Question

Jack Ltd. is a large, publicly held company that is considering leasing a warehouse to be used to manufacture steel rods. The current price of steel is $3,700 per ton. If the price of steel falls over the next six months, the company will purchase 500 tons of steel and produce 175,000 steel rods. Each steel rod will cost $21 to manufacture and the company plans to sell the rods for $34 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 38 percent.

Required:

Use the Black-Scholes model to determine the maximum amount that Jack Ltd. should be willing to pay for the lease. Assume the lease will be a one-off payment at time zero.