Aufgabe 1 A one-year-long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10 % per annum with continuous compounding. 1. What are the forward price and the initial value of the forward contract? 2. Six months later, the price of the stock is $45 and the risk-free interest rate is still 10 %. What are the forward price and the value of the forward contract?
Aufgabe 2 The two-month interest rates in Switzerland and the United State with continuous compounding are 3 % and 8 % per annum, respectively. The spot price of the Swiss franc is $0.6500. The future price for a contract deliverable in two months is $ 0.6600. What arbitrage opportunities does this create?
Aufgabe 3 The current price of silver is $9 per ounce. The storage costs are $0,24 per ounce per year payable quarterly in advance. Assuming that the interest rates of all maturities equal 10% per annum with continuous compounding, calculate the futures price of silver for delivery in nine months.
Aufgabe 4 A stock is expected to pay a dividend of $1 per share in two months and again in five month. The stock price is $50 and the risk-free rate of interest is 8 % per annum with continuous compounding for all maturities. An investor has just taken a short position in a six month forward contract on the stock. What are the forward price and the initial value of the forward contract? Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8 % per annum. What are the forward price and the value of the shot position in the forward contract?
Aufgabe 5 A bank offers a corporate client a choice between borrowing between cash at 11 % per annum and borrowing gold at 2 % per annum. (If gold is borrowed, interest and principal must be repaid in gold. Thus 100 ounces borrowed today would require 102 ounces to be repaid in one year.) The risk-free interest rate is 9.25 % per annum and storage costs are 0.5 % per annum. Discuss whether the rate of interest on the gold loan is too high or too low in relation to the rate of interest on the cash loan. The interest rates on the two loans are expressed with annual compounding. The risk-free rate and storage cost are expressed with continuous compounding.
Aufgabe 6 (B/M Chap. 17, PQ 15) Two firms, U and L, are identical except for their capital structure. Both will earn $150 in a boom and $50 in a slump. There is a 50 percent chance of each event. U is entirely equity-financed, and therefore shareholders receive the entire income. Its shares are valued at $500. L has issued $400 of risk-free debt at an interest rate of 10 percent, and therefore $40 of L s income is paid out as interest. There are no taxes or other market imperfections. Investors can borrow and lend at the risk-free rate of interest. (a) What is the value of L s stock? (b) Suppose that you invest $20 in U s stock. Is there an alternative investment in L that would give identical payoffs in boom and slump? What is the expected payoff from such strategy? (c) Now suppose that you invest $20 in L s stock. Design an alternative strategy with identical payoffs.
Aufgabe 7 (B/M Chap. 15, PQ 11/12) In 1998 the Pandora Box Company made a rights issue at $5 a share of one new share for every four shares held. Before the issue there were 10 million shares outstanding and the share price was $6. (a) What was the total amount of new money raised? (b) How many rights were needed to buy one new share? (c) What was the value of one right? (d) What was the prospective ex-rights price? (e) How far could the total value of the company fall before shareholders would be unwilling to take up their rights? Suppose that the company had decided to issue new stock at $4. How many shares would it have needed to sell to raise the same sum of money? Recalculate the answers to question (b) to (e). Show that the shareholders are just as well off if the company issues the shares at $4 rather then $5.