|Problem Set 2
SUGGESTED SOLUTIONS TO CHAPTER 4 PROBLEMS
1. From base price levels of 100 in 1987, West German and U.S. price levels in 1988 stood at 102 and 106, respectively. If the 1987 $/DM exchange rate was $0.54, what should the exchange rate be in 1988? In fact, the exchange rate in 1988 was DM 1 = $0.56. What might account for the discrepancy? (Price levels were measured using the consumer price index.)
Answer. If e1981 is the dollar value of the German mark in 1988, then according to purchasing power parity e1988/.54 = 106/102 or e1988 = $.5612. The discrepancy between the predicted rate of $.5612 and the actual rate of $.56 is insignificant and hence needs no explaining. Historically, however, discrepancies betweenthe PPP rate and the actual rate have frequently occurred. These discrepancies could be due to mismeasurement of the relevant price indices. Estimates based on narrower price indices reflecting only traded goods prices would probably be closer to the mark, so to speak. Alternatively, it could be due to a switch in investors' preferences from dollar to non dollar assets.
3. In early 1996, the short-term interest rate in France was 3.7%, and forecast French inflation was 1.8%. At the same time, the short-term German interest rate was 2.6% and forecast German inflation was 1.6%.
a. Based on these figures, what were the real interest rates in France and Germany?
Answer. The French real interest rate was 1.037/1.018 - 1 = 1.87%. The corresponding real rate in Germany was 1.026/1.016 - 1 = 0.98%.
b. To what would you attribute any discrepancy in real rates between France and Germany?
Answer. The most likely reason for the discrepancy is the inclusion of a higher inflation risk component in the French real interest rate than in the German real rate. Other possibilities are the effects of currency risk or transactions costs precluding this seeming arbitrage opportunity.
4. In July, the one year interest rate is 12% on British pounds and 9% on U.S. dollars.
a. If the current exchange rate is $1.63:1, what is the expected future exchange rate in one year?
Answer. According to the international Fisher effect, the spot exchange rate expected in one year equals 1.63 x 1.09/1.12 = $1.5863.
b.Suppose a change in expectations regarding future U.S. inflation causes the expected future spot rate to decline to $1.52:£1. What should happen to the U.S. interest rate?
Answer. If rus is the unknown U.S. interest rate, and assuming that the British interest rate stayed at 12% (because there has been no change in expectations of British inflation), then according to the IFE, 1.52/1.63 = (1+rus)/1.12 or rus = 4.44%.
5. If expected inflation is 100% and the real required return is 5%, what will the nominal interest rate be according to the Fisher effect?
Answer. According to the Fisher effect, the relationship between the nominal interest rate, r, the real interest rate a, and the expected inflation rate, i, is 1 + r = (1 + a)(1 + i). Substituting in the numbers in the problem yields 1 + r = 1.05 x 2 = 2.1, or r = 110%.
6. Suppose that in Japan the interest rate is 8% and inflation is expected to be 3%. Meanwhile, the expected inflation rate in France is 12%, and the English interest rate is 14%. To the nearest whole number, what is the best estimate of the one year forward exchange premium (discount) at which the pound will be selling relative to the French franc?
Answer. Based on the numbers, Japan's real interest rate is about 5% (8% 3%). From that, we can calculate France's nominal interest rate as about 17% (12% + 5%), assuming that arbitrage will equate real interest rates across countries and currencies. Since England's nominal interest rate is 14%, for interest rate parity to hold, the pound should sell at around a 3% forward premium relative to the French franc.
9. The inflation rate in Great Britain is expected to be 4% per year, and the inflation rate in Switzerland is expected to be 6% per year. If the current spot rate is £1 = SF 12.50, what is the expected spot rate in two years?
Answer. Based on PPP, the expected value of the pound in two years is 12.5 x (1.06/1.04)2 = SF12.99.
10. If the $:¥ spot rate is $1 = ¥218 and interest rates in Tokyo and New York are 6% and 12%, respectively, what is the expected $:¥ exchange rate one year hence?
Answer. According to the international Fisher effect, the dollar spot rate in one year should equal 218(1.06/1.12) = ¥206.32.
