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[1] Pure Discounts: For Component #1, Table 9-5A, cell D13; For Component #2, 9% per Schwert article. For Components #3A and #3B, see notes [3] and [4] below.
[2] Formula For Sellers™ Discount: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B. Formula For Buyers™ Discount: 1 (1 z)*(1 x j)/((1 (1 z)*x j)),
per equation [7-9a], used for Component #3A. Components #1 and #2 simply transfer the pure discount.
[3] We assume 2% incremental costs for the buyer, who would have to perform due diligence on the other member interests in addition to due diligence on the property itself.
[4] Our survey of brokers dealing with fractional LP interests found that brokerage fees for interests in LPs is similar to the standard 6% real estate commission. Therefore, we assume
that there are no incremental costs for the seller.
[5] Per Cost of Capital Quarterly-1999, SIC Code 6798 (REITs), 10 Yr Avg. Small Composite returns 10.38%. We add 3% for the incremental risk of a small operation with very low
[6] This equals the total returns minus expected distributions, Table 9-4, C9 minus C12.

Component 2, buyer™s monopsony power, and Components 3A and 3B,
buyers™ and sellers™ transactions costs.

Buyer™s Monopsony Power
The control stockholders of privately held ¬rms have no guarantee at all
that they can sell their ¬rms. The market for privately held businesses is
very thin. Most small and medium-sized ¬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 publicly 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 purchase.
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 to
the few who are interested. Therefore, a small, unexciting business will
have an additional component to the discount for lack of marketability
because of the additional bargaining power accruing to the buyers in thin
It is easy to think that component 2 might already be included in
component 1, i.e., they both derive from the long time it takes 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 hypo-
thetical case of a very exciting privately held ¬rm that has just discovered

PART 3 Adjusting for Control and Marketability
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. There-
fore, it would still be necessary to have a signi¬cant discount for com-
ponent 1, while component 2 would be zero. It may not take longer to
sell the corner dry cleaning store, but the ¬rst ¬rm is virtually guaranteed
to be able to sell at the highest price after its required marketing time,
whereas the dry cleaning store will have the additional uncertainty of
sale. Also, its few buyers would have more negotiating power than the
buyers of the ¬rm with the cure for cancer.
The results from Schwert, described in Chapter 7 of Quantitative Busi-
ness Valuation: A Mathematical Approach for Today™s Professionals, are rele-
vant here.12 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.13 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 33.7% 0.122/1.337 9.1%,
or approximately 9%. This is a useful benchmark for the second compo-
nent of DLOM. We have inserted it in Table 9-5C, B10.
It is quite possible that the buyer™s monopsony power for any subject
interest should be larger or smaller than 9%, depending on the facts and
circumstances of the situation. We are using Schwert™s measure of the
effect of multiple versus single bidders as a conservative estimate for
component 2. It may possibly have a downward bias because 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. A 9% buyer™s monopsony power discount (B10) for
the subject interest is a conservative assumption.

Transactions Costs
Transactions costs for both the buyer and the seller include: legal, ac-
counting, and appraisal fees, 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 ap-
praisal fees are for two main categories: the pre-transaction deal appraisal
to help buyer and/or seller establish the right price, and post-transaction,
tax-based appraisal for allocation of purchase price and/or valuation of
in-process R&D.
We are only interested in incremental transactions costs that occur as
a result of a fractional interest transaction. The buyer of a 2.80% member
interest would not only have to perform due diligence on the LLC itself,

12. G. William Schwert, ˜˜Markup Pricing in Mergers and Acquisitions.™™ Journal of Financial
Economics 41 (1996): 153“192.
13. We assume a successful purchase, a tender offer, and a cash deal.

