Question

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 $835 per ton. If the price of steel falls over the next six months, the company will purchase 325 tons of steel and produce 35,750 steel rods. Each steel rod will cost $29 to manufacture, and the company plans to sell the rods for $39 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 6 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. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Maximum amount

$

Answer 1

When solving a question dealing with real options, begin by identifying the
option-like features of the situation. First, since Sardano will only choose to
manufacture the steel rods if the price of steel falls, the lease, which gives the firm
the ability to manufacture steel, can be viewed as a put option. Second, since the
firm will receive a fixed amount of money if it chooses to manufacture the rods:
Amount received = 35,750 rods x ($39 - $29) = $357,500
The amount received can be viewed as the put option’s strike price (K). Third,
since the project requires Sardano to purchase 325 tons of steel and the current
price of steel is $835/ton, the current price of the underlying asset (S) to be used
in the Black-Scholes formula is:
“Stock” price = 325 tons x $835/ton = $271,375
Finally, since Sardano must decide whether to purchase the steel or not in 6
months, the firm’s real option to manufacture steel rods can be viewed as having a
time to expiration (t) of 6 months or ½ a year. In order to calculate the value of
this real put option, we can use the Black-Scholes model to determine the value of
an otherwise identical call option and then infer the value of the put using the put-
call parity relationship.