12. Suppose that on January 1, the cost of borrowing French francs for the year is 18%. During the year, U.S. inflation is 5%, and French inflation is 9%. At the same time, the exchange rate changes from FF 1 = $0.15 on January 1 to FF 1 = $0.10 on December 31. What was the real U.S. dollar cost of borrowing francs for the year?
Answer. During the year, the franc devalued by (.15 - .10)/.15 = 33.33%. The nominal dollar cost of borrowing French francs, therefore, was .18(1 - .3333) - .3333 = -21.33% (see Chapter 12). For each dollar's worth of francs borrowed on January 1, it cost only $0.7867 to repay the principal plus interest. With U.S. inflation of 5% during the year, the real dollar cost of repaying the principal and interest is $0.7867/1.05 = $0.7492. Subtracting the original $1 borrowed, we see that the real dollar cost of repaying the franc loan is -$0.2508 or a real dollar interest rate of -25.08%.
14. Assume the interest rate is 16% on pounds sterling and 7% on the Euro. At the same time, inflation is running at an annual rate of 3% in Germany and 9% in England.
a. If the Euro is selling at a one-year forward premium of 10% against the pound, is there an arbitrage opportunity? Explain.
Answer. According to interest rate parity, with a Euro rate of 7% and a 10% forward premium on the Euro against the pound, the equilibrium pound interest rate should be
1.07 x 1.10 - 1 = 17.7%
Since the pound interest rate is only 16%, there is an arbitrage opportunity. It involves borrowing pounds at 16%, converting them into Euro, investing them at 7%, and then selling the proceeds forward, locking in a pound return of 17.7%.
b. What is the real interest rate in Germany? in England?
Answer. The real interest rate in Germany is 1.07/1.03 -1 = 3.88%. The real interest rate in England is 1.16/1.09 -1 = 6.42%.
c. Suppose that during the year the exchange rate changes from Euro2.7/£1 to Euro2.65/£1. What are the real costs to a German company of borrowing pounds? Contrast this cost to its real cost of borrowing Euro.
Answer. At the end of one year, the German company must repay 1.16 for every pound borrowed. However, since the pound has devalued against the Euro by 1.85% (2.65/2.70 - 1 = -1.85%), the effective cost in Euro is 1.16 x (1 - 0.0185) - 1 = 13.85%. In real terms, given the 3% rate of German inflation, the cost of the pound loan is found as 1.1385/1.03 -1 = 10.54%.
As shown above, the real cost of borrowing Euro equals 3.88%, which is significantly lower than the real cost of borrowing pounds. What happened is that the pound loan factored in an expected devaluation of about 9% (16% - 7%), whereas the pound only devalued by about 2%. The difference between the expected and actual pound devaluation accounts for the approximately 7% higher real cost of borrowing pounds.
d. What are the real costs to a British firm of borrowing Euro? Contrast this cost to its real cost of borrowing pounds.
Answer. During the year, the Euro appreciated by 1.89% (2.70/2.65 - 1) against the pound. Hence, a Euro loan at 7% will cost 9.02% in pounds (1.07 x 1.0189 - 1). In real pound terms, given a 9% rate of inflation in England, this loan will cost the British firm 0.02% (1.0902/1.09 - 1) or essentially zero. As shown above, the real interest on borrowing pounds is 6.42%.
15. Suppose today's exchange rate is $0.62/Euro. The 6-month interest rates on dollars and Euro are 6% and 3%, respectively. The 6-month forward rate is $0.6185. A foreign exchange advisory service has predicted that the Euro will appreciate to $0.64 within six months.
a. How would you use forward contracts to profit in the above situation?
Answer. By buying Euro forward for six months and selling it in the spot market, you can lock in an expected profit of $0.0215 (0.64 - 0.6185) per Euro bought forward. This is a semiannual percentage return of 3.48% (0.0215/0.6185). Whether this profit materializes depends on the accuracy of the advisory service's forecast.
b. How would you use money market instruments (borrowing and lending) to profit?
Answer. By borrowing dollars at 6% (3% semiannually), converting them to Euro in the spot market, investing the Euro at 3% (1.5% semiannually), selling the Euro proceeds at an expected price of $0.64/Euro, and repaying the dollar loan, you will earn an expected semiannual return of 1.77%:
Return per dollar borrowed = (1/0.62) x 1.015 x 0.64 - 1.03 = 1.77%
c. Which alternatives (forward contracts or money market instruments) would you prefer? Why?
