INSTRUCTOR’S MANUAL MULTINATIONAL FINANCIAL MANAGEMENT , 9
TH
ED.
1. What is an interest rate swap? What is the difference between a basis swap and a coupon swap?
A NSWER .
An interest rate swap is an agreement between two parties to exchange interest payments in the same currency for a specific maturity on an agreed upon notional amount. The term notional refers to the theoretical principal underlying the swap. In the coupon swap, one party pays a fixed rate calculated at the time of trade as a spread to a particular Treasury bond, while the other side pays a floating rate that resets periodically throughout the life of the deal against a designated index. In a basis swap, a floating-rate liability tied to one reference rate, say,
LIBOR, is exchanged for a floating rate-liability with another reference rate, say, 90-day Treasury bills. Thus, coupon swaps convert fixed-rate debt into floating-rate debt (or vice versa), whereas the basis swap converts one type of floating-rate debt into another type of floating-rate debt.
2. What is a currency swap?
A
NSWER
.
A currency swap involves the exchange of principal plus interest payments in one currency for equivalent payments in another currency.
3. Comment on the following statement. "In order for one party to a swap to benefit, the other party must lose."
A NSWER .
Given that both parties to the swap freely enter into the swap transaction, both must perceive benefits.
The tax, financial market, and regulatory system arbitrage benefits associated with swaps are shared by both parties.
4. The Swiss Central Bank bans the use of Swiss francs for Eurobond issues. Explain how currency swaps can be used to enable foreign borrowers who want to raise Swiss francs through a bond issue outside of Switzerland to get around this ban.
A NSWER . Foreign borrowers can issue Eurodollar bonds and then swap the proceeds for Swiss francs. In this way, they can raise Swiss francs without violating the ban on issuing Swiss franc Eurobonds.
5. Explain how IBM can use a forward rate agreement to lock in the cost of a one-year $25 million loan to be taken out in six months. Alternatively, explain how IBM can lock in the interest rate on this loan by using
Eurodollar futures contracts. What is the major difference between using the FRA and the futures contract to hedge IBM’s interest rate risk?
A NSWER .
To lock in the rate on a one-year $25 million loan to be taken out in six months, IBM could buy a "6 x
12" FRA on LIBOR for a notional principal of $25 million. This means that IBM has entered into a six-month forward contract on 12-month LIBOR. Alternatively, IBM can lock in the interest rate on this loan by selling 25 $1 million 6-month futures contracts. However, this transaction will only protect IBM for the first three months of its loan. To hedge the remaining nine months of future loan, IBM would have to sell 25 $1 million 9-month, 12month, and 15-month futures contracts. The most important difference between using the FRA and the futures contract is that is that the latter is marked to market daily, meaning that gains and losses are settled in cash each day. In addition, the FRA involves entering into just one contract for the 12-month loan, whereas using the futures contract to hedge IBM’s interest rate risk involves entering into four separate three-month futures contracts.
1. What factors underlie the economic benefits of swaps?
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CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES
A NSWER .
For swaps to provide economic benefits, they must allow the transacting parties to engage in some form of tax, regulatory system, or financial market arbitrage. Thus, underlying the economic benefits of swaps are barriers that prevent other forms of arbitrage from functioning fully. This impediment must take the form of legal restrictions on spot and forward foreign exchange transactions, different perceptions by investors of risk and creditworthiness of the two parties, appeal or acceptability of one borrower to a certain class of investor, tax differentials, and so forth. If the world capital market were fully integrated, the incentive to swap would be reduced because fewer arbitrage opportunities would exist.
2. Comment on the following statement. "During the period 1987-1989, Japanese companies issued some $115 billion of bonds with warrants attached. Nearly all were issued in dollars. The dollar bonds usually carried coupons of 4% or less; by the time the Japanese companies swapped that exposure into yen (whose interest rate was as much as five percentage points lower than the dollar's), their cost of capital was zero or negative."
A NSWER .
This statement assumes that the warrants on these Japanese bonds, which are long-dated call options, are costless for the Japanese firms to issue. They are not. During this period, Japanese stock prices rose dramatically.
The net result was that Japanese firms did not issue cheap debt; instead, they issued expensive equity. That is, they issued equity at the exercise price on the warrants, which was typically far below the price at which they could have sold new stock in the marketplace.
3. Explain how Cisco Systems can use arbitrage to create a forward forward to fix the interest rate on a threemonth $10 million loan to be taken out in nine months. The loan will be priced off LIBOR.
A NSWER .
Cisco can lock in a three-month rate on a $10 million loan to be taken out in nine months by buying a forward forward or by creating its own through arbitrage. Specifically, Cisco can derive a nine-month forward rate on LIBOR3 by simultaneously lending the present value of $10 million for nine months and borrowing that same amount of money for 12 months.
4. Why do governments provide subsidized financing for some investments?
A NSWER .
Governments use subsidized financing to encourage programs and activities that are deemed to be worthy. For example, governments provide subsidized trade financing to boost exports and low-cost financing to projects expected to create jobs in regions with high unemployment. Often, these subsidies offset regulatory and other costs that are imposed on companies by the same governments.
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.
A NSWER .
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?
A NSWER .
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.
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INSTRUCTOR’S MANUAL MULTINATIONAL FINANCIAL MANAGEMENT , 9
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ED. 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?
A NSWER .
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?
A NSWER .
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?
A
NSWER
.
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.)
A NSWER .
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?
A NSWER .
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?
