CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES
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SUGGESTED SOLUTIONS TO CHAPTER 9 PROBLEMS 1. Dell Computers would like to borrow pounds, and Virgin Airlines wants to borrow dollars. Because Dell is better known in the United States, it can borrow on its own dollars at 7 percent and pounds at 9 percent, whereas Virgin can on its own borrow dollars at 8 percent and pounds at 8.5% a. Suppose Dell wants to borrow £10 million for two years, Virgin wants to borrow $16 million for two years, and the current ($/£) exchange rate is $1.60. What swap transaction would accomplish this objective? Assume the counterparties would exchange principal and interest payments with no rate adjustments. ANSWER. Virgin would borrow £10 million for two years and Dell would borrow $16 million for two years. The two companies would then swap their proceeds and payment streams. b. What savings are realized by Dell and Virgin? ANSWER. Assuming no interest rate adjustments, Dell would pay 8.5% on the £10 million and Virgin would pay 7% on its $16 million. Given that its alternative was to borrow pounds at 9%, Dell would save 0.5% on its borrowings, or an annual savings of £50,000. Similarly, Virgin winds up paying an interest rate of 7% instead of 8% on its dollar borrowings, saving it 1% or $160,000 annually. c.
Suppose, in fact, that Dell can borrow dollars at 7 percent and pounds at 9 percent, whereas Virgin can borrow dollars at 8.75 percent and pounds at 9.5 percent. What range of interest rates would make this swap attractive to both parties?
ANSWER. Ignoring credit risk differences, Virgin would have to provide Dell with a pound rate of less than 9%. Given that Virgin has to borrow the pounds at 9.5%, it would have to save at least 0.5% on its dollar borrowing from Dell to make the swap worthwhile. If Dell borrows pounds from Virgin at 9% - x. then Virgin would have to borrow dollars from Dell at 8.75% - (0.5% + x) to cover the 0.5% + x difference between the interest rate at which it was borrowing pounds and the interest rate at which it was lending those pounds to Dell. d.
Based on the scenario in part (c), suppose Dell borrows dollars at 7 percent and Virgin borrows pounds at 9.5 percent. If the parties swap their current proceeds, with Dell paying 8.75 percent to Virgin for pounds and Virgin paying 7.75 percent to Dell for dollars, what are the cost savings to each party?
ANSWER. Under this scenario, Dell saves 0.25% on its pound borrowings and earns 0.75% on the dollars it swaps with Virgin, for a total benefit of 1% annually. Virgin loses 0.75% on the pounds it swaps with Dell and saves 1% on the dollars it receives from Dell, for a net savings of 0.25% annually. 2. In May 1988, Walt Disney Productions sold to Japanese investors a 20-year stream of projected yen royalties from Tokyo Disneyland. The present value of that stream of royalties, discounted at 6 percent (the return required by the Japanese investors), was ¥93 billion. Disney took the yen proceeds from the sale, converted them to dollars, and invested the dollars in bonds yielding 10 percent. According to Disney's chief financial officer, Gary Wilson, "In effect, we got money at a 6 percent discount rate, reinvested it at 10 percent, and hedged our royalty stream against yen fluctuations--all in one transaction." a. At the time of the sale, the exchange rate was ¥124 = $1. What dollar amount did Disney realize from the sale of its yen proceeds? ANSWER. Disney realized 93,000,000,000/124 = $750,000,000 from the sale of its future yen proceeds. b. Demonstrate the equivalence between Walt Disney's transaction and a currency swap. (Hint: A diagram would help.)
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INSTRUCTORS MANUAL: MULTNATIONAL FINANCIAL MANAGEMENT, 10TH ED.
