CHAPTER 8 MANAGEMENT OF TRANSACTION EXPOSURE ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. How would you define transaction exposure? How is it different from economic exposure? Answer: Transaction exposure is the sensitivity of realized domestic currency values of the firm’s contractual cash flows denominated in foreign currencies to unexpected changes in exchange rates. Unlike economic exposure, transaction exposure is well-defined and shortterm. 2. Discuss and compare hedging transaction exposure using the forward contract vs. money market instruments. When do the alternative hedging approaches produce the same result? Answer: Hedging transaction exposure by a forward contract is achieved by selling or buying foreign currency receivables or payables forward. On the other hand, money market hedge is achieved by borrowing or lending the present value of foreign currency receivables or payables, thereby creating offsetting foreign currency positions. If the interest rate parity is holding, the two hedging methods are equivalent. 3. Discuss and compare the costs of hedging via the forward contract and the options contract. Answer: There is no up-front cost of hedging by forward contracts. In the case of options hedging, however, hedgers should pay the premiums for the contracts up-front. The cost of forward hedging, however, may be realized ex post when the hedger regrets his/her hedging decision. 4. What are the advantages of a currency options contract as a hedging tool compared with the forward contract? Answer: The main advantage of using options contracts for hedging is that the hedger can decide whether to exercise options upon observing the realized future exchange rate. Options thus provide a hedge against ex post regret that forward hedger might have to suffer. Hedgers can only eliminate the downside risk while retaining the upside potential. 5. Suppose your company has purchased a put option on the euro to manage exchange exposure associated with an account receivable denominated in that currency. In this case, your company can be said to have an ‘insurance’ policy on its receivable. Explain in what sense this is so. Answer: Your company in this case knows in advance that it will receive a certain minimum dollar amount no matter what might happen to the $/€ exchange rate. Furthermore, if the euro appreciates, your company will benefit from the rising euro. 6. Recent surveys of corporate exchange risk management practices indicate that many U.S. firms simply do not hedge. How would you explain this result? Answer: There can be many possible reasons for this. First, many firms may feel that they are not really exposed to exchange risk due to product diversification, diversified markets for their products, etc. Second, firms may be using self-insurance against exchange risk. Third, firms may feel that shareholders can diversify exchange risk themselves, rendering corporate risk management unnecessary. 7. Should a firm hedge? Why or why not? Answer: In a perfect capital market, firms may not need to hedge exchange risk. But firms can add to their value by hedging if markets are imperfect. First, if management knows about the firm’s exposure better than shareholders, the firm, not its shareholders, should hedge. Second, firms may be able to hedge at a lower cost. Third, if default costs are significant, corporate hedging can be justifiable because it reduces the probability of default. Fourth, if the firm faces progressive taxes, it can reduce tax obligations by hedging which stabilizes corporate earnings. 8. Using an example, discuss the possible effect of hedging on a firm’s tax obligations. Answer: One can use an example similar to the one presented in the chapter. 9. Explain contingent exposure and discuss the advantages of using currency options to manage this type of currency exposure. Answer: Companies may encounter a situation where they may or may not face currency exposure. In this situation, companies need options, not obligations, to buy or sell a given amount of foreign exchange they may or may not receive or have to pay. If companies either hedge using forward contracts or do not hedge at all, they may face definite currency exposure. 10. Explain cross-hedging and discuss the factors determining its effectiveness. Answer: Cross-hedging involves hedging a position in one asset by taking a position in another asset. The effectiveness of cross-hedging would depend on the strength and stability of the relationship between the two assets. PROBLEMS 1. Cray Research sold a super computer to the Max Planck Institute in Germany on credit and invoiced €10 million payable in six months. Currently, the six-month forward exchange rate is $1.10/€ and the foreign exchange advisor for Cray Research predicts that the spot rate is likely to be $1.05/€ in six months. (a) What is the expected gain/loss from the forward hedging? (b) If you were the financial manager of Cray Research, would you recommend hedging this euro receivable? Why or why not? (c) Suppose the foreign exchange advisor predicts that the future spot rate will be the same as the forward exchange rate quoted today. Would you recommend hedging in this case? Why or why not? (d) Suppose now that the future spot exchange rate is forecast to be $1.17/€. Would you recommend hedging? Why or why not? Solution: (a) Expected gain($) = 10,000,000(1.10 – 1.05) = 10,000,000(.05) = $500,000. (b) I would recommend hedging because Cray Research can increase the expected dollar receipt by $500,000 and also eliminate the exchange risk. (c) Since Cray Research can eliminate risk without sacrificing dollar receipt, I still would recommend hedging. (d) Now, hedging via forward contract involves an expected loss: -$700,000 = 10,000,000 (1.10 -1.17). Hedging thus becomes much less attractive. But if Cray Research is highly risk averse, it may still decide to hedge. The decision to hedge then critically depends on the firm’s degree of risk aversion. 