reasonable estimate”for real growth, totaling 3.00% (row 8). Adding

rows 6 and 7, which are net income margins and property appreciation,

we come to a forecast total returns from the property of 2.30% and 3.74%

(row 9).

Bradley Jones expects to retain 25% (row 10) of income for reinvest-

ment, which leaves one minus 25%, or 75% (row 11) for cash distributions.

Finally, we multiply the net income margins in row 7 by the expected

distributions of available income in row 11 to calculate expected distri-

butions in row 12. As the 1999 amount is negative, we use only the 1997“

1999 average of 0.55% in C12 as our forecast of distributions. Again, we

will use this forecast in Table 9-6 to calculate the fractional interest dis-

count using the Partnership Pro¬les approach.

VALUATION

Valuation Approaches

We have considered the following basic approaches in calculating the

fractional interest discount:

T A B L E 9-4

Cash Distributions

A B C

4 1999 1997“1999 Avg

5 Adjusted net income (Table 9-3: B34, B36) 9,704 10,240

6 Net asset value (Table 9-2, C22) 1,389,185 1,389,185

7 Net income margin 0.70% 0.74%

8 Property appreciation [1] 3.00% 3.00%

9 Total returns 2.30% 3.74%

10 Retention percentage [2] 25.00% 25.00%

11 Expected distributions 1-retention % 75.00% 75.00%

12 Expected distributions 0.52% 0.55%

[1] Assumed at CPI expected in¬‚ation of 2.5% (Survey of Professional Forecasters, www.phil.frb.org/¬les/spf/survq499.html), plus

real growth of 0.5%

[2] Bradley Jones expects the LLC to retain 25% of net income for future growth.

6. CPI expected in¬‚ation from Survey of Professional Forecasters, www.phil.frb.org/¬les/spf/

survq499.html.

PART 3 Adjusting for Control and Marketability

326

— Economic components approach.

— Partnership pro¬les database approach.

— Market approach”sales of unregistered private fractional

interests.

— Quantitative marketability discount model.

Selection of Valuation Approach

We have selected the Economic components approach, the Partnership

Pro¬les database approach, and the market approach”sales of unregis-

tered Private Fractional Interests as the appropriate ones for valuing the

member interests. These ¬rst two are more accurate and objective than

the QMDM, which was ineffective in its ability to model restricted stock

discounts.7 The third provides us with a market benchmark.

Economic Components Approach

In this valuation approach we quantify the underlying economic com-

ponents that make up the discount for lack of marketability (DLOM) and

for lack of control (DLOC). Chapter 7 of Quantitative Business Valuation:

A Mathematical Approach for Today™s Professionals, by Jay B. Abrams, ASA,

CPA, MBA, is the theoretical basis for this approach. We will refer to this

as ˜˜the chapter.™™ Much of the wording of this section is in the context of

valuing corporate stock, as that is the context of the chapter, but the logic

also applies to valuing interests in limited partnerships, general partner-

ships, TICs, and LLCs.

DLOC is relatively simple and has no subcomponents. However,

DLOM is more complicated. Abrams identi¬es four components of the

discount for lack of marketability in the chapter: Delay-to-sale, monop-

sony power, and incremental transaction costs for both the buyer and the

seller. The ¬rst component, delay-to-sale, is the economic impact of the

incremental time that it would take to sell the subject property (in this

case, the various member interests) beyond the time that it would nor-

mally take to sell the underlying property from which we draw our com-

parisons, i.e., a 100% interest in the property. The second component is

the monopsony power to the few buyers of small businesses (or other

illiquid investments). The third and fourth components are differentials

in transaction costs for both the buyer and seller between purchasing a

fractional interest compared to a 100% interest.

Table 9-5, section 1 shows the calculation of the combined discount

(DLOM DLOC) for the 2.80% member interests according to the eco-

nomic components approach. In Table 9-5, section 2 we calculate the dis-

count for lack of control. The calculation of the discount for lack of mar-

ketability is contained in Tables 9-5A, 9-5B, and 9-5C.

7. See Chapter 7 of Jay Abrams™ book Valuing Businesses: Advanced Techniques For Practitioners,

McGraw-Hill, to be published in November 2000.

