Problem set
1. Implications of PPP. Today's spot rate of the Mexican peso is $.10. Assume that purchasing power parity holds. The U.S. inflation rate over this year is expected to be 7%, while the Mexican inflation over this year is expected to be 3%. Wake Forest Co. plans to import from Mexico and will need 20 million Mexican pesos in one year. Determine the expected amount of dollars to be paid bythe Wake Forest Co. for the pesos in one year.
2. PPP and Real Interest Rates. The nominal (quoted) U.S. one-year interest rate is 6%, while the nominal one-year interest rate in Canada is 5%. Assume you believe in purchasing power parity. Youbelieve the real one-year interest rate is 2% in the U.S, and that the real one-year interest rate is 3% inCanada. Today the Canadian dollar spot rate at $.90. What do you think the spot rate of the Canadiandollar will be in one year?
3. PPP and Cash Flows. Boston Co. will receive 1 million euros in one year from selling exports. It did not hedge this future transaction. Boston believes that the future value of the euro will bedetermined by purchasing power parity (PPP). It expects that inflation in countries using the euro willbe 12% next year, while inflation in the U.S. will be 7% next year. Today the spot rate of the euro is$1.46, and the one-year forward rate is $1.50.
a. Estimate the amount of U.S. dollars that Boston will receive in one year when converting its euro receivables into U.S. dollars.
b. Today, the spot rate of the Hong Kong dollar is pegged at $.13. Boston believes that the Hong
Kong dollar will remain pegged to the dollar for the next year. If Boston Co. decides to convert its 1 million euros into Hong Kong dollars instead of U.S. dollars at the end of one year, estimate theamount of Hong Kong dollars that Boston will receive in one year when converting its euro receivables into Hong Kong dollars.
4. Influence of PPP. The U.S. has expected inflation of 2%, while Country A, Country B, and Country C have expected inflation of 7%. Country A engages in much international trade with the U.S. Theproducts that are traded between Country A and the U.S. can easily be produced by either country.Country B engages in much international trade with the U.S. The products that are traded betweenCountry B and the U.S. are important health products, and there are not substitutes for these productsthat are exported from the U.S. to Country B or from Country B to the U.S. Country C engages inmuch international financial flows with the U.S. but very little trade. If you were to use purchasingpower parity to predict the future exchange rate over the next year for the local currency of eachcountry against the dollar, do you think PPP would provide the most accurate forecast for thecurrency of Country A, Country B, or Country C? Briefly explain.
5. Forecasting the Future Spot Rate Based on IFE. Assume that the spot exchange rate of the Singapore dollar is $.70. The one-year interest rate is 11 percent in the United States and 7 percent in Singapore. What will the spot rate be in one year according to the IFE? What is the force that causesthe spot rate to change according to the IFE?
6. IFE. The one-year Treasury (risk-free) interest rate in the U.S. is presently 6%, while the one-year Treasury interest rate in Switzerland is 13%. The spot rate of the Swiss franc is $.80. Assume that youbelieve in the international Fisher effect. You will receive 1 million Swiss francs in one year.What is the estimated amount of dollars you will receive when converting the francs to U.S. dollars inone year at the spot rate at that time?
7. IFE. Beth Miller does not believe that the international Fisher effect (IFE) holds. Current one-year interest rates in Europe are 5 percent, while one-year interest rates in the U.S. are 3 percent. Bethconverts $100,000 to euros and invests them in Germany. One year later, she converts the euros backto dollars. The current spot rate of the euro is $1.10.
a. According to the IFE, what should the spot rate of the euro in one year be?
b. If the spot rate of the euro in one year is $1.00, what is Beth's percentage return from her strategy?
c. If the spot rate of the euro in one year is $1.08, what is Beth's percentage return from her strategy?
d. What must the spot rate of the euro be in one year for Beth's strategy to be successful?
8. Deriving the Forward Rate. Assume that annual interest rates in the U.S. are 4 percent, while interest rates in France are 6 percent. If the euro's spot rate is $1.10, what should the one-year forward rate of the euro be?
9. Implications of IRP. Assume that interest rate parity exists. You expect that the one-year nominal interest rate in the U.S. is 7%, while the one-year nominal interest rate in Australia is 11%. The spotrate of the Australian dollar is $.60. You will need 10 million Australian dollars in one year. Today,you purchase a one-year forward contract in Australian dollars. How many U.S. dollars will you needin one year to fulfill your forward contract?
10. Integrating CIP and IFE. Assume the following information is available for the U.S. and Europe:
U.S. Europe
Nominal interest rate 4% 6%
Expected inflation 2% 5%
Spot rate ----- $1.13
One-year forward rate ----- $1.10
a. Does CIP hold?
b. According to PPP, what is the expected spot rate of the euro in one year?
c. According to the IFE, what is the expected spot rate of the euro in one year?
11. Real Interest Rates, Expected Inflation, IRP, and the Spot Rate. The U.S. and the country of Rueland have the same real interest rate of 3%. The expected inflation over the next year is 6 percent in the U.S. versus 21% in Rueland. Interest rate parity exists. The one-year currency futures contract on Rueland's currency (called the ru) is priced at $.40 per ru. What is the spot rate of the ru?
12. IFE, Cross Exchange Rates, and Cash Flows. Assume the Hong Kong dollar (HK$) value is tied to the U.S. dollar and will remain tied to the U.S. dollar. Assume that interest rate parity exists.
Today, an Australian dollar (A$) is worth $.50 and HK$3.9. The one-year interest rate on the Australian dollar is 11%, while the one-year interest rate on the U.S. dollar is 7%. You believe in the international Fisher effect.You will receive A$1 million in one year from selling products to Australia, and will convert theseproceeds into Hong Kong dollars in the spot market at that time to purchase imports from HongKong. Forecast the amount of Hong Kong dollars that you will be able to purchase in the spot marketone year from now with A$1 million. Show your work.