Gary Levin is the chief executive officer of Mountain brook Trading Company. The board of directors has just granted Mr. Levin 25,000 at-the money European call options on the company's stock, which is currently trading at $55 per share. The stock pays no dividends. The options will expire in five years, and the standard deviation of the returns on the stock is 61 percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of 6 percent.

a. Use the Black-Scholes model to calculate the value of the stock options.

b. You are Mr. Levin's financial adviser. He must choose between the previously mentioned stock option package and an immediate $750,000 bonus. If he is risk-neutral, which would you recommend?

c. How would your answer to (b) change if Mr. Levin were risk-averse and he could not sell the options prior to expiration?