91Ó°ÊÓ

Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 30,000 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 45 percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of 6 percent. 1\. Use the Black-Scholes model to calculate the value of the stock options. 2\. 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? 3\. How would your answer to (b) change if Mr. Levin were risk-averse and he could not sell the options prior to expiration?

Sardano and Sons is a large, publicly held company that is considering leasing a warehouse. One of the company's divisions specializes in manufacturing steel, and this particlar warehouse is the only facility in the area that suits the firm's operations. The current price of steel is \(\$ 630\) per ton. If the price of steel falls over the next six months, the company will purchase 400 tons of steel and produce 45,000 steel rods. Each steel rod will cost \(\$ 16\) to manufacture, and the company plans to sell the rods for \(\$ 24\) each. It will take only a matter of days to produce and sell the steel rods. If the price of steel rises or remains the same, it will not be profitable to undertake the project, and the company will allow the lease to expire without producing any steel rods. Treasury bills that mature in six months yield a continuously compounded interest rate of 4.5 percent, and the standard deviation of the returns on steel is 45 percent. Use the Black- Scholes model to determine the maximum amount that the company should be willing to pay for the lease.