2. IBM purchased computer chips from NEC, a Japanese electronics concern, and was billed ¥250 million payable in three months. Currently, the spot exchange rate is ¥105/$ and the three-month forward rate is ¥100/$. The three-month money market interest rate is 8 percent per annum in the U.S. and 7 percent per annum in Japan. The management of IBM decided to use the money market hedge to deal with this yen account payable. (a) Explain the process of a money market hedge and compute the dollar cost of meeting the yen obligation. (b) Conduct the cash flow analysis of the money market hedge. Solution: (a). Let’s first compute the PV of ¥250 million, i.e., 250m/1.0175 = ¥245,700,245.70 So if the above yen amount is invested today at the Japanese interest rate for three months, the maturity value will be exactly equal to ¥25 million which is the amount of payable. To buy the above yen amount today, it will cost: $2,340,002.34 = ¥245,700,245.70/105. The dollar cost of meeting this yen obligation is $2,340,002.34 as of today. (b) __________________________________________________________________ Transaction CF0 CF1 __________________________________________________________________ 1. Buy yens spot -$2,340,002.34 with dollars ¥245,700,245.70 2. Invest in Japan - ¥245,700,245.70 ¥250,000,000 3. Pay yens - ¥250,000,000 Net cash flow - $2,340,002.34 __________________________________________________________________ 3. You plan to visit Geneva, Switzerland in three months to attend an international business conference. You expect to incur the total cost of SF 5,000 for lodging, meals and transportation during your stay. As of today, the spot exchange rate is $0.60/SF and the three-month forward rate is $0.63/SF. You can buy the three-month call option on SF with the exercise rate of $0.64/SF for the premium of $0.05 per SF. Assume that your expected future spot exchange rate is the same as the forward rate. The three-month interest rate is 6 percent per annum in the United States and 4 percent per annum in Switzerland. (a) Calculate your expected dollar cost of buying SF5,000 if you choose to hedge via call option on SF. (b) Calculate the future dollar cost of meeting this SF obligation if you decide to hedge using a forward contract. (c) At what future spot exchange rate will you be indifferent between the forward and option market hedges? (d) Illustrate the future dollar costs of meeting the SF payable against the future spot exchange rate under both the options and forward market hedges. Solution: (a) Total option premium = (.05)(5000) = $250. In three months, $250 is worth $253.75 = $250(1.015). At the expected future spot rate of $0.63/SF, which is less than the exercise price, you don’t expect to exercise options. Rather, you expect to buy Swiss franc at $0.63/SF. Since you are going to buy SF5,000, you expect to spend $3,150 (=.63x5,000). Thus, the total expected cost of buying SF5,000 will be the sum of $3,150 and $253.75, i.e., $3,403.75. (b) $3,150 = (.63)(5,000). (c) $3,150 = 5,000x + 253.75, where x represents the break-even future spot rate. Solving for x, we obtain x = $0.57925/SF. Note that at the break-even future spot rate, options will not be exercised. (d) If the Swiss franc appreciates beyond $0.64/SF, which is the exercise price of call option, you will exercise the option and buy SF5,000 for $3,200. The total cost of buying SF5,000 will be $3,453.75 = $3,200 + $253.75. This is the maximum you will pay for SF5,000. 0 0.579 0.64 (strike price) 4. Boeing just signed a contract to sell a Boeing 737 aircraft to Air France. Air France will be billed €20 million which is payable in one year. The current spot exchange rate is $1.05/€ and the one-year forward rate is $1.10/€. The annual interest rate is 6.0% in the U.S. and 5.0% in France. Boeing is concerned with the volatile exchange rate between the dollar and the euro and would like to hedge exchange exposure. (a) It is considering two hedging alternatives: sell the euro proceeds from the sale forward or borrow euros from Credit Lyonnaise against the euro receivable. Which alternative would you recommend? Why? (b) Other things being equal, at what forward exchange rate would Boeing be indifferent between the two hedging methods? Solution: (a) In the case of forward hedge, the future dollar proceeds will be (20,000,000)(1.10) = $22,000,000. In the case of money market hedge (MMH), the firm has to first borrow the PV of its euro receivable, i.e., 20,000,000/1.05 =€19,047,619. Then the firm should exchange this euro amount into dollars at the current spot rate to receive: (€19,047,619)($1.05/€) = $20,000,000, which can be invested at the dollar interest rate for one year to yield: $20,000,000(1.06) = $21,200,000. Clearly, the firm can receive $800,000 more by using forward hedging. (b) According to IRP, F = S(1+i$)/(1+iF). Thus the “indifferent” forward rate will be: F = 1.05(1.06)/1.05 = $1.06/€. 