Problem
Question 1
An oil company has zero coupon notes outstanding that mature one year from now. That is, each note promises to make a single payment of $1000 one year from now with no coupon payments between now and then. Unlike ordinary zeros, the note also promises investors a bonus payment equal to 15 times the amount by which the prevailing oil price on the maturity date exceeds $60 per barrel (for example, if the oil price is $62 at maturity, the holder receives $1000 plus 15 x $2 or $1030 in all; if the price of oil is below $60, the holder receives only $1000). The oil company's investment bankers estimate that the oil company could instead have issued a conventional one- year zero at a yield of about 8%. Suppose also that investors are convinced that the price of oil one year from now will be either $50 or $70 per barrel. Annual risk free rate is 3% and the current oil price per barrel is $60.
a) Explain how you could characterize each note as a combination of a conventional zero coupon note and an option. What kind of option is it, and who owns the option?
b) How much do you think the notes would have sold for originally if there had been no option attached? How much is the value of the option? (Use the binomial option pricing model). What is the total value of the notes?
c) Suppose that investors do not have good idea about what oil price will be in the next year. But, they believe that the annual standard deviation of oil prices is 20%. How much do you think the notes are worth?
Question 2
Sunburn Sunscreen has a zero coupon bond issue outstanding with $20,000 face value that matures in one year. The current market value of the firm's assets is $20,900. The standard deviation of the return on the firm's assets is 26% per year, and the annual risk-free rate is 6% per year, compounded continuously.
a) What is the market value of the firm's equity and debt?
b) Suppose the firm is considering two mutually exclusive investments. Project A has an NPV of $800, and Project B has an NPV of $1,300. As a result of taking Project A, the standard deviation of the return on the firm's assets will increase to 50% per year. If Project B is taken, the standard deviation will fall to 23%. What is the value of the firm's equity and debt if Project A is undertaken? If Project B is undertaken?
c) What does the example suggest to you about stockholder incentives?
Question 3
A Japanese electronics manufacturer is contemplating investing $1 billion (with all of the investment to be made at the outset) in a 10-year investment project in the U.S. The Japanese company is well known in world capital markets and is universally regarded as quite safe. To help finance the project, the company believes it could issue 10-year zero coupon bonds in the U.S. at a yield that would be very close to the current 10-year U.S. Treasury rate of 4%. Alternatively, the company could issue equivalent 10-year zero coupon debt in Japan at an interest rate of 2%. Assume for simplicity that both rates are annually compounded rates. The current spot exchange rate is 89.6 ¥/$.
a) The company's treasurer argues that the company should issue new debt in Japan, where the interest rate is lower. Do you agree? Briefly explain.
b) What do you expect the ¥/$ exchange rate to be 10 years from now? How does your forecast help you explain the current differential between interest rates in the U.S. and Japan?
c) The Japanese company wishes to use the foreign currency approach to estimate the project's NPV. The Japanese company's stock is listed on both the Tokyo and New York Stock Exchanges. In either location, the beta of the company's stock is 1.25. In the U.S., the historical risk premium of the market return over the 10-year government bond rate has been 6%. If the Japanese company issues $740,122,143 (face value) in 10-year zero coupon bonds in the U.S. to help finance the project, how much equity financing will it need to support the project? If all project cash flows are taxed at an effective rate of 35%, what weighted average cost of capital should the Japanese company use in evaluating the project (assume for simplicity that the total market value of the project will be approximately equal to the $1 billion investment outlay)?
Question 4
Wolfco management is currently considering a merger with Lambco. Both companies are in the same industry, and both companies' shares sell at a ratio of price to free cash flow of 10. If the two companies merged, there is no reason to believe that this valuation multiple would change.
Wolfco has 20 million shares outstanding, selling at a price of $22.50 per share. Lambco has 10 million shares outstanding. Neither company has any debt.
Lambco has revenues of $400 million per year and cash operating costs of $200 million per year. Annual depreciation expense is $100 million and annual capital expenditures are $110 million per year. Lambco also invests $20 million each year in additional net working capital. The corporate tax rate is 35%.
If Wolfco and Lambco were to merge, Wolfco believes that it could apply its superior inventory control and accounts receivable management techniques to Lambco and thereby cut Lambco's annual investment in net working capital in half. The two companies' management teams are now trying to negotiate the terms of a merger.
a) What is the value of Lambco to Wolfco?
b) Wolfco management proposes to pay $40 cash for each Lambco share. What is the Net Present Value (NPV) of this offer to Wolfco?
c) Lambco management counters with a proposal under which Wolfco would offer two Wolfco shares for each currently outstanding Lambco share. What is the NPV of this offer to Wolfco?
d) What are the primary factors that determine whether the final agreement will be closer to the terms of the cash offer in part (b) or the share exchange in part (c)?