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nent #1, the delay to sale of DLOM, for a privately held ¬rm. Note that
˜˜Value of Block”Post Discount™™ (Table 7-10, A7) is analogous to ˜˜Shares
Sold”$™™ (Table 7-5, A50), and ˜˜FMV“100% Marketable Minority Inter-
est™™ (Table 7-10, B8) is analogous to ˜˜Market Capitalization™™ (Table 7-5,
A51). The regression coef¬cients are in B5“B11. We insert the subject com-

T A B L E 7-10

Calculation of Component #1”Delay To Sale [1]


4 Coef¬cients Subject Co. Data Discount

5 Intercept 0.1292 NA 12.9%
Revenues2 [2]
6 5.39E 18 3.600E 13 0.0%
7 Value of block-post-discount [3] 4.39E 09 $4,331,435 1.9%
8 FMV-100% marketable minority interest 6.10E 10 $5,000,000 0.3%
9 Earnings stability 0.1381 0.4500 6.2%
10 Revenue stability 0.1800 0.3000 5.4%
11 Average years to sell 0.1368 1.0000 13.7%

12 Total Discount 13.4%
14 Value of block”pre-discount [4] $5,000,000

[1] Based on Abrams™ Regression #2 of Management Planning, Inc. data
Revenues2 $6,000,0002 (6 106)2 1013
[2] 3.6
[3] Equal to (value of block pre-discount) * (1 discount).
[4] Marketable minority interest FMV

PART 3 Adjusting for Control and Marketability
pany data in C6“C11, except for row 7, which we will discuss below. Our
subject company has $5 million in revenues (which, squared, equals 3.6
1013, per (C6), 100% marketable minority interest FMV of $5 million
(C8, analogous to market capitalization for the public companies in the
Management Planning, Inc. data), and earnings and revenue stability of
0.45 (C9) and 0.30 (C10), respectively.55 We estimate it will take one year
to sell the interest (C11).
Since we are valuing 100% of the capital stock of the ¬rm, the value
of the block of stock also has an FMV of $5 million (B14) before DLOM.56
The regression calls for the postdiscount FMV, which means we must
subtract the discount. The formula in cell C7 is: B14*(1 D12), i.e., the
postdiscount FMV equals the prediscount FMV (1 Discount). How-
ever, this is a simultaneous equation since the discount and the shares
sold in dollars each depend on the other. In order to be able to calculate
this, your spreadsheet should be set to allow recalculation with multiple
iterations. Otherwise you will get an error message with a circular ref-
erence.57 Column D is equal to column B column C, except for the y-
intercept in D5, which transfers directly from B5. Adding each of the
components in column D, we obtain a forecast discount of 13.4% (D12).

Limitations of the Regression. There may be combinations of subject
company data that can lead to strange results. This is especially true be-
1. The subject company data are near the end or outside of the
ranges of data in the regression of the MPI data.
2. There is very little variation in the range of the ˜˜average time to
sale™™ variable in our set. Most all of the restricted stock could be
sold between two and three years from the transaction date,
which is very little variation. Only 4 of the 53 sales were
expected to take less than two years (see below).
3. The R 2 is low.
4. The standard error of the y-estimate is fairly high”10%.
Regarding number 1, 47 of the 53 restricted stock sales in the MPI
database took place before the SEC circulated its Exposure Draft on June
27, 1995,58 to amend Rule 144(d) and (k) to shorten the waiting period

55. We do not explicitly show the detail of the calculations of earnings and revenue stability. Our
sample Restricted Stock Discount Study in Chapter 8, Table 8-1, shows these calculations.
56. Had we been valuing a 10% block of stock, B14 would have been $500,000.
57. If you create your own spreadsheet and make changes to the data, the simultaneous equation
is fragile, and it can easily happen that you may get error messages. When that happens,
you must put in a simple number in C7, e.g., $200,000, allow the spreadsheet to
˜˜recalibrate™™ and come back to equilibrium, then put in the correct formula. We do not have
this iterative problem with the other components of DLOM.
58. Revision of Holding Period Requirements in Rule 144; Section 16(a) Reporting of Equity Swaps
and Other Derivative Securities. File No. S7-17-95, SEC Release Nos. 33-7187; 34-35896; 17
CFR Parts 230 and 241; RIN 3235-AG53. The author expresses his gratitude to John Watson,
Jr., Esq., of Latham & Watkins in Washington, D.C., for providing him with a copy of the
exposure draft.

