Business 4079

International Financial Management Lakehead University Final Exam Suggested Answers Philippe Gr´egoire

Winter 2003

Time allowed: 3 hours. Instructions: Calculators are permitted. One 8.5 × 11 inches crib sheet is allowed. Please answer all questions in the exam booklets provided. The marks awarded for each question are in brackets. Good luck!

Part I (45 points). Answer all of the following questions. 1. (10 points) Countries that try to maintain a fixed or highly managed exchange rate may experience a currency crisis. A crisis, however, does not happen without reason. Conditions must be ripe for a crisis, such as: (i) large and growing government deficit; (ii) large and growing current account deficit; (iii) increasing inflation; (iv) large and/or growing foreign debt; (v) a slowing economy. Explain how these conditions may develop in an emerging market. Explain why these conditions make a country vulnerable to a currency crisis. Answer: (i) Large and growing government deficit How: Governments in emerging markets are usually heavily involved in building their country’s infrastructure (roads, dams, health care, etc.). They may 1

also be spending money to subsidize some industries in order to encourage their country’s development. At the same time, tax collections may be problematic (underground economy, tax evasion), which makes its difficult, if not impossible, to run a balanced budget. Why: The greater the government deficit, the less likely the latter will be able to bail out banks if ever they fail, and subsidy programs may end due to lack of money. Greater deficits may also force the government into more borrowing and it may induce the government to operate irresonsible monetary and/or fiscal policy. These factors make outside investors demand higher risk premia and/or simply pull their money out of the country. (ii) Large and growing current account deficit How: When a country’s currency is artificially maintained, some imported goods may become cheaper over time, especially goods from countries with fairly valued currencies. For example, if country A has an artificially maintained currency and country B has just devalued its currency, then goods from B are now much cheaper to inhabitants of A, who will purchase more of them. If, at the same time, B competes with A for some exported goods, then exports from A will diminish. These two effects together increase the current acount deficit. Why: An increasing current account deficit is an indication that the nominal exchange rate is not in line with demand and supply, thus opening the door to currency speculation. (iii) Increasing inflation How: This may arise because of an irresponsible monetary policy (printing money to pay off debt or to finance an election), or simply because a high expected inflation induces consumers to buy rather than to save, thus feeding the inflation problem. Why: Floating exchange rates are influenced by inflation differentials across countries. Hence, it may not be possible for a high inflation country to maintain its currency value at an artificial level for a long time, which attracts speculators. (iv) Large and/or growing foreign debt How: When investors demand a premium to hold assets in a country’s currency, interest rates may be lower outside the country. Foreign borrowing being cheaper, banks and governments tend to favour foreign debt over local debt. Why: The repayment of foreign debt becomes more costly, if not impossible, 2

to repay when a country’s currency is devalued, thus increasing the likelihood of default. (v) a slowing economy. How: This may be linked to a reduction in exports, too costly compared to another country’s exports, expecially if the latter country’s currency has just been devalued. Why: A slowing economy usually has less attractive investment opportunities and thus reduces capital inflows in the country. 2. True or False (1 point)? Explain (4 points). The balance of payments is a model developed by governments to control exchange rates. That is, if the balance of payments of a country is negative, then the government of that country will increase the exchange rate to encourage imports of goods. 3. True or False (1 point)? Explain (4 points). It has been shown empirically that purchasing power parity holds almost exactly across industrialized countries. The Big Mac Hamburger Standard, compiled by The Economist, is a living proof of that. 4. True or False (1 point)? Explain (4 points). If a country’s currency is expected to depreciate against the euro, say, and, at the same time, this country’s interest rates are lower than Germany’s interest rates, then covered and/or uncovered interest arbitrage opportunities exist. 5. True or False (1 point)? Explain (4 points). If the Japanese yen exchange rate were U125/$ at the beginning of 1998 and U100/$ at the end of 1998, then we could say that the yen has appreciated by 25% in 1998. 6. True or False (1 point)? Explain (4 points). When dealing with translation exposure, the foreign exchange loss/gain following a sudden change in exchange rates is always greater under the current-rate method than under the temporal method. 7. (5 points) Explain why competition in a firm’s home market may help the latter perform better in foreign markets. 8. True or False (1 point)? Explain (4 points). In multinational capital budgeting, a positive net present value of cash flows from the 3

project viewpoint necessarily means that the net present value of cash flows from the parent’s viewpoint is positive. Part II (55 points). Answer all of the following problems. 1. Hedging Transaction Exposure

On March 1, Redwall Pump Company sells a shipment

of pumps to Vollendam Dike Company of the Netherlands for on June 1,

E6,000, payable E2,000

E2,000 on September 1 and E2,000 on December 1. Even though the euro

has recently appreciated and is expected to appreciate in the near future, Redwall’s director of finance wonders whether the firm should hedge against a reversal of the euro trend. The spot rate on March 1 is $1.1000/E, and you have the following information about hedging instruments: (i) The 3-month forward exchange rate quote is $1.1060/E, the 6-month forward quote is $1.1100/E and the 9-month forward quote is $1.1140/E.

(ii) Redwall can borrow euros from the Frankfurt branch of its bank at 8% per annum. (iii) June put options are available at a strike price of $1.1000/E for a premium of 2%

per contract, September put options are available at $1.1000/E for a premium of 1.2%, and December put options are available at $1.1000/E for a premium of 0.7%.

(iv) Redwall can purchase June call options at a strike price of $1.1000/E for a premium of 3%, September call options at $1.1000/E for a 3.2% premium, and December call options at $1.1000/E for a 3.5% premium.

Redwall estimates its cost of equity capital to be 12% per annum, and is unable to raise funds with long-term debt. The average T-bills yield is 3.6% per annum. (a) (4 points) Describe how Redwall can hedge against a reversal of the euro trend using forward contracts. What is the present value (as of March 1) of this hedge? What is its future value (as of December 1)? Answer: Using forward contracts and discounting at Redwall’s cost of capital (which is 3% quarterly), we find a forward hedging present value of 2, 000 × 1.1060 2, 000 × 1.1100 2, 000 × 1.1140 + + = $6, 279.07. 2 1.03 (1.03) (1.03)3 On the other hand, the future value of this hedging strategy is 2, 000×1.1060×(1.03)2 + 2, 000×1.1100×(1.03)1 + 2, 000×1.1140 = $6, 861.31. 4

(b) (4 points) Describe how Redwall can hedge against a reversal of the euro trend using a money market hedge. What is the present value of this hedge? What is its future value? Answer: Under a money market hedge, Redwall would borrow today and invest the proceeds in its firm, and the loan would be such that the euro payments of Vollendam would pay it off completely. Redwall can borrow euros at 8% per annum, which means 2% quarterly. Hence, the loan that can be repaid with

E2,000 each quarter is

2, 000 2, 000 2, 000 + + = 2 1.02 (1.02) (1.02)3

E5,767.77.