Answer. The return per dollar in the forward market is substantially higher than the return using the money market speculation. Other things being equal, therefore, the forward market speculation would be preferred.
Chapter 11(a) problems
5. On January 1, the U.S. dollar:Japanese yen exchange rate is $1 = ¥250. During the year, U.S. inflation is 4% and Japanese inflation is 2%. On December 31, the exchange rate is $1 = ¥235. What are the likely competitive effects of this exchange rate change on Caterpillar Tractor, the American earth moving manufacturer, whose toughest competitor is Japan's Komatsu?
Answer. The real value of the yen changed from $.004000 (1/250) at the start of the year to $.004339 (1/235 x 1.04/1.02) at the end of the year, an increase of 8.47%. Caterpillar Tractor should benefit from this increase in the real value of the yen since Komatsu does most of its manufacturing in Japan. The inflation adjusted dollar cost of Japanese supplied components and labor will rise in line with the increase in the real value of the yen. Komatsu's raw materials and energy prices should not rise in dollar terms because these resources are imported.
7. In 1990, General Electric acquired Tungsram Ltd., a Hungarian light bulb manufacturer. Hungary's inflation rate was 28% in 1990 and 35% in 1991, while the forint (Hungary's currency) was devalued 5% and 15%, respectively, during those years. Corresponding inflation for the U.S. was 6.1% in 1990 and 3.1% in 1991.
a. What has happened to the competitiveness of GE's Hungarian operations during 1990 and 1991? Explain.
Answer. Since forint devaluations haven't kept pace with Hungary's roaring inflation, we know that the forint's real exchange rate has risen. Specifically, if the nominal exchange rate (dollar value of the forint) at the start of 1990 was e0, the forint's real value at the end of 1991 was:
0.95 x 0.85e0 x (1.28)(1.35)/[(1.061)(1.031)] = 1.276e0
This equation reflects the fact that if the nominal exchange rate (dollar value of the forint) at the start of 1990 was e0, then the 5% devaluation during 1990 left it at 0.95e0 by the end of 1990. A further 15% devaluation during 1991 would have left the nominal rate equal to 0.95 x 0.85e0 by the end of 1991.
Based on this equation, we can see that the real exchange rate increased by 27.6% during this two-year period. The sharp appreciation in the real value of the forint reduced the cost competitiveness of GE's Hungarian operations.
b. In early 1992, GE announced that it would cut back its capital investment in Tungsram. What might have been the purpose of GE's publicly announced cutback?
Answer. GE was trying to put pressure on the Hungarian government to devalue further the forint and thereby improve the cost competitiveness of its Tungsram manufacturing facilities. In effect, GE was telling the Hungarian government that it was in business to make a profit and that if it couldn't make a profit in Hungary because of the high forint and the resulting sharp jump in its costs, it was not going to invest there in the future.
11. Assess the likely consequences of a declining dollar on Fluor Corporation, the international construction engineering contractor based in Irvine, California. Most of Fluor's value added involves project design and management; most of its costs are for U.S. labor in design, engineering, and construction management services.
Answer. Fluor will benefit from a falling dollar since it will be more cost competitive vis a vis foreign contractors both at home and abroad. Its costs are primarily denominated and determined in dollars. Thus, when the dollar declines, these costs fall relative to those of its foreign competitors. Although many of the costs incurred on foreign projects are set in the local currency, these costs are the same for all potential competitors. Hence, in competing against foreign firms, Fluor will find that some of its costs are the same while other of its costs, particularly for the labor involved in design, engineering, and construction management services, are now lower.
14. The Edmonton Oilers (Canada) of the National Hockey League are two time defending Stanley Cup champions. (The Stanley Cup playoff is hockey's equivalent of football's Super Bowl or baseball's World Series.) As is true of all NHL teams, most of the Oilers' players are Canadian. How are the Oilers affected by changes in the Canadian dollar/U.S. dollar exchange rate?