CHAPTER 9 Sample Appraisal Report 327

T A B L E 9-5

Economic Components Approach: 2.80% Member Interest

A B C D E F G

5 Section 1: Combined Discounts

7 Pure Percent

8 Discount Remaining

9 31.3% 68.7% Discount-lack of marketability (Table 9-5C, D14)

10 26.0% 74.0% Discount-lack of control (E20)

11 50.8% Total % remaining 68.7% * 74.0%

12 49.2% Discount 1 total % remaining

15 Section 2: Discount-Lack of Control

17 Average premium ( P) for control [1] 40.7%

18 Discount-minority interest P/(1 P) 28.9%

19 Adjustment: for 2.80% member interest-subtract 90%

10% [2]

20 Discount-lack of control 26.0%

[1] Source: Mergerstat-1999, page 23. There is new research in Chapter 7 of Abrams™ book Quantitative Business Valuation: A Math-

ematical Approach for Today™s Professionals which suggests that control premiums for private ¬rms probably should be on the order

of 21 to 28% above the marketable minority level. This would imply a lower discount for lack of control. However, in private ¬rms

the possibility of wealth transfer from minority interests to control interests could very well increase DLOC. In Chapter 7, Abrams

also cited international voting rights premia (VRP) as high as 82 percent and an American outlier VRP 42 percent that might indicate

the value of control to be higher than 28 percent. Taking these data into consideration, we use the Mergerstat acquisition premium

to arrive at our DLOC.

[2] A 2.80% Member Interest should have more in¬‚uence than a typical minority interest in the stock market. We quantify this by

reducing the discount for lack of control by 10%, leaving 90% of the discount for lack of control.

Commentary to Table 9-5: Calculation of

Combined Discounts

Section 1: The Combined Discounts

In this section we show the combined effects of both discounts: for lack

of marketability and lack of control. Cell A9 contains the DLOM of 31.3%

from Table 9-5C, D14. Cell A10 contains the DLOC of 26.0%, calculated

in Section 2. The remaining value after the DLOM is 1 31.3% 68.7%

(B9). The remaining value after the DLOC is 1 26.0% 74.0% (B10).

Multiplying the two remaining values produces a total remaining value

of 68.7% 74.0% 50.8% (B11). The combined discount is 1 50.8%

49.2% (B14) for the 2.80% member interest.

Section 2: Discount for Lack of Control8

Minority interests typically have no cash ¬‚ow from their investments. The

control owners are able to divert corporate funds to themselves in the

form of high salaries, perks, etc., which give them cash ¬‚ow without

generating corporate taxes. Closely held business owners of C corpora-

tions generally do not declare dividends, which are not tax-deductible as

are salaries, bonuses, and perks. Minority shareholders have no cash ¬‚ow

8. The following paragraph is introducing valuation theory that is necessary, even though it is

couched in terms of minority share ownership in C corporations, which is not the current

assignment. We will modify the conclusions that arise from this discussion as appropriate

for this valuation assignment.

PART 3 Adjusting for Control and Marketability

328

from excess salaries and receive no dividends. The only way to get cash

¬‚ow is to pray for the company to sell, and even then the control share-

holder can sell his shares without taking the minority shareholders along.

Also, the minority shareholder cannot generally force the sale of the ¬rm

to achieve liquidity, with an important exception discussed below. The

position of a minority shareholder in a closely held company is usually

quite weak and vulnerable.

The standard valuation industry calculation of the minority interest

discount begins with measuring control premiums in acquisitions of pub-

licly held ¬rms. Such acquisitions generally take place at substantial pre-

miums. There is a value to control, and buyers pay for it.

On the contrary, there is negative value to a lack of control, and

buyers will discount value because of it. If we assume a 40% premium,

that means a company trading at $100 per share before being acquired

will be acquired at $140 per share, or a $40 per share or 40 per cent

premium. The other perspective is to say that there is a $40 discount for

minority interest from the control price of $140, i.e., the discount for lack

of control (DLOC). DLOC is then $40/140, or 28.6%. A more general for-

mula to calculate the minority interest discount is DLOC P/(1 P),

where P is the control premium in percentage.

The average control premium paid in 1998 was 40.7%9 (E17), which

implies a discount for lack of control of 28.9% (E18).

A 2.80% member interest has more in¬‚uence over policy than a typ-

ical minority interest in the stock market. Because of the 2.80% member

interest™s greater control, we reduce the discount for lack of control by

10%, leaving 90% (E19) of the minority interest discount. Multiplying

28.9% 90% 26.0% (E20), the discount for lack of control, which we

transfer to A10.

Commentary to Table 9-5A: Delay-to-Sale

Table 9-5A displays our calculation of the ¬rst of four components of

DLOM, the delay-to-sale. The chapter discusses how stock in privately

held ¬rms is illiquid. Most ¬rms of substance require a year or more to

sell. We begin the calculation by making a comparison of owning a pri-

vate ¬rm to holding restricted securities of a publicly traded ¬rm.