Tranlsating this amount in dollars using the spot rate of $1.1000/E, we obtain 5, 767.77 × 1.1000 = $6, 344.54, which is the present value of this hedge. If this money is invested in the firm, it will earn 3% quarterly and thus its value on December 1 will be 6, 344.54 × (1.03)3 = $6, 932.85. (c) (4 points) Describe how Redwall can hedge against a reversal of the euro trend using an options market hedge. What is the present value of this hedge? What is its future value? Answer: Redwall will receive euros and will be willing to resell them, and thus it needs to purchase put options in order to protect itself. The cost of each option is June put option:

2, 000 × 0.020 × 1.1000 = $44.00,

September put option: 2, 000 × 0.012 × 1.1000 = $26.40, December put option:

2, 000 × 0.007 × 1.1000 = $15.40.

Let VJ , VS and VD denote the value of the June, September and December put option, respectively, on June 1, September 1 and December 1. Let also SJ , SS and SD denote the spot exchange rate on June 1, September 1 and December 1, respectively. Then E[VJ ] = max { $2, 200 , $2, 000 × E[SJ ] } , E[VS ] = max { $2, 200 , $2, 000 × E[SS ] } , E[VD ] = max { $2, 200 , $2, 000 × E[SD ] } , 5

where E[·] means “expected value”. The present value of the options hedge (PVOH) is therefore PVOH =

E[VJ ] E[VS ] E[VS ] + + − $85.80, 2 1.03 (1.03) (1.03)3

and its future value is PVOH × (1.03)3 . (d) (3 points) What do you recommend to Redwall? Explain. Answer: First note that the forward hedge is definitely superior to the money market hedge, due to the steady increase in the forward rate from June to December, and also due to the little difference between Redwall’s borrowing rate and its WACC. According to the forward rates, there is no sign of a reversal of the euro trend and thus leaving the transaction unhedged may prove better than entering forward contracts. If, however, a reversal were to occur, it would likely be due to some highly unexpected event that may create some turmoil in foreign exchange markets. This implies an increase the volatility of exchange rates, and thus greater option values. Hence, purchasing put options seems reasonable in the present case. 2. Interest Rate Hedging

Using the information given in table 1 about government

zero-coupon bonds, answer the following questions. Maturity

Bond Yield

Bond Price

1 year

5.00%

0.952381

2 years

5.50%

0.898452

3 years

6.00%

0.839619

Table 1: Information on risk-free, zero-coupon, bonds. (a) (2 points) Compute the implied forward rate from year 1 to year 2 and the implied forward rate from year 2 to year 3. Answer: Let r0 (t1 , t2 ) denote the rate of interest (implied or actual), as of time 0, from year t1 to year t2 . The implied forward rates we are looking for are then denoted r0 (1, 2) and r0 (2, 3), and are such that (1 + r0 (0, 1))(1 + r0 (1, 2)) = (1 + r0 (0, 2))2 , (1 + r0 (0, 2))2 (1 + r0 (2, 3)) = (1 + r0 (0, 3))3 . 6

This gives us r0 (1, 2) =

(1 + r0 (0, 2))2 p0 (0, 1) − 1 = − 1, 1 + r0 (0, 1) p0 (0, 2)

r0 (2, 3) =

(1 + r0 (0, 3))3 p0 (0, 2) − 1, − 1 = 2 (1 + r0 (0, 2)) p0 (0, 3)

where p0 (t1 , t2 ) is the price as of time 0 of a zero-coupon bond issued in year t1 and that matures in year t2 . Hence, r0 (1, 2) =

p0 (0, 1) 0.952381 − 1 = − 1 = 6.00%, p0 (0, 2) 0.898452

r0 (2, 3) =

p0 (0, 2) 0.898452 − 1 = − 1 = 7.01%. p0 (0, 3) 0.839619

(b) (4 points) Suppose that XYZ Corporation has $100 of floating-rate debt with 3 years to maturity at LIBOR, meaning that every year XYZ pays that year’s current LIBOR. The rate that will prevail for the first year has already been set to 5% and thus is not random. On the other hand, the rates that will prevail in years 2 and 3, denoted r˜2 and r˜3 , will be determined by future market conditions and thus cannot be known in advance. XYZ would rather have fixed-rate debt and thus decides to enter into an interest rate swap agreement. Assuming that competition between swap dealers is such that the swap agreement has a zero net present value, what will be the fixed rate of interest demanded by the swap dealer? Answer: (The following calculations are on a per-dollar basis) Let R denote the fixed rate of interest that the swap dealer will charge to XYZ. Under the swap agreement, XYZ will pay R to the swap dealer each period, and the latter will pay r˜t to XYZ in year t. The swap dealer can hedge its position by entering forward rate agreements, where the forward rates would be as found in (a), i.e. 6.00% in year 2 and 7.01% in year 3. Under forward rate agreements, the swap would receive r˜2 − r0 (1, 2) in year 2 and r˜3 − r0 (2, 3) in year 3 (the interest rate in the first year being known, we don’t have to worry about it). The swap dealer’s cash inflow is then R − r0 (0, 1) in year 1, R − r0 (1, 2) in year 2, and R − r0 (2, 3) in year 3, and the present value of all these cash flows is 3 X R − r0 (0, 1) R − r0 (1, 2) R − r0 (2, 3) + + = p0 (0, t) (R − r0 (t − 1, t)) . 1 + r0 (0, 1) (1 + r0 (0, 2))2 (1 + r0 (0, 3))3 t=1

7

Competition among swap dealers implies that this present value is equal to zero, and thus 3 X

P3 p0 (0, t) (R − r0 (t − 1, t)) = 0

⇒

R =

t=1

t=1

p0 (0, t)r0 (t − 1, t) . P3 t=1 p0 (0, t)

