. 13
( 18)


not under any compulsion to buy and the latter is not under any com-
pulsion to sell, and when both parties have reasonable knowledge of
relevant facts.™™1
The scope of our engagement did not include a physical visit to the prop-
erties or your of¬ces, nor a separate valuation of the former.
For the fair market value of the properties, we relied on the appraisals
by ABC Real Estate Appraisals as of December 1998 and the estimate of
fair market value for the Dutch Flat property by Bradley Jones. All in-
formation regarding the LLC was provided by Bradley Jones and the
LLC™s attorney, David Hollander, Esq., and its accountant, David Sofer,

1. American Society of Appraisers Business Valuation Standards. Also, the wording is virtually
identical in Reg. § 1.170A-1(c)(2) (income tax, charitable contributions of property); see Reg.
§§ 20.2031-1(b) (second sentence) (estate tax), 25.2512-1 (second sentence) (gift tax).

PART 3 Adjusting for Control and Marketability
CPA. This information has been accepted, without additional veri¬cation,
as correctly re¬‚ecting the ¬nancial statements and value and nature of
the underlying assets, and is your responsibility.
In our opinion, based upon our investigation and analysis and subject to
the attached report and Statement of Limiting Conditions, the appropriate
fractional interest discount for the subject 2.80% and 2.25% member in-
terests is 48%. The fair market value of each 2.80% interest is $20,000,
and the fair market value of each 2.25% interest is $16,250.
We retain a copy of this letter in our ¬les, together with the ¬eld data
from which it was prepared. We consider these records con¬dential, and
we do not permit access to them by anyone without your authorization.
USPAP (Uniform Standards and Principals of Appraisal Practice) Certi-
I certify that to the best of my knowledge and belief that
— The statements of fact contained in this report are true and
correct, the reported analyses, opinions and conclusions are
limited only by the reported conditions, and they are our
personal, unbiased, professional analyses, opinions, and
— We have no present or prospective interest in the property that is
the subject of this report, and we have no personal interest or
bias with respect to the parties involved.
— Our compensation is not contingent on an action or event
resulting from the analyses, opinions, conclusions in this report
or the use thereof.
— Our analyses, opinions, and conclusions were developed, and
this report has been prepared, in conformity with the Uniform
Standards of Professional Appraisal Practice and the Business
Valuation Standards of the American Society of Appraisers.
— No one has provided signi¬cant professional assistance to me.
— I have passed the USPAP examination and am certi¬ed through
2001. Additionally, I am an Accredited Senior Appraiser (ASA)
with the American Society of Appraisers. My certi¬cation is
current through the year 2000.
Sincerely yours,

Jay B. Abrams, ASA, CPA, MBA

Chaffe, B. H., III. 1993. ˜˜Option Pricing as a Discount for Lack of Marketability in Private
Company Valuations,™™ Business Valuation Review (December).
Mercer, Z. Christopher. 1997. Quantifying Marketability Discounts. Memphis, Tenn.: Pea-

CHAPTER 9 Sample Appraisal Report 317
Purpose of the Report
Valuation of Considerations
Sources of Data
Signi¬cant Terms and Legal Issues
Economic Growth
Interest Rates
State and Local Economics
Commentary to Table 9-2: FMV Balance Sheets
Commentary to Table 9-3: Income Statements
Commentary to Table 9-4: Cash Distributions
Valuation Approaches
Selection of Valuation Approach
Economic Components Approach
Commentary to Table 9-5: Calculations of Combined Discounts
Section 1: The Combined Discounts
Section 2: Discount for Lack of Control
Commentary to Table 9-5A: Delay-to-Sale
Commentary to Table 9-5C: Calculation of DLOM
Buyer™s Monospony Power
Transactions Costs
Final DLOM
Commentary to Table 9-6: Partnership Pro¬les Approach”1999
Comparability of Partnership Pro¬les to the Subject Interest
Statistical Methodology
Regression Results of Partnership Pro¬les Database
Commentary to Table 9-6A: Correlation Matrix
Applying the Regression Equation
Adjustments to the Discount
Commentary to Table 9-7: Private Fractional Interest Sales
Comparability to the Subject Interest
Statistical Methodology
Regression Results of Partnership Pro¬les Database
Commentary to Table 9-8: Final Calculation of Fractional Interest
2.80% Member Interest

