Jared Lazarus has just been named the new chief executive officer of BluBell Fitness Centers, Inc. In addition to an annual salary of $417,500, his three-year contract states that his compensation will include 38,250 at-the-money European call options on the company’s stock that expire in three years. The current stock price is $22 per share, and the standard deviation of the returns on the firm’s stock is 60 percent. The company does not pay a dividend. Treasury bills that mature in three years yield a continuously compounded interest rate of 4.5 percent. Assume that Mr. Lazarus’s annual salary payments occur at the end of the year and that these cash flows should be discounted at a rate of 10 percent.
Use the Black–Scholes model to calculate the value of the stock options. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Stock options $______
Determine the total value of the compensation package on the date the contract is signed. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Compensation package $______