5. Suppose that Baltimore Machinery sold a drilling machine to a Swiss firm and gave the Swiss client a choice of paying either $10,000 or SF 15,000 in three months. (a) In the above example, Baltimore Machinery effectively gave the Swiss client a free option to buy up to $10,000 dollars using Swiss franc. What is the ‘implied’ exercise exchange rate? (b) If the spot exchange rate turns out to be $0.62/SF, which currency do you think the Swiss client will choose to use for payment? What is the value of this free option for the Swiss client? (c) What is the best way for Baltimore Machinery to deal with the exchange exposure? Solution: (a) The implied exercise (price) rate is: 10,000/15,000 = $0.6667/SF. (b) If the Swiss client chooses to pay $10,000, it will cost SF16,129 (=10,000/.62). Since the Swiss client has an option to pay SF15,000, it will choose to do so. The value of this option is obviously SF1,129 (=SF16,129-SF15,000). (c) Baltimore Machinery faces a contingent exposure in the sense that it may or may not receive SF15,000 in the future. The firm thus can hedge this exposure by buying a put option on SF15,000. 6. Princess Cruise Company (PCC) purchased a ship from Mitsubishi Heavy Industry. PCC owes Mitsubishi Heavy Industry 500 million yen in one year. The current spot rate is 124 yen per dollar and the one-year forward rate is 110 yen per dollar. The annual interest rate is 5% in Japan and 8% in the U.S. PCC can also buy a one-year call option on yen at the strike price of $.0081 per yen for a premium of .014 cents per yen. (a) Compute the future dollar costs of meeting this obligation using the money market hedge and the forward hedges. (b) Assuming that the forward exchange rate is the best predictor of the future spot rate, compute the expected future dollar cost of meeting this obligation when the option hedge is used. (c) At what future spot rate do you think PCC may be indifferent between the option and forward hedge? Solution: (a) In the case of forward hedge, the dollar cost will be 500,000,000/110 = $4,545,455. In the case of money market hedge, the future dollar cost will be: 500,000,000(1.08)/(1.05)(124) = $4,147,465. (b) The option premium is: (.014/100)(500,000,000) = $70,000. Its future value will be $70,000(1.08) = $75,600. At the expected future spot rate of $.0091(=1/110), which is higher than the exercise of $.0081, PCC will exercise its call option and buy ¥500,000,000 for $4,050,000 (=500,000,000x.0081). The total expected cost will thus be $4,125,600, which is the sum of $75,600 and $4,050,000. (c) When the option hedge is used, PCC will spend “at most” $4,125,000. On the other hand, when the forward hedging is used, PCC will have to spend $4,545,455 regardless of the future spot rate. This means that the options hedge dominates the forward hedge. At no future spot rate, PCC will be indifferent between forward and options hedges. 7. Consider a U.S.-based company that exports goods to Switzerland. The U.S. Company expects to receive payment on a shipment of goods in three months. Because the payment will be in Swiss francs, the U.S. Company wants to hedge against a decline in the value of the Swiss franc over the next three months. The U.S. risk-free rate is 2 percent, and the Swiss riskfree rate is 5 percent. Assume that interest rates are expected to remain fixed over the next six months. The current spot rate is $0.5974 a. Indicate whether the U.S. Company should use a long or short forward contract to hedge currency risk. b. Calculate the no-arbitrage price at which the U.S. Company could enter into a forward contract that expires in three months. c. It is now 30 days since the U.S. Company entered into the forward contract. The spot rate is $0.55. Interest rates are the same as before. Calculate the value of the U.S. Company’s forward position. Solution: a. The risk to the U.S. company is that the value of the Swiss franc will decline and it will receive fewer U.S. dollars on conversion. To hedge this risk, the company should enter into a contract to sell Swiss francs forward. b. S0 = $0.5974 T = 90/365 r = 0.02 rf = 0.05 0.5974 90/365 $0.5931 F(0,T) =(1.05)90/365 (1.02) = c. St = $0.55 T = 90/365 t = 30/365 T – t = 60/365 r = 0.02 rf = 0.05 $0.55 $0.5931 Vt (0,T) = (1.05)60/365 − (1.02)60/365 =−$0.0456 This represents a gain to the short position of $0.0456 per Swiss franc. In this problem, the U.S. company holds the short forward position. 8. Suppose that you are a U.S.-based importer of goods from the United Kingdom. You expect the value of the pound to increase against the U.S. dollar over the next 30 days. You will be making payment on a shipment of imported goods in 30 days and want to hedge your currency exposure. The U.S. risk-free rate is 5.5 percent, and the U.K. risk-free rate is 4.5 percent. These rates are expected to remain unchanged over the next month. The current spot rate is $1.50. a. Indicate whether you should use a long or short forward contract to hedge currency risk. b. Calculate the no-arbitrage price at which you could enter into a forward contract that expires in three months. c. Move forward 10 days. The spot rate is $1.53. Interest rates are unchanged. Calculate the value of your forward position. d. Using the text software spreadsheet TRANSEXP, replicate the analysis in Exhibit 8.8. Solution: a. The risk to you is that the value of the British pound will rise over the next 30 days and it will require more U.S. dollars to buy the necessary pounds