Chapter 22
1. Using Exchange Rates Take a look back at Figure 22.1 to answer the following questions: a. If you have $100, how many euros can you get? b. How many dollars is one euro worth? c. If you have five million euros, how many dollars do you have? d. Which is worth more, a New Zealand dollar or a Singapore dollar? e. Which is worth more, a Mexican peso or a Chilean peso? f. How many Mexican pesos can you get for a euro? What do you call this rate? g. Per unit, what is the most valuable currency of those listed? The least valuable?
1. Using the quotes from the table, we get: a. $100(€0.8206/$1) = €82.06 b. $1.2186 c. €5M($1.2186/€) = $6,093,103 d. Singapore dollar f. (P11.4850/$1)($1.2186/€1) = P13.9959/€ This is a cross rate. g. Most valuable: Bahrain dinar = $3.3920 Least valuable: Turkish lira = $0.00000067
2. Using the Cross-Rate Use the information in Figure 22.1 to answer the following questions: a. Which would you rather have, $100 or €100? Why? b. Which would you rather have, 100 Swiss francs or £100? Why? c. What is the cross-rate for Swiss francs in terms of British pounds? For British pounds in terms of Swiss francs?
2. a. You would prefer €100, since: (€100)($1.8301/€1) = $54.642 b. You would still prefer €100. Using the $/€ exchange rate and the SF/€ exchange rate to find the amount of Swiss francs €100 will buy, we get: (€100)($1.8301/€1)(SF .8008/$1) = SF 43.7572 c. Using the quotes in the book to find the SF/€ cross rate, we find: (SF .8008/$1)($1.8301/€1) = SF 0.4376/€1 The €/SF exchange rate is the inverse of the SF/€ exchange rate, so: €1/SF0.4376 = €2.2853/SF 1
3. Forward Exchange Rates Use the information in Figure 22.1 to answer the following questions: a. What is the three-month forward rate for the Japanese yen in yen per U.S. dollar? Is the yen selling at a premium or a discount? Explain. b. What is the six-month forward rate for Canadian dollars in U.S. dollars per Canadian dollar? Is the dollar selling at a premium or a discount? Explain. c. What do you think will happen to the value of the dollar relative to the yen and the Canadian dollar, based on the information in the figure? Explain.
3. a. F90 = ¥107.46 (per $). The yen is selling at a premium because it is more expensive in the forward market than in the spot market ($0.0092678 versus $0.0093058). b. F180 = $0.7409/C$1. The dollar is selling at a discount because it is less expensive in the forward market than in the spot market ($0.7425 versus $0.7409). c. The value of the dollar will fall relative to the yen, since it takes more dollars to buy one yen in the future than it does today. The value of the dollar will rise relative to the Canadian dollar, because it will take fewer dollars to buy one Canadian dollar in the future than it does today.
4. Using Spot and Forward Exchange Rates Suppose the spot exchange rate for the Canadian dollar is Can$1.26 and the six-month forward rate is Can$1.29. a. Which is worth more, a U.S. dollar or a Canadian dollar? b. Assuming absolute PPP holds, what is the cost in the United States of an Elkhead beer if the price in Canada is Can$2.49? Why might the beer actually sell at a different price in the United States? c. Is the U.S. dollar selling at a premium or a discount relative to the Canadian dollar?
d. Which currency is expected to appreciate in value? e. Which country do you think has higher interest rates—the United States or Canada? Explain.
4. a. The U.S. dollar, since one Canadian dollar will buy: (Can$1)/(Can$1.26/$1) = $0.7937 b. The cost in U.S. dollars is: (Can$2.49)/(Can$1.26/$1) = $1.9762 Among the reasons that absolute PPP doesn’t hold are tariffs and other barriers to trade, transactions costs, taxes, and different tastes.
c. The U.S. dollar is selling at a premium, because it is more expensive in the forward market than in the spot market (Can$1.29 versus Can$1.26). d. The Canadian dollar is expected to depreciate in value relative to the dollar, because it takes more Canadian dollars to buy one U.S. dollar in the future than it does today. e. Interest rates in the United States are probably lower than they are in Canada.
7. Interest Rates and Arbitrage The treasurer of a major U.S. firm has $30 million to invest for three months. The annual interest rate in the United States is .45 percent per month. The interest rate in Great Britain is .6 percent per month. The spot exchange rate is £0.53, and the three-month forward rate is £0.56. Ignoring transactions costs, in which country would the treasurer want to invest the company's funds? Why?