PART 3 Adjusting for Control and Marketability
Final Calculation of FMV of Fractional Interests

CHAPTER 9 Sample Appraisal Report 319
These considerations are outlined and described in Revenue Ruling 59-
60, 1959-1 CB 237, as modi¬ed by Revenue Ruling 65-193, 1965-2 CB 370,
and Revenue Ruling 77-287, IRB 1977-33. Although Revenue Ruling 59-
60 speci¬cally addresses itself to stock valuations for gift and estate tax
purposes, the principles set forth may be applied to a wide spectrum of
valuation problems, including those related to stockholder buy/sell
agreements, mergers and acquisitions, Employee Stock Ownership Plans,
corporate reorganizations, marital dissolutions, and bankruptcies. This re-
port will discuss these factors and address other items relevant to the
member interests to determine their effect upon the fair market value of
the LLC interests.

Sources of Data
1. Survey of Professional Forecasters™™ Federal Reserve Bank of
Philadelphia, November 19, 1999. Internet site http://
2. Operating Agreement of the LLC.
3. ABC Real Estate Appraisals.
4. Conversations with Bradley Jones.
5. LLC™s balance sheet and income statement.
6. Mrs. Tina Smith™s Federal Tax Returns from 1997 and 1998.
7. Survey of Professional Forecasters, www.phil.frb.org/¬les/spf/
8. Houlihan Lokey Howard & Zukin, Mergerstat Review”1999, p.
9. Cost of Capital Quarterly”1999, SIC Code #6798 (REITs),
Ibbotson Associates.
10. Management Planning, Inc. restricted stock data.
11. Partnership Pro¬les, Inc. secondary limited partnership data.
12. Jones, Roach & Caringella private sale data.

Tina M. Smith and her four children, listed below in Table 9-1, founded
the LLC on January 6, 1999. Mrs. Smith owned several properties, which
she contributed to the LLC. The original capital contributions and mem-
ber interests are as appears above in Table 9-1.
All four 5% members are children of Tina Smith. According to Brad-
ley Jones, the member interests are the same as of the valuation date,
even though there have been additional contributions.

Signi¬cant Terms and Legal Issues
The LLC is governed by its Operating Agreement dated January 6, 1999.
According to the Operating Agreement, the LLC is to be dissolved on
December 31, 2030, unless the term is extended by amendment to the
Operating Agreement or it is dissolved earlier.

CHAPTER 9 Sample Appraisal Report 321
T A B L E 9-1

Member Interests at Inception on 1/6/96

Member Initial Capital Contribution %

Tina M. Smitha $200,000 80%
Bradley J. Jones 10,000 5%
David R. Jones 10,000 5%
Larry T. Smith 10,000 5%
Lisa C. Dubliner 10,000 5%
Total $240,000 100%

Source: Exhibit A, Operating Agreement of the LLC.
As Trustee under the Tina M. Smith Revocable Living Trust, and amendments thereto, 9/11/90.

Section 11 of the Operating Agreement speci¬es a three-month right
of ¬rst refusal (ROFR) in which its other members have to buy out a
member who wants to sell.
Bradley J. Jones is the Manager of the LLC and has the right to bind
it legally. However, his authority is subject to the Management Commit-

The LLC™s ROFR is a moderate impairment of marketability and, there-
fore, fair market value. This happens because buyers are averse to in-
vesting their time in the due diligence process when they can be so easily
outbid by having their bid matched by insiders who have legal prefer-
ence. To be slightly conservative, we do not make an explicit adjustment
for this in our ¬nal calculation of the fractional interest discount.