There have been many studies that consistently ¬nd that the sellers

of restricted securities, who can choose to wait for two years10 and sell

9. Houlihan Lokey Howard & Zukin, Mergerstat Review”1999, p. 23. There is new research in

Chapter 7 of Abrams™ book Quantitative Business Valuation: A Mathematical Approach for

Today™s Professionals which suggests that control premiums for private ¬rms probably should

be on the order of 21“28% above the marketable minority level. This would imply a lower

discount for lack of control. However, in private ¬rms the possibility of wealth transfer from

minority interests to control interests could very well increase DLOC. In Chapter 7, Abrams

also cites international voting rights premia (VRP) as high as 82% and an American outlier

VRP 42% that might indicate the value of control to be higher than 28%. Taking these data

into consideration, we use the Mergerstat acquisition premium to arrive at our DLOC.

10. The SEC changed Rule 144 on April 29, 1997 to require only a one year instead of a two year

waiting period to sell restricted securities for nonaf¬liate owners. The studies we refer to

were conducted prior to April 29, 1997, and therefore measure the discount taken at the

time of sale instead of waiting two years.

CHAPTER 9 Sample Appraisal Report 329

T A B L E 9-5A

Calculation of Component #1: Delay to Sale [1]

A B C D

5 Coef¬cients Subject Co. Data Discount

6 Intercept 0.1292 NA 12.9%

Revenues2 (Table 9-3, B7)2

7 5.39E 18 6.76E 09 0.0%

8 Value of block-post-discount [2] 4.39E 09 $ 30,351 0.0%

9 FMV-100% interest in property (Table 9-2, C22) [3] 6.10E 10 $1,389,185 0.1%

10 Earnings stability (Table 9-5B, B40) 0.1381 0.1124 1.6%

11 Revenue stability (Table 9-5B, B21) 0.1800 0.1749 3.1%

12 Average years to sell [4] 0.1368 1.0000 13.7%

13 Total discount (transfer to Table 9-5C, B9) 22.0%

15 Block size in percent 2.80%

[1] This table is identical to Table 7-5, Regression #2 from Abrams™ book, with only subject™s data changed.

[2] Equal to fractional interest of FMV * (1-discount for delay to sale).

[3] In the restricted stock study, this was a marketable minority interest value. Due to the limitations of the data available, we must use the FMV of the whole property, which is a control

value.

[4] We normally assume it takes one year to sell such illiquid, fractional interests. A 3-month right of ¬rst refusal would tend to make this interest somewhat more dif¬cult than most to

sell. However, we take a conservative approach and assume it has no further impact. Thus, we remain with a one-year delay to sale.

all or part of their securities according to Rule 144 at the prevailing mar-

ket price, sell privately at an average discount of 35% (Pratt et al. 1996,

chap. 15). However, if a business takes one year on average to sell, what

is the discount? Furthermore, should every business be discounted

equally for an equal delay-to-sale, or do other business characteristics

in¬‚uence the delay-to-sale discount?

To answer these questions, Jay Abrams developed an original equa-

tion for the delay-to-sale discount. The equation was derived by perform-

ing regression analysis on the data from the Management Planning Study.

The Management Planning Study, presented as an entire chapter in Mer-

cer (1997), contains data on 49 restricted stock trades from 1980-1995. An

additional four restricted stock sales in 1996, obtained from Management

Planning, were added to the analysis.11 Abrams tested 37 independent

variables included in or derived from the Management Planning study.

Only the following 7 independent variables were statistically signi¬cant

at the 95% level.

# Independent Variable

1 Revenues squared.

2 Shares sold $: This is the post-discount dollar value of the transaction.

3 Market capitalization price per share times shares outstanding summed for all classes of

stock.

Earnings stability: the unadjusted R2 of the regression of net income as a function of time,

4

with time measured as years 1, 2, 3, . . . This is calculated in Quantitative Business

Valuation: A Mathematical Approach for Today™s Professionals in Table 7-5, regression

#1.

Revenue stability: the unadjusted R2 of the regression of revenue as a function of time,

5

with time measured as years 1, 2, 3, . . . This is calculated in Quantitative Business

Valuation: A Mathematical Approach for Today™s Professionals in Table 7-5, regression

#2.

