Problems with Black-Scholes
Serious flaws using Black-Scholes to model employee options
While the Black-Scholes model has been approved for use by the SEC for proxy disclosure and by FASB for footnote disclosure under APB 125, it was never designed for use in the compensation realm. Although useful in valuing options on the Chicago Board of Option Exchange, the Black-Scholes model lacks the ability to properly value employee stock options due to their unique nature. The flaws are not in the model, but in how the model is applied.
Options on the free market have a very short life span, are easily traded, and contain no restrictions on the way they are exercised. However, employee stock options typically extend over a period of ten years, cannot be freely exchanged, and contain restrictions on exercise such as vesting and an exercise window. Because of the Black-Scholes model's original intent for use, problems arise when outside variables such as the position of the company's stock, recent stock price performance, and the company's industry are not factored into the formula.
Using the Black-Scholes model, an option granted when the stock price is at an all-time high could be significantly overvalued. This appears to be counterintuitive because the assumption would be that a lower stock price would have greater opportunity to appreciate delivering greater value to the option holder. Additionally, the inputs of this model (dividend yield, volatility, risk-free rate) can be easily manipulated to significantly alter the end result. Therefore, the Black-Scholes model is not an accurate measure of determining the worth of an employee option and should not be used to do so.
While developing long-term incentive strategies, L&A utilizes the targeted gain approach to determine the number of options to be awarded based on the "value" of these options at an expected rate of appreciation of the company stock discounted for the risk-free rate. This method is straightforward and easily comprehended by executives, directors, and employees. For example an option granted at $20 has an expected life of 10 years, with the expected stock price appreciation at 15% per year and the discount rate at 5%. The formula for the targeted gain approach is as follows:
[(20 x 1.15) 10 - 20)]
(1.05) 10
The computed value for each stock option would be $37.39