Economic Growth
Forty-three forecasters surveyed by the Federal Reserve Bank of Phila-
delphia expect that the U.S. economy will expand at an annual rate of
3.7% in 1999™s fourth quarter and at an annual rate of 3.1% in 2000. The
forecasters see growth slipping a bit in the ¬rst quarter of 2000, to 2.3%,
but rebounding from that rate over the following three quarters. Unem-
ployment is expected to average 4.3% in 2000.3

Expectations for in¬‚ation, measured by the Consumer Price Index, over
the next 10 years are 2.50%. The expected in¬‚ation for 2000 is 2.50%.4 For
the purposes of this valuation, we forecast annual in¬‚ation at 3%.

3. ˜˜Survey of Professional Forecasters™™ Federal Reserve Bank of Philadelphia, November 19, 1999.
Internet site http://www.phil.frb.org/¬les/spf/survq499.html.
4. Ibid.

PART 3 Adjusting for Control and Marketability
Interest Rates
Three-month Treasury Bills are expected to average 5.1% in 2000, while
the yield on 10-year Treasury Bonds is expected to average 6.1.5

State and Local Economics
State and local economics are not suf¬ciently relevant to warrant research
in this report, as they are fully considered in the valuation of the real

The economic forecast for the United States appears moderately positive,
with modest growth and low in¬‚ation.

Commentary to Table 9-2: FMV Balance Sheets
Table 9-2 consists of a historical balance sheet of the LLC in column B
and a fair market value balance sheet in column C, both dated December
25, 1999, the valuation date. The source of the historical 1999 balance sheet
and income statement is the LLC™s internally generated statements as of
December 14, 1999.
Bradley Jones stated that he expects no other income, expenses, or
payments for the remainder of 1999, with one exception. The LLC will
pay his accrued salary of $1,600 on December 15. Additionally, there
would be another payment of his salary at the end of December, which
is after the December 25, 1999, valuation date. Technically, we should
accrue another ten days of his salary to the valuation date, but the dif-
ference is immaterial. Thus, we show an accrual of $3,200 for his entire
December salary in row 20.
The only difference between the amounts in columns B and C is that
we substitute the appraised fair market values for the properties in col-
umn C in place of the cost basis in column B. The historical balance sheet
is not relevant to the valuation analysis, and we present it in order to be
All fair market values of properties are appraised by ABC Real Estate
Appraisals, with the exception of Dover Field (Row 15), which is 2.77
acres of land and one studio. Bradley Jones estimates its fair market value
at $40,000.
The fair market value of the properties are $1,387,000 (C16), which
is approximately $667,000 above their cost basis. The net asset value, or
fair market value of the equity, is $1,389,185 (B22).

5. Ibid.

CHAPTER 9 Sample Appraisal Report 323
T A B L E 9-2

Balance Sheets 12/25/99 [1]


4 Assets: Historical FMV [2]

5 Cash 11,234 11,234
6 Computer equipment-net 1,251 1,251
7 Real estate:
8 4627-35 Bass St. 370,000
9 88 Apple Road, Julian 95,000
10 000 Pumpkin Patch [3] 40,000
11 37830 & 37848 Geese Rd., Ranchita 135,000
12 4463-65 Grape St. 215,000
13 852 Brown Ave. 300,000
14 1351 Kansas St. (80% owned by LLC) [4] 192,000
15 Dover Field 40,000
16 Total real estate [5] 719,254 1,387,000
17 Total assets 731,739 1,399,485

18 Liabilities
19 Security deposits 7,100 7,100
20 Accrued manager™s salary payable 3,200 3,200
21 Total liabilities 10,300 10,300
22 Total capital 721,439 1,389,185
23 Total liabilities & capital 731,739 1,399,485

