CHAPTER 7
Swaps
Practice Questions
Problem 7.1.
Companies A and B have been offered the following rates per annum on a $20 million five
year loan:
Fixed Rate
Floating Rate
Company A
5.0%
LIBOR+0.1%
Company B
6.4%
LIBOR+0.6%
Company A requires a floatingrate loan; company B requires a fixedrate loan. Design a
swap that will net a bank, acting as intermediary, 0.1% per annum and that will appear
equally attractive to both companies.
A has an apparent comparative advantage in fixedrate markets but wants to borrow floating.
B has an apparent comparative advantage in floatingrate markets but wants to borrow fixed.
This provides the basis for the swap. There is a 1.4% per annum differential between the
fixed rates offered to the two companies and a 0.5% per annum differential between the
floating rates offered to the two companies. The total gain to all parties from the swap is
therefore
1 4
0 5
0 9
% per annum. Because the bank gets 0.1% per annum of this gain, the
swap should make each of A and B 0.4% per annum better off. This means that it should lead
to A borrowing at LIBOR
0 3
% and to B borrowing at 6.0%. The appropriate arrangement
is therefore as shown in Figure S7.1.
Figure S7.1
Swap for Problem 7.1
Problem 7.2.
Company X wishes to borrow U.S. dollars at a fixed rate of interest. Company Y wishes to
borrow Japanese yen at a fixed rate of interest. The amounts required by the two companies
are roughly the same at the current exchange rate. The companies have been quoted the
following interest rates, which have been adjusted for the impact of taxes:
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Yen
Dollars
Company X
5.0%
9.6%
Company Y
6.5%
10.0%
Design a swap that will net a bank, acting as intermediary, 50 basis points per annum. Make
the swap equally attractive to the two companies and ensure that all foreign exchange risk is
assumed by the bank.
X has a comparative advantage in yen markets but wants to borrow dollars. Y has a
comparative advantage in dollar markets but wants to borrow yen. This provides the basis for
the swap. There is a 1.5% per annum differential between the yen rates and a 0.4% per annum
differential between the dollar rates. The total gain to all parties from the swap is therefore
1 5
0 4
1 1
% per annum. The bank requires 0.5% per annum, leaving 0.3% per annum for
each of X and Y. The swap should lead to X borrowing dollars at
9 6
0 3
9 3
% per annum
and to Y borrowing yen at
6 5
0 3
6 2
% per annum. The appropriate arrangement is
therefore as shown in Figure S7.2. All foreign exchange risk is borne by the bank.
Figure S7.2
Swap for Problem 7.2
Problem 7.3.
A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the
swap, sixmonth LIBOR is exchanged for 7% per annum (compounded semiannually). The
average of the bid
–
offer rate being exchanged for sixmonth LIBOR in swaps of all maturities
is currently 5% per annum with continuous compounding. The sixmonth LIBOR rate was
4.6% per annum two months ago. What is the current value of the swap to the party paying
floating? What is its value to the party paying fixed?
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 Spring '11
 Burns
 Derivative, Interest Rates, United States dollar, Forward contract, Interest rate swap

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