Chapter 21
Interest Rate and Foreign Currency Swaps
QUESTIONS
1. How does an interest rate swap work? In particular, what is the notional principal?
2. What is a currency swap? Describe the structure of and rationale for its cash flows.
3. What is a credit default swap? What happens in the event of default?
4. Banks quote interest rate and currency swaps using the 6-month LIBOR as a basis for both
transactions. How can a bank make money if it does not speculate on movements in either
interest rates or exchange rates?
Chapter 21: Interest Rate and Foreign Currency Swaps
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5. What is the AIC of a bond issue?
6. What is a comparative advantage in borrowing, and how could it arise?
Answer: Comparative advantage in borrowing means that the ratio of the borrowing cost in one
currency (one plus the interest rate) to the borrowing costs in another currency is not the same for two
7. What is basis point adjustment? Why is it not appropriate simply to add the basis point
differential associated with the first currency to the quoted swap rate that the firm will pay?
Answer: If a customer wants the financial intermediary to do a currency swap in which the financial
intermediary will pay the interest and principal on the customer’s outstanding bond, which has an
interest rate that is different from the interest rate that the intermediary is quoting, the financial
8. Discuss the sense in which a 5-year currency swap is a sequence of long-term forward contracts.
How do the implicit forward exchange rates in a currency swap differ from the long-term
forward exchange rates for those maturities?
Chapter 21: Interest Rate and Foreign Currency Swaps
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9. What are the determinants of the value of a currency swap as time evolves? Is it possible to
close out a swap before it has reached maturity?
Answer: When a swap is initiated, the cash flows of two bonds in different currencies are agreed to be
exchanged. These bond-like cash flows have the same present value at the current spot exchange rate.
PROBLEMS
1. General Motors (GM) wants to swap out of $15,000,000 of fixed interest rate debt and into
floating interest rate debt for 3 years. Suppose the fixed interest rate is 8.625% and the floating
rate is dollar LIBOR. What semiannual interest payments will GM receive, and what will GM
pay in return?
Answer: Because General Motors wants to swap out of the fixed interest rate debt into a floating
interest rate debt, it will receive the fixed interest rate side of the swap, and it would pay the semi–
annual LIBOR. Thus, it would receive 6 semiannual payments of
Financial Institution
General Motors
Time Period
Pays the
Fixed Rate
Receives the Floating
Rate
Pays the Floating Rate
Year 0.5
($646,875)
LIBOR/2 x $ 15 mill
(LIBOR/2 x $ 15 mill)
Year 1.0
($646,875)
LIBOR/2 x $ 15 mill
(LIBOR/2 x $ 15 mill)
Year 1.5
($646,875)
LIBOR/2 x $ 15 mill
(LIBOR/2 x $ 15 mill)
Year 2.0
($646,875)
LIBOR/2 x $ 15 mill
(LIBOR/2 x $ 15 mill)
Year 2.5
($646,875)
LIBOR/2 x $ 15 mill
(LIBOR/2 x $ 15 mill)
Year 3.0
($646,875)
LIBOR/2 x $ 15 mill
(LIBOR/2 x $ 15 mill)
Because the currency is the same, only a net interest payment is actually transferred between the
Chapter 21: Interest Rate and Foreign Currency Swaps
5
and you want to pay UBS dollars. UBS pays Swiss francs at 5.25%, and it receives dollars at 8.85%.
When you receive Swiss francs, you pay 6-month dollar LIBOR on the equivalent dollar amount, and
5. Suppose Viacom can issue $100,000,000 of debt at an AIC of 9.42%, whereas Gaz de France can
issue $100,000,000 of debt at an AIC of 10.11%. Suppose that the exchange rate is $1.35/€. If
Viacom issues euro-denominated bonds equivalent to $100,000,000, its AIC will be 8.27%,
whereas if Gaz de France issues such bonds, its AIC will be 9.17%. Which firm has a
comparative advantage when borrowing euros? Why?
Answer: Clearly, Viacom borrows at a lower rate than Gaz de France in both dollars (9.42% vs.
