share and that adequate information had to exist about the placement

and the corporation. The discounts ranged from 7 to 91 percent.
The authors also studied the effect on the discount caused by four determinants
of discounts that were outlined in Revenue Ruling 77-287:
1. Earnings
2. Sales
3. Trading market
4. Resale agreement provisions
“Profitability in the fiscal year preceding the placement did not seem to influ-
ence the discount; the 11 companies showing a profit in that year had a median
discount of 45 percent, while the 17 that were unprofitable had a median discount
of 46 percent.” However, the earnings patterns of the companies did have an
effect on the discounts. “On the average, companies that were profitable in each
of the five years prior to the date of placement appeared to sell restricted stock at
substantially smaller discounts from market than did those with two, three, or
four unprofitable years during the five-year period.” Companies that were prof-
itable all five of the prior years had a median discount of 34 percent. Those com-
panies with two to four years of profitability had a median discount of 39 percent,
whereas those with zero or one year of profitability had a median discount of 46
percent.
The magnitude of revenues for the companies also affected the discount per-
centages. Those companies with revenues from approximately $30 million to $275
million had a discount of 36 percent whereas those companies that had revenue in
the range of $500,000 to $1.6 million had a discount of 48 percent.
The authors concluded that of the 28 companies studied, there was not a sig-
nificant difference in the magnitude of the discount based on whether they were
traded on a major exchange or not. “The fact that there did not seem to be a rela-
tionship between the issuer’s trading market and discount might be attributable to
the development, since 1969, of the NASDAQ trading system.”
In terms of resale agreement or registration provisions including trigger or pig-
gyback rights, the authors indicate that:

the median discount for the ten placements involving resale agreement
provisions was 53 percent, versus a median discount for all twenty-eight
placements of 45 percent, a result that appears to be at odds with the
implications of RR 77-287. It should be noted that the promulgation of
Rule 144 in 1972, plus subsequent relaxations of this Rule, have
enhanced the marketability of restricted stock and thus made registration
rights less important.
The authors also discuss other considerations:
• The length of time the stock was held by the owner and the various factors under
Rule 144.
300 VALUATION DISCOUNTS AND PREMIUMS
• The length of time it would take to dispose of the restricted stock since “The
longer the time needed to dispose of the restricted stock, the greater the discount,
ceteris parabis.”
• The financial fundamentals of the issuer such that “The sounder the capitaliza-
tion of an issuer, the lower the discount tends to be.”
• The investor’s appraisals of the unrestricted stock being traded in the market-
place: “one would analyze the issuer’s relative price: earnings multiples, dividend
yields, and ratios of market price to tangible book value as compared with those
of comparable companies (rational investors require higher discounts from an
issuer whose stock they believe is overpriced).”
• The trading volume and volatility of the unrestricted stock: “The greater the
company’s trading volume, the greater the likelihood that upon expiration of
the resale restrictions, the restricted stock can be sold publicly without disrupt-
ing the market for the issuer’s unrestricted stock. A purchase of restricted stock
assumes less additional risk when the market for the issuer’s unrestricted stock
is stable.”
The authors go on to state that “In addition to being probative of discounts in
cases involving non-controlling restricted common stock interests issued in private
placements, these factors are equally important in the valuation of non-controlling

closely held common stock, qualified option stock . . . and other forms of restricted
ownership interest.”
Maher. Maher, Michael J., “Discounts for Lack of Marketability for Closely-
Held Business Interests,” Taxes (September 1976), pp. 562–571.
Period of Study
________________
Mean Discount of 35 percent 1969–1973
Median Discount of 33 percent 1969–1973
The author researched the purchases of restricted securities by investment com-
panies from 1969 to 1973. “The discounts were derived by comparing the cost to
the funds to the market value of unrestricted securities of the same class in the same
companies on the acquisition date.” Maher determined that the mean discount on
transactions occurring in this time frame was approximately 35 percent. The range
of discounts for the 34 transactions studied was 2.7 to 75.66 percent. Further analy-
sis reveals that 68 percent of the transactions occurred at discounts of 30 percent or
more, 35 percent occurred at discounts of 40 percent or higher, and 21 percent
occurred at a discount of 50 percent or greater.
Maher acknowledges that the investment companies discounted the purchases
to take into account the costs of registering the stocks, but he argues that the applied
discounts are considerably higher than the costs that investment companies would
incur to register the stock.
Maher justifies the 35 percent discount for lack of marketability by pointing
out that investors give up the opportunity to invest in other more marketable instru-
ments and that the investor “would continue to have his investment at the risk of
the business until the shares could be offered to the public or another buyer is
found.”
Empirical Evidence of Marketability Discounts 301
Gelman. Gelman, Milton, “An Economist-Financial Analyst’s Approach to
Valuing Stock of a Closely Held Company,” Journal of Taxation (June 1972),
pp. 353– 354.

