Accounting for Stock-Based Awards Using the Minimum Value Method

Abstract

Smith and Zimmerman [1976] suggested valuing employee stock options at the difference between the market price of the stock at the grant date and the present value of the exercise price of a simple call option on the stock discounted from the expiration date.' They also discussed modifications to this value to take account of the impact of dividends, differing income tax rates, and the problem of differential underdiversification across option holders. The purpose of this note is to extend the minimum value method by incorporating (a) random exercise prices which depend on stock prices, (b) fixed exercise price changes, and (c) ceilings on the amount of stock appreciation permitted in these awards. The minimum values which incorporate the first two extensions are obtained from the option models of Fischer [1978] and Merton [1973]. We derive the minimum value for the third extension from probability theory results for first-passage times for stochastic processes.