Gary Levin is the CEO of Mountain brook Trading Company. The board of directors has just granted Gary 30,000 at-the-money European call options on the company’s stock, which is currently trading at $50 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 56 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 Gary’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 Gary were risk averse and he could not sell the options prior to expiration?