Period of Study
________________
Mean and Median Discount 33 percent
1968–1970
The author evaluates the purchases of restricted securities by four investment
companies from 1968 through 1970. Restricted securities are interests in public cor-
porations that contain covenants limiting the resale of the securities by the investor
for periods of up to two years. Investment companies buy the stocks “directly from
the company, or, in some instances, from selling stockholders. . . . Since there is a
restriction on their transferability, restricted securities are usually purchased at a
price substantially below that of the freely-marketable securities of the same class as
the company.”
Using publicly available financial statements, the author compared the price
that the investment companies paid for the restricted securities of a corporation to
the market price of publicly traded securities of the same corporation. This study
was based on an analysis of publicly traded close-end investment companies that
specialized in and reported on restricted securities and letter stocks of public com-
panies. In 1970 the four investment companies “had letter stock investments in the
common stocks of 89 public companies.” Gelman analyzed these transactions and
determined that the mean and median discount of all 89 stock purchases was 33
percent.
It is significant to note that:
• 36 percent of the stocks exhibited discounts greater that 40 percent
• 59 percent of the stocks exhibited discounts greater than 30 percent
• 84 percent of the stocks exhibited discounts greater that 20 percent
Moroney. Moroney, Robert E., “Most Courts Overvalue Closely Held
Stocks,” Taxes (March 1973), pp. 144–156.
Period of Study
________________
Mean Discount of 35.6 percent, 1969–1973

Median Discount of 33 percent 1969–1973
Public records of the purchases of unregistered securities by investment com-
panies provide a basis for determining the size of the lack of marketability discounts
for closely held securities. Because the government restricts the sale of unregistered
stocks, they are less marketable than freely traded securities.
Beginning in 1969, the SEC required that registered investment companies
make public their internal restricted securities valuation methods and transaction
data (SEC Accounting Series Release No. 113, dated October 21, 1969, and
Accounting Series Release No. 118, dated December 23, 1970). By the end of 1968,
open-end and close-end registered investment companies held over $4.2 billion in
302 VALUATION DISCOUNTS AND PREMIUMS
restricted equity securities. A review of the prices at which investment companies
purchased 146 unregistered and restricted stocks reveals that the actual discount for
these securities was sometimes as great as 90 percent.
Moroney also investigated the published financial statements of the compa-
nies and reviewed the valuations prepared by the boards of directors of the firms
that were required by law to make good-faith estimates of value. Investment com-
panies’ board of directors consider several factors when evaluating the value of
their restricted securities holdings for their annual financial statement, including
the size of the security block, the size of the issuer, and the issuer’s presence in the
market.
Of the 146 transactions reviewed, the mean discount based on the original
purchase was 35.6 percent. Of further interest is that 64 percent of the transactions
occurred at a discount of 30 percent or greater, 40 percent occurred at a discount
of 40 percent or greater, and 23 percent occurred at a discount of 50 percent or
higher.
Trout. Trout, Robert R., “Estimation of the Discount Associated with the
Transfer of Restricted Securities,” Taxes (June 1977), pp. 381–385.
Period of Study
_________________

Mean Discount of 33.45 percent
1968–1972
To determine the appropriate lack of marketability discount on restricted secu-
rities, Trout analyzed 60 historical transactions of investment letter stock purchases
by mutual funds in the period from 1968 to 1972. Using multiple regression analy-
sis, he determined the relationship among the factors that influence the size of the
discount. These factors are:
• Exchange listing
• Number of shares outstanding
• Percent control, which is the number of shares purchased divided by the shares
outstanding
• Size of the purchase
• Value of the purchase
Trout enters actual transaction data for each of the variables and solves for the
coefficients of the variables. These coefficients describe the relationship that the
variables have to the size of the lack of marketability discount.
• Exchange Listing. The exchange listing variable accounts for the fact that stocks
traded on larger exchanges are generally more marketable than those that are
not, and will have lower discounts. Trout sets the variable to “one if the security
is listed on either the New York or the American Stock Exchange, and a value of
zero otherwise.” Analysis indicates that stocks traded on the above exchanges
will have an 8.39 percent lower discount than securities listed on smaller
exchanges.
• Number of Shares Outstanding. “The number of shares outstanding is a proxy
for the marketability of the shares purchased.” Securities with a greater number
Empirical Evidence of Marketability Discounts 303
of shares outstanding will be more marketable and therefore have a lower dis-
count. Analysis indicates that “the discount will be about four percentage points
smaller for each additional million shares of common stock of the issue which
are outstanding.”