CHAPTER 7 Adjusting for Levels of Control and Marketability 255
for selling restricted stock to one year from two years and for nonaf¬l-
iated shareholders to sell shares without restriction after two years in-
stead of three.
Two sales took place in 1995 (Esmor Correctional Services, Inc. and
Chantal Pharmaceuticals Corp.) after the SEC Exposure Draft, and four
sales took place in 1996 (ARC Capital, Dense Pac Microsystems, Inc., No-
bel Education Dynamics, Inc., and Unimed Pharmaceuticals). That means
the market knew there was some probability that this would become law
and might shorten the waiting period to sell the restricted stock it was
issuing, and the later the sale, the more likely it was at the time that the
Exposure Draft would become law and provide relief to the buyer of the
restricted stock.
Thus, we should expect that those sales would carry lower discounts
than earlier sales”and that is correct. The discounts on the 1996 sales
were signi¬cantly lower than discounts on the earlier sales, all other
things being equal. The discounts ranged from 16“23% on the 1996 sales.
However, the two post-Exposure Draft 1995 sales had higher-than-
average discounts, which is somewhat counterintuitive. It is true that the
1996 sales would be more affected because the relief from restrictions for
the 1995 sales were more likely to have lapsed from the passage of time
than the 1996 sales, if it would take a long time for the Exposure Draft
to become law. Nevertheless, the two 1995 sales remain anomalies.
The average years needed to sell the stock ranged from a low of 1.2
years for Dense Pac Microsystems to 2.96 years for Sudbury Holdings,
Inc., with the vast majority being between 2 and 3 years. Extrapolating
this model to forecast a restricted stock discount for a sale with a restric-
tion of 10 years, for example, leads to ridiculous results, and even more
than 4 years is very questionable.
The coef¬cient for average years to sell is 0.1368 (B11), which means
that for each year more (less) than the forecast we made for this subject
company of 1 year, the discount increases (decreases) by 13.68%, holding
all else constant. Thus, if we were to forecast for a 10-year restriction, we
would get a discount of 136.8%”a nonsense result.
Thus, the appraiser must exercise good judgment and common sense
in using these results. Mechanically using these regression formulas to all
situations can be dangerous. It may be necessary to run other regressions
with the same data, i.e., using different independent variables or different
transformations of the data, to accommodate valuation assignments with
facts that vary considerably with those underlying these data. Another
possible solution is to assume, for example, that when a particular subject
company™s R 2 is beyond the maximum in the MPI database, that it is
equal to the maximum in the MPI database. It may be necessary to use
the other models, i.e., BSOPM with inferred rather than explicit standard
deviations or the QMDM, for more extreme situations where the regres-
sion equation is strained by extreme data. Hopefully we will soon have
much more data, as there will be increasingly more transactions subject
to the relaxed Rule 144 restrictions.

Component #2: Buyer Monopsony Power
The control stockholder of a privately held ¬rm has no guarantee at all
that he or she can sell his or her ¬rm. The market for privately held

PART 3 Adjusting for Control and Marketability
businesses is very thin. Most small and medium-size ¬rms are unlikely
to attract more than a small handful of buyers”and even then probably
not more than one or two every several months”while the seller of pub-
licly traded stock has millions of potential buyers. Just as a monopolist
is a single seller who can drive up price by withholding production, a
single buyer”a monopsonist”can drive price down by withholding pur-
The presence of 100 or even 10 interested buyers is likely to drive
the selling price of a business to its theoretical maximum, i.e., ˜˜the right
price.™™ The absence of enough buyers may confer monopsony power on
the few who are interested. Therefore, a small, unexciting business will
have an additional component of the discount for lack of marketability
for the additional bargaining power accruing to the buyers in thin mar-
It is easy to think that component #2 may already be included in
component #1, i.e., they both derive from the long time to sell an illiquid
asset. To demonstrate that they are indeed distinct components and that
we are not double counting, it is helpful to consider the hypothetical case
of a very exciting privately held ¬rm that has just discovered the cure for
cancer. Such a ¬rm would have no lack of interested buyers, yet it still is
very unlikely to be sold in less than one year. In that year other things
could happen. Congress could pass legislation regulating the medical
breakthrough, and the value could decrease signi¬cantly. Therefore, it
would still be necessary to have a signi¬cant discount for component #1,
while component #2 would be zero. It may not take longer to sell the
corner dry-cleaning store, but while the ¬rst ¬rm is virtually guaranteed
to be able to sell at the highest price after its required marketing time,
the dry-cleaning store will have the additional uncertainty of sale, and its
few buyers would have more negotiating power than the buyers of the
¬rm with the cure for cancer.
The results from Schwert, described earlier in the chapter, are rele-
vant here. He found that the presence of multiple bidders for control of
publicly held companies on average led to increased premiums of 12.2%
compared to takeovers without competitive bidding. Based on the re-
gression in Table 4 of his article, we assumed a typical deal con¬guration
that would apply to a privately held ¬rm.59 The premium without an
auction was 21.5%. Adding 12.2%, the premium with an auction was
33.7%. To calculate the discount for lack of competition, we go in the
other direction, i.e., 12.2% divided by one plus 33.7% 0.122/1.337
9.1%, or approximately 9%. This is a useful benchmark for D 2.
However, it is quite possible that D 2 for any subject interest should
be larger or smaller than 9%. It all depends on the facts and circumstances
of the situation. Using Schwert™s measure of the effect of multiple versus
single bidders as our estimate of D 3 may possibly have a downward bias
in that the markets for the underlying minority interests in the same ¬rms
is very deep. So it is only the market for control of publicly held ¬rms
that is thin. The market for privately held ¬rms is thin for whole ¬rms
and razor thin for minority interests.