The rate charged by the swap dealer is therefore R =

0.952381 × 0.0500 + 0.898452 × 0.0600 + 0.839619 × 0.0701 = 5.96%. 0.952381 + 0.898452 + 0.839619

(c) (2 points) Explain how XYZ can hedge its interest rate exposure with forward rate agreements. Answer: Using the forward described above, XYZ could enter contracts that would pay r˜2 − r0 (1, 2) per dollar in year 2, and r˜3 − r0 (2, 3) per dollar in year 3, which is just what the swap dealer did in (b). Hence, if r˜t is actually greater than expected, i.e. greater than r0 (t − 1, t), t = 1, 2, XYZ receives money from the forward rate agreement that compensates for the higher interest payment it has to make on its loan. If, on the other hand, r˜t is lower than expected, then XYZ loses money on its forward rate agreement but is better off with respect to its loan payment. If fact, if the notional principal in the forward rate agreements is the amount of the loan, the rate paid in years 2 and 3 is r0 (1, 2) and r0 (2, 3), respectively. (d) (2 points) Explain how XYZ can hedge its interest rate exposure using Eurodollar contracts. Answer: Since XYZ is hurt on its loan contract when interest rates increase, it must choose hedging instruments that pay off when interest rates rises. In terms, of Eurodollar futures, XYZ has to sell futures contracts in order to hedge against the interest rate risk of its loan contract. 3. Translation Exposure

Table 2 provides the balance sheets as of December 31, 1993,

and December 31, 1994, of Click Enterprises, a wholly-owned subsidiary of a Canadian multinational corporation operating in Poland, and Table 3 represents Click’s 1994 income statement (note that there was no depreciation in 1994). All amounts are shown in millions of zloty, the local currency. Click has been acquired on Decenber 31, 1993, when the exchange rate was $0.50/zloty. The average exchange rate for 1994 was $0.48/zloty, and the exchange rate on December 31, 1994, was $0.45/zloty.

8

Click Enterprises of Poland 1993 and 1994 Balance Sheets Assets

Liabilities

1993

1994

1993

1994

50

100

Payables

100

200

Receivables

100

200

Long-Term Debt

400

500

Inventory

150

200

Common Stock

200

200

Net fixed assets

500

700

Retained Earnings

100

300

Total

800

1,200

Total

800

1,200

Cash

Table 2: Balance sheets for Problem 3. Click Enterprises of Poland 1994 Income Statement Revenues

1,000

Cost of goods sold

(500)

Other expenses

(300)

Net income

200

Table 3: Income statement for Problem 3. (a) (4 points) Assuming that the subsidiary in Poland is self-contained and that Poland is not considered a high inflation country, show the conversion to Canadian dollars of each financial statement. Answer: When the subsidiary is self-contained, the financial statements are translated using the current-rate method, which is what is done in tables 4 and 5. With the current-rate method, all items on the income statement are translated at the average exchange rate for 1994, which is $0.48/zloty, all assets and liabilities are translated at the rate prevailing on the balance sheet date, i.e. $0.50 for the 1993 entries and $0.45/zloty for the 1994 entries. Since the subsidiary has been acquired on December 31, 1993, retained earnings for 1993 are translated at the rate $0.50/zloty, and common stock is translated at the rate $0.50/zloty for both 1993 and 1994. (b) (4 points) Suppose now that, on December 31, 1994, Poland had experienced more than 100 percent inflation over the previous three years. Show the conversion to Canadian dollars of each financial statement. Answer: In this case, we have to translate using the temporal method. In this

9

Click Enterprises of Poland 1993 and 1994 Balance Sheets Assets

Liabilities

1993

1994

Cash

25

45

Payables

Receivables

50

90

Inventory

75

90

250

315

Net fixed assets Total

1994

50

90

Long-Term Debt

200

225

Common Stock

100

100

50

146

CTA

0

(21)

Total

400

540

Retained Earnings

540

400

1993

Table 4: Click’s balance sheets, current-rate translation. Click Enterprises of Poland 1994 Income Statement Revenues

480

Cost of goods sold

(240)

Other expenses

(144)

Net income

96

Table 5: Click’s income statement, current-rate translation. case, we have to be careful with fixed assets, costs of goods sold and inventory. Let’s do these one by one (i) Fixed Assets

In the 1993 balance sheet, fixed assets are translated at the

rate $0.50/zloty, the rate prevailing when the subsidiary was acquired. This gives us 500 × 0.50 = $250. In the 1994 balance sheet, we have $500 of 1993 assets and 700 − 500 = $200 of assets that have been acquired in 1994, and that will be translated at the 1994 average exchange rate. Hence, net fixed assets for 1994 are 500 × 0.050 + (700 − 500) × 0.48 = $346. (ii) Costs of Goods Sold COGS were 500 (amount in zlotys) in 1994. From this amount, 150 was taken from the firm’s inventory on Dec. 31, 1993, and is thus translated at the rate $0.50/zloty. The remaining amount, 500 − 150 = 350 has been purchased in 1994 and is thus translated at the 1994 average

10

exchange rate, i.e. $0.48/zloty. Translated 1994 COGS are then 150 × $0.50/zloty + 350 × $0.48/zloty = $243. (iii) Inventory For 1993, inventory is translated at its historical rate of $0.50/zloty, which gives $75. For 1994, we first need to find 1994 purchases, which are 200 + 500 − 150 = 550 zlotys. |{z} |{z} |{z} 1994 inv. 1993 inv. 1994 COGS 1994 purchases are translated at the 1994 average exchange rate, $0.48/zloty, so translated 1994 inventory is obtained as follows: 243 = $96. 75 + 550 |{z} |{z} {z0.48} − | × tr. 1993 inv. tr. 2002 COGS tr. 1994 pur. Regarding the remaining items, all monetary assets and liabilities are translated at the rate prevailing on the balance sheet date, while retained earnings include any imbalance, the difference being noted on the income statement. This is shown in tables 6 and 7. Click Enterprises of Poland 1993 and 1994 Balance Sheets Assets

