EXECUTIVE SUMMARY

Employee stock
options (ESOs) more closely resemble
warrants than traditional
options in that they result in the
issuance of additional shares of stock.
Like warrants, ESOs impact stock values
because they are dilutive.
To determine the
value of ESOs for a closely held
company, first determine the
fair value of common equity then allocate
that value between the common stock and
the ESOs .
The value of the
options and the value of the common
stock cannot be determined
independently, with the
remainder simply being allocated to the
other. Because the value of each
instrument is a function of the other,
their values must be determined
simultaneously.
The value of each of
a company’s potentially dilutive
instruments, including
outstanding ESOs, warrants or convertible
debt, must be included in the valuation of
any new ESOs being granted.
Because closely held
companies do not have historical
volatility data, special rules
apply when estimating expected volatility
for these companies.
Keith Sellers, CPA/ABV,
CVA, DBA, Yingping Huang,
Ph.D., OCP, CISSP, and Brett A.
King, Ph.D., serve on the faculty
of the College of Business, University of
North Alabama. Their email addresses are
kfsellers@una.edu, yingping@gmail.com
and baking@una.edu,
respectively. 
Until recently, nonpublic companies that
granted options, warrants or other types of
stockbased compensation to their employees were
not typically required to determine values for
these complex derivative instruments. Current
financial reporting standards such as FASB
Statement no. 123(R), ShareBased
Payment, as well as recent federal tax law
changes (IRC § 409A) are compelling companies to
value these financial instruments using stock
option valuation models developed for publicly
traded stock options. But several issues
are unique to the valuation of employee stock
options (ESOs) for closely held companies. Even
welldesigned option valuation models will yield
incorrect values if they are not modified to
address these unique issues. These problems are
not only a concern when the ultimate objective is
to value ESOs. The failure to correctly value
employee stock options can result in a material
error in the appraisal of the underlying common
shares.
OPTION VALUATION MODELS
Statement no. 123(R) does not prescribe a
specific option valuation model. Rather, it states
that “a lattice model (for example, a binomial
model) and a closedform model (for example, the
BlackScholesMerton formula) are among the
valuation techniques that meet the criteria
required by this Statement for estimating the fair
values of employee share options.”
However, the standard clearly states that the
appropriate method to use depends on the
“substantive characteristics of the instrument
being valued.” Since ESOs include characteristics
such as vesting schedules, anticipated employee
turnover and the possible early/suboptimal
exercise of the option, it is clearly more
appropriate to use a lattice model that can
incorporate these features. The HullWhite
approach is a lattice model that can be customized
to fit virtually any option feature including the
early exercise of options by employees, turnover
and employee exit rates both before and after
vesting, which can vary over the life of the
option. The model can incorporate
suboptimal exercise assumptions (the conditions
under which employees are expected to exercise
their options in terms of the stock price reaching
a specified multiple of the exercise price). Users
can also incorporate historical or projected
turnover and employee exit rate information into
the model. Specifically, given an employee
turnover rate, each node on the lattice contains a
probability that the employee will exercise a
vested option or forfeit an unvested option,
depending on its probability of being “in the
money” at that time.
EMPLOYEE SHARE OPTIONS—STOCK OPTIONS OR
WARRANTS? When a publicly traded
call option is exercised, the owner of the call
option receives an existing share from an assigned
call writer. The writing and exercising of such
options have no effect on the value of the
underlying shares. All basic option valuation
models, including lattice models, were
“constructed” to value these nondilutive,
publicly traded options. When valuing
employee stock options, it is critical to
understand that ESOs are more correctly identified
as warrants than options. Consistent with the
financial literature, warrants are similar to call
options, but the money (exercise price) goes to
the issuer, not an option underwriter. When a
warrant is exercised, the company issues new
shares of stock, so the number of outstanding
shares increases. In short, exercise of an ESO
results in the issuance of new shares. Since by
definition that issuance takes place at a price
that is below fair value, ESOs dilute the value of
common stock. This dilution impacts the
value of both the common shares of the company and
its ESOs. For publicly traded companies, the
dilutive effects are incorporated into observed
market prices. However, this mechanism is not
available for closely held companies that issue
ESOs. When valuing ESOs for a closely held
company, CPAs must rely on an appraised value of
common equity rather than an observed
marketdetermined price. However, if the company
has issued ESOs, this appraised value cannot
merely be attributed to common shares. Rather, it
must be allocated to both existing shares and all
outstanding ESOs. Through dilution, the issuance
of ESOs will directly impact the value of existing
common shares. Since the value of the underlying
shares is a direct input in the valuation of any
ESO, any change in the value of the underlying
common shares will impact ESO values. Thus, the
dilution simultaneously affects the value of both
the common shares and ESOs. The interrelationship
between stock and ESO value was addressed by FASB
in paragraph A38 of Statement no. 123(R):
“[E]xercise of employee share options results in
the issuance of new shares by the entity that wrote
the option (the employer), which increases the
number of shares outstanding. That dilution might
reduce the fair value of the underlying shares,
which in turn might reduce the benefit realized from
option exercise.” To correctly account for these
interrelationships, all new and existing ESOs and
the common stock must be valued simultaneously.
Since most option valuation models require stock
value as an input (as opposed to an output), these
models should be modified to let both stock value
and ESO value be determined simultaneously, with
fair value of equity being provided as an input.
The effects of these interrelationships on
value can be demonstrated with the following
examples. Assume that the value of common equity
for a nonpublic company has been independently
appraised at $5 million and there are 100,000
common shares outstanding. In the absence of any
ESOs, the stock would be worth $50 per share.