to make payment. To hedge this risk, you should enter a forward contract to buy British pounds. b. S0 = $1.50 T = 30/365 r = 0.055 rf = 0.045 $1.50 30/365 $1.5018 F(0,T) =(1.045)30/365 (1.055) = c. St = $1.53 T = 30/365 t = 10/365 T – t = 20/365 r = 0.055 rf = 0.045 $1.53 $1.5012 Vt (0,T) = (1.045)20/365 − (1.055)20/365 = $0.0295 Because you are long, this is a gain of $0.0295 per British pound. d. The answer is provided in Exhibit 8.8 of the textbook. MINICASE: AIRBUS’ DOLLAR EXPOSURE Airbus sold an aircraft, A400, to Delta Airlines, a U.S. company, and billed $30 million payable in six months. Airbus is concerned with the euro proceeds from international sales and would like to control exchange risk. The current spot exchange rate is $1.05/€ and six-month forward exchange rate is $1.10/€ at the moment. Airbus can buy a six-month put option on U.S. dollars with a strike price of €0.95/$ for a premium of €0.02 per U.S. dollar. Currently, six-month interest rate is 2.5% in the euro zone and 3.0% in the U.S. a. Compute the guaranteed euro proceeds from the American sale if Airbus decides to hedge using a forward contract. b. If Airbus decides to hedge using money market instruments, what action does Airbus need to take? What would be the guaranteed euro proceeds from the American sale in this case? c. If Airbus decides to hedge using put options on U.S. dollars, what would be the ‘expected’ euro proceeds from the American sale? Assume that Airbus regards the current forward exchange rate as an unbiased predictor of the future spot exchange rate. d. At what future spot exchange rate do you think Airbus will be indifferent between the option and money market hedge? Solution: a. Airbus will sell $30 million forward for €27,272,727 = ($30,000,000) / ($1.10/€). b. Airbus will borrow the present value of the dollar receivable, i.e., $29,126,214 = $30,000,000/1.03, and then sell the dollar proceeds spot for euros: €27,739,251 (=$29,126,214/$1.05/€). This is the euro amount that Airbus is going to keep. c. Since the expected future spot rate is less than the strike price of the put option, i.e., €0.9091< €0.95, Airbus expects to exercise the put option on $ and receive €28,500,000 = ($30,000,000)(€0.95/$). This is gross proceeds. Airbus spent €600,000 (=0.02x30,000,000) upfront for the option and its future cost is equal to €615,000 = €600,000 x 1.025. Thus the net euro proceeds from the American sale is €27,885,000, which is the difference between the gross proceeds and the option costs. d. At the indifferent future spot rate, the following will hold: €28,432,732 = ST (30,000,000) - €615,000. Solving for ST , we obtain the “indifference” future spot exchange rate, i.e., €0.9683/$, or $1.0327/€. Note that €28,432,732 is the future value of the proceeds under money market hedging: €28,432,732 = (€27,739,251) (1.025). Case Application: Richard May’s Options It is Tuesday afternoon, February 14, 2012. Richard May, Assistant Treasurer at American Digital Graphics (ADG), sits in his office on the thirty-fourth floor of the building that dominates Rockefeller Plaza’s west perimeter. Its Valentine’s Day and Richard and his wife have dinner reservations with another couple at Balthazar at 7:30. “I must get this hedging memo done,” thinks May, “and get out of here. Foreign exchange options? I had better get the story straight before someone in the Finance Committee starts asking questions. Let’s see, there are two ways in which I can envisage us using options now. One is to hedge a dividend due on September 15th from ADG Germany. The other is to hedge our upcoming payment to Matsumerda for their spring RAM chip statement. With the yen at 78 and increasing I’m glad we haven’t covered the payment so far, but now I’m getting nervous and I would like to protect my posterior. An option to buy yen on June 10 might be just the thing. Before we delve any further into Richard May’s musings, let us learn a bit about ADG, and about foreign exchange options. American Digital Graphics is a $12 billion sales company engaged in, among other things, the development, manufacture, and marketing of microprocessor-based equipment. Although 30 percent of the firm’s sales are currently abroad, the firm has full-fledged manufacturing facilities in only three foreign countries, Germany, Canada, and Brazil. An assembly plant in Singapore exists primarily to solder Japanese semiconductor chips onto circuit boards and to screw these into Brazilian-made boxes for shipment to the United States, Canada, and Germany. The German subsidiary has developed half of its sales to France, the Netherlands, and the United Kingdom, billing in euros. ADG Germany has accumulated a cash reserve of €900,000, worth $1,178,100 at today’s exchange rate. While the Hamburg office has automatic permission to repatriate €3 million, they have been urged to seek authorization to convert another €1 million by September 15th. The firm has an agreement to buy three hundred thousand RAM chips at ¥8000 each semi-annually, and it is this payment that will fall due on June 10th. The conventional means of hedging exchange risk are forward or future contracts. These, however, are fixed and inviolable agreements. In many practical instances the hedger is uncertain whether foreign currency cash inflow or outflow will materialize. In such cases, what is needed is the right, but not the obligation, to buy or sell a designated quantity of a foreign currency at a specified