3 binomial model gasworks inc has been approached to

3. Binomial Model Gasworks, Inc., has been approached to sell up to 5 million gallons of
gasoline in three months at a price of $2.05 per gallon. Gasoline is currently selling on the
wholesale market at $1.74 per gallon and has a standard deviation of 46 percent. If the risk-free
rate is 6 percent per year, what is the value of this option?
4. Real Options The Webber Company is an international conglomerate with a real estate division
that owns the right to erect an office building on a parcel of land in downtown Sacramento over
the next year. This building would cost $20 million to construct. Due to low demand for office
space in the downtown area, such a building is worth approximately $18.5 million today. If demand
increases, the building would be worth $22.4 million a year from today. If demand decreases, the
same office building would be worth only $17.5 million in a year. The company can borrow and
lend at the risk-free annual effective rate of 4.8 percent. A local competitor in the real estate
business has recently offered $750,000 for the right to build an office building on the land. Should
the company accept this offer? Use a two-state model to value the real option.
5. Real Options Jet Black is an international conglomerate with a petroleum division and is
currently competing in an auction to win the right to drill for crude oil on a large piece of land in
one year. The current market price of crude oil is $58 per barrel, and the land is believed to
contain 375,000 barrels of oil. If found, the oil would cost $35 million to extract. Treasury bills that
mature in one year yield a continuously compounded interest rate of 4 percent, and the standard
deviation of the returns on the price of crude oil is 50 percent. Use the Black–Scholes model to
calculate the maximum bid that the company should be willing to make at the auction.
INTERMEDIATE (QUESTIONS 6–8)

6. Real Options 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.