Answer. The fact that the Oilers are paid in Canadian dollars does not affect the answer to this question very much. While the C$ is the currency of denomination, the U.S.$ is the currency of determination. That is, the Canadian dollar salaries paid to the Oilers' players are just equal to what the players' salaries would be in U.S. dollars converted into Canadian dollars. Thus, the Edmonton Oilers are hurt by appreciation of the U.S.$ vis a vis the C$ and benefitted by U.S. dollar depreciation. Consider what would happen, for example, if the U.S.$ appreciates against the C$. If the Oilers' C$ salaries are not raised, they will find they are being paid less than players on U.S. hockey teams. The Oilers will be forced to raise the Canadian dollar equivalent of its players' salaries to keep them on a par with their U.S. rivals. Otherwise, the Edmonton Oilers will either lose players to U.S. teams or have a hostile team. Player nationality is irrelevant. Canadian teams compete in a world market for talent and must pay the market price.
15. South Korean companies such as Goldstar, Samsung, and Daewoo have captured more than 10% of the U.S. color TV market with their small, low priced TV sets. They are also becoming more significant exporters of videocassette recorders and small microwave ovens. What currency risk do these firms face?
Answer. These firms have benefitted greatly from the appreciation of the Japanese yen against the U.S. dollar because the won has not risen by nearly the same extent against the dollar. They have used their cost advantage vis à vis Japanese competitors to boost sales of low end consumer electronics products by cutting prices below the level at which the Japanese could make money. Yen depreciation or won appreciation would reduce their cost advantage. Similarly, they face currency risk because competitors in other nations, such as Taiwan or Thailand, might devalue their currencies against the won.
18. Black & Decker Manufacturing Co. of Towson, Maryland, has roughly 45% of its assets and 40% of its sales overseas. How does a soaring dollar affect its profitability, both at home and abroad?
Answer. Black & Decker has a rough balance between foreign sales and costs. Thus, as the dollar appreciates, both its sales revenue and its costs decline approximately in line with each other. This means that its profits will decline roughly in line with the rise of the dollar. (If both revenues and costs fall, say, 10%, then profit must also fall by 10%.) Dollar depreciation leads to corresponding increases in dollar revenues and costs. The bottom line is that B&D's profits fall as the dollar rises and rise as the dollar falls. If B&D didn't produce overseas, but instead exported from its U.S. plants, then currency changes would lead to much greater swings in its profits. Note that B&D's domestic profitability is also affected by currency changes since it faces competition in the U.S. from foreign companies such as Japan's Makita.
19. The shipbuilding industry is facing a worldwide capacity surplus. Although Japan currently controls about 50% of the world market, it is facing severe competition from the South Koreans. Japanese shipyards are extraordinarily productive, but at current price levels were just about breaking even with an exchange rate of ¥240 = $1. What are the likely effects on Japanese shipbuilders of a yen appreciation to ¥180 = $1? The South Korean won has maintained its dollar value.
Answer. The statement that "Japanese shipyards are extraordinarily productive" tells you that there is not much room for cost cutting by Japanese shipyards. Hence, Japanese shipyards will be devastated by a rise in the yen, as they were. As the yen appreciates against the won, South Korean shipyards gained a substantial cost advantage vis a via the Japanese. According to a story in the Wall Street Journal, "Japanese industry officials say ship buyers now automatically bypass Japanese makers, turning instead to Hyundai Corp. and other South Korean shipbuilders, which enjoy comparative reprieve on the currency front."
The only degree of freedom to adjust Japanese shipbuilder costs took place on the wage side. Japanese firms typically pay a substantial fraction of workers' wages in the form of a semi annual bonus that is tied to corporate profits. Thus, during hard times, labor costs fall automatically. However, this decrease in labor costs was not nearly enough and many Japanese shipyards went bankrupt. A spokesman for the Japan Ship Exporters Association said that they couldn't lower prices further. "They're already at the bottom. We can do nothing but watch competitors take away orders."
Japanese shipyards have responded by designing innovative ships for which demand is price inelastic. They are no longer competitive in the commodity ship business.
Chapter 11(b) problems
3. Gizmo, U.S.A. is investigating medium term financing of $10 million in order to build an addition to its factory in Toledo, Ohio. Gizmo's bank has suggested the following alternatives:
Type of loan
3-year U.S. dollar loan
3-year Euro loan
3-year Swiss franc loan
a. What information does Gizmo require to decide among the three alternatives?