• Percent Control. The amount of control measures both the premium for the
privilege of owning a controlling interest in the securities as well as the discount
for disposing of a large block of the security. The percent control has a small
negative affect on the discount: “the discount should decline by a little less than
1 percentage point for each additional 1 percent of control involved in the pur-
chase.”
• Size of the Purchase. The size variable “reflects the reduced discount necessary
for a purchase of a small number of shares of a restricted security that could eas-
ily be sold.” The analysis “indicates that small purchases of stock should have a
12.11 percentage point lower discount than purchases that amount to more than
1 percent of the outstanding shares.”
• Value of the Purchase. The value of purchase discount reflects “the value the
shares purchased would have if they were registered or unrestricted.” Analysis
indicates that “the discount will increase by 4.75 percentage points for each
additional million dollars of stock purchased.”
In summary, Trout’s model has a moderate ability to account for variations in
observed discounts. The analysis indicates that the size of the discount is strongly
affected by the discussed factors. The model does not explain all of the variations
among observed discounts, because other nontangible factors, such as purchase
agreements, the bargaining power of the seller, and the lack of an auction market,
affect the discount size.
Arneson. Arneson, George S., “Nonmarketability Discounts Should Exceed
Fifty Percent,” Taxes (January 1981), pp. 25–31.
Discount of 50 percent or Greater
Arneson evaluated studies of purchases of letter stock by investment compa-
nies. He referred to studies by Maher and Moroney that indicate the appropriate
discount for nonmarketability of an interest in a closely held company should be
around 35 percent. Arneson agreed with this rate for restricted securities but
pointed out that restricted securities of publicly traded companies are different from
interests in closely held businesses. He sees enough dissimilarity between the two

securities to argue that the discount rates on closely held securities should be above
the 35 percent level.
Arneson’s support for higher discounts included such factors as:
• Costs of flotation
• Lack of a preestablished market
• Risk
• Inability to market because of company size and history
• Noncash costs of underwriting
• Timing and length of time necessary to go public
304 VALUATION DISCOUNTS AND PREMIUMS
He concludes that the discount for lack of marketability for a closely-held com-
pany should be closer to 50 percent or greater.
• Costs of Flotation. Arneson evaluated the cost of flotation and determined that
the cost should include compensation to underwriters and other expenses. He
found that, on average, the compensation to underwriters was 8.41 percent and
other expenses were 4.02 percent of gross proceeds (based on 1,599 offerings to
the general public through securities dealers). For companies whose size of issue
was between $2 million and $5 million, the underwriters’ compensation was
8.19 percent and the other expenses were 3.71 percent. It is important to note
that other expenses include federal revenue stamps, state taxes, listing fees, print-
ing costs, and legal and accounting fees.
Arneson goes on to note that in addition to the other expenses, there was
other noncash compensation in the form of warrants or options in many situa-
tions. He indicates that such compensation has been prevalent among small
equity issues. He feels that “many closely-held companies would most likely
require such additional consideration, and in appraising the cost to market such
securities should be provided for.”
Arneson’s information comes from the Securities and Exchange Commission’s
“Costs of Flotation of Registered Issues, 1971-1972,” (December, 1974). He also
reviews a related study called “An Empirical Analysis of the Flotation Costs of

Corporate Securities,” Journal of Finance (September 1975) and “Unseasoned
Equity Financing,” Journal of Financial and Quantitative Analysis (June 1975).
The extra cost for warrants and options was approximately 12 percent.
• Preexisting Market. Using the same studies, Arneson presents evidence concern-
ing the wide difference in compensation paid to underwriters for stocks with no
previous market as opposed to stocks that already had established market posi-
tions. “On the average this amounted to 3.7 percent but varied with size and list-
ing exchanges.” The study also indicated that the discounts were higher for
stocks on regional exchanges and OTC compared to the New York Stock
Exchange and American Stock Exchange.
• Risk. Arneson feels that a thorough analysis of the company and the industry in
which it operates is an important element in setting risk. He feels that risk is
affected by the size of the company and that risk affects the costs of securities
flotation. Although he did not determine a specific factor, he indicated that risk
could be assessed on the basis of “an industry’s general market conditions, busi-
ness risk of a particular company and its financial risk, leverage, margins and the
like.”
• Ability to Market. “A serious weakness in utilizing flotational basis to determine
nonmarketability is that for very small companies, there is almost no possibility
that an underwriting could be carried out and a public market created.” Arneson
quotes in an article by Gerald A. Sears entitled “Public Offerings for Smaller
Companies,” published in the Harvard Business Review (September-October
1968), in which Sears lists the criteria for a company to market its stock suc-
cessfully: “The company should have a growth rate higher than its industry to
attract investors. Owner-managers accustomed to answering to no one in run-
ning their businesses must be able to adjust to operating in a sometimes uncom-
fortable spotlight of attention. The effect of public disclosure must not be to
compromise a company’s business.”
• Hidden but Real Costs. “Another cost for a privately-held company going pub-
lic is an ongoing one of audits, shareholder reports and relations, S.E.C. and state