Liabilities

1993

1994

Cash

25

45

Payables

1993

1994

50

90

Receivables

50

90

Long-Term Debt

200

225

Inventory

75

96

Common Stock

100

100

Net fixed assets

250

346

Retained Earnings

50

162

Total

400

577

Total

400

577

Table 6: Click’s balance sheets, temporal translation. (c) (4 points) What is Click’s translation exposure, in each year, under each method? Show how to calculate the translation gain or loss, for 1994, under each translation method, using the values obtained for Click’s translation exposure. Answer: (i) Current-Rate Method Under the current-rate method, translation exposure is net assets (N A). Let Si and S¯i denote the exchange rate on year i’s balance sheet date and the average exchange rate during year i, respectively, and let 11

Click Enterprises of Poland 1994 Income Statement Revenues

480

Cost of goods sold

(243)

Other expenses

(144)

Net income

93

Adjustment

19

Adj. net income

112

Table 7: Click’s income statement, temporal translation. N Ai = Ai − Li and ∆N Ai,i+1 denote net assets in year i’s balance sheet and the change in net assets from year i to year i + 1, respectively. Under the current-rate method, the translation gain for year i, denoted T Gi , is given by T Gi = Si − Si−1 N Ai−1 + Si − S¯i ∆N Ai−1,i . Note that this gives the change in CTA, not the CTA balance, except for the first year of operations. The translation gain in the present example is T G1994 = S1994 − S1993 N A1993 + S1994 − S¯1994 ∆N A1993,1994 = (0.45 − 0.50)(800 − 500}) + (0.45 − 0.48)(1, 200 − 700 − 300) | {z | {z } =300

=200

= −0.05 × 300 − 0.03 × 200 = −21. (ii) Temporal Method Under the temporal method, translation exposure is net monetary assets (N M A). As before, let Si and S¯i denote the exchange rate on year i’s balance sheet date and the average exchange rate during year i, respectively, and let N M Ai = M Ai − M Li and ∆N M Ai,i+1 denote net monetary assets in year i’s balance sheet and the change in net monetary assets from year i to year i + 1, respectively. Under the temporal method, the translation gain for year i, denoted T Gi , is given by T Gi = Si − Si−1 N M Ai−1 + Si − S¯i ∆N M Ai−1,i . In the present example, we have N M A1993 = 50 + 100 − 500 = − 350, N M A1994 = 100 + 200 − 700 = − 400, ∆N M A1993,1994 = − 400 − (−350) = − 50, 12

and thus the translation gain for 1994 is T G1994 =

S1994 − S1993 N M A1993 +

S1994 − S¯1994 ∆N M A1993,1994

= (0.45 − 0.50)(−350) + (0.45 − 0.48)(−50) = $19. (d) (3 points) Suppose now that, on January 1, 1995, the exchange rate suddenly jumps to $0.47/zloty. What is the gain or loss associated with this change under each translation method? Answer: Translation at the end of 1994 is 200 zlotys under the current-rate method and −400 zlotys under the temporal method. If the exchange rate increases by $0.02/zloty, the gain is 200 × 0.02 =

$4 under the current-rate method,

−400 × 0.02 = −$8 under the temporal method. 4. Covered Interest Arbitrage

Here are some prices in the international money market:

Spot rate = $0.75/DM; forward rate (one year) = $0.77/DM; interest rate in DM is 7% per year; interest rate in $ is 9% per year. (a) (4 points) Assuming no transaction costs, do covered arbitrage opportunities exist in the above situation? Describe the flows. Answer: Investing (resp. borrowing) $1 in Germany returns (resp. costs) 1 × 1.07 × 0.77 − 1 = $0.0985 0.75 with certainty after one year. On the other hand, investing (resp. borrowing) $1 in the U.S. returns (resp. costs) $0.09 per year. It is therefore possible to make a riskless profit of 0.0985 − 0.0900 = $0.0085 per dollar by borrowing in the U.S. and investing the proceeds in Germany. This arbitrage opportunity exists because the percent increase in the value of the DM,

0.77 − 0.75 = 2.67%, 0.75 is greater than the interest rate differential of 1.09 − 1.07 = 1.87% 1.07 13

between Germany and the U.S.. That is, investing in Germany returns more than the cost of borrowing in the U.S. because the deutschmark appreciation outweighs the interest rate differential. (b) (4 points) Suppose now that transaction costs in the foreign exchange market equal 0.35% per transaction. Do covered arbitrage opportunities still exist in this case? If so, describe the flows. Answer: In this case, investing $1 in Germany returns 1 × 0.9965 × 1.07 × 0.77 × 0.9965 − 1 = $0.0908, 0.75 which is still greater than what needs to be repaid if the dollar is borrowed in the U.S.. Thus arbitrage opportunities still exist. 5. Futures and Options (a) (4 points) On Monday morning, an investor takes a short position in a DM futures contract. The agreed-upon price is $0.6370 for DM 125,000. The initial margin requirement for a DM contract is $1,080 and the maintenance margin requirement is $800. At the close of trading on Monday, the futures price rises to $0.6460. At Tuesday close, the price falls to $0.6390. At Wednesday close, the price falls further to $0.6320 and the investor closes his position. Detail the daily settlement process, including margin calls, if any. What is the investor’s profit or loss? There are no transaction costs. Answer: (i) Monday close: The investors loses 125, 000 × (0.6460 − 0.6370) = $1, 125. The initial margin being $1,080, the investor’s account shows a deficit of $45. With a maintenance margin requirement of $800, this means that the investor receives a margin call of $845. (ii) Tuesday close: The investor gains 125, 000 × (0.6460 − 0.6390) = $875. The investor now has $1,675 in his account and there is no margin call. 14

(iii) Wednesday close: The investor gains 125, 000 × (0.6390 − 0.6320) = $875. The investor now has $2,550 in his account, which is closed by an offsetting contract. The investor’s profit is 2, 550 − 1, 080 = $1, 470. (b) (3 points) A trader simultaneously purchases a put option on the yen with strike price $0.0103/U for 2.81 hundredths of cent per yen, and sells a put option with strike price $0.0101/U for 1.6 hundredths of cent per yen. The two options have the same expiration date. Derive the trader’s profit as a function of the exchange rate that will prevail when the two options expire. Answer: Let ST denote the spot exchange rate (in 100th of cents per yen) at the expiration date. The trader’s profit (in 100th of cents per yen) at the expiration date, π, is then

π =

103 − 101 − 1.21 = 0.79

if ST < 101,

103 − S − 1.21 = 101.79 − S if 101 < S ≤ 103, −1.21

15

if S > 103.

