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Estimating the Control Premium
We begin the process of estimating the control premium by starting with
the voting rights premium (VRP) data, which show that there is a value
of the vote to individual shareholders. If the vote has value, then logically
control must have more value”but again only to an individual who is
really in control.
Our VRP analysis shows two levels of voting rights premium. The
gross premiums were 5.4% and 3.2% in the United States from the Lease,
McConnell, and Mikkelson study and the HLHZ study, and 13.3% in
England, per Megginson (1990). The net premiums”meaning those
above and beyond expected higher cash ¬‚ows to the voting stock”were
1“1.4%. For the valuation of most small and medium-size businesses, the
gross VRP is the more relevant measure, for reasons we will discuss
shortly.
The U.S. gross VRPs average 4.3%, i.e., the average of the 5.44% and
3.2% gross VRPs from Lease, McConnell, and Mikkelson and HLHZ ar-
ticles. According to Professor Megginson, we then need to add another
2% to 3%, say 2.5%, for the depressing effect on the VRP of the illiquidity
of the voting shares, which brings us to 6.8%, which we round to 7%.
Control must be worth at least three to four times the value of the
vote. That would place the value of control to an individual at at least
21“28%. It could easily be more. Currently, the only possible direct evi-
dence in the United States is the conglomerate control premium of 19.2%
in the Maquieira, Megginson, and Nail article, which is very close to the
above estimate. The VRP in Switzerland, Israel, and Milan of 20%, 45.5%,
and 82%, respectively, is another indication of the value of control when
minority shareholders are not well protected, again keeping in mind that
those were the value of the vote, not control.
Another piece of data indicating the value of control is the one outlier
in the Lease, McConnell, and Mikkelson study, which had a 42% VRP.
Such a high VRP in the United States is probably indicative of control
battles taking place and could rapidly reduce to a more normal VRP.
Thus, the voting shareholders probably could not rely on being able to
resell their shares at a similar premium at which they buy. That 42%
premium is evidence of the value of the vote in an extreme situation when
small blocks of shares would have a large impact on who has control.
The reason why the gross VRP is relevant for most businesses in the
process of inferring the value of control is that as long as the buyer of a
business can turn around and sell the business for the same control pre-
mium as he or she bought it, there is no loss in net present value of cash
¬‚ows, other than the pure control portion, which derives from the net
VRP.35 The buyer will eventually recoup the control premium later on as
a seller. That works as long as the business is small enough that its buyers


35. There is actually a second-order effect where this is not literally true. To the extent that the
owner is taking implicit dividends in the form of excess salary, there is some loss in present
value from this.


CHAPTER 7 Adjusting for Levels of Control and Marketability 227
will be either private individuals or private ¬rms. If the business grows
large enough to be bought by a public ¬rm or undergoes its own IPO,
then instead of recouping a private control premium, the owner may
receive an acquisition premium with synergies in the case of a buyout.
In the case of an IPO, the company will experience an increase in value
from increased marketability.36 Also, while the control premium will be
smaller, DLOM may also be smaller.
The best source of data for control premiums and DLOC for private
¬rms in the United States will probably come from a thorough analysis
of the international literature. The publicly traded ¬rms overseas are
probably better guidelines to use to understand the value of control than
United States ¬rms for two reasons. The ¬rst reason is that in most foreign
countries”especially those outside the United Kingdom”ownership of
public ¬rms is far more concentrated than it is in the United States. The
second reason is that the minority shareholders there are far more vul-
nerable to abuse by the control interests, which is closer to the case in
privately held ¬rms in the United States.
Unfortunately, that will have to remain as future research. In the
meantime, I would suggest that the 21“28% control premium based on
the gross VRP is probably reasonable to add to a marketable minority
FMV”at least for small and medium ¬rms. For large private ¬rms, that
range may still be right if a synergistic buy is likely in the future. Oth-
erwise, it is probably more appropriate to use a smaller control premium
based on the net VRP, which would be in the 3“6% range.
At this point, we need to compare our control premium inferred by
VRPs with going private premiums, as the latter is also a candidate for
our measure of the value of control. The median going private premium
of 24.1% (Table 7-1, E21) is right in the middle of our 21“28% range for
control calculated by VRPs. However, the mean going private premium
of 32.1% (Table 7-1, D21) is above our VRP-calculated range. Which is
more likely to be right?
The going private premiums have the advantage of being directly
calculated rather than indirectly inferred, so that is one point in their
favor. There is no consensus in the valuation profession in general
whether medians or means are better measures. All other things being
equal, then, it would make sense to use the median, as it is consistent
with the VRP-calculated control premium. I more often use means than
medians, which leaves me a little dissatis¬ed relying solely on the con-
sistency of the two measures.
There is other logic that convinces me that the lower measure of
control is more correct. What are the motivations for going private? The
management team may believe:
(1) The company is underpriced in the market.
(2) Removing the burdens of SEC reporting will increase
pro¬tability.