security reports, transfer agent, shareholder meetings and the like. For a small
company, these could represent a sizable additional annual expense.”
• Time and Timing. “Lettered stock could reasonably expect to become registered
and thus freely tradable in two to three years; however, it could take longer for
a closely-held company to prepare itself and have its stock marketed.” Arneson
goes on to talk about the fact that the general condition of the marketplace also
could dictate whether a company could go public. Several factors outside a firm
will influence its ability to market the equity:
• General level of business activity
• Level of interest rates
• Level of stock prices
• Availability of funds in the money markets
Willamette Management Associates Study
Period of Study
_________________
Median Discount of 31.2 percent
1981–1984
In a study of 33 transactions involving purchases of restricted securities from
1981 through 1984, Willamette Management compared the prices at which the
restricted securities were issued to the prices for comparable publicly traded stocks
from the issuing company. It found that the restricted securities sold at a median dis-
count of 31.2 percent.
“The slightly lower average percentage discounts for private placements during
this time may be attributable to the somewhat depressed pricing in the public stock
market, which in turn reflected the necessary economic conditions prevalent during
most of the period of the study.”
13
Management Planning Restricted Stock Studies.
14
An independent business

appraisal firm, Management Planning, Inc. (MPI) has compiled an analysis of the
discounts on restricted stocks as compared to their publicly traded counterparts that
includes data from 1980 through 1995. MPI reviewed all reported private place-
ments in that period, choosing transactions that met the following criteria:
• Restricted stock in the transaction had to have a publicly traded and actively held
common stock counterpart in the same company with the same rights as the
restricted stock.
• Data on the transaction had to be available.
• Publicly traded common stock counterpart had to sell at a price of at least $2 per
share.
• Company selling the stock must be domestic.
Empirical Evidence of Marketability Discounts 305
13
Shannon P. Pratt, Robert F. Reily, and Robert R. Schweihs, Valuing a Business: The Analysis
and Appraisal of Closely Held Companies, 4th ed. (New York: McGraw-Hill, Inc.), p. 400.
14
Christopher Z. Mercer, Quantifying Marketability Discounts (Peabody Publishing, L.P.,
1997), pp. 350–355. (Used with permission.) Note: This study has been updated. See
Chapter 5 of Handbook of Advanced Business Valuation, Robert F. Reilly and Robert P.
Schweihs, eds. (New York: McGraw-Hill, Inc., 2000).
306 VALUATION DISCOUNTS AND PREMIUMS
• The company selling the stock must not be described in disclosure documents as
being in a developmental stage.
According to MPI, the criteria mitigate abnormalities in discount data that may
be caused by market inefficiencies for certain inactive stocks or speculative stocks.
Over 200 private placements of restricted stock met the criteria. MPI further elimi-
nated any company “that suffered a loss in the fiscal year preceding the private
transaction,” any company with revenues less than $3 million (a start-up company),
and any transactions of stocks with known registration rights. Only 49 of the orig-
inal group of companies met the criteria. Exhibit 8.13 summarizes the results of the