Answer. It is useful to divide this problem into two issues: what is the expected cost and what is the risk of each alternative. Defining the terms "cost" and "risk" requires careful thought.
If we assume that (1) the international money markets are efficient and (2) the international Fisher effect holds (these are separate issues) then the expected cost of each loan is the same. If the market is anticipating that for the next three years the Euro and the Swiss franc will appreciate 6% and 10% annually, respectively, then the expected U.S. dollar cost of each loan is the same. If we are unwilling to make assumptions (1) and (2), then we need to use independent forecasts of the Euro and Swiss franc exchange rates to calculate the loan whose expected U.S. dollar cost is the lowest.
Even if the expected cost of each loan is the same, the risk associated with each loan may be different for Gizmo. This risk will depend on the currency denomination of assets that Gizmo holds as well as on the markets in which Gizmo buys its inputs and sells it outputs. For example, if Gizmo sells many products in Germany, then it probably has accounts receivable denominated in Euro. It can use these receivables to pay off a DM loan and avoid the risks that are associated with an uncertain $/Euro rate. If Gizmo desires a particular risk level, then it may rationally prefer a particular currency denomination for the loan. It may also be that forward markets are more developed in one currency or that unanticipated exchange rate changes are smaller in one currency, and therefore, the risks associated with that currency are smaller even if the expected costs are the same.
b. Suppose the factory will be built in Geneva, Switzerland, rather than Toledo. How does this affect your answer in part a?
Answer. If the factory in Geneva sells in Switzerland, then Gizmo has an asset which is essentially denominated in Swiss francs. This may establish a natural hedge against a Swiss franc loan and reduce the risk of this particular alternative. If the expected cost of each loan alternative if the same, and if the firm seeks to reduce total risk, then this information would suggest a Swiss franc loan.
But if the Swiss factory is exporting to the U.S., or is selling in the Swiss market and facing import competition, then some dollar financing or financing in the currency of the country in which its main competitors are located might be appropriate. If the objective is to minimize currency risk, the relative amount of financing to do in each currency will also depend on the sources of Gizmo's inputs, particularly the extent to which it uses Swiss labor. The more labor intensive the production process, the less useful Swiss franc financing will be in reducing Gizmo's exposure (since by using Swiss labor it already has Swiss franc outflows).
5. In September 1992, Dow Chemical reacted to the currency chaos in Europe by switching to Euro pricing for all its products in Europe. The purpose, said a Dow executive, was to shift currency risk from Dow to its European customers. Moreover, said the Dow executive, the policy was fairer: By setting the same DM price throughout Europe, Dow's new policy would nullify any advantage that a Dow customer in one company might have over competitors in another country based on currency swings.
a. What is Dow really trying to accomplish with its new pricing policy?
Answer. Dow was really trying to raise its prices in those European counties whose currencies devalued so as to preserve its dollar margins, which were eroding from the devaluations.
b. What is the likelihood that this new policy will reduce Dow's currency risk?
Answer. Not very likely. Unless all its leading competitors go along with Euro pricing (its U.S. and foreign competitors said that they wouldn't follow Dow but would continue doing business in local currencies), Dow will have to cut its Euro price every time the Euro appreciates or else lose market share. In other words, Dow can't use Euro pricing to avoid margin erosion when European currencies devalue against the dollar unless it is willing to sacrifice market share.
c. How are Dow's customers likely to respond to this new policy?
Answer. They will simply demand lower Euro prices if their currencies devalue. If Dow doesn't cut its Euro prices, many of them will buy from those of Dow's competitors who are willing to cut their dollar or Euro prices.
8. Cost Plus Imports is a West Coast chain specializing in low cost imported goods, principally from Japan. It has to put out its semiannual catalogue with prices that are good for six months. Advise Cost Plus Imports on how it can protect itself against currency risk.
Answer. A company such as Cost Plus will typically negotiate purchase contracts with the suppliers of its catalogue merchandise in advance. Cost Plus could hedge these purchases using forward contracts. A problem, though, is that if the foreign currencies devalue during the life of the catalogue, prices of substitute products for the items in the catalogue will likely come down somewhat. In this case, some customers who might have bought from Cost Plus will decide to buy the cheaper substitutes, costing Cost Plus sales. This is very likely here given the nature of Cost-Plus products: low cost goods presumably bought by a price sensitive clientele.
