˜˜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]

A B C D

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

254

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-

cause:

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

256

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-

chase.

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-

kets.

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

sides.

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)

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)

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

258

T A B L E 7-11

Estimates of Transaction Costs [1]

A B C D E F G H I

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%