# CHAPTER 9 SUGGESTED ANSWERS TO CHAPTER 9 QUESTIONS

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4 CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES Borrower Fixed-Rate Yen Available Floating-Rate Dollars Available Korea Development Bank 4.9% LIBOR % IBM 4.5% LIBOR % Difference 0.4% 0.55% Given the differences in rates between the two markets, the two parties can achieve a combined 15 basis point savings through IBM borrowing floating-rate dollars at LIBOR % and KDB borrowing fixed-rate yen at 4.9% and then swapping the proceeds. IBM would be able to borrow fixed-rate yen at 4.35% if all these savings were passed along to it in the swap. This could be accomplished by IBM providing KDB with floating-rate dollars at LIBOR %, saving KDB 0.55%, which then passed these savings along to IBM by swapping the fixed-rate yen at 4.9% % = 4.35%. Thus, the potential savings to IBM range from 0 to 0.15%. b. Assuming a notional principal equivalent to \$125 million, and a current exchange rate of 105/\$, what do these possible cost savings translate into in yen terms? ANSWER. At a current exchange rate of 105/\$, IBM's borrowing would equal 13,125,000,000 (125,000,000*105). A 0.15% savings on that amount would translate into 19,687,500 per annum ( 13,125,000,000*0.0015). c. Redo Parts a and b assuming that the parties use Bank of America, which charges a fee of 8 basis points to arrange the swap. ANSWER. In this case, the potential savings from a swap net out to 7 basis points. If IBM realizes all these savings, its borrowing cost would be lowered to 4.43% (4.5% %). The 7 basis point saving would translate into an annual saving of 9,187,500 ( 13,125,000,000*0.0007). 4. At time t, 3M borrows 12.8 billion at an interest rate of 1.2 percent, paid semiannually, for a period of two years. It then enters into a two-year yen/dollar swap with Bankers Trust (BT) on a notional principal amount of \$100 million ( 12.8 billion at the current spot rate). Every six months, 3M pays BT U.S. dollar LIBOR6, while BT makes payments to 3M of 1.3 percent annually in yen. At maturity, BT and 3M reverse the notional principals. a. Assume that LIBOR6 (annualized) and the /\$ exchange rate evolve as follows. Calculate the net dollar amount that 3M pays to BT ("-") or receives from BT ("+") each six-month period. Time (months) LIBOR6 /\$ (spot) Net \$ receipt (+)/payment (-) t 5.7% 128 t % 132 t % 137 t % 131 t % 123 ANSWER. The semiannual receipts, payments, and net receipts (payments) are computed as follows: Time (months) LIBOR6 /\$ (spot) Receipt Payment Net \$ receipt (+)/payment (-) t 5.70% 128 t % 132 \$630,303 \$2,700,000 \$2,069,697 t % 137 \$607,299 \$2,650,000 \$2,042,701 t % 131 \$635,115 \$2,950,000 \$2,314,885 t % 123 \$676,423 \$2,900,000 \$2,223,577 There is no payment or receipt at time t. The semiannual payment is calculated as \$100,000,000 x LIBOR6/2. The semiannual receipt is calculated as 12,800,000,000 x 0.013/2 x 1/S, where S is the current spot rate ( /\$). 4