price (exchange rate). This is precisely what a foreign exchange option provides. A foreign exchange option gives the holder the right to buy or sell a designated quantity of a foreign currency at a specified exchange rate up to or at a stipulated date. The terminal date of the contract is called the expiration date (or maturity date). If the option may be exercised before the expiration date, it is called an American option; if only at the expiration date, a European option. The party retaining the option is the option buyer; the party giving the option is the option seller (or writer). The exchange rate at which the option can be exercised is called the exercise price or strike price. The buyer of the option must pay the seller some amount, called the option price or the premium, for the rights involved. The important feature of a foreign exchange option is that the holder of the option has the right, but not the obligation, to exercise it. He will only exercise it if the currency moves in a favorable direction. Thus, once you have paid for an option you cannot lose, unlike a forward contract, where you are obliged to exchange the currencies and therefore will lose if the movement is unfavorable. The disadvantage of an option contract, compared to a forward or futures contract is that you have to pay a price for the option, and this price or premium tends to be quite high for certain options. In general, the option’s price will be higher the greater the risk to the seller (and the greater the value to the buyer because this is a zero-sum game). The risk of a call option will be greater, and the premium higher, the higher the forward rate relative to the exercise price; after all, one can always lock in a profit by buying at the exercise price and selling at the forward rate. The chance that the option will be exercised profitably is also higher, the more volatile is the currency, and the longer the option has to run before it expires. Returning to Richard May in his Rockefeller Center office, we find that he has been printing spot, forward and currency options and futures quotations from the company’s Bloomberg terminal. The option prices are quoted in U.S. cents per euro. Yen are quoted in hundredths of a cent. Looking at these prices, Richard realizes that he can work out how much the euro or yen would have to change to make the option worthwhile. Richard makes a mental note that ADG can typically borrow in the Eurocurrency market at LIBOR + 1% and lend at LIBID. “I’ll attach these numbers to my memo,” mutters May, but the truth is he has yet to come to grips with the real question, which is when, if ever, are currency options a better means of hedging exchange risk for an international firm than traditional forward exchange contracts or future’s contracts. Please assist Mr. May in his analysis of currency hedging for his report to ADG’s Finance Committee. In doing so, you may consult the highlighted market quotes in the following attachments. Solution: ADG’s euro receivable ADG has a €3,000,000 receivable in 214 days on September 15th. To assess alternative ways of hedging, the following data are relevant: The current spot exchange rate (S)=$1.3088/€, 7month forward exchange rate (F)=$1.3090, the dollar interest rate (bid)=0.78% and euro interest rate (ask)=1.40%; the put option on the euro with the strike (exercise) price of $1.31 selling for a premium of 5.09 cents per euro. Here we consider and compare three alternative hedging methods as in our discussions in the textbook: Forward, money market, and option hedges. Hedging with futures is often inconvenient due to the standardized maturities and contract size and also possibly thin trading. ▪ Forward hedge If ADG chooses to use forward contract, it just needs to sell its euro receivable at today’s forward exchange. ADG then is assured of receiving a guaranteed dollar amount of $3,927,000 on September 15th: (€3,000,000) ($1.3090/€) = $3,927,000. ▪ Money market hedge If ADG decides to use money market hedging, it first needs to borrow the present value (PV) of its euro receivable at 2.40% interest rate (=1.40%+1.0%): PV = (€3,000,000) / (1+0.024(214/360)) = 3,000,000 / 1.01427 = €2,957,802. It then would convert €2,957,802 at today’s spot exchange rate of $1.3088/€ into $3,871,171. If ADG invests this dollar amount at the dollar interest rate till September 15th, the future value (FV) of the investment will be: FV = ($3,871,171) (1+0.0078 (214/360) ) = $3,889,121. ▪ Option hedge If ADG chooses to hedge its euro receivable using currency options, it can purchase put options on three million euros with a $1.31 strike price at the premium of 5.09 cents per euro. This means that the firm has to spend the option cost upfront. The option costs, including the time value of money, would be: 153,408 = (€3,000,000) ($0.0509) [1+0.0078 (214/360) ]. If the future spot exchange rate turns out to be less than the strike price, i.e., if the euro becomes cheaper than the option strike price ($1.31), ADG will simply exercise its put option and exchange its euro receivable at the strike price, collect $3,776,592 (net of option costs), which is the guaranteed minimum net dollar proceeds: (€3,000,000) ($1.31) - $153,408 = $3,776,592. If the euro becomes stronger than the strike price, the firm will simply let its put option expire and convert its euro receivable at the future spot exchange rate. As can be seen from the following graph, forward hedging