Now assume that the company grants 10,000 ESOs
with an exercise price of $50 each. The options
have a maturity of 10 years and the typical
attributes and assumptions shown in Exhibit 1 are
used to value the options.
Based on this information,
the use of a typical HullWhite lattice model with
1,000 time steps yields an option value of $27.75
per option. However, this value does not reflect
the dilutive effect of the ESOs. Modifying the
option valuation model to use a bisection method
(see sidebar “ A Method for Partitioning Value”)
that simultaneously determines the
optimal stock price and option value yields the
results shown in Exhibit 2.
As can be seen, dilution materially reduced the
pershare or peroption value of both the stock
and the ESOs. For this reason, the value of both
the stock and the options can only be determined
simultaneously. This interrelationship of values
extends to any additional ESOs, warrants or
other dilutive instruments. For example, now
assume the same company already has an
additional 10,000 ESOs outstanding, which were
issued five years ago with an exercise price of
$30. The appraised value of equity would be
allocated as shown in Exhibit 3.
In summary, unless your
option valuation model can simultaneously
allocate values to stocks and all ESOs, it will
yield incorrect ESO values for closely held
companies. This, in turn, will result in
incorrect stock valuations. Statement no. 123(R)
states that “employee share options and similar
instruments will be estimated using
optionpricing models adjusted for the
unique characteristics of those
instruments” (italics added). Clearly, any
“offtheshelf” option valuation model must be
adjusted to incorporate the dilutive effects of
ESOs.
A
Method for Partitioning Value
When valuing the common stock and
ESOs of a closely held company, the
appraised total value of common equity
must first be determined using traditional
business valuation methods. This
value must then be allocated between the
various components of common equity, in
this case common stock and ESOs. While
this process is complicated by the fact
that the value of each component is a
function of the other component’s value,
one can assume that the correct value of
the company’s stock can be no less than
zero and no more than the total value of
common equity. Using this
information, the bisection method
determines the midpoint of this interval
and uses this midpoint as the stock price
to calculate a value for the options. If
the resulting sum of the option and stock
values exceeds the total value of equity,
the model understands that the midpoint
value is too high. The model then discards
values above the original midpoint, making
the midpoint the top of the remaining
interval of potentially correct stock
prices. The model then uses the midpoint
of the remaining possible stock prices and
performs this procedure again.
Thus, with each iteration, half of the
possible solutions are rejected. This
process is repeated until the total value
of the options and stock equals the total
value of equity (within a specified
tolerance, such as $0.01). The
authors have developed a software package
called the BVR/DVA 123R Compliance
Calculator that uses the method described
above. For more information, visit www.bvresources.com/123R.
 A final
relationship between employee stock options and
stock values should be mentioned. While the
appraised value of equity was held constant in the
preceding examples, the existence of ESOs may very
likely influence the appraised value of common
equity. A primary purpose of ESOs is to help
attract, reward and retain valuable employees. The
use of ESOs may allow the issuing company to pay
belowmarket cash compensation while reducing
employee turnover and improving productivity. In
other words, while the issuance of ESOs will
directly reduce stock values through dilution, the
business appraiser should consider their potential
impact on the amount, timing and uncertainty of
future cash flows and other key variables
affecting firm value.
ESTIMATING EXPECTED VOLATILITY
The need to partition value between shares
and ESOs is not the only issue when valuing
private vs. public companies. Volatility is a
critical input in any option valuation model
because a relatively small change in this estimate
can result in a large change in the value of the
option. Unfortunately, volatility can also be one
of the more difficult variables to estimate since
it requires a combination of empirical data,
advanced statistical techniques and the use of
professional judgment. The appropriate measure of
volatility, referred to as “expected volatility”
in Statement no. 123(R), is that which is expected
during the remaining life of the option. Expected
volatility is most often estimated using
historical price data. In fact, Statement no.
123(R), paragraph A21, states that “Historical
experience is generally the starting point for
developing expectations about the future.”
However, nonpublic companies have no
historical price volatility by which to estimate
expected volatility. For these companies, the
standard provides two alternative sources of
volatility information: 
Identify similar public
companies. If a company can
identify similar public companies, it should
consider the historical, expected or implied
volatility of those public companies’ shares to
help estimate expected volatility.

Identify an appropriate
index. If no similar public
companies can be identified, one should identify
and use the volatility of an appropriate
industry or subindustry index (see example at
paragraph A139 of Statement no. 123(R)).
In either case, one must exercise
judgment in identifying either appropriate similar
companies or an appropriate index. FASB has
determined that the choice of estimating future
volatility requires professional judgment that
cannot be prescribed, so it is up to the
individual performing the valuation to determine
(and support) which data and approach is most
appropriate for the specific options he or she is
valuing. In all cases, Statement no. 123(R)
cautions that companies should be consistent in
this and all critical inputs.
 AICPA
RESOURCES
JofA article
“
How to ‘Excel’ at Options
Valuation,” Dec. 05, page 57
Conference
Fair Value Measurement Workshop,
Feb. 28–29, New York City For more
information or to register, go to www.cpa2biz.com,
or call the Institute at 8887777077.
OTHER RESOURCES
Articles
“Accounting for Employee
Stock Options: A Practical Approach to
Handling the Valuation Issues,”
Journal of Derivatives
Accounting, Vol. 1, No. 1 (2004),
page 3
“How to Value Employee Stock
Options,” Financial Analysts
Journal, Vol. 60, No. 1 (Jan./Feb.
2004), page 114  