Chapter 17 Homework Problems

*PLEASE WORK OUT SOLUTIONS WITH FORMULAS SHOWN IN EXCEL* USE SEPARATE TABS FOR EACH PROBLEM CORRECT SOLUTIONS ARE PROVIDED BELOW (17-1) At today’s spot exchange rate 1 U.S dollar can be exchanged for 9 Mexican pesos or for 111.23 Japanese yen. You have pesos that you would like to exchange for yen. What is the cross rate between the yen and the peso; that is, how many yen would you receive for every peso exchanged?

(17-2) The nominal yield on 6-month T-bills is 7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5%. In the spot exchange market, 1 yen equals $0.009. If interest rate parity holds, what is the 6-month forward exchange rate?

(17-3) A computer costs $500 in the United States. The same model costs 550 euros in France. If purchasing power parity holds, what is the spot exchange rate between the euro and the dollar?

(17-4) If euros sell for $1.50 (U.S) per euro, what should dollars sell for in euros per dollar?

(17-5) Suppose that the exchange rate is 0.60 dollars per Swiss franc. If the franc appreciates 10% against the dollar, how many francs would a dollar buy tomorrow?

(17-6) Suppose the exchange rate between U.S dollars and the Swiss franc is SFr1.6 = $1 and the exchange rate between the dollar and the British pound is £1 = $1.50. What then is the cross rate between francs and pounds?

(17-7) Assume that interest rate parity holds. In both the spot market and the 90-day forward market, 1 Japanese yen equals 0.0086 dollar. In Japan, 90 day risk-free securities yield 4.6%. What is the yield on 90-day risk-free securities in the United States?

(17-8) In the spot market, 7.8 pesos can be exchanged for 1 U.S, dollar. A pair of headphones costs $15 in the United States. If purchasing power parity holds, what should be the price of the same headphones in Mexico?

(17-11) Boisjoly Watch Imports has agreed to purchase 15,000 Swiss watches for 1 million francs at today’s spot rate. The firm’s financial manager, James Desreumaux, has noted the following current spot and forward rates:

U.S. Dollar/Swiss Franc Swiss Franc/U.S. Dollar Spot

1.6590

0.6028

30-day forward

1.6540

0.6046

90-day forward

1.6460

0.6075

180-day forward

1.6400

0.6098

On the same day, Desreumaux agrees to purchase 15,000 more watches in 3 months at the same price of 1 million Swiss francs. a. What is the price of the watches, in U.S. dollars, if purchased at today’s spot rate? b. What is the cost, in dollars, of the second 15,000 batch if payment is made in 90 days and the spot rate at that time equals today’s 90-day forward rate? c. If the exchange rate for the Swiss franc is 0.50 to $1 in 90 days, how much will Desreumaux have to pay (in dollars) for the watches?

(17-12) Assume that interest rate parity holds and that 90-day risk-free securities yield 5% in the United States and 5.3% in Germany. In the spot market, 1 euro equals $1.40. What is the 90-day forward rate? Is the 90-day forward rate trading at a premium or a discount relative to the spot rate?

SOLUTIONS 17-1

$1 = 9 Mexican pesos; $1 = 111.23 Japanese yen; Cross exchange rate, yen/peso = ? Cross Rate:

Dollar Yen Yen  = . Peso Dollar Peso

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, then 1 peso = $0.1111. Yen/Peso = 0.1111 dollars per peso  111.23 yen per dollar = 12.358 yen per peso.

17-2

rNom, 6-month T-bills = 7%; rNom of similar default-free 6-month Japanese bonds = 5.5%; Spot exchange rate, e0: 1 Yen = $0.009; 6-month forward exchange rate = ft = ? ft (1  rh )  e 0 (1  rf )

.

rf = 5.5%/2 = 2.75%. rh = 7%/2 = 3.5%. e0 = $0.009. ft $0.009

=

1.0275 ft

= $0.00932

ft

= $0.00907.

1.035 1.0275

The 6-month forward exchange rate is 1 yen = $0.00907. 17-3

U. S. Computer = $500; French Computer = 550 euros; Spot rate between euro and dollar =? Ph = Pf(e0) $500 = 550 euros(e0) 500/550 = e0 $0.9091 = e0. 1 euro = $0.9091 or $1 = 1 / 0.9091 = 1.1000 euros.

17-4

Dollars should sell for 1/1.50, or 0.6667 euros per dollar.

17-5

The current exchange rate is 0.60 dollars per Swiss franc. A 10 percent appreciation will make it 0.66 dollars per Swiss franc. To find Swiss francs per dollar, divide 1 by the exchange rate: 1/0.66 = 1.5152 Swiss francs per dollar.

17-6

Cross rate = Swiss francs/dollars  dollars/pounds = Swiss francs/pounds = 1.6  1.5 = 2.4 Swiss francs per pound.

17-7

Spot rate = 1 yen = $0.0086; f t = 1 yen = $0.0086; r Nom of 90-day Japanese risk-free securities = 4.6%; rNom of 90-day U. S. risk-free securities = ?

ft (1  rh )  . Spot rate (1  rf ) rf = 4.6%/4 = 1.15%; rh = ?

(1  rh ) 1.0115 1 + rh = 1.0115 rh = 0.0115. 1 =

rNom = 1.15%  4 = 4.6%. 17-8

$1 = 7.8 pesos; headphones = $15.00; Price of headphones in Mexico = ? 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.

17-11 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. 17-12 rNom of 90-day U. S. risk-free securities = 5%; of 90-day German risk-free securities = 5.3%; Spot rate = 1 euro = $0.80; ft selling at premium or discount = ?

ft (1  rh )  . Spot rate (1  rf ) rh = 5%/4 = 1.25%; rf = 5.3%/4 = 1.325%; Spot rate = $1.40

ft 1.0125 = $1.40 1.01325 ft = 0.9993. $1.40 ft = $1.3990.

The forward rate is selling at a discount, since a euro buys fewer dollars in the forward market than it does in the spot. In other words, in the spot market $1 would buy 1/1.40 = 0.7143 euros, but at the forward rate $1 would buy 1/1.3990 = 0.7148 euros; therefore, the forward currency is said to be selling at a discount.