11. In addition, Management Planning provided a few small corrections to the original data.

PART 3 Adjusting for Control and Marketability

330

# Independent Variable

6 Average years to sell: This is the weighted average years to sell by a nonaf¬liate, based on

SEC Rule 144.

7 Price stability: this ratio is calculated by dividing the standard deviation of the stock price

by the mean of the stock price. The end-of-month stock prices for the 12 months prior

to the valuation date are used.

The regression has an adjusted R 2 of 59%. This means that 59% of

the variation in restricted stock discounts is explained by the regression

model. The subject of this report does not have the data necessary to

calculate the Price stability variable. Therefore, we need to use a modi¬ed

version of the regression which excludes price stability. We also rename

variables #2 and #3 ˜˜value of block”post-discount™™ and ˜˜FMV-100% in-

terest in the LLC™™ to better suit the context of this application. The ad-

justed R 2 of this alternate regression is 43%. The coef¬cients of the re-

gression equation appear in column B.

In order to employ Abrams™ equation, we must determine the para-

meters for the LLC. Column C contains the LLC™s parameters. Cell C7

contains the square of the LLC™s 1999 revenue, $6.76 billion, shown as

6.76E 09.

The value of block”post-discount variable actually depends on the

¬nal delay-to-sale discount, the dependent variable. Therefore, we must

derive the LLC™s input for this independent variable through an iterative

process. With the aid of a spreadsheet program, the task is simple. We

input the FMV of equity, $1,389,185, which comes from Table 9-2, C22,

times the percentage interest times one minus the delay-to-sale discount,

or $1,389,185 2.80% (1 D13) $30,351 (C8) for the LLC™s value of

block”post-discount and activate the iterative capability of the spread-

sheet program.

For the FMV-100% interest in the LLC (C9), we simply input the FMV

of the LLC™s equity, $1,389,185 from Table 9-2, C22.

To determine the LLC™s earnings and revenue stability, we perform

a regression analysis of the LLC™s earnings as a function of time and its

revenue as a function of time. The results of the regressions are in Table

9-5B. The R 2 of the earnings regression (Table 9-5B, B40) is the earnings

stability of 0.1124 in C10. The R 2 of the revenue regression (Table 9-5B,

B21) is the revenue stability of 0.1749 in C11.

Due to the circumstances of the subject member interests, one who

desires to sell such a member interest could easily search for several years

to ¬nd a buyer. We assume a one-year incremental delay to sale, which

is a conservative estimate (C12).

To calculate the actual discount for delay to sale, we multiply the

coef¬cients in column B by the LLC™s parameters in Column C. Then, we

add together the y-intercept value and the products of the coef¬cients

and the parameters, which yields a delay to sale discount of 22.0% (D13).

This ¬gure is inserted in Table 9-5C, cell B9.

Commentary to Table 9-5C: Calculation of DLOM

Table 9-5C is our calculation of DLOM. Component 1 was discussed in

our commentary to Table 9-5A. Therefore we begin with a discussion of

CHAPTER 9 Sample Appraisal Report 331

332

T A B L E 9-5B

Earnings and Revenue Stability

A B C D E F G H I

4 Year Year Revenue Income

5 1 1989 $89,044 $1,165

6 2 1990 $79,646 $8,033

7 3 1991 $89,894 $(34,588)

8 4 1992 $90,645 $(25,486)

9 5 1993 $73,825 $(24,984)

10 6 1994 $70,739 $19,203

11 7 1995 $61,853 $(18,186)

12 8 1996 $70,476 $6,916

13 9 1997 $82,054 $25,025

14 10 1998 $75,147 $15,400

15 11 1999 $82,220 $(9,704)

17 SUMMARY OUTPUT-REVENUE REGRESSION

19 Regression Statistics

20 Multiple R 0.418245668

21 R square 0.174929439

22 Adjusted R square 0.083254932

23 Standard error 8831.270953

24 Observations 11

26 ANOVA

27 df SS MS F Signi¬cance F

28 Regression 1 148819808.3 148819808.3 1.908157952 0.200494368

29 Residual 9 701922119.9 77991346.65

30 Total 10 850741928.2

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

33 Intercept 85664.6 5710.916139 15.00015022 1.128E 07 72745.6003 98583.5997 72745.6 98583.6

34 Year 1163.145455 842.0286469 1.381360906 0.200494368 3067.948041 741.6571321 3067.95 741.6571

36 SUMMARY OUTPUT-EARNINGS REGRESSION

38 Regression Statistics

39 Multiple R 0.335265099

40 R square 0.112402687

41 Adjusted R square 0.013780763