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 particular warehouse is the only facility in the area that suits the firm’s operations. The current price of steel is $670 per ton. If the price of steel falls over the next six months, the company will purchase 500 tons of steel and produce 55,000 steel rods. Each steel rod will cost $18 to manufacture, and the company plans to sell the rods for $29 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.
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