Cheryl Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Cheryl 35,000 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 53 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 Cheryl’s financial adviser. She must choose between the previously mentioned stock option package and an immediate $750,000 bonus. If she is risk-neutral, which would you recommend?

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