[1] The source of the historical balance sheet (and income statement) is the LLC™s internally drafted statement as of 12/14/99. Brad-
ley Jones expects no other income, expenses, or payments through the end of the year, with the exception of his own salary of
$3,200 per month. Technically, we should accrue that salary through 12/25/99. However, to facilitate the income statement analysis
for an entire year, it is preferable to accrue his salary through 12/31/99. The difference of six days of salary is immaterial to the
[2] All properties appraised by ABC Real Estate Appraisals as of 12/30/98 or 12/3/98, except for Dover Field, which is 2.77 acres of
land, plus one studio. Bradley Jones, LLC Manager, estimates its FMV at $40,000. All other assets and liabilities are per the LLC™s
12/14/99 Balance Sheet.
[3] This is vacant land.
[4] Four gifts of 5% each 20% Tenants-in-Common interests were already gifted to Bradley Jones, David R. Jones, Larry T. Smith,
and Lisa C. Dubliner. This is 80% of the appraised FMV.
[5] The historical numbers consist of the following:
Total buildings 494,005
Less accumulated depreciation-bldgs (116,310)
Buildings-net 377,695
Construction in progress (Brown Ave.) 44,864
Land 296,695
Total real estate 719,254
Bradley Jones reports that ABC Real Estate Appraisals told him verbally that the appropriate FMV for the Brown Ave. property,
which is the one with the construction-in-progress, is still the $300,000 at which it was appraised in 1998.

Commentary to Table 9-3: Income Statements
Table 9-3 presents income statement data for three years. Column B con-
tains a complete income statement for 1999. January 6, 1999, was the
inception of the LLC, so the income statement excludes January 1 through
January 5, when the properties were still owned by Tina M. Smith as an
individual. Additionally, the 1997 and 1998 income data, which appear
in columns D and C, respectively, are partial data taken from Mrs. Smith™s
tax returns”speci¬cally from Schedule E.
Row 32 shows net income as appears on the LLC™s income statement
and Mrs. Smith™s tax returns. Net income was $27,733, $17,843, and
$28,696 in 1997“1999, respectively (D32, C32, and B32).
Next, it is necessary to subtract salary for Bradley Jones™s services to
the properties. In 1997 and 1998 he was part-time and managed only one

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

Income Statements [1]


4 1999 1998 1997

5 Rental income 82,170
6 Late fees 50
7 Total income 82,220
8 Expenses:
9 Fire equipment maintenance 29
10 Auto 2,905
11 Bank charges 64
12 Dues & subscriptions 72
13 Equipment rental 396
14 Franchise fees 800
15 Insurance 5,284
16 Landscaping 1,535
17 Licenses and permits 623
18 Postage and delivery 241
19 Accounting 1,380
20 Consulting 1,750
21 Legal 1,500
22 Property taxes 10,576
23 Repairs 17,854
24 Supplies 6,169
25 Telephone 505
26 Gas & electric 430
27 Water 1,502
28 Rounding error 1
29 Total expenses 53,614
30 Net operating income 28,606
31 Interest income 90
32 Net income before adjustments [2] 28,696 17,843 27,733
33 Less management salary [3] 38,400 2,443 2,708
34 Adjusted net income [4] 9,704 15,400 25,025
35 1997“1999 average net income 30,721
36 1997“1999 total net income 10,240

[1] Sources: The LLC™s 12/14/99 Income Statement provided by Bradley Jones and Schedule E™s from Tina Smith™s 1997“1998 tax
[2] This amount equals net income on the LLC™s income statement.
[3] In 1999, Bradley Jones made $3,200 per month, which is arm™s-length. His salary was recorded as a draw against earnings, but
it should be charged as an expense. In earlier years, Mrs. Smith paid an outside property manager. Bradley managed one of her
properties, without pay. In 1997-1998, we subtract the same amount paid to the property manager as Bradley™s arm™s-length salary
in those years.
[4] This income statement is 1/1/99 to 12/14/99. Bradley Jones expects no more income or expense for the remainder of 1999, with
the exception of his own salary, which we have accrued.

of the properties, and he was unpaid. For those two years we subtracted
the same amount as Mrs. Smith paid her outside property manager”
approximately $2,400 to $2,700 (C33 and D33). In 1999, Mr. Jones worked
full-time for the LLC, and we subtract his actual (and arm™s-length) salary
of $38,400 (B33), which on the LLC™s income statement was charged as a
draw against pro¬ts.
We subtract row 33 from row 32 to arrive at adjusted net income in
row 34. Adjusted net loss was $9,704 (B34) in 1999. In 1997 and 1998
adjusted net income was $25,025 and $15,400 (D34 and C34). Total ad-
justed net income for the three years was $30,721 (B35), and the three-
year average was $10,240 (B36).

