siderable time that it takes to sell a privately held business in excess of

the near instantaneous ability to sell the publicly held stocks from which

we calculate our discount rates.

Psychology. Investors don™t like illiquidity. Medical and other emer-

gencies arise in life, causing people to have to sell their assets, possibly

including their businesses. Even without the pressure of a ¬re sale, it

usually takes three to six months to sell a small business and one year or

more to sell a business worth $1 million or more.

The selling process may entail dressing up the business, i.e., tidying

up the accounting records, halting the standard operating procedures of

charging personal expenses to the business, and getting an appraisal. Ei-

ther during or after the dress-up stage, the seller needs to identify poten-

tial buyers or engage a business broker or investment banker to do so.

This is also dif¬cult, as the most likely buyers are often competitors. If

the match doesn™t work, the seller is worse off, having divulged con¬-

dential information to his competitors. The potential buyers need to go

through their due diligence process, which is time consuming and ex-

pensive.

During this long process, the seller is exposed to the market. He or

she would like to sell immediately, and having to wait when one wants

to sell right away tries one™s patience. The business environment may be

CHAPTER 7 Adjusting for Levels of Control and Marketability 249

better or worse when the transaction is close to consummation. It is well

established in behavioral science”and it is the major principle on which

the sale of insurance is based”that the fear of loss is stronger than the

desire for gain (Tversky and Kahneman 1987). This creates pressure for

the seller to accept a lower price in order to get on with life.

Another important ¬nding in behavioral science that is relevant in

explaining DLOM and DLOC is ambiguity aversion (Einhorn and Ho-

garth 1986). The authors cite a paradox proposed by the psychologist

Daniel Ellsberg (Ellsberg 1961) (of Pentagon Papers fame), known as the

Ellsberg paradox.

Ellsberg asked subjects which of two gambles they prefer. In gamble

A the subject draws from an urn with 100 balls in it. They are red or

black only, but we don™t know how many of each. It could be 100 black

and 0 red, 0 black and 100 red, or anything in between. The subject calls

˜˜red™™ or ˜˜black™™ before the draw and, if he or she calls it right, wins $100;

otherwise, he or she gets nothing. In gamble B, the subject draws one ball

from an urn that has 50 red balls and 50 black balls. Again, if the subject

forecasts the correct draw, he or she wins $100 and otherwise wins noth-

ing.

Most people are indifferent between choosing red or black in both

gambles. When asked which gamble they prefer, the majority of people

had an interesting response (before we proceed, ask yourself which gam-

ble you would prefer and why). Most people prefer to draw from urn #2.

This is contrary to risk-neutral logic. The ¬nding of Ellsberg and Einhorn

and Hogarth is that people dislike ambiguity and will pay to avoid it.

Ambiguity is a second-order uncertainty. It is ˜˜uncertainty about un-

certainties,™™ and it exists pervasively in our lives. Gamble B has uncer-

tainty, but it does not have ambiguity. The return-generating process is

well understood. It is a clear 50“50 gamble. Gamble A, on the other hand,

is fuzzier. The return-generating process is not well understood. People

feel uncomfortable with that and will pay to avoid it.

It is my opinion that ambiguity aversion probably explains much of

shareholder level discounts. As mentioned earlier in the chapter, Jan-

kowske mentions wealth transfer opportunities and the protection of in-

vestment as economic bene¬ts of control. Many minority investors are

exposed to the harsh reality of having their wealth transferred away.

Many of those who do not experience that still have to worry about it

occurring in the future. The minority investor is always in a more am-

biguous position than a control shareholder.

In our regressions of the partnership pro¬les database that tracks the

results of trading in the secondary limited partnership markets (see Chap-

ter 9), we ¬nd that regular cash distributions are the primary determinant

of discounts from net asset value. Why would this be so? After all, there

have already been appraisals of the underlying properties, and those ap-

praisals certainly included a discounted cash ¬‚ow approach to valua-

tion.52 If the appraisal of the properties already considered cash ¬‚ow, then

52. In the regression we included a dummy variable to determine whether the discount from net

asset value depended on whether the properties were appraised by the general partner or

by independent appraiser. The dummy variable was statistically insigni¬cant, meaning that

the market trusts the appraisals of the general partners as much as the independent

appraisers.

PART 3 Adjusting for Control and Marketability

250

why would we consider cash ¬‚ow again in determining discounts? I

would speculate the following reasons:

1. If the general partner (GP) takes greater than arm™s-length fees

for managing the property, that would not be included in the

appraisal of the whole properties and would reduce the value of

the limited partner (LP) interest. It is a transfer of wealth from

the LP to the GP.

