Question

A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five years. Payments are made every six months. Suppose that company X defaults on the sixth payment date (end of year 3) when the interest rate (with semiannual compounding) is 8% per annum for all maturities. What is the loss to the financial institution? Assume that six-month LIBOR was 9% per annum halfway through year 3.

Please detailed calculations, do not use excel.

Answer 1

Solution

While calculating interest rate swaps, the LIBOR rate for the previous period is used. Hence, we will use 9%, which was the LIBOR rate midway through the third year to calculate the payment which was defaulted by company X.

The formula to calculate the payment due at the end of the third year is:

((Fixed interest rate received) * 180/360) - (LIBOR rate paid) * 180/360) * principal amount

we are multiplying the rates by 180/360, as the contract was biannual.

Hence, at the sixth instalment of the contract, at the end of the third year, the amount due to the financial institution was:

(0.10*180/360) - (0.09*180/360) * $10,000,000 = $50,000

Since company X defaulted, the loss to the financial institution was $50,000