dominates money market hedging. If the future spot rate exceeds the indifference rate, S* = $1.36, option hedging becomes preferable; otherwise, forward hedging is preferable. Dollar receipt from euro receivable hedging alternatives ADG’s yen payable ADG has a ¥2,400 million payable in 4 months. The relevant market data include: The current spot exchange rate of $0.01274/¥, four-month forward exchange rate of $0.01274/¥, four-month call option on yen with the strike price set at 127 cents for 100 yen that is selling for 3.11 cents per 100 yen. ADG’s borrowing interest rate in dollars is 0.62%, while lending interest rate in yen is 0.18%. ▪ Forward hedge If ADG decides to use forward contract to hedge its yen payable, it just needs to purchase the yen payable amount forward at today forward exchange rate. The dollar cost of doing so will be $30,576,000 = (¥2,400,000,000) ($0.01274/¥). ▪ Money market hedge Money market hedging would require borrowing the PV of the yen payable in dollars, $30,558,123.50 = [(¥2,400,000,000)/(1+0.0018(117/360)] ($0.01274), and converting the dollar amount borrowed into yen and invest for four months at the yen interest rate to receive, ¥2,400,000,000 = ($30,558,123.50/$0.01274/¥)(1+0.0018(117/360)). When ADG receives the maturity value of the yen investment, it will use the yen amount to make payment to Matsumerda. Lastly, in four month, ADG will pay back the dollar loan: $30,719,012 = ($30,558,123.50) (1+0.0162(117/360)). ▪ Option hedge In the case of hedging with option, ADG will need to buy call option on its yen payable. If ADG decides to buy options with strike price set at $0.0127 per dollar trading for 3.11 cents per 100 yens, the option cost (including the time value of money) will be, $747,783 = (¥2,400,000,000)($0.000311)[1+0.0057(117/360)] = ($746,400)(1.0018525) If the yen appreciates beyond the strike price of the call option, K=$0.0127/¥, ADG will simply exercise its option and the max dollar cost of securing the yen payable amount will be, $31,227,783 = (¥2,400,000,000)($0.0127/¥) + $747,783. As can be seen from the graph below, forward hedge dominates money market hedge as the dollar cost will be always lower with forward hedge than with money market hedge. If the exchange rate becomes lower than the indifference rate, S*=$0.0124, call option hedge would be preferable; otherwise, forward hedge would be preferable. The indifference rate can be identified from solving the following equation for S*: 30,576,000 = (2,400,000,000) S* +747,783. Dollar cost from yen payable hedging alternatives Management of Transaction Exposure Chapter Eight Chapter Outline • Forward Market Hedge • Money Market Hedge • Options Market Hedge • Cross-Hedging Minor Currency Exposure • Hedging Contingent Exposure • Hedging Recurrent Exposure with Swap Contracts • Hedging Through Invoice Currency • Hedging via Lead and Lag • Exposure Netting • Should the Firm Hedge? • What Risk Management Products Do Firms Use? Forward Market Hedge: Imports • If you expect to owe foreign currency in the future, you can hedge by agreeing today to buy the foreign currency in the future at a set price by entering into a long position in a forward contract. Forward Market Hedge: Exports • If you are going to receive foreign currency in the future, agree to sell the foreign currency in the future at a set price by entering into short position in a forward contract. Importer’s Forward Market Hedge A U.S.-based importer of Italian shoes has just ordered next year’s inventory. Payment of €100M is due in one year. If the importer buys €100M at the forward exchange rate of $1.50/€, the cash flows at maturity look like this: Exporter’s Futures Market Cross-Currency Hedge Your firm is a U.K.-based exporter of bicycles. You have sold €750,000 worth of bicycles to an Italian retailer. Payment (in euros) is due in six months. Your firm wants to hedge the receivable into pounds. Country U.S. $ equiv. Currency per U.S. $ Britain (£62,500) $2.0000 £0.5000 1 Month Forward $1.9900 £0.5025 3 Months Forward 6 Months Forward 12 Months Forward $1.9800 £0.5051 $2.0000 £0.5000 $2.1000 £0.4762 Euro (€125,000) $1.4700 €0.6803 1 Month Forward $1.4800 €0.6757 3 Months Forward 6 Months Forward $1.4900 €0.6711 $1.5000 €0.6667 12 Months Forward $1.5100 €0.6623 Sizes of forwards on this exchange are £62,500 and €125,000. Exporter’s Futures Market Cross-Currency Hedge • The exporter has to convert the €750,000 receivable first into dollars and then into pounds. • If we sell the €750,000 receivable forward at the six-month forward rate of $1.50/€, we can do this with a SHORT position in 6 six-month euro futures contracts. €750,000 6 contracts = €125,000/contract ▪Selling the €750,000 forward at the six-month forward rate of $1.50/€ generates $1,125,000: $1.50 $1,125,000 = €750,000 × €1 ⚫At the six-month forward exchange rate of $2/£, $1,125,000 will buy £562,500. We can secure this trade with a LONG position in 9 six-month pound futures contracts: £562,500 9 contracts = £62,500/contract Short position in 6 six-month euro futures on €125,000 at $1.50/€1 Long position in 9 six-month pound futures on £62,500 at $2.00/£1 Exporter’s Futures Market Cross-Currency Hedge: Cash Flows at Maturity Importer’s Money Market Hedge • This is the same idea as covered interest arbitrage. • To hedge a foreign currency payable, buy the present value of that foreign currency payable today and put it in the bank at interest. – Buy the present value of the foreign currency payable today at the spot exchange rate. – Invest that amount at the foreign rate. – At maturity your investment will have grown enough to cover your foreign currency payable. Importer’s Money Market Hedge A U.S.