1.The William Companies (WMB) owns and operates natural gas pipelines that deliver 12% of the natural gas consumed in the United States. WMB is concerned that a major hurricane could disrupt its Gulfstream pipeline, which runs 691 miles through the Gulf of Mexico. In the event of a disruption, the firm anticipates a loss of profits of $65 million. Suppose the likelihood of a disruption is 3% per year, and the beta associated with such a loss is −0.25. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium?
2.Genentech’s main facility is located in South San Francisco. Suppose that Genentech would experience a direct loss of $450 million in the event of a major earthquake that disrupted its operations. The chance of such an earthquake is 2% per year, with a beta of −0.5.
a. If the risk-free interest rate is 5% and the expected return of the market is 10%, what is the actuarially fair insurance premium required to cover Genentech’s loss?
b. Suppose the insurance company raises the premium by an additional 15% over the amount calculated in part (a) to cover its administrative and overhead costs. What amount of financial distress or issuance costs would Genentech have to suffer if it were not insured to justify purchasing the insurance?
3.Your firm imports manufactured goods from China. You are worried that U.S.–China trade negotiations could break down next year, leading to a moratorium on imports. In the event of a moratorium, your firm expects its operating profits to decline substantially and its marginal tax rate to fall from its current level of 40% to 10%.
An insurance firm has agreed to write a trade insurance policy that will pay $500,000 in the event of an import moratorium. The chance of a moratorium is estimated to be 10%, with a beta of −1.5. Suppose the risk-free interest rate is 5% and the expected return of the market is 10%.
a. What is the actuarially fair premium for this insurance?
b. What is the NPV of purchasing this insurance for your firm? What is the source of this gain?
4.Your firm faces a 9% chance of a potential loss of $10 million next year. If your firm implements new policies, it can reduce the chance of this loss to 4%, but these new policies have an upfront cost of $100,000. Suppose the beta of the loss is 0, and the risk-free interest rate is 5%.
a. If the firm is uninsured, what is the NPV of implementing the new policies?
b. If the firm is fully insured, what is the NPV of implementing the new policies?
c. Given your answer to part (b), what is the actuarially fair cost of full insurance?
d. What is the minimum-size deductible that would leave your firm with an incentive to implement the new policies?
e. What is the actuarially fair price of an insurance policy with the deductible in part (d)?
5.BHP Billiton is the world’s largest mining firm. BHP expects to produce 2 billion pounds of copper next year, with a production cost of $0.90 per pound.
a. What will be BHP’s operating profit from copper next year if the price of copper is $1.25,$1.50, or $1.75 per pound, and the firm plans to sell all of its copper next year at the going price?
b. What will be BHP’s operating profit from copper next year if the firm enters into a contract to supply copper to end users at an average price of $1.45 per pound?
c. What will be BHP’s operating profit from copper next year if copper prices are described as in part (a), and the firm enters into supply contracts as in part (b) for only 50% of its total output?
d. Describe situations for which each of the strategies in parts (a), (b), and (c) might be optimal.
6.Your utility company will need to buy 100,000 barrels of oil in 10 days time, and it is worried about fuel costs. Suppose you go long 100 oil futures contracts, each for 1000 barrels of oil, at the current futures price of $60 per barrel. Suppose futures prices change each day as follows:
a. What is the mark-to-market profit or loss (in dollars) that you will have on each date?
b. What is your total profit or loss after 10 days? Have you been protected against a rise in oil prices?
c. What is the largest cumulative loss you will experience over the 10-day period? In what case might this be a problem?
7.Suppose Starbucks consumes 100 million pounds of coffee beans per year. As the price of coffee rises, Starbucks expects to pass along 60% of the cost to its customers through higher prices per cup of coffee. To hedge its profits from fluctuations in coffee prices, Starbucks should lock in the price of how many pounds of coffee beans using supply contracts?