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The ¬rst component of DLOM is the economic disadvantage of the con-
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-

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