36. The appraiser must consider the issue of restricted stock discounts in this case.




PART 3 Adjusting for Control and Marketability
228
(3) If the going private transaction is a division of a public
company, it can operate more ef¬ciently without interference
and the burden of overhead from the corporate people.
(4) The management group and the buyout group want to be in
control of the company.
Item (1) implies that the universe of going private transactions may
have a sample bias with respect to the valuation of privately held ¬rms.
However, to the extent that (1) is true, that portion of the control premium
is inapplicable to the valuation of private ¬rms, as we presume that the
valuation is done correctly up to this point. Item (2) is also inapplicable
to the valuation of private ¬rms, as this represents a performance im-
provement to the going private ¬rm that is unavailable to the ¬rm that
has always been private. Therefore, that portion of the going private pre-
mium represented by the economic ef¬ciencies of being private also does
not belong in our calculation of the value of control.
Item (3) is a performance improvement and not really a value of
control itself. It represents improvements in cash ¬‚ow, and thus could be
considered a control premium to the extent that we believe that the av-
erage going private ¬rm would achieve the same amount of performance
improvements that an already private ¬rm could expect with new man-
agement, but I ¬nd that very speculative.
A direct measurement of the premium associated with item (4) would
be the closest to our VRP approach to calculating the value of control.
However, I ¬nd it hard to believe that there is a single shareholder who
is in control in the large going private transactions recorded in Mergerstat.
Who is in control of the buyout group? Management?
I think that the composition of the observed going private premium
is a mixture of all four items above and probably others of which I am
unaware. It is likely that some of the going private premium is irrelevant
to the valuation of private ¬rms, some of it is for performance improve-
ments that might be applicable to private ¬rms, and some is for the value
of control itself, although the latter certainly is less for going private trans-
actions than it is for true control of a ¬rm by a single individual.
Let™s make a wild guess as to how the four components comprise
the going private premium. Suppose each item is one-fourth of the pre-
mium, i.e.:
(1) Company underpriced 8%
(2) Remove SEC reporting 8%
(3) Eliminate corporate overhead 8%
(4) Control 8%
Total”Mean 32%
If this were the true breakdown of the going private premium, then the
value of pure control would be only 8%. But, perhaps that is reasonable
in a situation where control is not concentrated in a single individual but
rather is spread among a few people in the buyout group and a few
people in management. This would tell us fairly little about how to apply
it to an already private company.




CHAPTER 7 Adjusting for Levels of Control and Marketability 229
Ultimately, I am more comfortable with the VRP inference of the
value of control than the going private premium, as it makes a clean
separation of performance improvements from control. In any case, it
seems clear that the mean going private premium is probably too high
as a measure of the value of control, and we should stick with the 21“
28% control premium.

DLOC
It is my opinion that Nath is correct in his assertion that both DLOM and
DLOC are needed from the marketable minority interest.37 Bolotsky dis-
agrees with this more in form than in substance. He asks”logically
enough”how one can subtract a DLOC from an interest that has no
control attributes to it. The answer is that control matters much less in
publicly held ¬rms in the United States than it does in privately held
¬rms. The public minority shareholder has little fear of control share-
holders ruining the company or abusing the minority shareholders. Even
if he or she does, there are remedies such as class action lawsuits, take-
overs, shareholder meetings, etc. that the private minority shareholder
can only wish for.
I suggest that Bolotsky™s 2 2 levels of value chart, as depicted in
38
Figure 7-2, is still too simple. Using his own very innovative and per-
ceptive framework of differing shareholder attributes, it is possible to see
why it may still be appropriate to subtract an incremental DLOC in val-
uing a private minority interest. Figure 7-3 is my own expansion of Bol-
otsky™s 2 2 levels of value chart. Here I have split minority interests
into well treated and exploited. Most U.S. public minority interests are
well treated, and the values are in row 2, column 2 of Figure 7-3. Most
private minorities in the United States are poorly treated or, if not, may
have to fear being poorly treated with a change in control ownership or
a change in attitude of the existing owners. Thus, most U.S. private mi-
norities are in row 3, column 2. The DLOC calculated as the ¬‚ip side of
the control premium going from a well-treated minority to control is in-
suf¬cient to measure the lower position of an exploited minority. You will


F I G U R E 7-3

3 2 Levels of Value Chart


Public Private

Control x x
Minority (well treated) x x
Minority (exploited) x x




37. This distinction is more important vis-a-vis Mercer™s original position than it is in using his
`
quantitative marketability discount model.
38. In fairness, his 2 2 levels of value chart is his own simpli¬cation of his more complicated
system.