CHAPTER 9 Sample Appraisal Report 325
Commentary to Table 9-4: Cash Distributions
In Table 9-4, we calculate the margins from net income and property
appreciation as well as cash distributions. We use the ¬rst two items in
our calculations in Table 9-5C, and we use the latter in Table 9-6.
We begin with adjusted net income of $9,704 (B5, from Table 9-3,
B34) for 1999 only and $10,240 (C5, from Table 9-3, B36) for the average
of 1997“1999. We then divide that by the net asset value of $1,389,185
(Row 6, from Table 9-2, C22) to arrive at the net income margins of
0.70% and 0.74% (Row 7).
We assume property appreciation at 2.5% for in¬‚ation6 and 0.5%”a
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 Approaches
We have considered the following basic approaches in calculating the
fractional interest discount:

T A B L E 9-4

Cash Distributions


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/

PART 3 Adjusting for Control and Marketability
— Economic components approach.
— Partnership pro¬les database approach.
— Market approach”sales of unregistered private fractional
— 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


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
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]


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

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

PART 3 Adjusting for Control and Marketability
# 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

T A B L E 9-5B

Earnings and Revenue Stability


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)


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


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
38 Regression Statistics

39 Multiple R 0.335265099
40 R square 0.112402687
41 Adjusted R square 0.013780763
42 Standard error 20145.2116
43 Observations 11


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
T A B L E 9-5C

Calculation of DLOM: 2.80% Member Interest


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
[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]



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


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
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

Applying the Regression Equation
We apply the above regression equation to the LLC in Table 9-6, Rows
26 to 32. First, we repeat the regression x-coef¬cients from B21 to B23 in
B27 to B29. The LLC™s data are in C27 to C29. The triple-net-lease dummy
variable equals zero, as the LLC™s properties are not subject to TNLs. We
multiply the x-coef¬cients in B27 to B29 by the LLC™s data in C27 to C29
to come to the regression results for the LLC in D27 to D29, which we
subtotal in D30 as 1.3%. We then repeat the y-intercept of 38.7% from
B20 in D31 and add that to the subtotal, to come to a discount before
adjustments of 37.5% (D32).

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

Correlation Matrix


4 Avg Disc Debt / MVA98 RYld98 RYld97 RYld96 RYld95 C MF R MH RST Combo Parking Eq Dist TNL Indep
5 Avg disc 1.00
6 Debt / MVA98 0.61 1.00
7 RYld98 0.80 0.61 1.00
8 RYld97 0.64 0.42 0.78 1.00
9 RYld96 0.68 0.48 0.81 0.76 1.00
10 RYld95 0.65 0.47 0.75 0.72 0.88 1.00
11 C 0.07 0.12 0.00 0.11 0.15 0.15 1.00
12 MF 0.00 0.28 0.04 0.14 0.12 0.04 0.19 1.00
13 R 0.01 0.06 0.01 0.02 0.02 0.01 0.08 0.14 1.00
14 MH 0.16 0.13 0.07 0.04 0.01 0.04 0.09 0.16 0.07 1.00
15 RST 0.52 0.35 0.40 0.34 0.43 0.41 0.15 0.28 0.12 0.13 1.00
16 Combo 0.20 0.02 0.21 0.18 0.26 0.15 0.20 0.36 0.15 0.17 0.29 1.00
17 Parking 0.09 0.09 0.01 0.01 0.02 0.02 0.05 0.09 0.04 0.04 0.07 0.09 1.00
18 Eq dist 0.14 0.05 0.09 0.09 0.21 0.11 0.04 0.14 0.08 0.31 0.42 0.29 0.17 1.00
19 TNL 0.51 0.22 0.43 0.36 0.46 0.44 0.09 0.34 0.03 0.16 0.82 0.24 0.09 0.51 1.00
20 Indep 0.20 0.37 0.30 0.16 0.16 0.20 0.27 0.43 0.07 0.07 0.40 0.16 0.14 0.11 0.47 1.00
T A B L E 9-6B