CHAPTER 9 Sample Appraisal Report 335
but also on the other members. Thus, the buyer would experience addi-
tional due diligence costs, which we estimate at 2% (B11). For the seller,
we assume a zero incremental brokerage cost (B12).
Transactions costs are different than the ¬rst two components of
DLOM. For Components 3A and 3B we need to explicitly calculate the
present value of the occurrence of transactions costs every time the in-
terest sells. The reason is that, unlike the ¬rst two components, transac-
tions costs are actually out-of-pocket costs that leave the system. They are
paid to attorneys, accountants, appraisers, and investment bankers or
business brokers. Additionally, the internal management of both the
buyer and the seller must spend signi¬cant time on the project to make
it happen, and they often have to spend time on failed acquisitions before
being successful.
We need to distinguish between the buyer™s transactions costs and
the seller™s costs. This is because the buyer™s transactions costs are always
relevant, whereas the seller™s transactions costs for the immediate trans-
action reduce the net proceeds to the seller but do not reduce FMV. How-
ever, before the buyers are willing to buy, they should be saying, ˜˜It™s
true, I don™t care about the sellers™ costs. That™s their problem. However,
10 years or so down the road when it™s my turn to be the seller, I do care
about that.™™ To the extent that sellers™ costs exceed the brokerage cost of
selling publicly-traded stock, in 10 years my buyer will pay me less be-
cause of those costs, and therefore I must pay my sellers less because of
my costs as a seller in Year 10. Additionally, the process goes on forever,
because in Year 20, my buyer becomes a seller and faces the same prob-
lem.™™ Thus, we need to quantify the present value of periodic buyer™s
transactions costs through an in¬nity of time beginning with the imme-
diate sale and sellers™ transactions costs that begin with the second sale
of the business. With the following two formulas, we can adjust the sell-
ers™ and buyers™ transactions costs to present value and calculate the re-
sulting discount as follows:
Formula for NPV of buyers™ costs
1 g
x J)
(1 z)(1
D3A 1 , where x
z)x J
1 (1 1 r
Formula for NPV of sellers™ costs
D3B 1
z)x j
1 (1
In the above equations, D is the discount for transactions costs, g is
the growth rate of the business, r is the discount rate of the business, j is
r, ’ 0
the average number of years between transactions, and g x
1. The derivation of these two equations appears in the Mathematical
Appendix to Chapter 7 of Quantitative Business Valuation: A Mathematical
Approach for Today™s Professionals. An analysis of partial derivatives in the
Mathematical Appendix shows that the discount, i.e., DLOM, always in-
creases with increases in growth (g) and transactions costs (z) and always
decreases with increases in the discount rate (r) and the average number
of years between sales ( j). The converse is true as well. Decreases in the
independent variables have the opposite effect of increases on DLOM.

PART 3 Adjusting for Control and Marketability
To apply these equations to the LLC, we must determine a discount
rate, a growth rate, and an average number of years between sales. Our
assumptions for these variables are in section 2 of Table 9-5C. We assume
a 13.38% discount rate (E18). We derive the discount rate by adding the
following components:
1. The 10-year average rate of return on investment for a small
composite of Real Estate Investment Trusts of 10.38%;14 plus
2. A 3% premium for incremental risk of a small operation with
very low pro¬ts, based on professional judgment.
The expected growth rate for the LLC is the expected total returns
minus expected distributions, or Table 9-4, cell C9 minus C12, or 3.74%
3.18% (Table 9-5C, E19).15
“ 0.55%
The present value of the 2% pure discount for buyers™ incremental
transactions costs is 3.2% (C11), and it is zero (C12) for the sellers™ zero
incremental transactions costs. As we explained above, there is no need
to adjust the ¬rst two DLOM components.

Final DLOM
To calculate the ¬nal DLOM, we must ¬rst compute the value remaining
after each discount. The remaining values after the four discounts are
100% 22% 78% (D9), 100% 9.0% 91% (D10), 100% 3.2%
96.8% (D11), and 100% 0% 100.0% (D12). The total remaining value
is the product of the remaining values of all the components of DLOM,
78.0% 91.0% 96.8% 100.0% 68.7% (D13). Subtracting the total
remaining value from one yields a total DLOM of 31.3% (D14). We insert
this ¬gure in Table 9-5, cell A9.