PART 3 Adjusting for Control and Marketability
230
see this later in the chapter in the section on international voting rights
premia, where we examine the difference in market value of voting versus
nonvoting stock in international public markets. When minority rights
are poorly protected, the voting rights premium is as high as 82%, i.e.,
voting stock sells for an 82% higher price than nonvoting stock. Control
must be very valuable in Milan!
It often may be appropriate to use control premia from other coun-
tries to calculate a DLOC that is appropriate for U.S. minorities. Then one
can use Jankowske™s formula to make the incremental adjustment. Thus,
it is my opinion that we should subtract both an incremental DLOC and
DLOM from the marketable minority value to arrive at a private minority
value. However, this is an area that requires further research.
It is important to understand that those are not six unique and dis-
crete cells in the ¬gure. While public or private is an either/or concept,
both the degree of control and how well treated are the minority interests
are continuums. Thus, there are not only six values that one could cal-
culate as DLOM, but an in¬nity of values, depending on the magnitudes.
In my correspondence with Mike Bolotsky, he agrees in substance
with this view. He prefers to think in a multidimensional matrix of fac-
tors, labeled something like ˜˜SEC oversight and enforcement power,™™ in-
stead of a control issue. Even so, I will quote from his letter to me. ˜˜In
valuing private minority interests that are either poorly treated, which is
typical of most, or even have reason to fear being poorly treated, I think
it is reasonable to subtract DLOC. However, we cannot learn what that
is from the American public stock markets, where minority interests are
well protected administratively and legally.™™ I agree completely.
That is a research task to be done in the future. In the meantime, the
above simpli¬cation works and is easier than a multifactor matrix.
What measure of control premium should we use to calculate DLOC?
Starting with a marketable minority FMV, we have to decide whether we
are coming down to a well-treated private minority or an exploited pri-
vate minority interest. Additionally, even a well-treated private minority
today may turn into a poorly treated minority tomorrow, and the fear of
that alone should create a positive DLOC from the marketable minority
level. I would suggest again that the 40% range for the foreign VRPs and
the American outlier in the Lease, McConnell, and Mikkelson study
(which, by coincidence, are similar to American acquisition premiums)
plus some additional amount for control being more valuable than the
vote, is a reasonable range from which to calculate DLOC. One caveat: if
you are valuing an ˜˜exploited™™ minority interest and have not added back
excessive salaries taken by the control shareholders, the 40 % range con-
trol premium would translate to a 28.6% DLOC, which might be exces-
sive, depending on the magnitude of excessive salary. The reason for this
is that the 40 % VRP may, to some extent, represent excess salaries to
holders of voting shares. Therefore, if we have already accounted for it
in the discounted cash ¬‚ow, we do not want to double-count and take
the full discount.
It is important to note that, given the previous analysis, I do not
consider the decrease in value from a public ˜˜control™™ value to a mar-




CHAPTER 7 Adjusting for Levels of Control and Marketability 231
ketable minority level to be DLOC. It tells us nothing about control. It
only tells us the magnitude of synergies in acquisitions. I would not use
it go from a private control interest to a private minority interest.

DISCOUNT FOR LACK OF MARKETABILITY (DLOM)
Three quantitative models for calculating DLOM have appeared in the
professional literature: Jay Abrams™ economic components model
(Abrams 1994a),39 Z. Christopher Mercer™s quantitative marketability dis-
count model (Mercer 1997), and Larry Kasper™s discounted time to market
model (Kasper 1997). In this section we will review Mercer™s and Kasper™s
work. In the next section we will cover Abrams™ model in greater depth.

Mercer™s Quantitative Marketability Discount Model
Mercer presents the quantitative marketability discount model (QMDM)
in his impressive volume devoted entirely to the topic of discount for
lack of marketability. His book contains much important research in the
¬eld and does an excellent job of summarizing prior research and iden-
tifying and discussing many of the important issues involved in quanti-
fying DLOM. I consider his book mandatory reading in the ¬eld, even
though I will present my own competing model that I contend is superior
to the QMDM. I will not attempt to give more than a bare summary of
his work”not because it is not important, but for the opposite reason: it
is too important to be adequately represented by a summary.
With that caveat in mind, the QMDM is based on calculating the net
present value of forecast cash ¬‚ows to shareholders in a business entity.
His key concept is that one can evaluate the additional risk of minority
ownership in an illiquid business entity compared to ownership of pub-
licly traded stock and quantify it. The appraiser evaluates a list of various
factors that affect risk (Mercer 1997, p. 323) and quanti¬es the differential
risk of minority ownership of the private ¬rm compared to the public
¬rm or direct ownership of the underlying assets”whichever is appro-
priate”and discounts forecast cash ¬‚ows to present value at the higher
risk-adjusted rate of return to calculate the discount.
To simplify the calculations, Mercer usually assumes a growing an-
nuity. He presents an approximate formula for the present value of an
annuity with growth (p. 276). In using the QMDM, one improvement the
appraiser can make is to use the exact annuity discount factors (ADFs)
with growth that we developed in Chapter 3 and that we repeat below.
n
1 1 g
ADF 1
r g 1 r
ADF with perpetual growth: End-of-year formula (3-6b)
n
1 r 1 g
ADF 1
r g 1 r
ADF with perpetual growth: midyear formula (3-10a)


