43 Observations 11

45 ANOVA

46 df SS MS F Signi¬cance F

47 Regression 1 462537437.2 462537437.2 1.139733262 0.313506838

48 Residual 9 3652465953 405829550.4

49 Total 10 4115003391

51 Coef¬cients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

52 Intercept 15685.85455 13027.29977 1.204075658 0.259270779 45155.67649 13783.9674 45155.7 13783.97

53 Year 2050.581818 1920.770561 1.067582906 0.313506838 2294.506377 6395.670013 2294.51 6395.67

333

T A B L E 9-5C

Calculation of DLOM: 2.80% Member Interest

A B C D E F G

4 Section 1: Calculation of the Discount For Lack of Marketability

6 1 Col. [C]

7 Pure Discount PV of Perpetual Remaining

8 Component z [1] Discount [2] Value

9 1 22.0% 22.0% 78.0% Delay to sale-1 yr (Table 9-5A, D13)

10 2 9.0% 9.0% 91.0% Buyer™s monopsony power-thin markets

11 3A 2.0% 3.2% 96.8% Transactions costs-buyers [3]

12 3B 0.0% 0.0% 100.0% Transactions costs-sellers [4]

13 Percent remaining 68.7% Total % remaining components 1 2 3A 3B

14 Final discount 31.3% Discount 1 Total % Remaining

16 Section 2: Assumptions and Intermediate Calculations:

18 Discount rate r [5] 13.38%

19 Constant growth rate g [6] 3.18%

20 Intermediate calculation: x (1 g)/(1 r) 0.9101

21 Avg # years between sales j 10

[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

pro¬ts.

[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

markets.

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

334

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

xj

1

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

336

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

Approach”199916

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

partnershippro¬les.com).

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

338

T A B L E 9-6

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

A B C D E F G

4 SUMMARY OUTPUT

6 Regression Statistics

7 Multiple R 0.839306575

8 R square 0.704435526

9 Adjusted R square 0.693752473

10 Standard error 0.079631408

11 Observations 87

13 ANOVA

14 df SS MS F Signi¬cance F

15 Regression 3 1.254399586 0.41813 65.93953 6.66022E-22

16 Residual 83 0.526316376 0.00634

17 Total 86 1.780715963

19 Coef¬cients Std Error t Stat P-value Lower 95% Upper 95%

20 Intercept 0.387231995 0.023 16.5698 7.73E-28 0.340750627 0.433713

21 Debt / MVA98 0.115269034 0.043 2.66025 0.00937 0.029086922 0.201451

22 RYld98 2.29555895 0.320 7.17703 2.75E-10 2.931724028 1.659394

23 TNL 0.07286963 0.022 3.35275 0.001207 0.116098278 0.029641

26 Variable X-Coef¬cient Client Data Regress

27 Debt / MVA98 (B33) 0.115269034 0.0% 0.0%

28 RYld98 (Table 9-4, C12) 2.29555895 0.005528601 1.3%

29 TNL 0.07286963 0 0.0%

30 Subtotal 1.3%

31 Intercept 38.7%

32 Discount before adjustments 37.5%

33 Adjustments:

34 No public registration [2] 15.0%

35 Increased in¬‚uence [3] 5.0%

36 Total adjustments 10.0%

37 Discount 47.5%

39 Calculation of Debt / MVA98

40 Debt 0

41 MVA98 (market value of assets-1998) [4] 1,389,185

42 Debt / MVA98 0.0%

[1] Based on the data in Table 9-6B.

[2] The Partnership Pro¬les LPs are publicly registered, which is not true of the Member interests. Thus, the latter should bear a larger discount for that factor.

[3] The Partnership Pro¬les Limited Partners have no in¬‚uence over the Partnership, while the subject Member interests do. We decrease the discount to account for that difference.

[4] Table 9-2, C22.

¬rms are riskier than equity-¬nanced ¬rms, and the higher the risk, the

higher the discount. The negative signs to the other two variables”yield

and triple-net lease”mean that investors consider LPs with higher cash

yields and triple-net leases to be lower risk, which is also true. Thus, our

regression results make intuitive sense. Also, higher cash yields make up

for some of the disadvantage of lack of marketability.

The yields were signi¬cant in nonlinear forms, that is, natural loga-

rithms, denoted as ln, and inverses. Additionally, the cumulative yield

CHAPTER 9 Sample Appraisal Report 339

since inception was also statistically signi¬cant. While these additional

independent variables did add to the adjusted R 2 and lowered the stan-

dard error of the y-estimate, they did not dramatically improve the re-

gression results, and it is far easier and more practical to work with a

much simpler equation.

Commentary to Table 9-6A: Correlation Matrix

Table 9-6A is a correlation matrix. Looking down column B, we can see

that the average discount is strongly negatively correlated to yields (B7“

B10), the restaurant dummy variable (B15), and triple-net leases (B19).

This means that high cash distributions to LPs drive down discounts,

which is intuitive.

Triple-net leases (TNL) also result in lower discounts, which is also

intuitive, because TNL landlords have far less operating risk than other

landlords. The correlation of discounts to restaurants is really an indirect

relationship, because there is a strong positive correlation of 82% (L19)

between TNL and restaurants. In other words, it means that most restau-

rants are on a TNL.

The average discount is strongly positively related only to leverage

(Debt/MVA98) (B6). Looking down column C, we can see that leverage

is strongly negatively related to yields. This also makes sense, as highly

leveraged partnerships have to worry about making their debt payments

before they consider making cash distributions.

It is signi¬cant that the yields across time are highly correlated. For

example, the 1998 yields are 78%, 81%, and 75% correlated to the 1997,

1996, and 1995 yields, respectively, as can be seen in cells D8 through

D10.

By using the 1998 yield as the only yield appearing as an indepen-

dent variable in the regression equation, we still indirectly pick up the

earlier yields because they are so highly correlated. Using only one year™s

yield has the additional bene¬t of removing the problem of multicolli-

nearity. When the subject interest 1998 and earlier yields are uncorrelated,

then it is necessary to use a more long-run value for the 1998 yields. For

example, if 1998 yields are extraordinarily high (low) and expected to

decrease (increase) in the future, then it is appropriate to eliminate the

extraordinary part of the subject interest™s yield and only use that portion

which one would reasonably expect to continue in the future with normal

growth.

Applying the Regression Equation