First National Bank has made a 5-year, $100 million fixed-rate loan at 10%. Annual interest payments are $10 million, and all principal will be repaid in year 5. The bank wants to swap the fixed interest payment into floating-rate payments. If the bank could borrow at a fixed rate of 8% for 5 years, what is the notional principal of the swap?

Question

Quizplus · Accepted Answer

To swap from fixed to floating, First National Bank would enter into an interest rate swap where they receive a fixed rate of 10% and pay a floating rate based on a benchmark such as LIBOR. They would receive payments from the borrower of $10 million per year, and pay a floating rate.

To offset the risk of receiving a fixed rate and paying a floating rate, First National Bank would enter into a second swap where they pay a fixed rate of 8% and receive a floating rate. This swap would effectively convert their fixed payment obligations into floating payment obligations.

To determine the notional principal of the second swap, we can set the present value of the fixed payments equal to the present value of the floating payments. The present value of the fixed payments is $50 million (5 years x $10 million per year). The present value of the floating payments is $40 million (5 years x $8 million per year). Therefore, the notional principal of the swap would be $125 million ($50 million / 0.4).

So, the answer would be C.

First National Bank Has Made a 5-Year, $100 Million Fixed-Rate