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Name: Problem Set 4 Assigned Problem 1 Suppose the exchange rate between U.S. dollars and Swiss francs is SF 1.41 = $1.00, and the exchange rate between the U.S. dollar and the euro is $1.00 = 1.64 euros. What is the crossrate of Swiss francs to euros? Assigned Problem 2 Assume that the U.S. is the home country. Suppose 1 U.S. dollar equals 1.60 Canadian dollars in the spot market. Six-month Canadian securities have an annualized return of 6% (and thus a 6-month periodic return of 3%). Six-month U.S. securities have an annualized return of 6.5% and a 6-month periodic return of 3.25%. If interest rate parity holds, what is the U.S. dollar-Canadian dollar exchange rate in the 180-day forward market? Assigned Problem 3 In 1985, a given Japanese imported automobile sold for 1,476,000 yen, or $8,200. If the car still sold for the same amount of yen today but the current exchange rate is 144 yen per dollar, what would the car be selling for today in U.S. dollars? Assigned Problem 4 Suppose Stack Pool Inc. had inventory in Britain valued at 240,000 pounds one year ago. The exchange rate for dollars to pounds was 1 = 2 U.S. dollars. This year the exchange rate is 1 = 1.82 U.S. dollars. The inventory in Britain is still valued at 240,000 pounds. What is the gain or loss in inventory value in U.S. dollars as a result of the change in exchange rates? Assigned Problem 5 Taco Trucking, a U.S.-based company, is considering expanding its operations into a foreign country. The required investment at Time = 0 is $10 million. The firm forecasts total cash inflows of $4 million per year for 2 years, $6 million for the next 2 years, and then a possible terminal value of $5 million. In addition, due to political risk factors, Taco believes that the gross terminal value will be only $5 million. However, the government of the host country will block 20% of all cash flows. Thus, cash flows that can be repatriated are 80% of those projected. Taco's cost of capital is 15%, but it adds one percentage point to all foreign projects to account for exchange rate risk. Under these conditions, what is the project's NPV? Solutions to Module 4 Practice Problems Solution to Practice Problem 1 - Cross rates Problem (17-1) Textbook page 720 $1 = 9 Mexican pesos; $1 = 111.23 Japanese yen; Cross exchange rate, yen/peso = ? Dollar Yen Yen Cross Rate = = Peso Peso Dollar Note that an indirect quotation is given for Mexican; however, the cross rate formula requires a direct quotation. The indirect quotation is the reciprocal of the direct quotation. Since $1 = 9 pesos, 1 peso = $0.1111. Yen/Peso = 0.1111 dollars per peso 111.23 yen per dollar = 12.358 yen per peso Solution to Practice Problem 2 - Cross rates Problem (17-6) Textbook page 721 Cross rate = Swiss francs/dollars dollars/pounds = Swiss francs/pounds = 1.6 1.5 = 2.4 Swiss francs per pound. Solution to Practice Problem 3 - Exchange gains and losses Problem (17-9) Textbook page 721 The U. S. dollar liability of the corporation falls from (0.10 dollars per peso)(50,000,000 pesos) = $5,000,000 to (0.09 dollars per peso)(50,000,000 pesos) = $4,500,000, corresponding to a gain of 500,000 U. S. dollars for the corporation. However, the real economic situation might be somewhat different. For example, the loan is presumably a long-term loan. The exchange rate will surely change again before the loan is paid. What really matters, in an economic sense, is the expected present value of future interest and principal payments denominated in U. S. dollars. There are also possible gains and losses on inventory and other assets of the firm. A discussion of these issues quickly takes us outside the scope of this textbook. Solution to Practice Problem 4 - Results of exchange rate changes Problem (17-10) Textbook page 721 The automobile's value has increased because the dollar has declined in value relative to the yen. The 1983 cost in yen was (245 yen per dollar)(8,000 dollars) = 1,960,000 yen. At an exchange rate of 80 yen per dollar, this is (1,960,000 yen)/(80 yen per dollar) = $24,500.00 Page 1 of 3 Solutions to Module 4 Practice Problems Solution to Practice Problem 5 - Interest rate parity According to interest rate parity: f t (1 + rh ) = e 0 (1 + rf ) rf = 5.5%/2 = 2.75%. rh = 7%/2 = 3.5%. Spot rate: e0 = $0.009 ft 1.035 = $0.009 1.0275 1.0275 ft = $0.00932 Forward rate: ft = $0.00907 The 6-month forward exchange rate is 1 yen = $0.00907 Solution to Practice Problem 6 - Purchasing power parity Problem (17-8) Textbook page 721 $1 = 7.8 pesos Price of headphones in U.S. = $15.00; Price of headphones in Mexico = ? According to purchasing power parity: Ph = Pf (Spot rate). 1 Peso = 1/7.8 = $0.1282 $15 = Pf($0.1282) $15 = 117 pesos $0.1282 Check: Spot rate = $15/117 pesos = $0.1282 for 1 peso Solution to Practice Problem 7 - Spot and forward rates Problem (17-11) Textbook pages 721-722 a. (1,000,000 Swiss francs) / (0.6028 Swiss francs per dollar) = $1,658,925 b. (1,000,000 Swiss francs) / (0.6075 Swiss francs per dollar) = $1,646,091 c. If the exchange rate is 0.500 Swiss francs per dollar when payment is due in 3 months, the SFr. 1,000,000 will cost: (1,000,000 Swiss francs)/(0.500 Swiss francs per dollar) = $2,000,000, which is more than the spot price today and more than purchasing a forward contract for 90 days. Page 2 of 3 Solutions to Module 4 Practice Problems Solution to Practice Problem 8 - International capital budgeting a. If a U.S.-based company undertakes the project, the rate of return for the project is a simple calculation, as is the net present value. NPV = -$1,000 + $1,200/1.14 = $52.63 Rate of return = ($1,200 - $1,000)/$1,000 or $1,200/$1,000 - 1 = 0.020 or 20%. b. According to the interest rate parity, the following condition holds: Forward exchange rate Spot exchange rate Forward exchange rate 1.62 Forward exchange rate 1.62 Forward exchange rate 1 + rSwiss 1 + rUS 1.045 = 1.0725 = = 0.97436 = 1.5785 Swiss Francs per U.S. $ c. First, we must adjust the cash flows to reflect Solitaire's home currency. Year 0 1 CF ($) -1,000 1,200 CF (Swiss Francs) -1,620.00 = -1,000 1.62 1,894.20 = 1,200 1.5785 Using the Swiss Franc-denominated cash flows, the appropriate NPV and rate of return can be found. NPV = -1,620 + 1,894.20/1.14 = 41.58 Swiss Francs Rate of return = 1,894.20 SF/1,620 SF - 1 = 0.1691 or 16.91% Page 3 of 3