2. Even if the GP takes an arm™s-length management fee, he or she

still determines the magnitude and the timing of the

distributions, which may or may not be convenient for the

individual LPs.

3. LPs may fear potential actions of the GP, even if he or she never

takes those actions. The LP only knows that information about

the investment that the GP discloses and may fear what the GP

does not divulge”which, of course, he or she won™t know. The

LPs may hear rumors of good or bad news and not know what

to do with it or about it.

The bottom line is that investors don™t like ignorance, and they will

pay less for investments that are ambiguous than for ones that are not”

or that are, at least, less ambiguous”even if both have the same expected

value.

Our paradigm for valuation is the two-parameter normal distribu-

tion, where everything depends only on expected return and expected

risk. Appraisers are used to thinking of risk only as either systematic risk,

measured by , or total risk in the form of , the historical standard

deviation of returns. The research on ambiguity avoidance adds another

dimension to our concept of risk, which makes our task more dif¬cult

but affords the possibility of being more realistic.

It is also noteworthy that the magnitude of special distributions, i.e.,

those coming from a sale or re¬nancing or property, was statistically in-

signi¬cant. Investors care only about what they feel they can count on,

the regular distributions.

Black“Scholes Options Pricing Model. One method of modeling

the economic disadvantage of the period of illiquidity is to use the Black“

Scholes options pricing model (BSOPM) to calculate the value of a put

on the stock for the period of illiquidity. A European put, the simplest

type, is the right to sell the stock at a speci¬c price on a speci¬c day. An

American put is the right to sell the stock on or before the speci¬c day.

We will be using the European put.

The origins of using this method go back to David Chaffe (Chaffe

1993), who ¬rst proposed using the BSOPM for calculating restricted

stock discounts for SEC Rule 144 restricted stock. The restricted stock

discounts are for minority interests of publicly held ¬rms. There is no

admixture of minority interest discount in this number, as the restricted

stock studies in Pratt™s Chapter 15 (Pratt, Reilly, and Schweihs 1996) are

minority interests both pre- and posttransaction.

Then Abrams (1994a) suggested that owning a privately held busi-

ness is similar to owning restricted stock in that it is very dif¬cult to sell

CHAPTER 7 Adjusting for Levels of Control and Marketability 251

a private ¬rm in less than the normal due diligence time discussed above.

The BSOPM is a reasonable model with which to calculate Component

#1 of DLOM, the delay to sale discount.

There is disagreement in the profession about using BSOPM for this

purpose. Chapter 14 of Mercer™s book (Mercer 1997) is entitled, ˜˜Why

Not the Black“Scholes Options Pricing Model Rather Than the QMDM?™™

Mercer™s key objections to the BSOPM are:53

1. It requires the standard deviation of returns as an input to the

model. This input is not observable in privately held companies.

2. It is too abstract and complex to meaningfully represent the

thinking of the hypothetical willing investor.

Argument 2 does not matter, as the success of the model is an em-

pirical question. Argument 1, however, turned out to be more true than

I would have imagined. It is true that we cannot see or measure return

volatility in privately held ¬rms. However, there are two ways that we

indirectly measured it. We combined the regression equations from re-

gressions #1 and #2 in Table 4-1 to develop an expression for return vol-

atility as a function of log size, and we performed a regression of the

same data to directly develop an expression for the same. We tried using

both indirect estimates of volatility as inputs to the BSOPM to forecast

the restricted stock discounts in the Management Planning, Inc. data, and

both approaches performed worse than using the average discount. Thus,

argument 1 was an assertion that turned out to be correct.

When volatility can be directly calculated, the BSOPM is superior to

using the mean and the QMDM. So, BSOPM is a competent model for

forecasting when we have ¬rm-speci¬c volatility data, which we will not

have for privately-held ¬rms.

Other Models of Component #1. The regression equation developed

from the Management Planning, Inc. data is superior to both the non-

¬rm-speci¬c BSOPM and the QMDM. Thus, it is, so far, the best model

to measure component #1, the delay to sale component, as long as the

expected delay to sale is one to ¬ve (or possibly as high as six) years.

The QMDM is pure present value analysis. It has no ability to quan-

tify volatility”other than the analyst guessing at the premium to add to

the discount rate. It also suffers from being highly subjective. None of the

components of the risk premium at the shareholder level can be empiri-

cally measured in any way.

