Third National Bank has made a 10-year,$25 million fixed-rate loan at 12%.Annual interest payments are $3 million,and all principal will be repaid in year 10.The bank wants to swap the fixed interest payments into floating-rate payments.If the bank could borrow at a fixed rate of 10% for 10 years,what is the notional principal of the swap?

Question

Quizplus · Accepted Answer

The bank wants to swap the fixed interest payments into floating-rate payments. Therefore, it needs to find a counterparty who is willing to pay it the fixed interest payments of $3 million annually and receive floating-rate payments in return.

The bank can enter into an interest rate swap where it agrees to pay the counterparty a fixed rate of 12% and receive a floating rate based on LIBOR. The payments in the interest rate swap will offset the fixed interest payments on the loan, leaving the bank with only the floating-rate payments.

To determine the notional principal of the swap, we need to calculate the present value of the fixed interest payments of $3 million annually for 10 years at a rate of 10%.

PV = PMT x [1 - (1 + r)-n]/r

PV = $3 million x [1 - (1 + 0.10)-10]/0.10
PV = $20.947 million

This means that the bank needs a counterparty who is willing to enter into an interest rate swap with a notional principal of $20.947 million.

However, since the bank has a $25 million loan, it will need to receive floating-rate payments based on a notional principal of $25 million. This means that the counterparty will be paying floating-rate payments based on a notional principal of $25 million and receiving fixed interest payments based on a notional principal of $30 million.

Therefore, the answer is D) $30 million.

Third National Bank Has Made a 10-Year,$25 Million Fixed-Rate Loan