International Financial Management Lakehead University Final Exam Suggested Answers Philippe Gr´egoire

Winter 2003

Time allowed: 3 hours. Instructions: Calculators are permitted. One 8.5 × 11 inches crib sheet is allowed. Please answer all questions in the exam booklets provided. The marks awarded for each question are in brackets. Good luck!

Part I (45 points). Answer all of the following questions. 1. (10 points) Countries that try to maintain a fixed or highly managed exchange rate may experience a currency crisis. A crisis, however, does not happen without reason. Conditions must be ripe for a crisis, such as: (i) large and growing government deficit; (ii) large and growing current account deficit; (iii) increasing inflation; (iv) large and/or growing foreign debt; (v) a slowing economy. Explain how these conditions may develop in an emerging market. Explain why these conditions make a country vulnerable to a currency crisis. Answer: (i) Large and growing government deficit How: Governments in emerging markets are usually heavily involved in building their country’s infrastructure (roads, dams, health care, etc.). They may 1

also be spending money to subsidize some industries in order to encourage their country’s development. At the same time, tax collections may be problematic (underground economy, tax evasion), which makes its difficult, if not impossible, to run a balanced budget. Why: The greater the government deficit, the less likely the latter will be able to bail out banks if ever they fail, and subsidy programs may end due to lack of money. Greater deficits may also force the government into more borrowing and it may induce the government to operate irresonsible monetary and/or fiscal policy. These factors make outside investors demand higher risk premia and/or simply pull their money out of the country. (ii) Large and growing current account deficit How: When a country’s currency is artificially maintained, some imported goods may become cheaper over time, especially goods from countries with fairly valued currencies. For example, if country A has an artificially maintained currency and country B has just devalued its currency, then goods from B are now much cheaper to inhabitants of A, who will purchase more of them. If, at the same time, B competes with A for some exported goods, then exports from A will diminish. These two effects together increase the current acount deficit. Why: An increasing current account deficit is an indication that the nominal exchange rate is not in line with demand and supply, thus opening the door to currency speculation. (iii) Increasing inflation How: This may arise because of an irresponsible monetary policy (printing money to pay off debt or to finance an election), or simply because a high expected inflation induces consumers to buy rather than to save, thus feeding the inflation problem. Why: Floating exchange rates are influenced by inflation differentials across countries. Hence, it may not be possible for a high inflation country to maintain its currency value at an artificial level for a long time, which attracts speculators. (iv) Large and/or growing foreign debt How: When investors demand a premium to hold assets in a country’s currency, interest rates may be lower outside the country. Foreign borrowing being cheaper, banks and governments tend to favour foreign debt over local debt. Why: The repayment of foreign debt becomes more costly, if not impossible, 2

to repay when a country’s currency is devalued, thus increasing the likelihood of default. (v) a slowing economy. How: This may be linked to a reduction in exports, too costly compared to another country’s exports, expecially if the latter country’s currency has just been devalued. Why: A slowing economy usually has less attractive investment opportunities and thus reduces capital inflows in the country. 2. True or False (1 point)? Explain (4 points). The balance of payments is a model developed by governments to control exchange rates. That is, if the balance of payments of a country is negative, then the government of that country will increase the exchange rate to encourage imports of goods. 3. True or False (1 point)? Explain (4 points). It has been shown empirically that purchasing power parity holds almost exactly across industrialized countries. The Big Mac Hamburger Standard, compiled by The Economist, is a living proof of that. 4. True or False (1 point)? Explain (4 points). If a country’s currency is expected to depreciate against the euro, say, and, at the same time, this country’s interest rates are lower than Germany’s interest rates, then covered and/or uncovered interest arbitrage opportunities exist. 5. True or False (1 point)? Explain (4 points). If the Japanese yen exchange rate were U125/$ at the beginning of 1998 and U100/$ at the end of 1998, then we could say that the yen has appreciated by 25% in 1998. 6. True or False (1 point)? Explain (4 points). When dealing with translation exposure, the foreign exchange loss/gain following a sudden change in exchange rates is always greater under the current-rate method than under the temporal method. 7. (5 points) Explain why competition in a firm’s home market may help the latter perform better in foreign markets. 8. True or False (1 point)? Explain (4 points). In multinational capital budgeting, a positive net present value of cash flows from the 3

project viewpoint necessarily means that the net present value of cash flows from the parent’s viewpoint is positive. Part II (55 points). Answer all of the following problems. 1. Hedging Transaction Exposure

On March 1, Redwall Pump Company sells a shipment

of pumps to Vollendam Dike Company of the Netherlands for on June 1,

E6,000, payable E2,000

E2,000 on September 1 and E2,000 on December 1. Even though the euro

has recently appreciated and is expected to appreciate in the near future, Redwall’s director of finance wonders whether the firm should hedge against a reversal of the euro trend. The spot rate on March 1 is $1.1000/E, and you have the following information about hedging instruments: (i) The 3-month forward exchange rate quote is $1.1060/E, the 6-month forward quote is $1.1100/E and the 9-month forward quote is $1.1140/E.

(ii) Redwall can borrow euros from the Frankfurt branch of its bank at 8% per annum. (iii) June put options are available at a strike price of $1.1000/E for a premium of 2%

per contract, September put options are available at $1.1000/E for a premium of 1.2%, and December put options are available at $1.1000/E for a premium of 0.7%.

(iv) Redwall can purchase June call options at a strike price of $1.1000/E for a premium of 3%, September call options at $1.1000/E for a 3.2% premium, and December call options at $1.1000/E for a 3.5% premium.

Redwall estimates its cost of equity capital to be 12% per annum, and is unable to raise funds with long-term debt. The average T-bills yield is 3.6% per annum. (a) (4 points) Describe how Redwall can hedge against a reversal of the euro trend using forward contracts. What is the present value (as of March 1) of this hedge? What is its future value (as of December 1)? Answer: Using forward contracts and discounting at Redwall’s cost of capital (which is 3% quarterly), we find a forward hedging present value of 2, 000 × 1.1060 2, 000 × 1.1100 2, 000 × 1.1140 + + = $6, 279.07. 2 1.03 (1.03) (1.03)3 On the other hand, the future value of this hedging strategy is 2, 000×1.1060×(1.03)2 + 2, 000×1.1100×(1.03)1 + 2, 000×1.1140 = $6, 861.31. 4

(b) (4 points) Describe how Redwall can hedge against a reversal of the euro trend using a money market hedge. What is the present value of this hedge? What is its future value? Answer: Under a money market hedge, Redwall would borrow today and invest the proceeds in its firm, and the loan would be such that the euro payments of Vollendam would pay it off completely. Redwall can borrow euros at 8% per annum, which means 2% quarterly. Hence, the loan that can be repaid with

E2,000 each quarter is

2, 000 2, 000 2, 000 + + = 2 1.02 (1.02) (1.02)3

E5,767.77.

