Executive compensation is almost synonymous with equity compensation given that 60% or more of executive pay is aligned with equity instruments. The two most prevalent pricing models used to value equity compensation are Black Scholes and Binomial (Lattice). Understanding the fundamental design of these models can aid the executive compensation practitioner to manage the information requirements for disclosure, to assess effective equity plan designs, and to enhance compensation communications.
Since 2005, the accounting regulations Financial Accounting Standard (FAS) 123R and its subsequent replacement, ASC 718, in 2009, have required companies to report the fair value (FV) of all equity-based compensation which becomes an expense that directly affects the income statement. The Black Scholes or Binomial models are used by most (if not all) publicly traded corporations to report the FV of equity compensation. These models take into consideration plan design characteristics, allow for sensitivity analysis with volatility assumptions, and reflect exercise behavior realities. The standard inputs to both models are:
Current stock price
Risk free interest rate
Expected dividends on stock
Expected stock price volatility
Expected term of option
Companies are required to disclose in Annual Reports / 10-K filings the assumptions and input values used in these valuation models. Determining the value for expected term relies on the behavior of employees who hold options and is less predictable. For private firms (who tend to use Black Scholes), the expected volatility of their stock is also less predictable since they have no trading history like public firms. The stock price, exercise price, risk free interest rate, and expected dividends tend to be more stable inputs to the models.
According to a June 2010 Radford Survey, the number of companies adopting the Binomial model for FV calculations has increased over 1149% since 2003 (see http://www.radford.com/home/ccg/valuation_services/Binomial_Model.pdf). The Binomial (Lattice) model is more dynamic, lends itself to simulation techniques, and allows for a range of values for volatility, risk free interest rate, and expected term. Becton Dickinson adopted the Binomial model in 2004 and its recent Annual Report disclosed sets of 3-years of assumptions and inputs used in the valuing its stock appreciation rights (SARs):
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For both models, there is a generic version plus several variations that capture granular assumptions to make the models more predictive, albeit more complex. Depending on the complexity of the equity programs, the business model in which the organization operates, and the cost/benefit trade-off of adopting a more complex pricing model, it can incorporate one or more of these additional variables:
- Expected holding period and exercise history (both pre- and post-termination).
- Vesting period and company-specific exercise rules.
- Termination rate or forfeiture rate (the probability of a vested option being canceled).
- Blackout periods and arrangements for automatic exercise.