–based importer of Italian bicycles owes €100,000 to an Italian supplier in one year. – The spot exchange rate is $1.50 = €1.00. – The one-year interest rate in Italy is i€ = 4%. – The importer can hedge this payable by buying €96,153.85 = and investing €96,153.85 at 4% in Italy for one year. At maturity, he will have €100,000 = €96,153.85 × (1.04). Dollar cost today = $144,230.77 = €96,153.85 × Importer’s Money Market Hedge • With this money market hedge, we have redenominated a one-year €100,000 payable into a $144,230.77 payable due today. • If the U.S. interest rate is i$ = 3%, we could borrow the $144,230.77 today and owe $148,557.69 in one year. $148,557.69 = $144,230.77 × (1.03) €100,000 $148,557.69 = S($/€)× (1+ i€)T ×(1+ i$)T Importer’s Money Market Hedge: Cash Flows Now and at Maturity Spot Foreign Exchange Market Exporter’s Money Market Hedge Importer’s Money Market Cross-Currency Hedge Your firm is a U.K.-based importer of bicycles. You have bought €750,000 worth of bicycles from an Italian firm. Payment (in euros) is due in one year. Your firm wants to hedge the payable into pounds. – Spot exchange rates are $2/£ and $1.55/€ – The interest rates are 3% in €, 6% in $ and 4% in £, all quoted as an APR. What should you do to redenominate this 1-year €denominated payable into a £-denominated payable with a 1-year maturity? Importer’s Money Market Cross-Currency Hedge • Sell pounds for dollars at spot exchange rate, buy euro at spot exchange rate with the dollars, invest in the euro zone for one year at i€ = 3%, all such that the future value of the investment equals €750,000. Using the numbers we have: – Step 1: Borrow £564,320.39 at i£ = 4%. – Step 2: Sell pounds for dollars, receive $1,128,640.78. – Step 3: Buy euro with the dollars, receive €728,155.34. – Step 4: Invest in the euro zone for 12 months at 3% APR (the future value of the investment equals €750,000). – Step 5: Repay your borrowing with £586,893.20. (see next slide for where the numbers come from) Where Do the Numbers Come From? The present value of the euro payable = €728,155.34 = $1.55 The dollar cost of buying the present value of the euro payable today Cost today in pounds of the present dollar value of the euro payable FV in pounds of the cost in pounds of being able to pay the supplier €750,000 = $1,128,640.78 = €728,155.34 × €1 £1 $2 £564,320.39 = $1,128,640.78 × £586,893.20 = £564,320.39 × (1.04) Importer’s Money Market Cross-Currency Hedge: Cash Spot Foreign Exchange Market Spot Foreign Exchange Market Options • A motivated financial engineer can create almost any risk-return profile that a company might wish to consider. • An important consideration when using options is the hedge ratio that we covered in the last chapter. • Without due consideration of the hedge ratio, the careless use of options can undo attempts at hedging. Using Options to Hedge: Exports • A British exporter who is owed €100,000 in one period has many choices: – Buy call options on the pound with a strike in dollars while also buying put options on the euro with a strike in dollars. – Buy call options on the pound with a strike in euros. – Buy put options on the euro with a strike in pounds. • For any options market hedge, the exporter should use the hedge ratio to know how many options are needed. – Spot rates are S0(£/€) = £0.80/€, S0($/€) = $2.00/€, S0($/£) = $2.50/£; i£ = 15½% and i€ = 5%. – In the next year, suppose that there are two possibilities: • S1(£/€) = £1.00/€ or • S1(£/€) = £0.75/€ Options Market Cross-Currency Hedge At first it seems logical that a British exporter with a €100,000 receivable should buy 10 put options on €10,000—but that doesn’t work well.£10,000 10 × p0 = £2,077.92 (strike price of £.80/€)up The hedge ratio of this option is − 1/5 p1 = £0 S (£/€) = £1.00/€ p1up – p down1 €10,000 = £8,000 H = S1up – S1down p0 = £207.79 £7,500 = £0 – £500 = – £500 = −1/ pdown = £500 5 1 £10,000 – £7,500 £2,500 S1(£/€) = £0.75/€ With a hedge ratio of –0.20 our exporter would actually be better hedged with a long position in 50 PHLX puts. 10 Puts on €10,000 (Strike £8,000) is Not a Hedge Out-of-the-Money: Put T = 1 Spot Market Option S1(£/€) = £1.00/€ Dealer K0(£/€) = £0.80/€ customer 10×p0 = £2,077.92 The future value of the £100,000 Sell €100,000 Buying Exporter €100,000 S1(£/€) = £1.00/€. Notice that our exporter doesn’t have a hedge when he buys 10 put options. Put £80,000S1(£/€) = £0.75/€ Option Buying K0(£/€) = £0.80/€ Dealer Exporter €100,000 receivable net of the cost of 10 options is either £97,600 = £100,000 − £2,077.92 × 1.155 or £77,600 = £80,000 − £2,077.92 × 1.155 Long 50 Puts = Perfect Hedge 50 × p0 = £10,389.61 Option OutS1(-£/€) = £1.00/€of-the-Money: Put £100,000 T = 1 Spot MarketSell €100,000 Dealer K0(£/€) = £0.80/€ Buying Exporter €100,000 S1(£/€) = £1.00/€. T = 1 Spot Market Buy €400,000 customer S1(£/€) = £0.75/€. In-the-Money Puts S1(£/€) = £0.75/€ Put K0(£/€) = £0.80/€ Buying £400,000 The future value of the Exporter Option receivable net of the cost of 50 puts is €500,000 Dealer £88,000 = £100,000 − £10,389.61 × 1.155 or £88,000 = £400,000 − £10,389.61 × 1.155 − £300,000 Options Hedges and Money Market Hedges and Forward Market Hedges • The next two slides show that the hedge of buying 50 puts has the exact same payoffs as a forward market hedge and a money market hedge. • Recall the story: A British exporter is owed €100,000 in one period. • S0(£/€) = £0.80/€, S0($/€) = $2.00/€, S0($/£) = $2.50/£ – i£ = 15½% and i€ = 5% – In the next year, there are two possibilities: • S1(£/€) = £1.00/€ or • S1(£/€) = £0.75/€ Money Market Cross-Currency Hedge Perfect hedge whether S1(£/€) = £1.00/€ or S1(£/€) = £0.75/€. Forward Market Cross-Currency Hedge A U.K.