ANSWER. In a currency/interest rate swap, one party trades a stream of payments in one currency, at one interest rate, for a stream of payments in a second currency, at a second interest rate. Disney's stream of yen royalties can be treated as a yen bond, which it traded for a dollar bond, with dollar payments. The only difference between the Disney swap and a traditional swap is that the latter usually involve cash outflows whereas the Disney swap involves cash inflows. c. Comment on Gary Wilson's statement. Did Disney achieve the equivalent of a free lunch through its transaction? ANSWER. Gary Wilson is committing the economist's unpardonable sin: He is comparing apples with oranges, in this case, a 6% yen interest rate with a 10% dollar interest rate. The international Fisher effect tells us that the most likely reason that the yen interest rate is 4 percentage points less than the equivalent dollar interest rate is because the market expects the dollar to depreciate by about 4% annually against the yen. 3. Suppose that IBM would like to borrow fixed-rate yen, whereas Korea Development Bank (KDB) would like to borrow floating-rate dollars. IBM can borrow fixed-rate yen at 4.5 percent or floating-rate dollars at LIBOR + 0.25 percent. KDB can borrow fixed-rate yen at 4.9 percent or floating-rate dollars at LIBOR + 0.8 percent. a. What is the range of possible cost savings that IBM can realize through an interest rate/currency swap with KDB? ANSWER. The cost to each party of accessing either the fixed-rate yen or the floating-rate dollar market for a new debt issue is as follows: Borrower Korea Development Bank IBM Difference
Fixed-Rate Yen Available 4.9% 4.5% 0.4%
Floating-Rate Dollars Available LIBOR + 0.80% LIBOR + 0.25% 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 + 0.25% 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 + 0.25%, saving KDB 0.55%, which then passed these savings along to IBM by swapping the fixed-rate yen at 4.9% - 0.55% = 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% - 0.07%). 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 $100 million (¥12.8 billion at the current spot rate). Every six months, 3M pays BT U.S. dollar LIBOR6, while
CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES
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BT makes payments to 3M of 1.3 percent annually in yen. At maturity, BT and 3M reverse the notional principals.
a. Assume that LIBOR6 (annualized) and the ¥/$ 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)
t
5.7%
128
t+6
5.4%
132
t + 12
5.3%
137
t + 18
5.9%
131
t + 24
5.8%
123
Net $ receipt (+)/payment (-)
ANSWER. The semiannual receipts, payments, and net receipts (payments) are computed as follows: Time (months) t t+6 t + 12 t + 18 t + 24
LIBOR6 ¥/$ (spot) Receipt Payment Net $ receipt (+)/payment (-) 5.70% 128 5.40% 132 $630,303 $2,700,000 $2,069,697 5.30% 137 $607,299 $2,650,000 $2,042,701 5.90% 131 $635,115 $2,950,000 $2,314,885 5.80% 123 $676,423 $2,900,000 $2,223,577
There is no payment or receipt at time t. The semiannual payment is calculated as $100,000,000 x LIBOR6/2. The semiannual receipt is calculated as 12,800,000,000 x 0.013/2 x 1/S, where S is the current spot rate (¥/$). b.
What is the all-in dollar cost of 3M's loan?
ANSWER. The net payments made semiannually by 3M are shown in the table below. The net payment is computed as the LIBOR6 payment made to BT less the dollar value of the 0.05% semiannual difference between the yen interest received and the yen interest paid (shown in the column labeled “Receipt.”) Time (months) T T+6 T + 12 T + 18 t + 24
c.
LIBOR6 5.70% 5.40% 5.30% 5.90% 5.80%
¥/$ (spot) Receipt Payment Net payment 128 -$100,000,000 132 $48,485 $2,700,000 $2,651,515 137 $46,715 $2,650,000 $2,603,285 131 $48,855 $2,950,000 $2,901,145 123 $52,033 $2,900,000 $102,847,967 IRR 2.75% Annualized 5.50%
Suppose 3M decides at t + 18 to use a six-month forward contract to hedge the t + 24 receipt of yen from BT. Six-month interest rates (annualized) at t + 18 are 5.9% in dollars and 2.1% in yen. With this hedge in place, what fixed dollar amount would 3M have paid (received) at time t + 24? How does this amount compare to the t + 24 net payment computed in part a?
