Employee Stock Option Valuation
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, suboptimal, 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 FAS 123R (now ASC 718) compliant Excel functions which can be used for the valuation and analysis of options granted under an employee stock option plan (ESOP). The international IFRS 2 and the US FAS 123R (ASC 718) both specify that an option-pricing model be applied to ESOs to estimate their fair value as at their grant date. The Hoadley ESO analysis software 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 an example of a simple ESOP grant schedule produced in Excel using the ESO2
function (see below). Click above picture to enlarge
|Types of ESO|
ESOs fall into three broad categories:
|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.
|where the exercise price is linked to a market or industry index,
where vesting is conditional on the company's stock outperforming an index
within a specified period of time, or where vesting is based on relative TSR performance
against a peer group of stocks (Relative TSR plans). More
|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.
These three types of ESOs are handled by the Hoadley Finance Add-in for Excel, and are described below.
Note that Restricted
Stock Units (RSUs) can generally be valued using the same valuation
models as ESOs with the option term equal to the vesting period.
|Market-Leveraged Stock Units (MSUs)|
An MSU is a leveraged equity instrument for employee compensation where the number of shares received at the end of a vesting period depends on the ratio of the stock price at that time to the stock price at the time of the grant.
The Finance Add-in for Excel includes a function for
valuing MSUs. More information.
|Standard ESO Functions|
The Hoadley Finance Add-in for Excel includes functions designed specifically for the valuation and analysis of "standard" employee stock options: options with one or more fixed exercise (strike) prices where the executives are rewarded based on the amount by which the stock price at time of exercise exceeds the strike price. ESOs may include performance hurdles.
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 FAS 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 -- FAS 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.
|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 FAS 123R.
|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.
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.
Other optional key features available in the ESO4 function include:
|Time varying exercise
prices: options with multiple exercise prices that take effect at
|Capped Stock Appreciation Rights
(SARs): Valuation of SARs with a cap on the maximum benefit
Taking account of recurring blackout periods during
which employees may not exercise their options.
|ESO5: "Enhanced" plus variable interest rates, dividends and volatilities; black-out periods; performance hurdles|
Includes 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.
The ESO5 model can also be used to value Restricted Stock Units (RSUs) with performance vesting conditions.
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.
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.
Total shareholder return (TSR) targets: The type of option described above 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. The template allows for the specification of Multiple TSR hurdle levels if
required, each with a different vesting percentage. Achievement of
the highest performance target would result in 100% of options
vesting. Lower levels of achievement would result in
correspondingly lower vesting percentages.
|Relative Performance Plans|
The terms of some ESOPs include market-based performance hurdles -- market conditions --where ESO valuation is linked to the performance of the company relative to a market or industry index, or where vesting percentages depend on the relative performance of company, as measured by Total Shareholder Return (TSR), with respect to a peer group of stocks.
The three main types of relative
performance-related ESOs are described below.
|Vesting conditional on outperforming an index|
Vesting in some ESOPs or Performance Share plans is contingent on the company's 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 relative to the index is not achieved then the options are forfeited.
Performance hurdles are often specified as a schedule of one or more targets (expressed in terms of the percentages by which the company's TSR must beat the index for the options or performance shares to vest) and a corresponding vesting percentage for each target point. Vesting occurs on a sliding scale using linear interpolation for outperformance falling between specified percentage points.
A valuation template application designed
to value these types of ESO and Performance Share plans is available on
request. The application uses 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 to value these
relative performance plans.
|Relative TSR against a peer group|
In an increasing number of Relative Total Shareholder Return (TSR) plans, vesting depends on the performance of the company relative to that of a peer group of companies. At the end of the vesting period ("test date") the percentile ranking of the company's TSR within the peer group determines the percentage of options or performance shares (performance rights) that will vest.
A valuation template is available to corporate users of the Finance Add-in for Excel to value this type of relative TSR plan. The template uses a combination of Monte Carlo simulation and a trinomial lattice to model the performance of the company's stock and the individual stocks within the selected peer group (typically 15 to 30 industry peers) taking into account their individual volatilities and correlations. The add-in includes tools to calculate these measures from historical data.
For very large peer groups, for example a group consisting of all the companies in the S&P 500 index, a simplified "single index" model can be used. With the single index model, instead of directly specifying the correlations between each of the assets, asset betas and volatilities are used to infer asset cross-correlations based on each asset's implied correlation with the peer group (usually an index). Use of the single index model with large peer groups both simplifies the inputs required and greatly reduces Monte Carlo simulation time.
The percentage of options that will vest at each percentile
ranking point is calculated according to a user-defined vesting schedule. Vesting percentages which fall between defined
percentile points are calculated based on a sliding scale (linear
|Indexed strike ESOs|
Another less 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.
The Hoadley Finance Add-in for Excel contains a function for valuing indexed strike ESOs. Based on the Hull-White model, this function extends this model to take 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 standard ESO4 function, the
indexed strike function will allow for dividend yields, correlations and
volatilities which vary over the term of the option for both the index
and the stock.
|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.
|Restricted Stock (RS) Buybacks|
When restricted stock (note: restricted stock, not restricted stock units) is issued to employees the company's right to buy back a certain percentage of the stock at the grant price (which may be zero), should the employee leave during the vesting period, constitutes a call option. The call option reduces the cost to the company of issuing the stock and so should be valued.