10.11%) and euros (8.27% vs. 9.17%). Viacom therefore has an absolute borrowing advantage in
6. Suppose in problem 5 that because of currency risk, Viacom would prefer to have dollar debt,
and Gaz de France would prefer to have euro debt. How could an investment bank structure a
currency swap that would allow each of the firms to issue bonds denominated in the currency in
which the firm has a comparative advantage while respecting the firms’ preferences about
currency risks?
Answer: Because Viacom has a comparative advantage in borrowing euros, it should borrow euros
and swap into dollars. Gaz de France should do the opposite, that is, borrow dollars and swap into
7. Suppose Sony issues $100,000,000 of 5-year dollar bonds. Nomura will handle the bond issue for
Chapter 21: Interest Rate and Foreign Currency Swaps
6
a fee of 1.875%. Sony’s bonds will be priced at par if they carry a coupon of 8.5%. As the swap
trader for Mitsubishi UFJ (MUFJ), you have been quoting the following rates on 5-year swaps:
U.S. dollars: 8.00% bid and 8.10% offered against the 6-month dollar LIBOR
Japanese yen: 4.50% bid and 4.60% offered against the 6-month dollar LIBOR
Sony would like to do the dollar bond issue, but it prefers to have fixed-rate yen debt. If MUFJ
gets the proceeds of the dollar bond issue, giving Sony an equivalent amount of yen, and MUFJ
agrees to make the dollar interest payments associated with Sony’s dollar bonds, what yen
interest payments should MUFJ charge Sony? What is Sony’s all-in cost in yen? The current
spot exchange rate is ¥98.50/$.
Answer: The following exhibit provides the analysis, which is explained below.
Sony‘s Dollar Bond Issue and Cash Flows in the Swap into Yen with MUFJ
extra extra Effective
dollar yen yen
Year notional $ dollars notional ¥ interest interest cash flows
098.13 -100.00 -98.13 9,850.00 9,665.31
0.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
1 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
1.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
2 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
2.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
3 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
3.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
4 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
4.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14
5 -104.25 104.00 104.25 -10,076.55 0.25 22.59 -10,099.14
AIC 4.49% 4.00% 4.49% 2.30% 2.75%
Annual AIC 9.17% 8.16% 9.17% 4.65% 5.57%
Swap Receipts (+) and Payment (-)
with MUFJ
(All cash flows are in millions of dollars or yen)
Dollar Bond Issue
The first thing to determine is the dollar proceeds of the bond issue. Because it is priced at par, Sony will
receive 1.875% less than the $100 million provided by investors:
$100,000,000
(1 – 0.01875) = $98,125,000
This amount will be given to MUFJ in exchange for an equal amount of yen:
$98,125,000
¥98.50/$ = ¥9,665,312,500
Chapter 21: Interest Rate and Foreign Currency Swaps
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8. Assume that 1 year has passed since you entered into the transaction described in problem 4.
Assume that the new spot exchange rate is CHF1.45/$ and that UBS is now quoting the
following interest rates on 4-year swaps:
U.S. dollars: 7.50% bid and 7.60% offered against the 6-month dollar LIBOR
Swiss francs: 6.75% bid and 6.85% offered against the 6-month dollar LIBOR
If you close out the swap transaction of problem 4, what net dollar cash flow will you
experience? Explain why this is the correct amount. You can assume that the term structures of
interest rates in both currencies are flat.
Answer: You owe eight additional semi-annual payments of $850,962 and a final principal payment
of $19,230,769. The present value of these cash flows at 3.80% = 7.60%/2 is $20,046,721. At the
9. Go to
https://www.verizon.com/about/sites/default/files/annual_reports/2016/downloads/Veriz
on-AnnualReport2016.pdf to find the 2016 Annual Report of Verizon, a large
telecommunications company. Determine whether they use interest rate and/or
currency swaps and why.
Answer: Verizon uses both interest rate and currency swaps. On p. 28, the 2016 annual report states,
Chapter 21: Interest Rate and Foreign Currency Swaps
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Cross Currency Swaps
• We enter into cross currency swaps to exchange British Pound Sterling and Euro-denominated
debt into U.S. dollars and to fix our future interest and principal payments in U.S. dollars, as well
as to mitigate the effect of foreign currency transaction gains or losses. These swaps are