-based exporter sold a €100,000 order to an Italian retailer. Payment is due in 1 year and the exporter used a forward hedge. S0(£/€) = £0.80/€, S0($/€) = $2.00/€, Euro Forward Contract Counterparty Pound Forward Contract Counterparty Perfect hedge whether S1(£/€) = £1.00/€ or S1(£/€) = £0.75/€. Call-Buying Importer Consider a British importer who owes €100,000 in one year. c1 = £0 H = up down c1 –c1 = £2,000– £0 = £2,000 = 4 The importer can use a money market or forward market hedge £10,000 to redenominate this into a £88,000 liability. He could also use OTC call options on the euro c = £2,000 with a pound strike. £8,000 c0 = £900.43 With a hedge ratio of .80 our importer can hedge with a long position in 1 OTC call on €125,000.£7,500 down S1up – S1down £10,000 – £7,500 £2,500 5 1 Call on €125,000 = Perfect Import Hedge receivable net of the cost of the call is In-the-Money Calls: £88,000 = £75,000 + £13,000 or SK10((£/€) = £1.00/€£/€) = £0.80/€ £88,000 = £100,000 + £13,000 − £25,000 Cross-Hedging Minor Currency Exposure • The major world currencies are the U.S. dollar, Canadian dollar, British pound, euro, Swiss franc, Mexican peso, and Japanese yen. • Everything else is a minor currency (for example, the Swedish krona). • It is difficult, expensive, and sometimes even impossible to use financial contracts to hedge exposure to minor currencies. Cross-Hedging Minor Currency Exposure • Cross-hedging involves hedging a position in one asset by taking a position in another asset. • The effectiveness of cross-hedging depends upon how well the assets are correlated. – An example would be a U.S. importer with liabilities in Swedish krona hedging with long or short forward contracts on the euro. If the krona is expensive when the euro is expensive, or even if the krona is cheap when the euro is expensive, it can be a good hedge. But they need to co-vary in a predictable way. Hedging Recurrent Exposure with Swaps • Recall that swap contracts can be viewed as a portfolio of forward contracts. • Firms that have recurrent exposure can usually hedge their exchange risk at a lower cost with swaps than with a program of hedging each exposure as it comes along. • It is also the case that swaps are available in longer-terms than futures and forwards. Exposure Netting • A multinational firm should not consider deals in isolation, but should focus on hedging the firm as a portfolio of currency positions. • Once the residual exposure is determined, we hedge that. • Multilateral netting is an efficient and cost-effective mechanism for settling interaffiliate foreign exchange transactions and thus determining the firm’s residual exposure. • In the following slides, a firm faces the following exchange rates: £1.00 = $2.00 €1.00 = $1.50 SFr 1.00 = $0.90 Exposure Netting Exposure Netting Exposure Netting: How to Double Check Your Answer • It’s always good practice to check your work. • It’s better for you to find your mistakes than for your professor to (or your boss!). • You can check your work in exposure netting by adding up each subsidiary’s debits and credits. • When you’re done, check that you haven’t destroyed or “created” any money. • A new example follows for practice checking answers. $25$20 +$55+$45 –$20+$75 $60$140 $100 $60+$40 $140 Alternative Solution $60 $140 Netting with Central Depository Some firms use a central depository as a cash pool to facilitate funds mobilization and reduce the chance of misallocated funds. Central depository Other Hedging Strategies • Hedging through invoice currency. – The firm can shift, share, or diversify: • Shift exchange rate risk by invoicing foreign sales in home currency • Share exchange rate risk by pro-rating the currency of the invoice between foreign and home currencies • Diversify exchange rate risk by using a market basket index • Hedging via lead and lag. – If a currency is appreciating, pay those bills denominated in that currency early; let customers in that country pay late as long as they are paying in that currency. – If a currency is depreciating, give incentives to customers who owe you in that currency to pay early; pay your obligations denominated in that currency as late as your contracts will allow. Should the Firm Hedge? • Not everyone agrees that a firm should hedge. – Hedging by the firm may not add to shareholder wealth if the shareholders can manage exposure themselves. – Hedging may not reduce the non-diversifiable risk of the firm. Therefore, shareholders who hold a diversified portfolio are not benefitted when management hedges. What Risk Management Products do Firms Use? • Most U.S. firms meet their exchange risk management needs with forward, swap, and options contracts. • The greater the degree of international involvement, the greater the firm’s use of foreign exchange risk management. Solution Manual for International Financial Management Cheol S. Eun, Bruce G. Resnick 9780077861605
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