Employee Stock Options Valuation
Excel Add-in
Standard option pricing models
cannot be used to determine the value of employee stock options (ESOs). Vesting
conditions (both time and performance-based), forfeiture of unvested and out-of-the-money options when employees leave
the company, non-tradability of ESOs (usually resulting in earlier,
sub-optimal, exercise by employees),
blackout periods, and other considerations make ESO
valuation more complex than standard option valuation.
Employee stock options (sometimes called executive stock
options) also tend to have a much longer
duration than standard options (many years vs a few months for most
exchange traded options) during which time interest rates, dividend
yields, and the underlying stock volatility may change significantly from their values at ESO grant date.
Changes in these key variables can have a substantial impact on ESO
valuation.
The Hoadley Finance Add-in for Excel provides IFRS 2 and FASB 123R compliant Excel functions which can be used for the valuation of
options granted under an employee stock option plan (ESOP). The
international IFRS 2 and the US FASB 123R both specify that an
option-pricing model be applied to ESOs to estimate their fair value as at
their grant date. The Hoadley ESO functions can be used to expense
ESOs at their grant date, and then to "mark to market" at subsequent
reporting dates if required as well.
The above picture is a simple example of an ESOP grant
schedule produced in Excel using the ESO2 function (see below). Click above
picture to enlarge.
ESOs fall into
three broad categories:
 | Standard |
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with one or more fixed exercise prices determined at the grant date.
Vesting conditions may or may not include a hurdle with
respect to company performance targets being met. Most ESOPs fall into this category.
More information
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| Index-related |
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where the exercise price
is linked to a market or industry index, or where vesting is
conditional on the company's stock outperforming an index within a specified period of
time. More information
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| Forward Start |
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where the exercise price is set at a future date
("grant date")
some time after the valuation date based on the stock price
at that future time. More information
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These three types of ESOs are handled by the
Hoadley Finance Add-in for Excel, and are described below.
There are six Excel functions
designed specifically for the valuation of "standard" employee stock
options: options with a fixed exercise (strike) price where the executives
are rewarded based on the amount by which the stock price at time of
exercise exceeds the fixed strike. Unlike general option pricing
software, these functions are designed specifically for ESOP valuation and
take into account vesting requirements, employee turnover rates, and
employee exercise behaviour. The functions can be used in your
Excel spreadsheets to calculate the expense to an organization of options
granted under this type of employee share option plan (ESOP). A
company would normally select one of the following functions for ESO
valuation depending on the terms of its ESOP and the level of valuation sophistication required:
Values
employee stock options in accordance with the basic US Financial Accounting Standards Board (FASB)
123 standard. Takes into account a vesting period (time vesting) and
employee exit rates during the vesting period.
Values employee stock
options in accordance with the
Hull-White "enhanced" version of FASB 123R. The Hull-White model
would be more practical and easier to use than the ESO1 basic model for
most companies. In particular,
it does not require companies to estimate the expected life (ie expected time until
exercised) of an option - something which is not possible to do with any
degree of accuracy. The ESO2 function prices options using a
trinomial lattice model (as recommended in the FASB December 2004
statement --
FASB 123R) and
defines the conditions under which employees are expected to exercise
their options after vesting in terms of the stock price reaching a
specified multiple of the exercise price
(also recommended in FASB 123R).
Employee exit/forfeiture rates (both pre and post vest) can be specified.
For more information on the Hull-White ESO valuation model,
see
Hull-White overview.
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ESO3: "Enhanced" plus variable interest rates and dividends |
Values employee stock
options
in accordance with the Hull-White model as for the ESO2 function, but in
addition incorporates a zero coupon yield curve over the term of the
option
(time varying interest rates). This enables the interest rate
yield curve to be taken into account in ESO valuation. The function also handles dividend yields which vary over
the term of the option. Both are recommended by FASB 123R.
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ESO4: "Enhanced" plus time varying interest rates, dividends,
volatilities and exercise prices; black-out periods |
Includes everything in the
ESO3 function (ie term structure of rates and yields) and in
addition incorporates a term structure of volatilities -- stock
volatility which varies over the term of the option -- using a flexible
recombining trinomial lattice. The function will also handle time
varying exercise prices. Specifying time varying
volatility rather than one constant volatility can make a
significant difference to ESO valuation when, for example, it is expected
that a company will move from a growth phase (with higher volatility) to a more
mature phase (lower volatility) in the future.
The ESO4 function will
will also take account of recurring blackout periods during
which employees may not exercise their options.
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ESO5: "Enhanced" plus variable interest rates, dividends and
volatilities; black-out periods; performance hurdles |
Includes everything in the
ESO4 function (ie term structure of rates, yields and volatilities, and
optional specification of blackout periods) and in addition handles the
most common type of performance-vested (incentive-based, or market-based) options:
options for which vesting is
contingent on a share price target being hit at some time during the life of
the option. Share
price targets for this type of ESO may increase over time. For instance,
the terms of an ESOP might stipulate that each year the
performance target will be increased by 15%. And the type of employee
stock option where a share
price target must be reached within a specified period of time
for the option to vest -- eg within the
first two years -- can also be handled by the function. For this type
of option if the share price target is not reached within the specified
period of time the options will be forfeited.The target share price(s) can be used in conjunction with
time vesting to specify a minimum vesting period. An option would then
become vested (unconditional) once both the vesting period had expired
and the share price target had been hit. Once a target share price
has been hit then, subject to any time vesting constraints, the option will
be deemed to have vested even if the share price subsequently falls back
below the target price.
Note that this type of option is not the same as ESOPs where
the option vests only if the share price is above a target at the end of the
vesting period. Valuation of these
ESOPs with an absolute total shareholder
return (TSR) hurdle can be handled by a combined
Monte Carlo simulation and trinomial lattice approach.