Is the QMDM useless? No. It may be the best model in some sce-

narios. As mentioned before, one of the limitations of my restricted stock

discount regression is that because the restricted stocks had so little range

in time to marketability, the regression equation performs poorly when

the time to marketability is substantially outside that range”above ¬ve

to six years. Not all models work in all situations. The QMDM has its

place in the toolbox of the valuation professional. It is important to un-

53. Actually, Chapter 14 is co-authored by J. Michael Julius and Matthew R. Crow, employees at

Mercer Capital.

PART 3 Adjusting for Control and Marketability

252

derstand its limitations in addition to its strengths, which are ¬‚exibility

and simplicity.

The BSOPM is based on present value analysis, but contains far more

heavy-duty mathematics to quantify the probable effects of volatility on

investor™s potential gains or losses. While the general BSOPM did not

perform well when volatility was measured indirectly, we can see by

looking at the regression results that Black“Scholes has the essence of the

right idea. Two of the variables in the regression analysis are earnings

stability and revenue stability. They are the R2 from regressions of earn-

ings and revenues as dependent variables against time as the independent

variable. In other words, the more stabile the growth of revenues and

earnings throughout time, the higher the earnings and revenue stability.

These are measures of volatility of earnings and revenues, which are the

volatilities underlying the volatility of returns. Price stability is another

of the independent variables, and that is the standard deviation of stock

price divided by the mean of returns (which is the coef¬cient of variation

of price) and then multiplied by 100.

Thus, the regression results demonstrate that using volatility to mea-

sure restricted stock discounts is empirically sound. The failure of the

non-¬rm-speci¬c BSOPM to quantify restricted stock discounts is a mea-

surement problem, not a theoretical problem.54

An important observation regarding the MPI data is that MPI ex-

cluded startup and developmental ¬rms from its study. There were no

¬rms that had negative net income in the latest ¬scal year. That may

possibly explain the difference in results between the average 35% dis-

counts in most of the other studies cited in Pratt™s Chapter 15 (Pratt,

Reilly, and Schweihs 1996) and MPI™s results. When using my regression

of the MPI data to calculate component #1 for a ¬rm without positive

earnings, I would make a subjective adjustment to increase the discount.

As to magnitude, we have to make an assumption. If we assume that the

other studies did contain restricted stock sales of ¬rms with negative

earnings in the latest ¬scal year, then it would seem that those ¬rms

should have a higher discount than the average of that study. With the

average of all of them being around 33“35%, let™s say for the moment

that the ¬rms with losses may have averaged 38“40% discounts, all other

things being equal (see the paragraph below for the rationale). Then 38“

40% minus 27% in the MPI study would lead to an upward adjustment

to component #1 of 11% to 13%. That all rests on an assumption that this

is the only cause of the difference in the results of the two studies. Further

research is needed on this topic.

We can see the reason that ¬rms with losses would have averaged

higher discounts than those who did not in the x-coef¬cient for earnings

stability in Table 7-10, cell B9, which is 0.1381. This regression tells us

the market does not like volatility in earnings, which implies that the

54. There is a signi¬cant difference between forecasting volatility and forecasting returns. Returns

do not exhibit statistically signi¬cant trends over time, while volatility does (see Chapter 4).

Therefore, it is not surprising that using long-term averages to forecast volatility fail in the

BSOPM. The market is obviously more concerned about recent than historical volatility in

pricing restricted stock. That is not true about returns.

CHAPTER 7 Adjusting for Levels of Control and Marketability 253

market likes stability in earnings. Logically, the market would not like

earnings to be stable and negative, so investors obviously prefer stable,

positive earnings. Thus, we can infer from the regression in Table 7-10

that, all other things being equal, the discount for ¬rms with negative

earnings in the prior year must be higher than for ¬rms with positive

earnings. Ideally, we will eventually have restricted stock data on ¬rms

that have negative earnings, and we can control for that by including

earnings as a regression variable.

It is also worth noting that the regression analysis results are based

on the database of transactions from which we developed the regression,

while the BSOPM did not have that advantage. Thus, the regression had

an inherent advantage in this data set over all other models.

Abrams™ Regression of the Management Planning, Inc. Data. As

mentioned earlier in the chapter, there are two regression equations in

our analysis of the MPI data. The ¬rst one includes price stability as an

independent variable. This is ¬ne for doing restricted stock studies. How-

ever, it does not work for calculating Component #1 in a DLOM calcu-

lation for the valuation of a privately held ¬rm, whether a business or a

family limited partnership with real estate. In both cases there is no ob-

jective market stock price with which to calculate the price stability.

Therefore, in those types of assignments, we use the less accurate second

regression equation that excludes price stability.

Table 7-10 is an example of using regression #2 to calculate compo-