7. $30M(1.0045)3 = $30,406,825.23 If we invest in Great Britain, we must exchange the dollars today for pounds, and exchange the pounds for dollars in three months. After making these transactions, the dollar amount we would have in three months would be: ($30M)(£0.53/$1)(1.0060)3/(£0.56/$1) = $28,907,001.13 We should invest in U.S.
Suppose the current exchange rate for the Polish zloty is PLN 3.84. The expected exchange rate in three years is PLN 4.02. What is the difference in the annual inflation rates for the United States and Poland over this period? Assume that the anticipated rate is constant for both countries. What relationship are you relying on in answering?
8. Using the relative purchasing power parity equation: Ft = S0 × [1 + (hFC – hUS)]t We find: PLN 4.02 = PLN3.84[1 + (hFC – hUS)]3 hFC – hUS = (PLN4.02/PLN3.84)1/3 – 1 hFC – hUS = .0154 Inflation in Poland is expected to exceed that in the U.S. by 1.54% over this period.
10. Exchange Rates and Arbitrage Suppose the spot and six-month forward rates on the Norwegian krone are NOK 6.43 and NOK 6.52, respectively. The annual risk-free rate in the United States is 5 percent, and the annual risk-free rate in Norway is 7 percent. a. Is there an arbitrage opportunity here? If so, how would you exploit it? b. What must the six-month forward rate be to prevent arbitrage?
10. a. If IRP holds, then: F180 = (NOK 6.43)[1 + (.07 – .05)]1/2 F180 = NOK 6.494 Since given F180 is NOK 6.52, an arbitrage opportunity exists; the forward premium is too high. Borrow NOK1 today at 7% interest. Agree to a 180-day forward contract at NOK 6.52. Convert the loan proceeds into dollars: NOK 1 ($1/NOK 6.43) = $0.15552
Invest these dollars at 5%, ending up with $0.15931. Convert the dollars back into krone as $0.15931(NOK 6.52/$1) = NOK 1.03869 Repay the NOK 1 loan, ending with a profit of: NOK1.03869 – NOK1.07180/365 = NOK 0.00476
b. To find the forward rate that eliminates arbitrage, we use the interest rate parity condition, so: F180 = (NOK 6.43)[1 + (.07 – .05)]1/2 F180 = NOK 6.494
12. Spot versus Forward Rates Suppose the spot and three-month forward rates for the yen are ¥131.30 and ¥129.76, respectively. a. Is the yen expected to get stronger or weaker? b. What would you estimate is the difference between the inflation rates of the United States and Japan?
12. a. The yen is expected to get stronger, since it will take fewer yen to buy one dollar in the future than it does today. b. hUS – hJAP (¥129.76 – ¥131.30)/¥131.30 hUS – hJAP = – .0117 or –1.17% (1 – .0117)4 – 1 = –.0461 or –4.61% The approximate inflation differential between the U.S. and Japan is – 4.61% annually.
Suppose the spot exchange rate for the Hungarian forint is HUF 215. Interest rates in the United States are 4.2 percent per year. They are 8.6 percent in Hungary. What do you predict the exchange rate will be in one year? In two years? In five years? What relationship are you using?
13. We need to find the change in the exchange rate over time so we need to use the relative purchasing power parity relationship: Ft = S0 × [1 + (hFC – hUS)]t Using this relationship, we find the exchange rate in one year should be: F1 = 215[1 + (.086 – .042)]1 F1 = HUF 224.46
The exchange rate in two years should be: F2 = 215[1 + (.086 – .042)]2 F2 = HUF 234.34 And the exchange rate in five years should be: F5 = 215[1 + (.086 – .042)]5 F5 = HUF 266.65
14. Capital Budgeting You are a U.S. firm that is evaluating a proposed expansion of an existing subsidiary located in Switzerland. The cost of the expansion would be 27.0 million francs (CHF). The cash flows from the project would be CHF 7.5 million per year for the next five years. The dollar required return is 12 percent per year, and the current exchange rate is CHF 1.72. The going rate on Eurodollars is 8 percent per year. It is 6 percent per year on Euroswiss.
