Problem 1:
You hold stock X with price $100 that can increase by 10% or decrease by 10% in a year. The interest rate is 5%.
a) Suppose that you want to ensure that you'll get a minimum of $100 in a year regardless of the evolution of the stock price. Which derivative security will you have to purchase to ensure that your financial position will be at least $100 in a year? (Note: You are allowed to purchaseust one derivative security. Please describe the simplest security that allows you to get a minimum of $100 regardless of what happens to stock X_ Also please ignore the cost of purchasing such security, i_e_, assume that in a year you want to have $100 gross of the cost of acquiring such security. )
b) Value the derivative security described in a).
c) Suppose that there is no derivatives market but that bonds and the stock can be traded (and short-sold if needed). Design a pori-folio position in stock and T-b ills that ensures you a payoff similar to the derivative security described in a).
Problem 2:
An associate of yours is offering your firm to buy an oil-well that will produce 1,000,000 barrels of oil next year (assume for simplicity that the oil is available at the end of the year) and it will be closed forever after that Suppose that the operating expenses are $100 per barrel. Suppose that the forward price for oil delivered one year from today is Si20liziarrei and that the risk-free interest rate is 8%.
a) What is the value of the oil well?
b) Describe an alternative set of investments (i_e_, tracking portfolio) that gives the same payoffs than the oil-well_
c) Keep the same assumptions as above about production capability, interest rates and forward prices for oil, but assume now that your production costs are $150 per barrel instead. What is the value of the oil-well?
d) Suppose that an oil analyst tells you that he believes the oil price will be $2009barrel a year from now (and you believe that he is right). What is then the value of the oil well? Explain.
Problem 3:
A gold mine will produce all of its output two years from now. The mine has a reserve of 100 pounds of gold. The gold can be extracted at no cost and sold in year 2. We have the following data:
- The two-year forward price of gold is S10.000 per pound today.
- In year 2. gold price will be either 514.000 per pound. or S8.000 per pound.
- The one-year risk-free rate is 10%. The risk-free rate will remain at 10% next year too.
1. What is the value of the gold mine today?
2. Suppose that the mine owner receives today an offer for the mine for S1.1 million. The offer is valid for two years and the mine owner can wait until year two and decide whether to take the offer or keep operating the mine himself after observing the year-2 gold price. What is the value of the mine today?
3. Now suppose that there is some uncertainty about the reserves of the mine. The mine's reserves are either 100 pounds or zero. with each outcome equally likely. In year 1. the mine owner will learn whether the reserves are 100 pounds or zero. Suppose that the mine owner receives an offer today for the mine that is conditional on the reserves. The bidder offers S1.1 million if reserves prove to be 100 pounds. but only S55.000 if the reserve turns out to be zero. In either case, the payment is to be received in year 2 if the offer is accepted. Value the mine now.
Problem 4:
A project has an expected free cash flow of S100 million a year from now (no other cash flows afterwards). We have identified a comparison firm with similar investments. The equity beta of the comparison firm is 1.4. and it has a DIE ratio 1. We plan to have a at ratio of 0.75 for the project. The risk-free rate is 5%. and the market risk premium is 10%. The tax rate is 30%.
a) Use the WACC method to calculate the value of the project. Assume that both the comparison firm and out firm have risk-free debt and risk-free tax shields.
b) Now suppose the comparison firm has risk-free debt, but the project's debt is risky. Specifically. the beta of our bonds is 0.2. and the yield-to-maturity of the bond is 8%. The tax shields will be utilized fully 90% of the time. Assume that the debt and the tax shields are equally risky. Calculate the WACC in this scenario and find the value of the project.