7 INSTRUCTOR S MANUAL MULTINATIONAL FINANCIAL MANAGEMENT, 9 TH ED. 2. Square Corp. has not tapped the Swiss-franc public debt market because of concern about a likely appreciation of that currency and only wishes to be a floating-rate dollar borrower, which it can be at LIBOR + 3/8%. Circle Corp. has a strong preference for fixed-rate Swiss-franc debt, but it must pay ½ of 1% more than the 5 1/4% coupon that Square Corp.'s notes would carry. Circle Corp., however, can obtain Eurodollars at LIBOR flat (a zero margin). What is the range of possible cost savings to Square from engaging in a currency swap with Circle? ANSWER. Square Corp. can borrow fixed-rate Swiss francs at 5.25% and floating-rate dollars at LIBOR + 3/8%. Meanwhile Circle Corp. can borrow fixed-rate Swiss francs at 5.75% and floating-rate dollars at LIBOR flat. The logical set of transactions under these circumstances would be (1) Square borrows fixed-rate francs, (2) Circle borrows floating-rate dollars, and (3) the companies then swap the payment streams. The maximum benefit to Square arises when it provides fixed- rate francs to Circle at 5.75% (Circle is no worse off under this scenario) and receives floating-rate dollars at LIBOR, which is Circle's cost of funds (Circle is again no worse off under this scenario). This swap will cut Square's cost of funds to LIBOR - 0.5%, which is a savings of 0.875%. At worst, Square will receive no benefit from the swap (otherwise it will not enter into it). Thus, the range of possible cost savings to Square from engaging in a currency swap with Circle is from 0% up to 0.875%. 3. Nestle rolls over a \$25 million loan priced at LIBOR3 on a three-month basis. The company feels that interest rates are rising and that rates will be higher at the next roll-over date in three months. Suppose the current LIBOR3 is %. a. Explain how Nestle can use an FRA at 6% from Credit Suisse to reduce its interest rate risk on this loan. ANSWER. Nestle can use the FRA priced at 6% to lock in today LIBOR3 of 6% at its next rollover date three months from now. Whatever happens to LIBOR3 at the rollover date, Nestle will pay LIBOR3 of 6% in three months time. b. In three months, interest rates have risen to 6.25%. How much will Nestle receive/pay on its FRA? What will be Nestle's hedged interest expense for the upcoming three-month period? ANSWER. According to Equation 9.1 in the chapter, Nestle will receive an amount of interest (it will be a recipient because LIBOR3 on the rollover date exceeds the rate agreed to on its FRA) computed as follows: days (LIBOR - forward rate)( ) Interest payment= notional principalx 360 days 1+ LIBORx( ) 360 Substituting in the figures from the problem yields an interest payment from Credit Suisse of \$15,385: Interest payment = \$25,000,000x 90 ( )( ) 360 = \$15, x( ) 360 c. After three months, interest rates have fallen to 5.25%. How much will Nestlé receive/pay on its FRA? What will be Nestle s hedged interest expense for the next three-month period? 7

8 CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES ANSWER. Under this interest rate scenario, Nestle must pay to Credit Suisse an amount equal to \$46,268: 4. Ford has a \$20 million Eurodollar deposit maturing in two months that it plans to roll over for a further six months. The company's treasurer feels that interest rates will be lower in two months time when rolling over the deposit. Suppose the current LIBOR6 is 7.875%. a. Explain how Ford can use an FRA at 7.65% from Banque Paribas to lock in a guaranteed six-month deposit rate when it rolls over its deposit in two months. ANSWER. Ford today can enter into the FRA and guarantee itself a six-month deposit rate in two months time of 7.65%. Specifically, Ford will sell a "2 x 6" FRA on LIBOR at 7.65% to Banque Paribas for a notional principal of \$20 million. This means that Banque Paribas Trust has entered into a two-month forward contract on six-month LIBOR. Two months from now, if LIBOR6 is less than 7.65%, Banque Paribas will pay Ford the difference in interest expense. If LIBOR6 exceeds 7.65%, Ford will pay Banque Paribas the difference. b. After two months, LIBOR6 has fallen to 7.5%. How much will Ford receive/pay on its FRA? What will be Ford's hedged deposit rate for the next six-month period? ANSWER. In this case, Ford will receive from Banque Paribas \$20,000,000 x ( )/2 = \$15,000, giving it an annualized hedged deposit rate of 7.65% for the next six months. c. In two months, LIBOR6 has risen to 8%. How much will Ford receive/pay on its FRA? What will be Ford's hedged deposit rate for the next six months? ANSWER. In this case, Ford will pay Banque Paribas \$20,000,000 x ( )/2 = \$35,000, giving it as before an annualized hedged deposit rate of 7.65% for the next six months. 8

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