In stock options analysis there are three mainstream methodologies and approaches used to calculate an employee stock option value, these are:
- Closed form models like Black–Scholes model, also known as the Black-Scholes-Merton model (“BSM” or “Black-Scholes”), and its modifications such as the Generalized Black-Scholes model (“GBM”);
- Monte Carlo Path Dependent Simulation methods; and
- Binomial Lattice.
The Black-Scholes model, while theoretically correct and elegant, is insufficient and inappropriately applied when it comes to quantifying the fair market value of employee stock options, this is because the BSM is applicable only to the calculation of European options without dividends, where the holder of the option can exercise the option only on its maturity date and the underlying stock does not pay dividends.
Most employee stock options are American type options with dividends, where the holder can execute the option at any time up to and including the maturity date while the underlying stock pays dividends. In addition, employee stock options have a time to vesting before the employee can execute the option, which may be contingent upon the company/or person attaining a specific performance level (e.g., profitability, growth rate, attain certain sales level, the stock price hitting a minimum barrier before the options become live), and are subject to forfeitures when the employee leaves the company or is terminated prematurely before reaching the vested period. All of these real-life scenarios make the Black-Scholes model insufficient and inappropriate when used to place a fair market value on the stock option grant.
Generally speaking, the Black–Scholes model typically overstates the fair market value of employee stock options where there is sub-optimal early exercise behavior coupled with vesting requirements, and employee forfeitures occur, or when the risk free rates, dividends, and volatilities change over the life of the option. In fact, companies using the Black–Scholes model to value and expense employee stock options may be significantly overstating their true expense, typically incurring hundreds of thousands to tens of millions of dollars in overstated expenses per year.
The Black–Scholes model takes into account only the following inputs: stock price, strike price, time to maturity, a single risk free rate, and a single volatility. The GBM accounts for the same inputs as well as a single dividend rate. Hence, in accordance with FAS 123 R requirements, the Black–Scholes model and the GBM fail to account for real life conditions.
The Monte Carlo Path Dependent Simulation Methods are appropriate for complex stock options where the complexity of the option itself makes closed form approached such as Black-Scholes intractable. Rather than solve the differential equations that define the option value in relation to the underlying stock price, a Monte Carlo model determines the value of the option for a set of randomly generated economic scenarios (e.g. future stock prices, option exercise behavior, stock price vs. stock index behavior). The resulting simulation yields an expected value for the option.
The Binomial Lattice Valuation Methodology can be customized to include the above mentioned input variables plus multiple risk-free rates changing over time, multiple volatilities changing over time, multiple dividend rates changing over time, plus all other real-life factors including but not limited to vesting periods, changing sub-optimal early exercise behaviors, multiple blackout periods, and changing forfeiture rates over time. It is important to note that the customized Binomial Lattice results revert to the GBM if the “real life conditions” are negligible. Therefore, in accordance with FAS 123 (R), which prefers the binomial lattice, we will utilize the customized Binomial Lattice Valuation Methodology to calculate the fair market value of the employee stock options. It is important to note that valuation results through the use of binomial lattices tend to approach those derived from the closed model solutions, hence we always utilize the BSM and GBM models to benchmark the binomial lattice results. The results from the closed model solutions are typically used in conjunction with the binomial lattice approach when presenting a complete employee stock option valuation solution. Our valuation will take into consideration many factors that influence the fair market value of stock options including, but not limited to, the following:
- The stock price;
- The strike prices;
- The time to maturity;
- The risk-free rate;
- The dividend; and
The Binomial Lattice approach will also address the following input items:
- Time to vesting;
- Changing forfeiture rate;
- Changing suboptimal exercise behavior multiples;
- Black-out dates;
- Changing risk-free rates;
- Changing dividends; and
- Changing volatilities over time.
Foxboro Consulting Group, Inc.’s stock option valuation study will be executed in accordance with practices currently accepted and utilized by the financial and valuation communities and in conformity with the National Association of Certified Valuators & Analysts (NACVA), the American Institute of Certified Public Accountants (AICPA) Statement of Standards for Valuation Services (“SSVS”), The Institute of Business Appraisers (IBA), and the Uniform Standards of Professional Appraisal Practice (USPAP) promulgated by the Appraisal Standards Board of the Appraisal Foundation, and the Appraisal Standards Board of the Appraisal Foundation.
If you have additional questions or wish to discuss this topic further, you can contact: Ronald J. Adams, CPA, CVA, ABV, CBA, CFF, FVS, CGMA, Managing Director – Valuations, at (774) 719-2236 – office; or at (508) 878-8390 – mobile; or e-mail him at: firstname.lastname@example.org .