A valuation template application for this type of option is
available on request.
Time to vest: The IFRS 2 standard stipulates
that with performance vested options where the performance target is based
on the underlying stock price, the average time the options remain un-vested
must be estimated for expensing purposes. The add-in includes a
function to calculate the information required to satisfy this IFRS 2
requirement: The pre-vest time (the time options are expected to remain
unvested, including those which expire without vesting), the "first hit" time
(the time until a performance target is first hit) and the
probability that the option will vest.
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Index-Related ESO Functions |
The terms of some ESOPs
include market-based performance hurdles based on the
performance of the company relative to a market or industry index. The two
main types of index-related ESOs are described below.
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Vesting conditional on outperforming an index
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Vesting in some ESOPs is conditional on the company stock outperforming a
market or industry
index during the vesting period. The performance hurdle is, in effect, a
relative total shareholder return (TSR) hurdle, which can be contrasted
with the absolute TSR hurdle described under the ESO5 section
above. If the performance hurdle is not
achieved then the options are forfeited.
A combination of correlated
Monte Carlo Simulation (to simultaneously simulate the performance of the
stock and the index taking into account the correlation between the two) and a trinomial lattice is used to value this type of
option. A valuation template application is
available on request.
Another relatively common type of ESO has a strike (exercise price)
that varies (up or down) with an industry or market index.
With this type
of Indexed ESO, employees are
compensated only for out-performance relative to the index, and not for absolute
stock performance, a large component of which may be due to the rising
market tide.
Indexed ESOs may therefore provide executives with a greater incentive
to perform compared with normal ESOs. And as indexed ESOs are usually
less expensive
than non-indexed ESOs more
options
can be issued for the same cost to the firm.
The Hoadley Finance Add-in for Excel contains two
functions for valuing indexed strike ESOs:
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ESO3Indexed: "Enhanced" Hull-White plus variable dividends.
Based on the
Hull-White model, this function also takes into account the
volatility of the relevant index, and the correlation between the index and
the firm's stock in calculating the fair value of the options.
Volatilities and correlations can be measured using the volatility and
correlation tools and functions in the Hoadley Finance Add-in.
Like the ESO3 function, the ESOIndexed function will handle
dividend yields which vary over the term of the option.
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ESO4Indexed: "Enhanced" Hull-White plus variable dividends and
volatilities; black-out periods This function is similar to the ESO3Indexed function
described above but in addition will handle volatilities (both of the index
and the stock) and correlations which vary over the term of the option.
Like the ESO4 function, the functions will also handle
recurring blackout periods.
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Forward Start ESO Function |
Some companies issue ESOs which are valued "today" for
expensing purposes but which are granted at some date in the future.
The exercise price is determined at that future date based on the stock
price at that time. For example a new employee may be promised ESOs at specific dates in the
future, conditional on remaining with the company.
The exercise prices of these options will not be known at the
valuation date, but will be set to be at-the-money (or proportionally
in- or out-of-the-money) at the future grant dates. These ESOs are
known as "forward start", or "deferred strike" options.
The Hoadley Finance Add-in for Excel includes a function
(ESO4ForwardStart) which can be used to value forward start ESOs. The
basic model used is the
Hull-White model
(including enhancements for yield and volatility term structures, and
black-out periods) but which has been enhanced to handle the forward start
characteristics of this type of option.
The functions are used in Excel
spreadsheets in the same way as you would use the standard Excel functions
like AVERAGE, SUM and NPV. Apart from knowing how to use simple Excel
functions, no programming or other technical knowledge is required.
Each function is fully documented in
a context-sensitive help file. A working example of each function is
also provided.
One of the key inputs for option valuation is volatility.
Unlike exchange traded options which tend to be relatively short term in
nature, employee stock options are usually long term (eg ten years) and valuations are highly sensitive
to variations in volatility estimates. However, estimating
volatility over a long term period is more difficult than over shorter
periods.
Listed companies: The Hoadley
Finance Add-in for Excel contains functions for
estimating volatility, including the GARCH
model which is generally regarded as the best model for forecasting the
long-term volatility trend (term structure) required for ESOP valuation.
A Historic Volatility
Calculator, which automates the process of retrieving stock price
history from Yahoo Finance and calculating current and forecast volatility
using the GARCH model, is included with the Finance Add-in for Excel.
The Historic Volatility
Calculator, using the GARCH model, produces key information needed to
estimate volatility over the duration of a long term option, including
current volatility, the long term mean and the rate at which current
volatility is likely to revert to the long term mean.
Unlisted or newly listed companies: For unlisted
companies, or newly listed companies without a stable history of closing
prices, the usual approach is to use the Historic Volatility Calculator to calculate the volatility of other
similar public
companies
(eg in same industry and/or at a similar stage of
development). This is the method recommended in paragraph A22 of the FASB 123R December 2004 statement. These volatility calculations would
provide a solid basis for estimating the volatility of the unlisted or
newly listed company. Note that basing the volatility on the volatility of
a relevant stock index would not
normally be used as the
volatility of an index, would typically be less
than the volatility of an individual stock.
The ESO functions are included in the corporate/commercial version
(ie purchased under a
corporate/commercial license) of the
Hoadley Finance Add-in
for Excel. This software also includes functions for volatility
estimation.
A corporate/commercial license
for the Finance Add-in for Excel is required to use these functions in
an organization for any purpose. The ESO functions may
not be used when purchased on-line under a private-use/personal license.
Contact Peter Hoadley
for corporate/commercial license enquiries.
You will receive a response to your
enquiry normally within an hour and always within six hours depending on
your time-zone.
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