MPI study.
Exhibit 8.13 Management Planning Inc., Restricted Stock Study—Summary of Transaction Data
Revenues Earnings Market Cap. Indicated
($MM) ($MM) ($MM) Discount %
________ _________ ___________ __________
Mean 47.5 2.1 80.4 27.7
Median 29.8 0.7 43.5 28.8
Minimum 3.2 0.1 3.4 0.0
Maximum 293.0 24.0 686.5 57.6
To test the correlation between certain factors and the restricted stock discount,
MPI divided the transactions into four quartiles. Two of the 49 companies were
omitted from the quartiles because they were financial companies. The results of
MPI’s analysis indicated that some factors had a clear correlation to the restricted
stock discount while others had some or no correlation to the restricted stock dis-
count.
Factors with a Clear Correlation. A number of factors were reviewed in each
quartile to confirm whether they appeared to affect the restricted stock discount:
• Revenues
• Recent earnings
• Market price/share
• Price stability
• Earnings stability
The analysis indicated that revenues and recent earnings had an inverse rela-
tionship with the restricted stock discount. Restricted stocks in companies with
higher revenues or earnings generally were subject to lower discounts than compa-
nies with lower revenues or earnings. Companies whose stock sold at higher prices
per share had lower restricted stock discounts. MPI stated that “lower share prices
are sometimes associated with more speculative or risky companies.” MPI measured
price stability “by taking the standard deviation of the stock prices divided by the
mean of the stock prices and is based on month-end stock prices for the twelve

months prior to the transaction date.” The restricted stock discounts are higher for
Empirical Evidence of Marketability Discounts 307
companies with a history of lower price stability. Earnings stability was measured
based on the fiscal year net income data of the 10 years prior to the transaction date.
Companies with more stable earnings have lower restricted stock discounts.
Exhibit 8.14 illustrates the result of MPI’s analysis of the above factors. In
ranking revenues, earnings, market price/share, and earnings stability, the first quar-
tile represents the higher end and the fourth quartile represents the lower end of the
range. For price stability, the first quartile represents the lower end and the fourth
quartile represents the higher end of the range.
Exhibit 8.14 Management Planning, Inc., Restricted Stock Study—Factors with Clear Correlation to
Restricted Stock Discounts
15
1st Quartile 2nd Quartile 3rd Quartile 4th Quartile
%%%%
__________ __________ __________ __________
Revenues Median 18.7 22.2 31.5 36.6
Mean 21.8 23.9 31.9 34.7
Earnings Median 16.1 30.5 32.7 39.4
Mean 18.0 30.0 30.1 34.1
Market Median 23.3 22.2 29.5 41.0
Price/Share Mean 23.3 24.5 27.3 37.3
Price Median 34.6 31.6 19.2 19.4
Stability Mean 34.8 33.3 21.0 22.0
Earnings Median 14.1 26.2 30.8 44.8
Stability Mean 16.4 28.8 27.8 39.7
Factors with Some Correlation. The following factors showed some correla-
tion with the restricted stock discounts:
• Market capitalization
• Number of shares in block

• Time to sell according to SEC Rule 144 restrictions (dribble out period, the num-
ber of three-month periods)
• Number of weeks trading volume to sell
• Block size/trading volume (percent), 10-year revenue
• 10-year earnings growth and revenue stability
The analysis indicated that these factors generally followed a predictable pat-
tern. Companies with larger market capitalization tended to have lower discounts.
Larger blocks of stock tended to have higher discounts. The longer the period
required to sell the stock based on the Rule 144 restrictions, the higher the
restricted stock discount tended to be. The higher the block size as a percent of
annual trading volume, the higher the discount tended to be. Companies with
15
Ibid., p. 357.
308 VALUATION DISCOUNTS AND PREMIUMS
greater revenue and earnings growth and revenue stability tended to have lower
discounts.
Exhibit 8.15 illustrates the result of MPI’s analysis of the above factors. In
ranking market capitalization, block size, weeks to sell, block size/trading volume
(percent), revenue and earnings growth, and revenue stability, the first quartile rep-
resents the higher end and the fourth quartile represents the lower end of the range.
For the SEC Rule 144 three-month period, the first quartile represents the longest
period and the fourth quartile represents the shortest.
Exhibit 8.15 Management Planning, Inc., Restricted Stock Study—Factors with Some Correlation
to Restricted Stock Discounts
16
1st Quartile 2nd Quartile 3rd Quartile 4th Quartile
%%%%
__________ __________ __________ __________
Market Median 29.9 25.4 26.9 22.5
Capitalization Mean 33.0 26.2 26.0 26.3