Partnership Pro¬les Database: Price-to-Value Discounts”1999


5 Name Avg Disc
6 Aetna Real Estate Associates 23%
7 ChrisKen Partners Cash Income 28%
8 Consolidated Capital Inst. Props. 1 28%
9 Consolidated Capital Inst. Props. 2 35%
10 First Capital Inst. Real Estate 4 21%
11 HCW Pension Real Estate Fund 29%
12 I.R.E. Pension Investors II 40%
13 John Hancock Realty Income Fund II 12%
14 Murray Income Properties I 25%
15 Murray Income Properties II 25%
16 Rancon Income Fund I 39%
17 Realty Parking Properties I 8%
18 Realty Parking Properties II 28%
19 Wells Real Estate Fund II-A 8%
20 Wells Real Estate Fund III-A 31%
21 Wells Real Estate Fund IV-A 38%
22 Wells Real Estate Fund VI-A 26%
23 Wells Real Estate Fund VII-A 25%
24 Wells Real Estate Fund VIII-A 24%
25 Wells Real Estate Fund IX-A 24%
26 Wells Real Estate Fund X-A 20%
27 Windsor Park Properties 6 15%
28 Angeles Income Properties II 30%
29 Angeles Opportunity Properties 37%
30 Angeles Partners XII 34%
31 ChrisKen Growth & Income II 16%
32 Consolidated Capital Inst. Props. 3 25%
33 Consolidated Capital Properties III 28%
34 Davidson Growth Plus 41%
35 Davidson Income Real Estate 38%
36 Multi-Bene¬t Realty Fund ™87-1 (A units) 29%
37 Nooney Income Fund II 42%
38 Shelter Properties VII 35%
39 Uniprop Man. Hous. Com. Inc. Fund I 45%
40 Uniprop Man. Hous. Com. Inc. Fund II 41%
41 Windsor Park Properties 3 38%
42 Windsor Park Properties 5 27%
43 Windsor Park Properties 7 46%
44 Angeles Income Properties III 42%
45 Angeles Income Properties IV 42%
46 Angeles Income Properties 6 29%
47 Angeles Partners IX 36%
48 Angeles Partners XI 25%
49 Consolidated Capital Properties V 52%
50 Davidson Diversi¬ed Real Estate I 62%

Adjustments to the Discount
For Lack of Public Registration. The Partnership Pro¬les database
consists exclusively of ¬rms that are publicly registered, though privately
traded. The lack of public registration of the member interests renders
them less marketable than the Partnership Pro¬les database. Therefore
we must increase the fractional interest discount for that factor. We as-
sume that a 15% increase is reasonable (D34).

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

Partnership Pro¬les Database: Price-to-Value Discounts”1999


5 Name Avg Disc
51 Davidson Diversi¬ed Real Estate II 61%
52 Davidson Diversi¬ed Real Estate III 38%
53 First Capital Income Properties XI 41%
54 First Capital Income & Growth Fund XII 44%
55 First Dearborn Income Properties 58%
56 Multi-Bene¬t Realty Fund ™87-1 (B units) 57%
57 InLand Capital Fund 47%
58 Inland Land Appreciation Fund I 45%
59 Inland Land Appreciation Fund II 48%
60 Scottsdale Land Trust 46%
61 CNL Income Fund III 9%
62 CNL Income Fund V 9%
63 CNL Income Fund VI 15%
64 CNL Income Fund VII 11%
65 CNL Income Fund VIII 16%
66 CNL Income Fund IX 11%
67 CNL Income Fund X 12%
68 CNL Income Fund XI 17%
69 CNL Income Fund XII 13%
70 CNL Income Fund XIII 15%
71 CNL Income Fund XIV 8%
72 CNL Income Fund XV 6%
73 CNL Income Fund XVI 14%
74 CNL Income Fund XVIII 7%
75 Carey Institutional Properties 28%
76 Corporate Property Associates 10 16%
77 Corporate Realty Income Fund I 27%
78 DiVall Income Properties 3 12%
79 DiVall Insured Income Properties 2 1%
80 John Hancock Realty Income Fund III 12%
81 Net 1 LP 23%
82 Net 2 LP 28%
83 Capital Mortgage Plus 23%
84 Capital Source LP 15%
85 Capital Source LP II 22%
86 Krupp Government Income Trust 10%
87 Krupp Government Income Trust II 15%
88 Krupp Insured Mortgage LP 9%
89 Krupp Insured Plus LP 15%
90 Krupp Insured Plus II 11%
91 Krupp Insured Plus III 2%
92 Paine Webber Insured Mortgage 1-B 21%
93 Max 61.7%
94 Min 0.8%
95 Mean 26.8%
96 Std deviation 14.4%

