1. Suppose that some time ago a financial institution entered into a swap where it agreed to make semiannual payments at a rate of 3.5% per annum and receive LIBOR on a notional principal of $300 million. The swap now has a remaining life of 1.15 years. Payments will therefore be made 0.15, 0.65, and 1.15 years from today. The risk-free rates with continuous compounding for maturities of 0.15, 0.65, and 1.15 years are 2.8%, 3.2%, and 3.4%, respectively. We suppose that the forward LIBOR rates for the 0.15-to-0.65 year and the 0.65-to-1.15 year periods are 3.4% and 3.7%, respectively, with semiannual compounding. The LIBOR rate applicable to the exchange in 0.15 years was determined 0.35 years ago. Suppose it is 2.9% with semiannual compounding.
What is the value of the swap (in $ millions)?
2. Microsoft can borrow at 3.5% or at LIBOR plus 10 basis points. General Motors can borrow at 4.5% or at LIBOR plus 30 basis points. Suppose that Microsoft borrows fixed and General Motors borrows floating. If they enter into a swap with each other where the apparent benefits are shared equally, Microsofts effective borrowing rate will be LIBOR plus how many basis points? (Note: the answer may be positive or negative)
3. Suppose that the continuously compounded risk-free interest rates for 1-year, 2-year, and 3-year investments in Japan are 3.6%, 3.9%, and 4.1% per annum, respectively. Suppose further that the continuously compounded risk-free interest rates for 1-year, 2-year, and 3-year investments in the United States are 2.8%, 3.2%, and 3.5% per annum, respectively. A financial institution has entered into a currency swap in which it receives 4.5% per annum in yen and pays 3.9% per annum in dollars once a year. The principals in the two currencies are $50 million and 6,000 million yen. The swap will last for another three years, and the current exchange rate is 115 yen per dollar.
What is the yen cash flow at time 2 (in millions)?
4. Suppose that the continuously compounded risk-free interest rates for 1-year, 2-year, and 3-year investments in Japan are 3.6%, 3.9%, and 4.1% per annum, respectively. Suppose further that the continuously compounded risk-free interest rates for 1-year, 2-year, and 3-year investments in the United States are 2.8%, 3.2%, and 3.5% per annum, respectively. A financial institution has entered into a currency swap in which it receives 4.5% per annum in yen and pays 3.9% per annum in dollars once a year. The principals in the two currencies are $50 million and 6,000 million yen. The swap will last for another three years, and the current exchange rate is 115 yen per dollar.
What is the value of the swap (in $ millions)?
5. Suppose that some time ago a financial institution entered into a swap where it agreed to make semiannual payments at a rate of 3.5% per annum and receive LIBOR on a notional principal of $300 million. The swap now has a remaining life of 1.15 years. Payments will therefore be made 0.15, 0.65, and 1.15 years from today. The risk-free rates with continuous compounding for maturities of 0.15, 0.65, and 1.15 years are 2.8%, 3.2%, and 3.4%, respectively. We suppose that the forward LIBOR rates for the 0.15-to-0.65 year and the 0.65-to-1.15 year periods are 3.4% and 3.7%, respectively, with semiannual compounding. The LIBOR rate applicable to the exchange in 0.15 years was determined 0.35 years ago. Suppose it is 2.9% with semiannual compounding.
What is the floating cash flow at time 1.15 (in $ millions)?
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