Block Size Median 29.9 30.0 27.0 19.6
(Shares) Mean 31.8 29.6 26.6 23.2
Three-Month Median 30.7 29.9 27.9 19.6
Period to Trade Mean 30.4 30.1 26.6 24.2
# of Weeks Median 30.7 30.8 28.4 19.6
Trading Volume Mean 32.4 29.1 25.6 24.2
to Sell
Block Size/ Median 30.7 30.8 28.4 19.6
Trading Mean 32.4 29.1 25.6 24.2
Revenue Median 28.2 25.0 28.0 39.4
Growth Mean 26.2 25.0 29.1 31.7
Earnings Median 24.3 17.7 35.2 34.2
Growth Mean 26.2 19.5 33.7 32.6
Revenue Median 29.1 12.6 34.3 41.0
Stability Mean 27.4 15.6 34.7 34.4
FMV Opinions Study. FMV Opinions, Inc., reviewed 243 restricted stock
transactions from 1980 through April 1997. This study was initially reported in
Valuation Strategies
17
in 2001 with a follow-up article in Business Valuation
Update.
18
All transactions were prior to the Rule 144 amendment in 1997 that
reduced the holding period from two years to one year. The overall mean (average)
discount in the study is 22.1 percent and the median discount is 20.1 percent. The
standard deviation of the sample is 16.0 percent. The median discount for exchange-
traded securities is 15.3 percent, while the median discount for over-the-counter
traded securities is 22.4 percent.
16
Ibid., p. 359.

17
Robak and Hall, “Bringing Sanity to Marketability Discounts: A New Data Source,”
Valuation Strategies, Vol. 4, No. 6 (July/August 2001).
18
Robak, Espen, “FMV Introduces Detailed Restricted Stock Study,” Shannon Pratt’s
Business Valuation Update, Vol. 7, No. 11 (November 2001).
The FMV Study also provides an analysis of the 243 transactions by SIC Code.
As there are too few transactions per SIC code to be meaningful, the authors
grouped the transactions into SIC code ranges. The study concludes that financial
descriptors such as size, risk, profitability, and liquidity are the most important
determinants of the discount for the lack of marketability, not business type.
Risk had a significant effect on the size of the discounts. The study showed that
smaller, less-profitable entities and those with a higher degree of balance sheet risk
had the highest discounts. The study also found a correlation between the size of the
discount and the stock price. The DLOM increases significantly with decreasing
stock prices. Other inferences drawn from the FMV study (including revenue,
income, dividend payments, dollar block size, book value, market value, and trad-
ing volume) also confirm the relationship between risk and the lack of marketabil-
ity discount.
Johnson Study. The Johnson study
19
observed 72 transactions during the
years 1991 to 1995. The range of the discounts was from a negative 10 percent (a
premium) to 60 percent. The study points to an average discount of 20 percent,
which is lower than past studies. The author attributes the decline in the size of the
discounts to the increased number of investors who entered the market for restricted
stocks in this five-year period following the SEC adoption of Rule 144A, which
allowed qualified institutional investors to trade unregistered securities without fil-
ing registration statements. The holding period for restricted stocks in this study was
two years.

The study also considered the effect of such factors as profitability, size, trans-
action amount, and the holding period on the amount of the discount for lack of
marketability. The average DLOM was 16 percent when the company reported pos-
itive earnings compared to 23 percent when the company reported a loss. This
spread in the average discount remained constant for each year net income was
examined. The relationship between the magnitude of the discount and the size of
the company is clearly direct. The average discount was 13 percent for companies
with sales greater than $200 million compared to 23.5 percent for companies with
sales of less than $10 million.
Columbia Financial Advisors, Inc. Columbia Financial Advisors, Inc. (CFAI)
performed two studies; one examined only private equity placements over the
period January 1, 1996, through April 30, 1997, and the other study examined only
private common equity placements over the period January 1, 1997, through
December 31, 1998. The second study was notable in that it is the first study to con-
sider DLOM after the 1997 Rule 144 change that reduced the holding period for
restricted stocks from two years to one.
In the first study, CFAI analyzed 23 transactions and found an average discount
of 21 percent. The discounts ranged from 0.8 to 67.5 percent; the median was 14
percent. The study offers this explanation of the decline in the size of DLOM from
the earlier studies:
Empirical Evidence of Marketability Discounts 309
19
Johnson, Bruce, “Restricted Stock Discounts, 1991– 95,” Shannon Pratt’s Business
Valuation Update, Vol. 5, No. 3 (March 1999), pp. 1–3.
These discounts are generally lower than the discounts recorded in the
earlier studies noted above which generally indicated discounts of
approximately 35 percent. The increase in volume of privately placed
stock (Rule 144A) in the past several years offers an explanation. As
activity in a market increases, more and better information becomes
available. In addition, there are now more participants in the market for

