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Letter of Opinion
November 18, 1998
Mr. Robert Smith
2633 Elm Way
La Jolla, CA 92037
Dear Mr. Smith:
In accordance with your instructions, we have made a determination of
the Discount for Lack of Marketability (DLOM) necessary to calculate the
fair market value (FMV) of the common stock that you received in ENCO,
Inc. (˜˜ENCO,™™ or ˜˜the Company™™) as of August 11, 1997, the date that
you sold your company, Smith Metals, to ENCO. The stock is restricted
according to SEC Rule 144, and it becomes marketable one year after the
date of your sale. ENCO trades on Nasdaq, and the closing price of its
freely trading shares on August 11, 1997 was 2 3/8, or $2.375.
It is our understanding that this appraisal will be used for income tax
purposes. The DLOM and related FMV, as determined within our report,
shall not be used for other purposes or dates without our written consent,
as they can be misleading and dangerous.
The de¬nition of fair market value is:
The price at which property [in this case, the capital stock of the Company]
would change hands between a willing seller and a willing buyer, when neither
is under compulsion to buy and when both have reasonable knowledge of the
relevant facts.1
The scope of our engagement included discussions with you and Len
Storm, Esq., Vice President and Legal Secretary of ENCO, as to the se-
curities laws that apply, as he understands them. Per your instructions,
we assume Len Storm™s understanding of the timing of your ability to
sell your ENCO stock to be correct. If his information were incorrect, that
would cause a change in the related DLOM.
Based upon our investigation and analysis and subject to the attached
report and Statement of Limiting Conditions, it is our opinion that the
restricted stock discount (the DLOM) is 20.5%. The closing price of
ENCO, Inc. common stock on August 11, 1997, was $2.375 per share.2 The


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).
2. Source: American Online, Prophet Line.




PART 3 Adjusting for Control and Marketability
294
20.5% discount is $0.486 per share, leaving the fair market value of the
restricted stock on that date at $1.889 per share (see Table 8-3 of the report
for those calculations).
We retain a copy of this letter in our ¬les, together with ¬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 of Professional Appraisal Practice) Certi¬ca-
tion:
I certify that to the best of my knowledge and belief:
— 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
conclusions.
— 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 or use of
this report.
— 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 the
person signing this report.
— I have passed the USPAP examination and am certi¬ed through
the year 2001. I am an Accredited Senior Appraiser with the
American Society of Appraisers, with certi¬cation current to the
year 2000.
Sincerely yours,


Jay B. Abrams, ASA, CPA, MBA




CHAPTER 8 Sample Restricted Stock Discount Study 295
INTRODUCTION
Background
Stock Ownership
Purpose of the Appraisal
No Economic Outlook Section
Sources of Data
VALUATION
Commentary to Table 8-1: Regression Analysis of Management
Planning Data
Previous Restricted Stock Studies
Change in SEC Rule 144
The Data
Commentary to Table 8-1A: Revenue and Earnings Stability
Commentary to Table 8-1B: Price Stability
Valuation Using Options Pricing Theory
Options Theory
Black“Scholes Put Option Formula
Chaffe™s Article: Put Options to Calculate DLOM of Restricted
Stock
Commentary to Table 8-2: Black-Scholes Calculation of DLOM for
ENCO, Inc.
Commentary to Table 8-2A: Annualized Standard Deviation of
Continuously Compounded Returns
Commentary to Table 8-3: Final Calculation of Discount
Conclusion of Discount for Lack of Marketability
ASSUMPTIONS AND LIMITING CONDITIONS
APPRAISER™S QUALIFICATIONS




PART 3 Adjusting for Control and Marketability
296
INTRODUCTION
Background
On August 11, 1997, Robert Smith sold his company, Smith Metals, LLC,
to ENCO, Inc. (˜˜ENCO,™™ or ˜˜the Company™™) and received 500,000 shares
of ENCO Common Stock that is subject to the greater of two sets of
restrictions in transfer:
1. The sales contract with ENCO: According to Section 2.12(b)(v),
Robert Smith must wait one year to sell his ENCO stock.
2. In accordance with SEC Rule 144, Robert Smith must wait one
year to begin selling his stock, at which point he can make
quarterly sales equal to the greater of:
(a) Rule 144 (e)(1)(i): 1% of the outstanding shares. With 112.5 million
shares outstanding at the valuation date (the date of sale), 1% is
1.125 million shares.
(b) Rule 144 (e)(1)(ii): The average weekly trading volume for the four
weeks preceding the date of sale. The average weekly trading
volume for the month preceding the sale was 900,000 shares. Thus,
(2)(a) predominates, and 1.125 million is the maximum sale per
quarter according to Rule 144 after the one-year waiting period.
The sale did not qualify as a tax-free reorganization, and you need the
fair market value of the ENCO stock to compute your capital gains tax.


