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 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.