restricted stocks due to Rule 144A and, therefore, increased liquidity.
This would tend to decrease discounts because better information results
in less risk and thus a lower required rate of return. The lower discounts
in this particular study may also reflect, to some degree, the market’s
anticipation of the SEC’s change in the holding period from two years to
one year, although we have no way to verify this. Since June 1995, the
SEC proposed amendment to Rule 144 was published for public com-
ment. Therefore, knowledgeable private placement and Rule 144A mar-
ket participants were most likely aware of the proposed changes.
20
The average discount for the second study, after the Rule 144 holding period
was shortened to one year, was 13 percent. The range of discounts in the second
study, which analyzed 15 transactions, was 0 to 30 percent; the median was 9 per-
cent. According to CFAI, “The lower discounts in this study in all probability reflect
the market’s reaction to the SEC’s change in the holding period from two years to
one year.”
The CFAI study also noted other market evidence to support declining dis-
counts following the Rule 144 holding period change. Tetra Tech, Inc., a publicly
traded environmental engineering firm, is active in industry acquisitions and typi-
cally uses its restricted stock for acquisitions. The Tetra Tech Form 10-K for the fis-
cal year ending September 30, 1999, included the following statement in the
footnotes to its September 30, 1999, financial statements: “The Company values
stock exchanged in acquisitions based on extended restriction periods and economic
factors specific to the Company’s circumstances. During fiscal 1998 and 1999, stock
exchanged in acquisitions was discounted by 15 percent. During fiscal 1997, the dis-
count on stock exchanged in acquisitions ranged from 16 to 28 percent.”
The CFAI study concluded that while discounts for restricted stocks are declin-
ing, “the studies conducted after 1990 are not relevant for purposes of determining
discounts for lack of marketability for privately held stock, because they reflect the
increased liquidity in the market for restricted securities. Such increased liquidity is

not present in privately held securities.”
Overall Observations of Studies
The following list presents some interesting observations after reviewing these
empirical studies:
• The smaller the company (revenues, earnings, market capitalization), the larger
was the discount for lack of marketability.
• Issuers of restricted stock may be better credit risks.
310 VALUATION DISCOUNTS AND PREMIUMS
20
Aschwald, Kathryn F., “Restricted Stock Discounts Decline as Result of 1-Year Holding
Period—Studies After 1990 ‘No Longer Relevant’ for Lack of Marketability Discounts,”
Shannon Pratt’s Business Valuation Update, Vol. 6, No. 5 (May 2000), pp. 1–5.
Quantitative Tools 311
• Issuers of restricted stock are publicly traded companies that have an active mar-
ket for their stock. Owners of stock in a closely held business have no access to
an active market for their stock. Closely held businesses are unlikely to ever be
publicly traded.
• Many publicly traded companies reflect annual dividends and/or an established
record of capital appreciation in their share price. Many closely held businesses
cannot offer this.
• Purchasers of restricted stock are institutional investors whose investment goals
and criteria are far different from those of the individual purchaser of a closely
held business interest.
• Institutional investors have different levels of risk perception and risk tolerance
from purchasers of closely held business stock.
• Purchasers of restricted securities usually intend to market the purchased securi-
ties in the future and assume a ready market will exist at that time. Purchasers
of stock in closely held companies have little or no expectation to market the
stock in the future; if they expect to market the stock, they assume a limited mar-
ket will exist for them to do so.

• Investments of venture capital companies in OTC nonreporting companies most
closely resemble purchases by closely held business owners.
• Venture capital investments are generally of relatively short duration, suggesting
even higher discounts for the typically longer positions in closely held business
stock.
• When an analyst applies a discount to a closely held company interest that is
equal to the discount observed in restricted stock of a publicly traded company,
the implication is that the restricted stock is comparable to the closely held stock.
• Blind reliance on empirical studies or discounts allowed by the courts is over-
simplistic as each valuation has its own unique facts and circumstances that must
be reflected in the selection of discounts.
• Valuation analysts who rely solely on empirical studies without analysis may
understate discounts and overstate value.
• Valuation analysts often fail to support discounts with sound reasoning and con-
sidered analysis.
• In the valuation of stock in most closely held businesses, the average discounts
observed in the restricted stock studies may be considered the minimum discount
applicable in many situations.
QUANTITATIVE TOOLS
Investor’s Discounted Cash Flow Models
John C. Harper, Jr., and J. Peter Lindquist wrote one of the early articles on the use
of a “shareholders’” DCF model. In their article they present a straightforward
example
21
:
21
John C. Harper, Jr., and J. Peter Lindquist, “Quantitative Support for Large Minority
Discounts in Closely Held Corporations,” The Appraisal Journal (April 1983).
Let us demonstrate by a simple but realistic example of how this dis-
count is calculated and the impact it can have on today’s value of a share