Commentary to Table 9-6: Partnership Pro¬les
The May/June 1999 edition of The Partnership Spectrum, a statistical com-
pendium published by Partnership Pro¬les, Inc., contains a wealth of data
about trades in the secondary limited partnership market, including the
average discount at which each partnership sold from its valuation. Table
9-6B shows the partnerships and their related discounts.

Comparability of Partnership Pro¬les to the Subject Interest
The member interests are fairly comparable to the LP interests in the
Partnership Pro¬les database. An ideal database to value the member
interests would be one that contained information on the selling prices,
discounts from underlying net asset value, and other relevant factors that
could affect discounts for member interests of a size and nature similar
to the subject of our valuation. This would be an ˜˜apples-to apples™™ com-
parison. Because of the differences between the member interests we are

14. Cost of Capital Quarterly”1999, SIC Code #6798 (REITs), Ibbotson Associates.
15. There is an apparent, but not real, rounding error.
16. The author regrets that because this section contains so many statistical concepts and so much
necessary statistical jargon, it is dif¬cult reading (refer to Partnership Pro¬les, Inc. website at

CHAPTER 9 Sample Appraisal Report 337
valuing and the Partnership Pro¬les LP interests, we make adjustments
to the calculated discount as discussed later.

Statistical Methodology
We performed extensive multiple regression analysis of the database. As
independent variables, we tested regular (Ryields) and special distribu-
tion yields (Syields) for 1992“1998, in simple form as well as quadratic,
natural logarithms, and inverses; cumulative cash distributions as a per-
centage of 1998 FMV; unrealized capital gains; leverage; FMV; property
type; triple/net leases; and independent versus General Partner appraisal.
Logarithms and reciprocals of zero have been converted to logarithms
and reciprocals of 0.001. We removed all variables with statistical signif-
icance under 95% and repeated the regression.17

Regression Results of Partnership Pro¬les Database
The top of Table 9-6 shows the overall regression results. R 2 and adjusted
R 2 are 70.4% (B8) and 69.4% (B9), respectively.18 This means that the re-
gression model explains 69.4% of the variation in the discounts.
The standard error of the y-estimate is 7.96% (B10). We can form an
approximate 95% con¬dence interval around the regression estimate by
adding and subtracting two standard errors, or approximately 15.9%.
There are three independent variables in the ¬nal regression:
1. Leverage: The ratio of debt to the December 31, 1998, market
value of assets (Debt/MVA98).
2. 1998 regular yield (Ryld98),19
3. A dummy variable for triple-net leases (TNL).
The regression equation is:
Average Discount 0.387 (0.115 Leverage) (2.296 1998 Yield)
(0.073 TNL)
The y-intercept and the x-coef¬cients appear in cells B20 to B23. The
y-intercept of 0.387 means that when all the independent variables have
a zero value, then the average discount from net asset value is 38.7%. All
three independent variables are zero when the LP has no leverage, cash
distributions, or triple-net leases.
The signs of the x-coef¬cients are important. The positive sign to the
leverage variable means that increased ¬nancial leverage increases the
discount from net asset value. This is intuitively appealing, as leveraged

17. The statistical signi¬cance level is the degree of con¬dence that we have that the coef¬cient of
the independent variable is not really zero. A 90% signi¬cance level, e.g., means we are 90%
certain that the coef¬cient of that variable is really not zero instead of the measure that we
obtained from the regression.
18. The adjusted R2 is a downward adjustment to remove the effects of irrelevant variables
randomly increasing R2.
19. This variable excludes special distributions. Also, the database did show ¬rst quarter 1999
distributions for many of the partnerships and second quarter distributions for some, but
using sporadic data such as this would cloud our results. Therefore, we used distributions
for the ¬rst prior full year, 1998, which all partnerships reported.

PART 3 Adjusting for Control and Marketability
T A B L E 9-6

Regression Analysis of Partnership Pro¬les Database”1999 [1]



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