1. JPMorgan Chase and Facebook agree on an interest rate swap on September 25, 2018 on a notional principal of $500 million. JPMorgan Chase will make annual floating payments according to the 1-year LIBOR plus 50 basis points. Facebook in return will make annual fixed-rate payments. The first cash flow exchange will occur on September 25, 2019. The contract will last for a period of 5 years, i.e., there will be a total of 5 payments for each company. On September 25, 2018, the following LIBOR zero rates and continuously compounded risk-free interest rates are as follows: LIBOR Zero Rate (%) Forward LIBOR (%) Risk-free Rate (%) Maturity 1 year 3.00 2.25 2 years 3.25 2.50 3 years 3.75 2.75 4.00 3.00 4 years 5 years 4.25 3.50 a) (2 points) If there is no cash settlement at the initiation of the contract, what should be the fair fixed rate that Facebook should pay? (Hint: Follow the steps and tables in the interest rate swap example for GE and MSFT in lecture slides. Step 1: Compute the forward LIBOR rate. Step 2: Compute the total present value of floating-rate payments. Step 3: Assume the fixed rate is % and compute the total present value of fixed-rate payments. Step 4: Equate the total present value of payments on the two sides and solve for the fair swap rate.) b) (0.5 points) If Facebook prefers a fixed rate of 5% annually, what cash settlement is needed between the parties on September 25, 2018 in order to have a fair contract? c) (1.5 points) On September 25, 2020, the LIBOR zero rates and risk-free interest rates become: Maturity 1 year 2 years LIBOR Zero Rate %) Forward LIBOR (%) 3.50 Risk-free Rate (%) 2.75 3.75 3.00 3 years 4.00 3.25 Compute the value of the swap to Facebook (assuming it pays a 5% fixed rate). (Hint: Follow the steps and tables in the "Valuation after Contract Initiation" example for GE and MSFT in lecture slides. Step 1: Compute the forward LIBOR rate. Step 2: Compute the total present value of floating-rate payments. Step 3: Compute the total present value of fixed-rate payments. Step 4: Take the difference between the two total present values and be careful with the sign.) 2. (1.5 points) Alibaba Group entered a currency swap with Goldman Sachs three years ago. 1. JPMorgan Chase and Facebook agree on an interest rate swap on September 25, 2018 on a notional principal of $500 million. JPMorgan Chase will make annual floating payments according to the 1-year LIBOR plus 50 basis points. Facebook in return will make annual fixed-rate payments. The first cash flow exchange will occur on September 25, 2019. The contract will last for a period of 5 years, i.e., there will be a total of 5 payments for each company. On September 25, 2018, the following LIBOR zero rates and continuously compounded risk-free interest rates are as follows: LIBOR Zero Rate (%) Forward LIBOR (%) Risk-free Rate (%) Maturity 1 year 3.00 2.25 2 years 3.25 2.50 3 years 3.75 2.75 4.00 3.00 4 years 5 years 4.25 3.50 a) (2 points) If there is no cash settlement at the initiation of the contract, what should be the fair fixed rate that Facebook should pay? (Hint: Follow the steps and tables in the interest rate swap example for GE and MSFT in lecture slides. Step 1: Compute the forward LIBOR rate. Step 2: Compute the total present value of floating-rate payments. Step 3: Assume the fixed rate is % and compute the total present value of fixed-rate payments. Step 4: Equate the total present value of payments on the two sides and solve for the fair swap rate.) b) (0.5 points) If Facebook prefers a fixed rate of 5% annually, what cash settlement is needed between the parties on September 25, 2018 in order to have a fair contract? c) (1.5 points) On September 25, 2020, the LIBOR zero rates and risk-free interest rates become: Maturity 1 year 2 years LIBOR Zero Rate %) Forward LIBOR (%) 3.50 Risk-free Rate (%) 2.75 3.75 3.00 3 years 4.00 3.25 Compute the value of the swap to Facebook (assuming it pays a 5% fixed rate). (Hint: Follow the steps and tables in the "Valuation after Contract Initiation" example for GE and MSFT in lecture slides. Step 1: Compute the forward LIBOR rate. Step 2: Compute the total present value of floating-rate payments. Step 3: Compute the total present value of fixed-rate payments. Step 4: Take the difference between the two total present values and be careful with the sign.) 2. (1.5 points) Alibaba Group entered a currency swap with Goldman Sachs three years ago