Valuation of restricted stock buyback rights must take into account the number of vesting periods and their timing, the percentage of employees expected to leave during each vesting period and the time-dependent percentage of the grant which the firm can buy back during each vesting period.
The Finance Add-in for includes a
function to value buyback rights on unvested restricted stock
|Maket-Leveraged Stock Units (MSUs)|
A Market-Leveraged Stock Unit (MSU) is an employee equity compensation instrument where the number of shares received at the end of a vesting period depends on the ratio of the stock price at that time to the stock price at the time of the grant.
The Finance Add-in for Excel includes a function for valuing MSUs using a trinomial lattice. Key features include:
to handle companies which expect future volatility to be different
from current volatility (eg those transitioning from a development
stage to a more mature stage).
Basing the payout ratio of an MSU at the vesting date on either the
actual share price at that date, or on the average share
price during a period preceding the vesting date.
|Floors and caps:
Specification of floors and caps for the payout ratio (the number of
units issued to the employee at the end of the vesting period).
Valuation of an MSU with either partial or full dividend protection,
or without dividend protection. Dividend protection compensates
employees, either partially or fully, for the negative impact on the
vesting-date share price of dividends paid on the underlying shares
during the vesting period.
turnover. Adjustment to the MSU value to account for
employees expected to leave the firm during the vesting period.
valuation. Ability to value an MSU at the grant
date or at a later date using the share price, volatilities,
dividend yield etc prevailing at the time of valuation.
In addition to the above "vanilla" MSUs, application templates using Monte Carlo simulation are available on request to corporate license holders for the valuation of MSUs with performance targets which must be met in order for the MSUs to vest. As for performance ESOs, MSU performance plans can be based on:
|Absolute Total Shareholder Return (TSR). One or more TSR hurdle levels
(targets) can be specified, each with a different vesting
percentage. Achievement of the highest performance target
would result in 100% of options vesting. Lower levels of
achievement would result in correspondingly lower vesting percentages.
performance against a market index. Performance
hurdles are specified as a schedule of one or more targets
(expressed in terms of the percentages by which the company's TSR must beat the index for the
MSUs to vest)
and a corresponding vesting percentage for each target point. Vesting
occurs on a sliding scale for outperformance
falling between specified percentage points.
|Relative TSR performance against a peer group. Vesting of MSUs depends on the performance of the company relative to that of a peer group of companies. At the end of the vesting period ("test date") the percentile ranking of the company's TSR within the peer group determines the percentage of MSUs that will vest according to a user-defined vesting schedule.|
Like warrants, the exercise of most employee stock options normally results in additional shares being issued by the company which are sold to the option holders for the strike price. As the strike price is less than the market price this dilutes the interests of existing shareholders.
How should dilution be handled when valuing ESOs?
For publicly traded companies the impact of dilution on ESO (and warrant) valuations can be ignored providing that ESO valuations are based on the stock price after the ESO grant has been announced. This is because, in efficient markets, the post-grant-announcement stock price would incorporate the potential dilution effect from all outstanding ESOs and warrants and therefore the dilution impact should not be considered again when the options are valued.
See the two papers on the Hull-White model for discussions on why dilution can be ignored for publicly listed companies.
For closely held companies the impact of dilution should not be ignored. Unlike public companies, there is no market price for closely held (private) companies which incorporates information about the potential dilution from outstanding ESOs and warrants. So the impact of dilution, which can be significant, must be explicitly considered when valuing private company equity instruments.
With public companies, each tranche of options with identical terms can be valued independently of every other tranche. This is not the case with private companies where the stock price and the instruments being valued are mutually dependent: the value of the company's shares depends on the value of all outstanding ESOs and warrants, and the value of these instruments, in turn, depends on the value of the company's shares.
The valuation process must take this interdependence into account. Both existing shareholder equity, and all outstanding instruments which could potentially dilute existing shareholders interests, must be valued together.
A valuation template application which can be used to value new and existing ESO grants (and warrants) in private companies is available on request for corporate users of the Hoadley Finance Add-in for Excel.
The valuation template uses an iterative procedure to simultaneously value a
company's shares and all outstanding ESOs and warrants, and to allocate the
company's equity across existing shares and other equity instruments. Tax savings
from option expenses will be included if required. ie the company's per
share value and the value of all outstanding ESOs and warrants are calculated on
a fully diluted after-tax basis. ESOs and warrants are also valued on
a normal "stand-alone" (undiluted) basis so the impact of dilution can be easily
seen for each option grant.
|Using the Functions|
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 FAS 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 volatility on the
volatility of a relevant stock index would not normally be
correct as the volatility of an index
would typically be less than the volatility of an individual
|Licensing & Purchase|
The Executive Stock Option (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
enquiries. You will receive a response to your enquiry
normally within an hour and always within six hours depending on your