Tranlsating this amount in dollars using the spot rate of $1.1000/E, we obtain 5, 767.77 × 1.1000 = $6, 344.54, which is the present value of this hedge. If this money is invested in the firm, it will earn 3% quarterly and thus its value on December 1 will be 6, 344.54 × (1.03)3 = $6, 932.85. (c) (4 points) Describe how Redwall can hedge against a reversal of the euro trend using an options market hedge. What is the present value of this hedge? What is its future value? Answer: Redwall will receive euros and will be willing to resell them, and thus it needs to purchase put options in order to protect itself. The cost of each option is June put option:

2, 000 × 0.020 × 1.1000 = $44.00,

September put option: 2, 000 × 0.012 × 1.1000 = $26.40, December put option:

2, 000 × 0.007 × 1.1000 = $15.40.

Let VJ , VS and VD denote the value of the June, September and December put option, respectively, on June 1, September 1 and December 1. Let also SJ , SS and SD denote the spot exchange rate on June 1, September 1 and December 1, respectively. Then E[VJ ] = max { $2, 200 , $2, 000 × E[SJ ] } , E[VS ] = max { $2, 200 , $2, 000 × E[SS ] } , E[VD ] = max { $2, 200 , $2, 000 × E[SD ] } , 5

where E[·] means “expected value”. The present value of the options hedge (PVOH) is therefore PVOH =

E[VJ ] E[VS ] E[VS ] + + − $85.80, 2 1.03 (1.03) (1.03)3

and its future value is PVOH × (1.03)3 . (d) (3 points) What do you recommend to Redwall? Explain. Answer: First note that the forward hedge is definitely superior to the money market hedge, due to the steady increase in the forward rate from June to December, and also due to the little difference between Redwall’s borrowing rate and its WACC. According to the forward rates, there is no sign of a reversal of the euro trend and thus leaving the transaction unhedged may prove better than entering forward contracts. If, however, a reversal were to occur, it would likely be due to some highly unexpected event that may create some turmoil in foreign exchange markets. This implies an increase the volatility of exchange rates, and thus greater option values. Hence, purchasing put options seems reasonable in the present case. 2. Interest Rate Hedging

Using the information given in table 1 about government

zero-coupon bonds, answer the following questions. Maturity

Bond Yield

Bond Price

1 year

5.00%

0.952381

2 years

5.50%

0.898452

3 years

6.00%

0.839619

Table 1: Information on risk-free, zero-coupon, bonds. (a) (2 points) Compute the implied forward rate from year 1 to year 2 and the implied forward rate from year 2 to year 3. Answer: Let r0 (t1 , t2 ) denote the rate of interest (implied or actual), as of time 0, from year t1 to year t2 . The implied forward rates we are looking for are then denoted r0 (1, 2) and r0 (2, 3), and are such that (1 + r0 (0, 1))(1 + r0 (1, 2)) = (1 + r0 (0, 2))2 , (1 + r0 (0, 2))2 (1 + r0 (2, 3)) = (1 + r0 (0, 3))3 . 6

This gives us r0 (1, 2) =

(1 + r0 (0, 2))2 p0 (0, 1) − 1 = − 1, 1 + r0 (0, 1) p0 (0, 2)

r0 (2, 3) =

(1 + r0 (0, 3))3 p0 (0, 2) − 1, − 1 = 2 (1 + r0 (0, 2)) p0 (0, 3)

where p0 (t1 , t2 ) is the price as of time 0 of a zero-coupon bond issued in year t1 and that matures in year t2 . Hence, r0 (1, 2) =

p0 (0, 1) 0.952381 − 1 = − 1 = 6.00%, p0 (0, 2) 0.898452

r0 (2, 3) =

p0 (0, 2) 0.898452 − 1 = − 1 = 7.01%. p0 (0, 3) 0.839619

(b) (4 points) Suppose that XYZ Corporation has $100 of floating-rate debt with 3 years to maturity at LIBOR, meaning that every year XYZ pays that year’s current LIBOR. The rate that will prevail for the first year has already been set to 5% and thus is not random. On the other hand, the rates that will prevail in years 2 and 3, denoted r˜2 and r˜3 , will be determined by future market conditions and thus cannot be known in advance. XYZ would rather have fixed-rate debt and thus decides to enter into an interest rate swap agreement. Assuming that competition between swap dealers is such that the swap agreement has a zero net present value, what will be the fixed rate of interest demanded by the swap dealer? Answer: (The following calculations are on a per-dollar basis) Let R denote the fixed rate of interest that the swap dealer will charge to XYZ. Under the swap agreement, XYZ will pay R to the swap dealer each period, and the latter will pay r˜t to XYZ in year t. The swap dealer can hedge its position by entering forward rate agreements, where the forward rates would be as found in (a), i.e. 6.00% in year 2 and 7.01% in year 3. Under forward rate agreements, the swap would receive r˜2 − r0 (1, 2) in year 2 and r˜3 − r0 (2, 3) in year 3 (the interest rate in the first year being known, we don’t have to worry about it). The swap dealer’s cash inflow is then R − r0 (0, 1) in year 1, R − r0 (1, 2) in year 2, and R − r0 (2, 3) in year 3, and the present value of all these cash flows is 3 X R − r0 (0, 1) R − r0 (1, 2) R − r0 (2, 3) + + = p0 (0, t) (R − r0 (t − 1, t)) . 1 + r0 (0, 1) (1 + r0 (0, 2))2 (1 + r0 (0, 3))3 t=1

7

Competition among swap dealers implies that this present value is equal to zero, and thus 3 X

P3 p0 (0, t) (R − r0 (t − 1, t)) = 0

⇒

R =

t=1

t=1

p0 (0, t)r0 (t − 1, t) . P3 t=1 p0 (0, t)