A NSWER .
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:
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CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES
Borrower
Korea Development Bank
IBM
Fixed-Rate Yen Available Floating-Rate Dollars Available
4.9% LIBOR + 0.80%
4.5% LIBOR + 0.25%
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 + 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?
A NSWER .
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.
A NSWER .
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
$100 million (¥12.8 billion at the current spot rate). Every six months, 3M pays BT U.S. dollar LIBOR6, while
BT makes payments to 3M of 1.3 percent annually in yen. At maturity, BT and 3M reverse the notional principals. a. Assume that LIBOR6 (annualized) and the ¥/$ exchange rate evolve as follows. Calculate the net dollar amount that 3M pays to BT ("-") or receives from BT ("+") each six-month period.
Net $ receipt (+)/payment (-) t + 6 t + 12 t + 18 t + 24
5.4%
5.3%
5.9%
5.8%
132
137
131
123
A NSWER .
The semiannual receipts, payments, and net receipts (payments) are computed as follows:
Time (months) LIBOR6 ¥/$ (spot) Receipt Payment Net $ receipt (+)/payment (-) t + 6 t + 12 t + 18 t + 24
5.40%
5.30%
5.90%
5.80%
132
137
131
123
$630,303
$607,299
$635,115
$676,423
$2,700,000
$2,650,000
$2,950,000
$2,900,000
$2,069,697
$2,042,701
$2,314,885
$2,223,577
There is no payment or receipt at time t. The semiannual payment is calculated as $100,000,000 x LIBOR6/2. The semiannual receipt is calculated as 12,800,000,000 x 0.013/2 x 1/S, where S is the current spot rate (¥/$).
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INSTRUCTOR’S MANUAL MULTINATIONAL FINANCIAL MANAGEMENT , 9
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ED. b. What is the all-in dollar cost of 3M's loan?
A NSWER .
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) LIBOR6 ¥/$ (spot) Receipt Payment Net
T + 6
T + 12
T + 18 t + 24
5.40%
5.30%
5.90%
5.80%
132
137
131
123
$48,485
$46,715
$48,855
$52,033
$2,700,000
$2,650,000
$2,950,000
$2,900,000
IRR
-$100,000,000
$2,651,515
$2,603,285
$2,901,145
$102,847,967
2.75%
Annualized 5.50% c. Suppose 3M decides at t + 18 to use a six-month forward contract to hedge the t + 24 receipt of yen from BT.
Six-month interest rates (annualized) at t + 18 are 5.9% in dollars and 2.1% in yen. With this hedge in place, what fixed dollar amount would 3M have paid (received) at time t + 24? How does this amount compare to the t + 24 net payment computed in part a?
A NSWER .
Given the interest rates presented in the problem, we can use interest rate parity to compute the 6-month forward rate at time t + 18 as ¥128.58/$: f
180
= 131x
1 +
0.021
2
0.059
1 +
2
= ¥128.58
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.
A NSWER .
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?
A NSWER .
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%.
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CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES
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 an 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?
A NSWER .
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?
A NSWER .
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.
1. Company A, a low-rated firm, desires a fixed-rate, long-term loan. A currently has access to floating interest rate funds at a margin of 1.5% over LIBOR. Its direct borrowing cost is 13% in the fixed-rate bond market. In contrast, company B, which prefers a floating-rate loan, has access to fixed-rate funds in the Eurodollar bond market at 11% and floating-rate funds at LIBOR + ½%. a. How can A and B use a swap to advantage?
A NSWER .
Based on the numbers presented, there is an anomaly between the two markets: One judges that the difference in credit quality between the two firms is worth 200 basis points, whereas the other determines that this difference is worth only 100 basis points. The parties can share among themselves the difference of 100 basis points by engaging in a currency swap. This transaction would involve A borrowing floating-rate funds and B borrowing fixed-rate funds and then swapping the proceeds. b. Suppose they split the cost savings. How much would A pay for its fixed-rate funds? How much would B pay for its floating-rate funds?
A NSWER .
If they split the cost savings, the resulting costs to the two parties would be 12.5% for A and LIBOR for
B, calculated as follows:
Party
Counterparty A
Counterparty B
Normal Funding Cost
13.00%
LIBOR + 1/2%
Cost After Swap
12.50
LIBOR
Difference
.50%
.50%
Total 1.00%
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INSTRUCTOR’S MANUAL MULTINATIONAL FINANCIAL MANAGEMENT , 9
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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?
A NSWER .
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 5.4375%. a. Explain how Nestle can use an FRA at 6% from Credit Suisse to reduce its interest rate risk on this loan.
A NSWER .
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?
A NSWER .
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:
Interest payment = notional principal x
(LIBOR forward
1 + LIBOR x( rate)( days
360
) days
360
)
Substituting in the figures from the problem yields an interest payment from Credit Suisse of $15,385:
Interest payment = $25,000,00 0 x
(0.0625
0.06)(
1 + 0.0625
x(
90
360
90
360
)
)
= $15,385 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?
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CHAPTER 9: SWAPS AND INTEREST RATE DERIVATIVES
A NSWER .
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.
A NSWER .
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?
A NSWER .
In this case, Ford will receive from Banque Paribas $20,000,000 x (0.0765 - 0.075)/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?
A NSWER .
In this case, Ford will pay Banque Paribas $20,000,000 x (0.08 - 0.0765)/2 = $35,000, giving it–as before– an annualized hedged deposit rate of 7.65% for the next six months .
8