39. There is no name for the model in the article cited. I have named it since.




PART 3 Adjusting for Control and Marketability
232
Note that the ¬rst terms on the right-hand-side of equations (3-6b) and
(3-10a) are the end-of-year and midyear Gordon models. As
n
1 g
n’ ’0
,
1 r
and the ADF reduces to the Gordon model with which we are all familiar.
In his Chapter 12, Mercer reiterates his opposition to a DLOM for
controlling interests from his original article (Mercer 1994). His primary
objection seems to be that the control owner has control of cash ¬‚ows
until he or she sells the business, at which time there is no longer DLOM.
I disagree, as the ability to enjoy cash ¬‚ows one day at a time and to
instantaneously actualize the present value of all cash ¬‚ow to perpetuity
are quite different, the difference being measured by the DLOM that Mr.
Mercer suggests does not exist.
In support of his belief that a DLOM is inappropriate for a controlling
interests, Mercer (p. 340) cites an article (Phillips and Freeman 1995) that
¬nds that after controlling for size, margin, and industry, privately held
¬rms do not sell for lower multiples than publicly held ¬rms when the
buyer is another publicly held ¬rm. There are a few problems with this
study:
1. Since the buyers are all publicly held ¬rms, once the sellers™
businesses are absorbed into the buyers™, there is no DLOM that
applies anymore. When a privately held ¬rm sells to a publicly
held ¬rm, ignoring any other differences such as potential
synergies, there are at least two FMVs for the seller: a ˜˜¬‚oor
FMV,™™ which is the FMV of the standalone business, including
DLOM, and a ˜˜ceiling FMV,™™ which is the FMV without DLOM.
The seller should not be willing to sell below the ¬‚oor FMV, and
the buyer should not be willing to pay more than the ceiling
FMV. An actual transaction can take place anywhere between
the two, and Mergerstat will record that as the FMV. The articles
by Schwert (1996) and Bradley, Desai, and Kim (1988) cited
earlier in this chapter show that the lion™s share of excess
returns in acquisitions go to the seller. Thus, it is normal that
the buyer pays top dollar, which would mean that the seller
would insist that the buyer forgo the DLOM, which disappears
in any case after the transaction. Therefore, at a minimum, the
Phillips/Freeman article™s applicability is limited to privately
held ¬rms that are large enough to attract the attention of and
be acquired by publicly held buyers.
2. In both regressions”the Mergerstat and the SDC database”
banks show up as having different valuations than all other
industries. However, the signs of the regression coef¬cients for
banks are opposite in the two regressions. The regression of the
Mergerstat database demonstrates at the 99.99% signi¬cance
level that buyers pay lower multiples of sales for banks than for
other industries, and the regression of the SDC database
demonstrates at the 99.99% signi¬cance level that buyers pay
higher multiples of sales for banks than other industries! There



CHAPTER 7 Adjusting for Levels of Control and Marketability 233
were several other inconsistencies in the results of the two
regressions.
3. The log“log form of regression that Phillips and Freeman used
can have the effect of making large variations look small. The
standard errors of their regressions were very high. The
standard error of the Mergerstat regression was 0.925. Two
standard errors is 1.85. Exponentiating, the 95% con¬dence
interval is approximately equal to multiplying the (value/sales)
estimate by two standard errors on either side of the regression
estimate. The high side of the 95% con¬dence interval is e1.85
6.36 times the regression estimate, and the low side is e 1.85
0.157 times the regression estimate. Let™s put some speci¬c
numbers into their equation to see what the con¬dence intervals
look like. Let™s assume we are forecasting the value of the
common stock as a percentage of sales for a ¬rm over $100
million in value that is neither a bank, a private placement, nor
a subsidiary. Their regression equation is ln(Value/Sales)
3.242 0.56 ln net margin 0.45 ln (1/PE of the S&P 500).
Let™s assume a 5% after-tax margin and an average PE for the
S&P 500 of 15, so 1/PE 0.067. Then, ln(Value/Sales) 3.242
(0.56 ln 0.05) (0.45 ln 0.067) 3.242 1.678 1.219
e0.345
0.345. Thus, the regression estimate of (Value/Sales)
1.413, or value is approximately 1.4 times sales, which seems
high. If sales are $100, then net income after taxes is $5, which
when multiplied by a PE ratio of 15 leads to a value of $75,

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