The rate charged by the swap dealer is therefore R =

0.952381 × 0.0500 + 0.898452 × 0.0600 + 0.839619 × 0.0701 = 5.96%. 0.952381 + 0.898452 + 0.839619

(c) (2 points) Explain how XYZ can hedge its interest rate exposure with forward rate agreements. Answer: Using the forward described above, XYZ could enter contracts that would pay r˜2 − r0 (1, 2) per dollar in year 2, and r˜3 − r0 (2, 3) per dollar in year 3, which is just what the swap dealer did in (b). Hence, if r˜t is actually greater than expected, i.e. greater than r0 (t − 1, t), t = 1, 2, XYZ receives money from the forward rate agreement that compensates for the higher interest payment it has to make on its loan. If, on the other hand, r˜t is lower than expected, then XYZ loses money on its forward rate agreement but is better off with respect to its loan payment. If fact, if the notional principal in the forward rate agreements is the amount of the loan, the rate paid in years 2 and 3 is r0 (1, 2) and r0 (2, 3), respectively. (d) (2 points) Explain how XYZ can hedge its interest rate exposure using Eurodollar contracts. Answer: Since XYZ is hurt on its loan contract when interest rates increase, it must choose hedging instruments that pay off when interest rates rises. In terms, of Eurodollar futures, XYZ has to sell futures contracts in order to hedge against the interest rate risk of its loan contract. 3. Translation Exposure

Table 2 provides the balance sheets as of December 31, 1993,

and December 31, 1994, of Click Enterprises, a wholly-owned subsidiary of a Canadian multinational corporation operating in Poland, and Table 3 represents Click’s 1994 income statement (note that there was no depreciation in 1994). All amounts are shown in millions of zloty, the local currency. Click has been acquired on Decenber 31, 1993, when the exchange rate was $0.50/zloty. The average exchange rate for 1994 was $0.48/zloty, and the exchange rate on December 31, 1994, was $0.45/zloty.

8

Click Enterprises of Poland 1993 and 1994 Balance Sheets Assets

Liabilities

1993

1994

1993

1994

50

100

Payables

100

200

Receivables

100

200

Long-Term Debt

400

500

Inventory

150

200

Common Stock

200

200

Net fixed assets

500

700

Retained Earnings

100

300

Total

800

1,200

Total

800

1,200

Cash

Table 2: Balance sheets for Problem 3. Click Enterprises of Poland 1994 Income Statement Revenues

1,000

Cost of goods sold

(500)

Other expenses

(300)

Net income

200

Table 3: Income statement for Problem 3. (a) (4 points) Assuming that the subsidiary in Poland is self-contained and that Poland is not considered a high inflation country, show the conversion to Canadian dollars of each financial statement. Answer: When the subsidiary is self-contained, the financial statements are translated using the current-rate method, which is what is done in tables 4 and 5. With the current-rate method, all items on the income statement are translated at the average exchange rate for 1994, which is $0.48/zloty, all assets and liabilities are translated at the rate prevailing on the balance sheet date, i.e. $0.50 for the 1993 entries and $0.45/zloty for the 1994 entries. Since the subsidiary has been acquired on December 31, 1993, retained earnings for 1993 are translated at the rate $0.50/zloty, and common stock is translated at the rate $0.50/zloty for both 1993 and 1994. (b) (4 points) Suppose now that, on December 31, 1994, Poland had experienced more than 100 percent inflation over the previous three years. Show the conversion to Canadian dollars of each financial statement. Answer: In this case, we have to translate using the temporal method. In this

9

Click Enterprises of Poland 1993 and 1994 Balance Sheets Assets

Liabilities

1993

1994

Cash

25

45

Payables

Receivables

50

90

Inventory

75

90

250

315

Net fixed assets Total

1994

50

90

Long-Term Debt

200

225

Common Stock

100

100

50

146

CTA

0

(21)

Total

400

540

Retained Earnings

540

400

1993

Table 4: Click’s balance sheets, current-rate translation. Click Enterprises of Poland 1994 Income Statement Revenues

480

Cost of goods sold

(240)

Other expenses

(144)

Net income

96

Table 5: Click’s income statement, current-rate translation. case, we have to be careful with fixed assets, costs of goods sold and inventory. Let’s do these one by one (i) Fixed Assets

In the 1993 balance sheet, fixed assets are translated at the

rate $0.50/zloty, the rate prevailing when the subsidiary was acquired. This gives us 500 × 0.50 = $250. In the 1994 balance sheet, we have $500 of 1993 assets and 700 − 500 = $200 of assets that have been acquired in 1994, and that will be translated at the 1994 average exchange rate. Hence, net fixed assets for 1994 are 500 × 0.050 + (700 − 500) × 0.48 = $346. (ii) Costs of Goods Sold COGS were 500 (amount in zlotys) in 1994. From this amount, 150 was taken from the firm’s inventory on Dec. 31, 1993, and is thus translated at the rate $0.50/zloty. The remaining amount, 500 − 150 = 350 has been purchased in 1994 and is thus translated at the 1994 average

10

exchange rate, i.e. $0.48/zloty. Translated 1994 COGS are then 150 × $0.50/zloty + 350 × $0.48/zloty = $243. (iii) Inventory For 1993, inventory is translated at its historical rate of $0.50/zloty, which gives $75. For 1994, we first need to find 1994 purchases, which are 200 + 500 − 150 = 550 zlotys. |{z} |{z} |{z} 1994 inv. 1993 inv. 1994 COGS 1994 purchases are translated at the 1994 average exchange rate, $0.48/zloty, so translated 1994 inventory is obtained as follows: 243 = $96. 75 + 550 |{z} |{z} {z0.48} − | × tr. 1993 inv. tr. 2002 COGS tr. 1994 pur. Regarding the remaining items, all monetary assets and liabilities are translated at the rate prevailing on the balance sheet date, while retained earnings include any imbalance, the difference being noted on the income statement. This is shown in tables 6 and 7. Click Enterprises of Poland 1993 and 1994 Balance Sheets Assets

