Problem:
Jared Lazarus has just been named the new chief executive officer of Blubell Fitness Centers, Inc. In addition to an annual salary of $400,000, his three year contract states that his compensation will include 10,000 at-the-money European call options on the company's stock that expires in three years. The current stock price is $40 per share, and the deviation of the returns on the firm's stock is 68 percent. The company does not pay a dividend. Treasury bills that mature in three years yield a continuously compounded interest of 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 9 percent. Using the Black-Scholes model to calculate the value of the stock options, determine the total value of the compensation package on the date the contract is signed.