A New Stock Option Plan and Its Valuation

ABSTRACT This new option plan allows the holder to purchase an underlying asset at a discount proportional to the asset's market price, and the proportion decreases with an employee's seniority. This option would provide strong incentives to improve executive and employee performance and loyalty. Compared to existing plans, this option would create less incentive to increase company risk or to reduce dividend payment, and it would not be too generous. We derive the value of this option for the general case of a dividend-paying stock and where the option's exercise price reflects a time-varying discount factor. The derived value incorporates the optimal exercise time. INTRODUCTION Existing stock option plans and previous research on stock option plans focus on executive compensation packages. Realizing the stronger incentives of stock options, more companies have started to offer stock options to their non-executive employees recently. Existing stock options have several disadvantages while creating incentives to increase stock price. (Smith & Watts, 1982, 1992; Agrawal & Mandelker, 1987; Lambert et al., 1989; Jensen & Murphy, 1990; DeFusco et al., 1990; Yermack, 1995; Tufano, 1996; Hall, 1998; Schrand & Unal, 1998; Core & Guay, 1998; Johnson & Tian 2000). Often, shareholders complain that some options are too generous and do not provide the right incentives to executives. Researchers find that existing stock options, traditional or nontraditional, create strong incentives to increase company risk and to reduce dividend payments. Executives compensated with stock options may take actions to increase company risk because an increase in stock price volatility increases the value of an executive stock option (Agrawal & Mandelker, 1987; Tufano, 1996; Schrand &Unal, 1998). Johnson and Tian (2000) find that five out of the six nontraditional options they examine create stronger incentives than the traditional option to increase company risk. Also, executives may reduce dividends in order to increase their option payoffs because, ceteris paribus, dividend payments reduce expected terminal stock prices and thus the value of call options that are not dividend protected (Lambert et al., 1989). Johnson and Tian (2000) report that three out of the six nontraditional options create stronger incentives to reduce dividend yield. In this paper, we present a new type of option that would create strong incentives to improve performance and loyalty of both executives and non-executive employees, while reducing the incentive to increase stock price volatility or to reduce dividend payments. We also analyze the value of the option. (For valuing traditional executive stock option plans, see Smith, 1976, and for valuing nontraditional executive stock options, see Johnson and Tian, 2000). This option is a non-standard, American-style call option whose exercise price is a proportion of the price of its underlying asset. The option under consideration is different from existing call options in that its exercise price is not a fixed price but, rather, a proportion of the price of its underlying asset. For example, an option might give its owner the right to buy a share of common stock at a price equal to 80 percent of the stock's market price at any time prior to the option's expiration date. Since its exercise price is a portion of the underlying asset's price, the option is always in the money as long as the value of the underlying asset is greater than zero. A potential use for such an option may be for employers who wish to provide performance-sensitive compensation to their employees. Companies are increasingly issuing stock and/or conventional stock options to employees in compensation contracts. An alternative, which is a hybrid of stocks and conventional stock options, would be to compensate employees in the form of options to buy company stock at a proportional discount. …