Liabilities

1993

1994

Cash

25

45

Payables

1993

1994

50

90

Receivables

50

90

Long-Term Debt

200

225

Inventory

75

96

Common Stock

100

100

Net fixed assets

250

346

Retained Earnings

50

162

Total

400

577

Total

400

577

Table 6: Click’s balance sheets, temporal translation. (c) (4 points) What is Click’s translation exposure, in each year, under each method? Show how to calculate the translation gain or loss, for 1994, under each translation method, using the values obtained for Click’s translation exposure. Answer: (i) Current-Rate Method Under the current-rate method, translation exposure is net assets (N A). Let Si and S¯i denote the exchange rate on year i’s balance sheet date and the average exchange rate during year i, respectively, and let 11

Click Enterprises of Poland 1994 Income Statement Revenues

480

Cost of goods sold

(243)

Other expenses

(144)

Net income

93

Adjustment

19

Adj. net income

112

Table 7: Click’s income statement, temporal translation. N Ai = Ai − Li and ∆N Ai,i+1 denote net assets in year i’s balance sheet and the change in net assets from year i to year i + 1, respectively. Under the current-rate method, the translation gain for year i, denoted T Gi , is given by T Gi = Si − Si−1 N Ai−1 + Si − S¯i ∆N Ai−1,i . Note that this gives the change in CTA, not the CTA balance, except for the first year of operations. The translation gain in the present example is T G1994 = S1994 − S1993 N A1993 + S1994 − S¯1994 ∆N A1993,1994 = (0.45 − 0.50)(800 − 500}) + (0.45 − 0.48)(1, 200 − 700 − 300) | {z | {z } =300

=200

= −0.05 × 300 − 0.03 × 200 = −21. (ii) Temporal Method Under the temporal method, translation exposure is net monetary assets (N M A). As before, let Si and S¯i denote the exchange rate on year i’s balance sheet date and the average exchange rate during year i, respectively, and let N M Ai = M Ai − M Li and ∆N M Ai,i+1 denote net monetary assets in year i’s balance sheet and the change in net monetary assets from year i to year i + 1, respectively. Under the temporal method, the translation gain for year i, denoted T Gi , is given by T Gi = Si − Si−1 N M Ai−1 + Si − S¯i ∆N M Ai−1,i . In the present example, we have N M A1993 = 50 + 100 − 500 = − 350, N M A1994 = 100 + 200 − 700 = − 400, ∆N M A1993,1994 = − 400 − (−350) = − 50, 12

and thus the translation gain for 1994 is T G1994 =

S1994 − S1993 N M A1993 +

S1994 − S¯1994 ∆N M A1993,1994

= (0.45 − 0.50)(−350) + (0.45 − 0.48)(−50) = $19. (d) (3 points) Suppose now that, on January 1, 1995, the exchange rate suddenly jumps to $0.47/zloty. What is the gain or loss associated with this change under each translation method? Answer: Translation at the end of 1994 is 200 zlotys under the current-rate method and −400 zlotys under the temporal method. If the exchange rate increases by $0.02/zloty, the gain is 200 × 0.02 =

$4 under the current-rate method,

−400 × 0.02 = −$8 under the temporal method. 4. Covered Interest Arbitrage

Here are some prices in the international money market:

Spot rate = $0.75/DM; forward rate (one year) = $0.77/DM; interest rate in DM is 7% per year; interest rate in $ is 9% per year. (a) (4 points) Assuming no transaction costs, do covered arbitrage opportunities exist in the above situation? Describe the flows. Answer: Investing (resp. borrowing) $1 in Germany returns (resp. costs) 1 × 1.07 × 0.77 − 1 = $0.0985 0.75 with certainty after one year. On the other hand, investing (resp. borrowing) $1 in the U.S. returns (resp. costs) $0.09 per year. It is therefore possible to make a riskless profit of 0.0985 − 0.0900 = $0.0085 per dollar by borrowing in the U.S. and investing the proceeds in Germany. This arbitrage opportunity exists because the percent increase in the value of the DM,

0.77 − 0.75 = 2.67%, 0.75 is greater than the interest rate differential of 1.09 − 1.07 = 1.87% 1.07 13

between Germany and the U.S.. That is, investing in Germany returns more than the cost of borrowing in the U.S. because the deutschmark appreciation outweighs the interest rate differential. (b) (4 points) Suppose now that transaction costs in the foreign exchange market equal 0.35% per transaction. Do covered arbitrage opportunities still exist in this case? If so, describe the flows. Answer: In this case, investing $1 in Germany returns 1 × 0.9965 × 1.07 × 0.77 × 0.9965 − 1 = $0.0908, 0.75 which is still greater than what needs to be repaid if the dollar is borrowed in the U.S.. Thus arbitrage opportunities still exist. 5. Futures and Options (a) (4 points) On Monday morning, an investor takes a short position in a DM futures contract. The agreed-upon price is $0.6370 for DM 125,000. The initial margin requirement for a DM contract is $1,080 and the maintenance margin requirement is $800. At the close of trading on Monday, the futures price rises to $0.6460. At Tuesday close, the price falls to $0.6390. At Wednesday close, the price falls further to $0.6320 and the investor closes his position. Detail the daily settlement process, including margin calls, if any. What is the investor’s profit or loss? There are no transaction costs. Answer: (i) Monday close: The investors loses 125, 000 × (0.6460 − 0.6370) = $1, 125. The initial margin being $1,080, the investor’s account shows a deficit of $45. With a maintenance margin requirement of $800, this means that the investor receives a margin call of $845. (ii) Tuesday close: The investor gains 125, 000 × (0.6460 − 0.6390) = $875. The investor now has $1,675 in his account and there is no margin call. 14

(iii) Wednesday close: The investor gains 125, 000 × (0.6390 − 0.6320) = $875. The investor now has $2,550 in his account, which is closed by an offsetting contract. The investor’s profit is 2, 550 − 1, 080 = $1, 470. (b) (3 points) A trader simultaneously purchases a put option on the yen with strike price $0.0103/U for 2.81 hundredths of cent per yen, and sells a put option with strike price $0.0101/U for 1.6 hundredths of cent per yen. The two options have the same expiration date. Derive the trader’s profit as a function of the exchange rate that will prevail when the two options expire. Answer: Let ST denote the spot exchange rate (in 100th of cents per yen) at the expiration date. The trader’s profit (in 100th of cents per yen) at the expiration date, π, is then

π =

103 − 101 − 1.21 = 0.79

if ST < 101,

103 − S − 1.21 = 101.79 − S if 101 < S ≤ 103, −1.21

15

if S > 103.