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#### Problem 7

###### Finance

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 floating-rate loan; company B requires a fixed-rate 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.

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:

 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.

Problem 7.4.

Explain what a swap rate is. What is the relationship between swap rates and par yields?

Problem 7.5.

A currency swap has a remaining life of 15 months. It involves exchanging interest at 10% on £20 million for interest at 6% on \$30 million once a year. The term structure of risk-free interest rates in the United Kingdom is flat at 7% and the term structure of risk-free rates in the United States is flat at 4% (both with annual compounding). The current exchange rate (dollars per pound sterling) is 1.5500. What is the value of the swap to the party paying sterling? What is the value of the swap to the party paying dollars?

Problem 7.6.

Explain the difference between the credit risk and the market risk in a financial contract.

Problem 7.7.

A corporate treasurer tells you that he has just negotiated a five-year loan at a competitive fixed rate of interest of 5.2%. The treasurer explains that he achieved the 5.2% rate by borrowing at six-month LIBOR plus 150 basis points and swapping LIBOR for 3.7%. He goes on to say that this was possible because his company has a comparative advantage in the floating-rate market. What has the treasurer overlooked?

Problem 7.8.

Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts.

Problem 7.9.

Companies X and Y have been offered the following rates per annum on a \$5 million 10-year investment:

 Fixed Rate Floating Rate Company X 8.0% LIBOR Company Y 8.8% LIBOR

Company X requires a fixed-rate investment; company Y requires a floating-rate investment. Design a swap that will net a bank, acting as intermediary, 0.2% per annum and will appear equally attractive to X and Y.

Problem 7.11.

Companies A and B face the following interest rates (adjusted for the differential impact of taxes):

 A B US Dollars (floating rate) LIBOR+0.5% LIBOR+1.0% Canadian dollars (fixed rate) 5.0% 6.5%

Assume that A wants to borrow U.S. dollars at a floating rate of interest and B wants to borrow Canadian dollars at a fixed rate of interest. A financial institution is planning to arrange a swap and requires a 50-basis-point spread. If the swap is equally attractive to A and B, what rates of interest will A and B end up paying?

Problem 7.15.

Why is the expected loss to a bank from a default on a swap less than the expected loss from the default on a loan to the counterparty with the same principal?

Assume no other transactions between the bank and the counterparty, that the swap is cleared bilaterally, and that no collateral is provided by the counterparty in the case of either the swap or the loan.

Problem 7.16.

A bank finds that its assets are not matched with its liabilities. It is taking floating-rate deposits and making fixed-rate loans. How can swaps be used to offset the risk?

Problem 7.17.

Explain how you would value a swap that is the exchange of a floating rate in one currency for a fixed rate in another currency.

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