14. a. Implicitly, it is assumed that interest rates won’t change over the life of the project, but the exchange rate is projected to decline because the Euroswiss rate is lower than the Eurodollar rate.
b. We can use relative purchasing power parity to calculate the dollar cash flows at each time. The equation is: E[St] = (CHF 1.72)[1 + (.06 – .08)]t E[St] = 1.72(.98) t So, the cash flows each year in U.S. dollar terms will be:
And the NPV is: NPV = –$15,697,674.42 + $4,449,454.20/1.12 + $4,540,259.39/1.122 + $4,632,917.74/1.123 + $4,727,467.08/1.124 +$4,823,946.00/1.125 NPV = $933,766.18
c. Rearranging the relative purchasing power parity equation to find the required return in Swiss francs, we get: RSFr = 1.12[1 + (.06 – .08)] – 1 RSFr = 9.76%
So the NPV in Swiss francs is: NPV= CHF 1,606,077.83 Converting the NPV to dollars at the spot rate, we get the NPV in U.S. dollars as: NPV = (CHF 1,606,077.83)($1/CHF 1.72) NPV = $933,766.18
Additional Questions
1. Suppose the euro is quoted at 0.7064 80 in London, and the pound sterling is quoted at 1.6244-59 in Frankfurt. Is there a profitable arbitrage situation? Describe it.
Answer. Sell euros for £0.7080/€ in London. Use the pounds to buy euros for €1.6244/£ in Frankfurt. This is equivalent to buying pounds for £0.6156. There is a net profit of £0.0924 per pound bought and sold–a percentage yield of 13.05% (0.0924/0.7080).
2. As a foreign exchange trader at Sumitomo Bank, one of your customers would like a yen quote on Australian dollars. Current market rates are: Spot 30-day ¥101.37-85/U.S.$1 15-13 A$1.2924-44/U.S.$1 20-26
a. What bid and ask yen cross rates would you quote on spot Australian dollars? b. What outright yen cross rates would you quote on 30-day forward Australian dollars? c. What is the forward premium or discount on buying 30-day Australian dollars against yen delivery?
Answer. By means of triangular arbitrage, we can calculate the market quotes for the Australian dollar in terms of yen as ¥78.31-81/A$1 These prices can be found as follows. For the yen bid price for the Australian dollar, we need to first sell Australian dollars for U.S. dollars and then sell the U.S. dollars for yen. It costs A$1.2944 to buy U.S.$1. With U.S.$1 we can buy ¥101.37. Hence, A$1.2944 = ¥101.37, or A$1 = ¥78.31. This is the yen bid price for the Australian dollar
The yen ask price for the Australian dollar can be found by first selling yen for U.S. dollars and then using the U.S. dollars to buy Australian dollars. Given the quotes above, it costs ¥101.85 to buy U.S.$1, which can be sold for A$1.2924. Hence, A$1.2924 = ¥101.85, or A$1 = ¥78.81. This is the yen ask price for the Australian dollar. As a foreign exchange trader, you would try to buy Australian dollars at slightly less than ¥78.31 and sell them at slightly more than ¥78.81. Buying and selling Australian dollars at the market price will leave you with no profit. How much better than the market prices you can do depends on the degree of competition you face from other traders and the extent to which your customers are willing to shop around to get better quotes.
Answer. Given the swap rates, we can compute the outright forward direct quotes for the yen and Australian dollar by adding or subtracting the forward points as follows Spot 30-day 30-day outright rates
By means of triangular arbitrage, we can then calculate the market quotes for the 30-day forward Australian dollar in terms of yen as ¥78.04-58/A$1 These prices can be found as follows. For the yen bid price for the forward Australian dollar, we need to first sell Australian dollars forward for U.S. dollars and then sell the U.S. dollars forward for yen. It costs A$1.2970 to buy U.S.$1 forward. With U.S.$1 we can buy ¥101.22. Hence, A$1.2970 = ¥101.22, or A$1 = ¥78.04. This is the yen bid price for the forward Australian dollar.
The yen ask price for the Australian dollar can be found by first selling yen forward for U.S. dollars and then using the U.S. dollars to buy forward Australian dollars. Given the quotes above, it costs ¥101.72 to buy U.S.$1, which can be sold for A$1.2944. Hence, A$1.2944 = ¥101.71, or A$1 = ¥78.58. This is the yen ask price for the forward Australian dollar.
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