For Additional In¬‚uence of Private versus Public Interest. The
member interests should have more in¬‚uence than the small LP interests
from which we calculated the regression coef¬cients, and they actually
do have a vote. We reduce the discount by 5% in D35.
The adjustments for lack of public registration and additional in¬‚u-
ence are both reasonable estimates. In total, our net adjustments are 10%

CHAPTER 9 Sample Appraisal Report 343
(D36). Adding D32 and D36, the total discount for the LLC interest is
47.5% (D37).

Benchmarks for Net Effect of the Adjustments. The x-coef¬cients
for the dummy variables can give us a feel for how the discount might
vary if Partnership Pro¬les had data available on trades of LLCs with
assets more similar to our subject. The coef¬cient for the triple-net lease
dummy variable is 7.2%. In earlier years, typical coef¬cients for other
dummy variables have ranged from 5“12%. Therefore, the net adjust-
ment for no public registration and increased in¬‚uence of 10% appears
There is another way to benchmark the net adjustments. According
to Jay Abrams™ conversations with brokers who sell LP interests, shifting
from selling a publicly registered LP interest to a private LP interest adds
approximately 7“10 months in the selling time, which is 58“83% of one
year. If we multiply that by the ˜˜Average Years to Sell™™ x-coef¬cient of
0.1368 in Abrams™ book20, we get an increase in discount of 8“11%. In the
book, there was another regression21, and the ˜˜Average Years to Sell™™ x-
coef¬cient for that one was 0.1722. Using that instead of the 0.1368 leads
to estimates of the net adjustment of 10“14%. Furthermore, it is reason-
able to assume that the decrease in discount from the ˜˜increased in¬‚u-
ence™™ factor in the private LP is offset by the increase in the discount for
the additional monopsony power to the buyer of the private LP interest.
Thus, 8% to 14% is a reasonable range for net adjustments.

Commentary to Table 9-7: Private Fractional Interest Sales
Robert Jones, a real estate appraiser with the ¬rm Jones, Roach & Car-
ingella in San Diego, provided us with actual transaction data for illiquid
fractional interests in real estate. Table 9-7 shows the detail and our anal-
ysis of the interests and their related discounts.

Comparability to the Subject Interest
The member interests are very comparable to the fractional interests in
Table 9-7. The main difference is that the subject member interest repre-
sents ownership in several properties, not just one.

Statistical Methodology
We performed simple and multiple regression analysis of the database.
As independent variables, we tested the transaction amount (Price), the
percentage interest (Size), the FMV of the entire property, and dummy
variables for the time period of the transaction (pre-1990) and whether
the interest was a GP interest in a general partnership. We did not have
yield data.

20. Table 7-5, p. 240, cell B54. In other words, the regression in the book shows that for each year
of inability to sell, restricted stocks experience a discount of 13.68%.
21. Applicable when the subject company has been publicly traded for at least six months, and
thus historical stock prices are available to calculate the ˜˜Price Stability™™ variable. See Table
7-5, p. 239, cell B26.

PART 3 Adjusting for Control and Marketability


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