The existence of quantity risk in addition to price risk suggests that Cost Plus should hedge less than 100% of its projected sales. As an alternative, Cost Plus could buy call options to cover its foreign purchases. If the foreign currencies drop below the call option price, the firm won't exercise its options; if they rise above the call price, Cost Plus will exercise them.
11. Lyle Shipping, a British company, has chartered out ships at fixed U.S. dollar freight rates. How can Lyle use financing to hedge against its exposure? How will your recommendation affect Lyle's translation exposure? Lyle uses the current rate method to translate foreign currency assets and liabilities. However, the charters are off balance sheet items.
Answer. Since Lyle has chartered out its ships in dollars, it has fixed dollar revenues. By financing its ship purchases with dollars, Lyle can offset these contractual dollar inflows with contractual dollar outflows.
Accountants will note that Lyle bears significant translation exposure. As the dollar rises against the pound, Lyle will show losses on its dollar debt and vice versa when the dollar falls. But gains or losses on the debts will be canceled out over time by changes in its operating cash flows. In 1984, when the dollar rose, its chairman pointed out that "Although foreign exchange losses have now been provided for in full on all loans and leases as if they had been repayable at 30 June 1984, it must be borne in mind that these are secured against ships chartered out at fixed freight rates, the U.S. dollar income from which will be sufficient to service both the interest and capital on the underlying loans. This future income will offset the exchange losses now provided for."
13. In 1985, Japan Airlines (JAL) bought $3 billion of foreign exchange contracts at ¥180/$1 over 11 years to hedge its purchases of U.S. aircraft. By 1994, with the yen at about ¥100/$1, JAL had incurred more than $1 billion in cumulative foreign exchange losses on that deal.
a. What was the economic rationale behind JAL's hedges?
Answer. Most likely, JAL had signed contracts to take delivery of planes in the future and was using forward contracts to protect itself against a rise in the value of the dollar that would increase the yen cost of buying the planes. Alternatively, the forward contracts could have been used to hedge purchases of U.S. planes financed by borrowing dollars.
b. Did JAL's forward contracts constitute an economic hedge? That is, is it likely that JAL's losses on its forward contracts were offset by currency gains on its operations?
Answer. The answer to this question depends on whether JAL's yen operating profits are negatively correlated with the yen's value. If a stronger yen means lower yen operating profits, then these forward contracts would constitute an economic hedge. Some factors to consider in deciding whether this is likely to be the case are as follows. First, a good part of JAL's costs are for Japanese flight crews, whose pay is denominated and determined in yen. To the extent that fares are determined in dollars (in part because JAL is competing with U.S. airlines, JAL's yen profits will vary inversely with the yen's value). At the same time, a stronger yen will induce more Japanese to travel to the U.S. but fewer Americans to visit Japan, increasing outbound volume but reducing inbound volume. Where the balance lies is an empirical question. It turns out that JAL has been hurt by yen appreciation and is now looking to cut costs, primarily by reducing its Japanese work force through job buyouts and hiring foreigners. It has also focused more on serving leisure travelers since the yen's strength has led unprecedented numbers of Japanese tourists to travel abroad.
16. In 1990, a Japanese investor paid $100 million for an office building in downtown Los Angeles. At the time, the exchange rate was ¥145/$1. When the investor went to sell the building five years later, in early 1995, the exchange rate was ¥85/$1 and the building's value had collapsed to $50 million.
a. What exchange risk did the Japanese investor face at the time of his purchase?
Answer. The risk is that the value of the dollar would fall against the yen and that the dollar revenues would not keep up with the decline in the value of the dollar.
b. How could the investor have hedged his risk?
Answer. The investor could have financed his purchase of the building by borrowing dollars, so that the very same event that led to a decline in the yen value of his asset--namely, a dollar decline-- would simultaneously reduce the yen cost of the liability used to finance that asset. He could also have taken out a long-dated forward contract to hedge the yen value of his building. Nothing would have protected the investor from the decline in the building's dollar price.