ANSWER. Given the interest rates presented in the problem, we can use interest rate parity to compute the 6-month forward rate at time t + 18 as ¥128.58/$:
0.021 2 = ¥128.58 f 180 = 131x 0.059 1+ 2 1+
3M will pay out $2.9 million (0.059/2 x $100,000,000) and receive $647,056 (0.013/2 x 12,800,000 x 1/128.58). The latter figure is calculated by converting its yen receipt into dollars at the forward rate of ¥128.58/$. 3M’s net payment equals $2,252,944 ($2,900,000 - $647,056). This amount is $29,367 more than the net payment of $2,223,577 it would have made otherwise. d.
Does it make sense for 3M to hedge its receipt of yen from BT? Explain.
ANSWER. No. As it now stands, 3M receives yen and pays out yen, resulting in a zero net exposure on the swap (aside from the net 0.05% semiannual yen receipt). Hedging would expose 3M to currency risk and negate the purpose of the cross-currency swap, which is to allow 3M to engage in arbitrage while being shielded from currency risk. 5.
Suppose LIBOR3 is 7.93 percent and LIBOR6 is 8.11 percent. What is the forward forward rate for a LIBOR3 deposit to be placed in three months?
ANSWER. Through arbitrage, the future value in six months of $1 invested today must be the same whether we invest at LIBOR3 today and enter into a forward forward for the following three months or invest at LIBOR6 today. That is, (1 + LIBOR3/4)(1 + r/4) = 1 + LIBOR6/2 where r equals the forward forward rate for a LIBOR3 deposit to be placed in three months. Substituting in numbers from the problem, we have 1.0198(1 + r/4) = 1.04055. Solving this equation yields r = 8.13%. 6.
Suppose that Skandinaviska Ensilden Banken (SEB), the Swedish bank, funds itself with three-month Eurodollar time deposits at LIBOR. Assume that Alfa Laval comes to SEB seeking a one-year, fixed-rate loan of $10 million, with interest to be paid quarterly. At the time of the loan disbursement, SEB raises three-month funds at 5.75%, but has to roll over this funding in three successive quarters. If it does not lock in a funding rate and interest rates rise, the loan could prove to be unprofitable. The three quarterly re-funding dates fall shortly before the next three Eurodollar futures-contract expirations in March, June, and September.
a.
At the time the loan is made, the price of each contract is 94.12, 93.95, and 93.80. Show how SEB can use Eurodollar futures contracts to lock in its cost of funds for the year. What is SEB's hedged cost of funds for the year?
ANSWER. The formula for the locked-in LIBOR, r, given a price P of a Eurodollar futures contract is r = 100 - P. Using this formula, the solution r for each of the contracts is 5.82%, 6.05%, and 6.2%. So SEB can lock in a cost for its $10 million loan equal to $10,000,000 x (1 + 0.0575/4)(1 + 0.0582/4)(1 + 0.0605) (1 + 0.062/4) = $10,608,927, which is equivalent to a one-year fixed interest rate of 6.09%. Effectively, what this procedure does is to roll over the principal and cumulative interest payment each quarter until it is paid off in a lump sum at the end of the fourth quarter. b.
Suppose that the settlement prices of the March, June, and September contracts are, respectively, 92.98, 92.80, and 92.66. What would have been SEB's unhedged cost of funding the loan to Alfa Laval?
ANSWER. We can solve this problem by using the insight that at the time of settlement, arbitrage will ensure that the settlement price for a Eurodollar futures contract will be virtually identical to the actual LIBOR on that date. Given the stated prices at settlement, actual LIBOR on each rollover date was 7.02%, 7.2%, and 7.34%. Based on these figures, the unhedged cost of the loan is $10,000,000 x (1 + 0.0575/4)(1 + 0.0702/4)(1 + 0.072/4)(1 + 0.0734/4) = $10,700,379. This is equivalent to an annual rate of 7.00%, or 91 basis points more than the hedged cost of the loan.