Stock Ownership
ENCO is publicly traded on Nasdaq with a ticker symbol of ENCO.
Through the sale of Smith Metals, Robert Smith acquired less than 1% of
ENCO™s stock.


Purpose of the Appraisal
The purpose of this appraisal is to calculate the discount for lack of mar-
ketability (DLOM) needed to ascertain the fair market value for income
tax purposes of the 500,000 shares of ENCO stock owned by Robert Smith.
Your instructions are that we are to assume the market price is the fair
market value of the unrestricted stock”a reasonable assumption”and
that the only calculation necessary to produce the fair market value of
the restricted stock is the DLOM.
The term fair market value is de¬ned as ˜˜the amount at which prop-
erty [in this case, the capital stock of the Company] would change hands
between a willing buyer and a willing seller, when the former is not under
any compulsion to buy and the latter is not under any compulsion to sell,
and when both parties have reasonable knowledge of relevant facts.™™3


3. 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).




CHAPTER 8 Sample Restricted Stock Discount Study 297
No Economic Outlook Section
The Economic Outlook, a standard section in business valuations, is ir-
relevant in this study. This section would be relevant in valuing ENCO
stock, but that is not our assignment. The same is true of a History of the
Company section. Thus, we proceed to the Valuation section.


Sources of Data
1. Financial statements sent by Len Storm, Esq., Vice President and
Legal Secretary of ENCO.
2. Copy of ENCO stock certi¬cate issued to Robert Smith including
copies of the ™33 Act legend and contractual legend.
3. One-year secondary market Treasury Bill rate as of 8/11/97
from the Federal Reserve Bank of St. Louis, internet web site
http://www.stls.frb.org.
4. America Online, Prophet Line stock quotes.
5. Restricted stock transaction data from Management Planning,
Inc., Princeton, New Jersey.


VALUATION
We use two valuation methodologies in calculating the restricted stock
discount. The ¬rst is based on our own statistical analysis using multiple
regression of data collected by Management Planning, Inc.4 The second
involves using a Black“Scholes put option as a proxy for the discount.


Commentary to Table 8-1: Regression Analysis of
Management Planning Data
Previous Restricted Stock Studies
There have been 10 studies of sales of restricted stocks.5 In the ¬rst nine
studies the authors did not publish the underlying data and merely pre-
sented their analysis and summary of the data. Additionally, only the
Hall/Polacek study contains data beyond 1988, theirs going through 1992.
The Management Planning Study contains data on trades from 1980“
1996. Thus, it is superior to the other studies in two ways: the detail of
the data exists, and the data are more current. Therefore, we use the
Management Planning study exclusively.

Change in SEC Rule 144
On April 29, 1997, SEC Rule 144 changed from a two-year holding period
to a one-year holding period for limited sales of stock. We should expect
the shortening of the period of restriction to decrease the discount. The
latest Management Planning data contain four observations with ex-


4. Published in Mercer (1997), chap. 12. Also, MPI provided us with four additional data points
and some data corrections.
5. See Mercer, p. 69 for a summary of the results of the ¬rst nine studies.


PART 3 Adjusting for Control and Marketability
298
pected holding periods of less than two years, which will enable us to
statistically infer the effect of the change in Rule 144 on DLOM.

The Data
Table 8-1 is two pages long. The ¬rst one and one-quarter pages contain
data on 53 sales of restricted stock between 1980“1996. Column A is num-
bered 1 through 53 to indicate the sale number. Column C, our dependent
(Y) variable, is the restricted stock discount for each transaction.
Columns D through J are our seven statistically signi¬cant indepen-
dent variables, which we have labeled X1, X2, . . . X7. Below is a descrip-
tion of the independent variables:


# Independent Variable

1 Revenues squared.
2 Shares sold”$: the post-discount dollar value of the traded restricted shares.
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
4
of time, with time measured as years 1, 2, 3, . . . We calculate this in Table 8-1A,
regression #1.
Revenue stability: the unadjusted R2 of the regression of revenue as a function of
5
time, with time measured as years 1, 2, 3, . . . We calculate this in Table 8-1A,
regression #2.
6 Average years to sell: 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. Management Planning used the end-of-
month stock prices for the 12 months prior to the valuation date.




We regressed 30 other independent variables included in the Man-
agement Planning study, and all were statistically insigni¬cant. We re-
strict our commentary to the seven independent variables that were sta-
tistically signi¬cant at the 95% level.
Table 8-1, page 2 contains the regression statistics. Adjusted R2 is
59.47% (C66), a reasonable though not stunning result for such an anal-
ysis. That means the regression model accounts for 59.47% of the varia-
tion in the restricted stock discounts. The other 40.53% of variation in the
discounts that remains unexplained are due to two possible sources: other
signi¬cant independent variables of which we (and Management Plan-
ning) do not know and random variation.
The standard error of the y-estimate is 8.7% (C67 rounded). We can

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