59. We assume a successful purchase, a tender offer, and a cash deal.

CHAPTER 7 Adjusting for Levels of Control and Marketability 257
Component #3: Transactions Costs
Transactions costs in selling a privately held business are substantially
more than they are for selling stock in publicly traded ¬rms. Most stock
in publicly traded ¬rms can be sold with a broker™s fee of 1“2%”or less.

Table 7-11: Quantifying Transactions Costs for Buyer and
Seller. Table 7-11 shows estimates of transactions costs for both the
buyer and the seller for the following categories: legal, accounting, and
appraisal fees (the latter split into posttransaction, tax-based appraisal for
allocation of purchase price and/or valuation of in-process R&D and the
pretransaction ˜˜deal appraisal™™ to help buyer and/or seller establish the
right price), the opportunity cost of internal management spending its
time on the sale rather than on other company business, and investment
banking (or, for small sales, business broker) fees. The ¬rst ¬ve of the
categories appear in columns B through F, which we subtotal in column
G, and the investment banking fees appear in column H. The reason for
segregating between the investment banking fees and all the others is
that the others are constantly increasing as the deal size (FMV) decreases,
while investment banking fees reach a maximum of 10% and stop in-
creasing as the deal size decreases.
Rows 6“9 are transactions costs estimates for the buyer, while rows
13“16 are for the seller. Note that the buyer does not pay the investment
banking fees”only the seller pays. Rows 20“23 are total fees for both
Note that the subtotal transactions costs (column G) are inversely
related to the size of the transaction. For the buyer, they are as low as
0.23% (I6) for a $1 billion transaction and as high as 5.7% (I9) for a $1
million transaction. We summarize the total in Rows 27“30 and include
the base 10 logarithm of the sales price as a variable for regression.60 The
purpose of the regression is to allow the reader to calculate an estimated
transactions costs for any size transaction.
The buyer regression equation is:
Buyer Subtotal Transaction Cost
0.1531 (0.0173 log10 Price)
The regression coef¬cients are in cells B48 and B49. The adjusted R2
is 83% (B37), which is a good result. The standard error of the y-estimate
is 0.9% (B38), so the 95% con¬dence interval around the estimate is ap-
proximately two standard errors, or 1.8%”a very good result.
The seller regression equation is:
Seller Subtotal Transaction Cost
0.1414 (0.01599 log10 Price)
The regression coef¬cients are in cells B67 and B68. The adjusted R2 is
82% (B56), which is a good result. The standard error of the y-estimate is

60. Normally we use the natural logarithm for regression. Here we chose base 10 because the logs
are whole numbers and are easy to understand. Ultimately, it makes no difference which
one we use in the regression. The results are identical either way.

PART 3 Adjusting for Control and Marketability
T A B L E 7-11

Estimates of Transaction Costs [1]


4 Buyer
Tax Deal
5 Deal Size Legal [2] Acctg Appraisal Appraisal [3] Internal Mgt [4] Subtotal Inv Bank Total

6 $1 billion 0.10% 0.02% 0.02% 0.00% 0.09% 0.23% 0.00% 0.23%


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