of stock. A friend of John Smith’s is approaching retirement and has
offered to sell Smith his 10 percent common stock interest in Acme
Services, Inc., which is controlled by members of the William Jones fam-
ily. What can Smith afford to pay for this stock?
Today’s value: Smith analyzes the performance of the company
using the Revenue Ruling 59-60 guidelines, then discusses his opinions
with Bill Jones, current president of the company. They agree that $100
per share is a fair value if 100 percent of the stock were to be sold today.
The article also presents that the company will grow 10 percent per year for the
next 10 years at which time Jones is to retire and “may” sell the company. Smith
used a 25 percent annual return on investment given the risks of a private company
investment.
If the sale of the company is expected to be in the tenth year, then a buyer
should not pay any more than $28, or a 72 percent discount from the original $100.
The expected or anticipated year of sale can be most difficult to determine as the
controlling shareholder’s age, health, mental well-being, and “exit strategy” all
affect the decisions to sell.
This example shows that a minority interest with very little market is near
worthless. Furthermore, the discount that we see in this example may be a combined
discount of both lack of control and lack of marketability because the $100 per
share price is an “enterprise” or controlling value, and the present value in the tenth
year of $28 may represent “cash equivalent” or marketable minority interest value,
thus including both discounts.
Quantitative Marketability Discount Model
In 1997 Z. Christopher Mercer published a book entitled Quantifying
Marketability Discounts that expanded on the concepts presented in the
Harper/Lindquist article. Mercer’s book presents a model for analyzing marketabil-
ity discounts and includes excellent overviews of restricted stock studies, IPO stud-
ies, and Tax Court cases.
The quantitative marketability discount model (QMDM) model requires five

key inputs:
• Marketable minority value of the stock
• Expected growth rate of a marketable minority shareholder interest
• Expected holding period
• Required rate of return for a nonmarketable minority interest
• Expected dividend payments
Some analysts have observed that the discount derived in this approach may
appear to combine discounts both for lack of control and marketability. Mercer,
however, disagrees. In Business Valuation, Discounts and Premiums, he states:
A number of appraisers have suggested that the QMDM may be captur-
ing elements of the minority interest discount as well as the marketabil-
312 VALUATION DISCOUNTS AND PREMIUMS
ity discount. There has been a recent exchange on this issue in Shannon
Pratt’s Business Valuation Update in vol. 7, no. 3 (March 2001) pp. 7-
10 and vol. 7, no. 5 (May 2001) pp. 9-10. Assuming, as I do, that it is
appropriate for appraisers to make normalizing adjustments in the devel-
opment of marketable minority valuation indications, the QMDM cap-
tures the appropriate marketability discount. The rationale for my
position on normalizing adjustments is outlined in Dr. Pratt’s book, Cost
of Capital—Estimation and Applications, in Appendix D which he asked
me to write relating to the use of ValuSource PRO Software. Some
appraisers assume that such normalizing adjustments for discretionary
owner compensation and expenses are inappropriate in minority interest
appraisals because they reflect elements of control not available to
minority shareholders. They further assume that the diminution of value
resulting from the “leakage” of discretionary cash flows reflects elements
of a minority interest discount. Under these assumptions, which I do not
believe to be correct, the QMDM captures elements of the minority
interest discount.
22

Option Pricing Models
In 1993 David B. Chaffe III published an article about his theory that the Black-
Scholes pricing model could be used to determine the amount of a marketability dis-
count.
23
Mr. Chaffe uncovered relationships in the comparison of his computation
of the marketability discount with that of the transaction data. He found that the
European option, which is exercisable only at the end of the option period, could be
an appropriate model for the SEC Rule 144 holding period of restricted shares.
Substituting certain inputs of the model to express conditions of a restricted stock,
he was able to produce results similar to those of the restricted stock studies. His
analysis was presented in Business Valuation Review, December 1993, “Option
Pricing as a Proxy for Discount for Lack of Marketability in Private Company
Valuations.”
Quantitative Tools 313
22
Pratt, Shannon P., Business Valuation Discounts and Premiums (New York: John Wiley &
Sons, Inc., 2001), p. 184.
23
David B. Chaffe III, “Option Pricing as a Proxy for Discount for Lack of Marketability in
Private Company Valuations,” Business Valuation Review (December 1993).
The QMDM represents continued theoretical development of the con-
cept of the marketability discount. Some appraisers have adopted some
form of the framework for analyzing discounts that Mercer has pre-
sented but most agree that if used, it should be in conjunction with the
use of traditional discount studies.
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