consider a one-year forward contract on gold. Suppose that it costs $2 per ounce per year to store gold with payment being made at the end of the year. Assume that the spot price is $450 per ounce and the risk-free rate is 7% per annum for allmaturities. Assume continuous compounding. (a) What is the forward price F (0, 1) that does not result in arbitrage profit? (b) If the forward price is $460, do you get any arbitrage profit opportunity? If so, what is your strategy? (You need to providemore than "buy low, sell high".)

Answer information:Step 1:Given :Rate of Interest = R = 7% per annumSpot Price = S(0) = $ 450 per…

Answered: consider a one-year forward contract on…

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter8: Basic Stock Valuation

Section: Chapter Questions

Problem 4MC

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a. If the spot price of gold is $1,500 per troy ounce, the risk-free interest rate is 2%, and storage and insurance costs are zero, what should be the forward price of gold for delivery in one year? Use an arbitrage argument to prove your answer.b. Show how you could make risk-free arbitrage profits if the forward price is $1,550.
This question will compare two different arbitrage situations. Recall that arbitrage should equalize rates of return. We want to explore what this implies about equalizing prices. In the first situation, two assets, A and B, will each make a single guaranteed payment of $100 in 1 year. But asset A has a current price of $80 while asset B has a current price of $90.a. Which asset has the higher expected rate of return at current prices? Given their rates of return, which asset should investors be buying and which asset should they be selling?b. Assume that arbitrage continues until A and B have the same expected rate of return. When arbitrage ceases, will A and B have the same price?Next, consider another pair of assets, C and D. Asset C will make a single payment of $150 in one year while D will make a single payment of $200 in one year. Assume that the current price of C is $120 and that the current price of D is $180.c. Which asset has the higher expected rate of return at current…
Suppose the gold price is $300/oz., the 1-year forward price is 310.686, and the continuously compounded risk-free rate is 5%. a. What is the lease rate? b. Demonstrate a cash-and-carry strategy that provides the zero cash flow at time 0 and the maturity date. (You borrow to buy gold, sell the gold forward, and lend the gold, earning the lease rate.) c. What is the return on a cash-and-carry strategy in which gold is not loaned? (You borrow to buy gold and sell the gold forward.)
2. An investment has an installed cost of $412,670. The cash flows over the four-year life of the investment are projected to be $212,817, $153,408, $102,389, and $72,308. If the discount rate is zero, what is the NPV? If the discount rate is infinite, what is the NPV? At what discount rate is the NPV just equal to zero? Sketch the NPV profile for this investment based on these three points.
You are given the following data on gold markets. What is the level of arbitrage profits that can earned? • Current spot price of gold = $1,275 • Futures price for a 1-year contract = $1,300 • 1-year risk free interest rate = 3% • Assume that there are no carrying costs or yield on buying/selling gold.
Suppose you are offered a project with the following payments: Year Cash Flows 0 $ 9,800 1 −5,300 2 −4,000 3 −3,100 4 −1,700 a. What is the IRR of this offer? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. b. If the appropriate discount rate is 15 percent, should you accept this offer? c. If the appropriate discount rate is 21 percent, should you accept this offer? d-1. What is the NPV of the offer if the appropriate discount rate is 15 percent? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. d-2. What is the NPV of the offer if the appropriate discount rate is 21 percent? Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
Investment X offers to pay you $4,700 per year for 9 years, whereas Investment Y offers to pay you $6,400 per year for 5 years. a. If the discount rate is 8 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b. If the discount rate is 20 percent, what is the present value of these cash flows?
Investment X offers to pay you $7,500 per year for 9 years, whereas Investment Y offers to pay you $10, 200 per year for 5 years. a. If the discount rate is 6 percent, what is the present value of these cash flows? Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. b. If the discount rate is 22 percent, what is the present value of these cash flows? Note: Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16. a. Present value of Investment X at 6 percent Present value of Investment Y at 6 percent b. Present value of Investment X at 22 percent Present value of Investment Y at 22 percent
B and C
3. (a) Consider a forward contract on an asset S with maturity T = 10 years. The asset S pays no dividends and the spot price at time 0 is S(0) = £56. The continuously compounded interest rate is r = 2% per annuum. Calculate the forward price F(0,T). (b) Consider the setting of (a). Suppose that you can enter a forward con- tract on S (long or short) with forward price of F(0,T) = £70 and maturity T = 10. Assume that you are also allowed to trade any number of zero coupon bonds with maturity T = 10, and any number of the underlying stock S. Construct an arbitrage. (c) (d) Consider a 6-month forward contract written on 100Kg of coffee beans. Assume that the spot price is £10 per Kg and that the continuously compounded risk free rate is r 5% per annum. Suppose that storing the coffee beans incurs an unknown cost, due halfway the contract. What are the storage costs if the forward price is £1005? - Consider the following market: There are only two times t = 0 and 1 years. The annual…
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