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

The loss of the financial institution is $413,000

Explanation:

Let's say that after 3 years the financial institution will receive:

0.5 * 10% of $10million

= 0.5 * 0.1 * 10000000

= $500,000

Then, they will pay 0.5 * 9% of $10M

= 0.5 * 0.09 * 10000000

= $450,000

Therefore, their immediate loss would be $500000 - $450000

= $50000.

Let's assume that forward rates are realized to value the rest of the swap.

The forward rates = 8% per annum.

Therefore, the remaining cash flows are assumed that floating payment is

0.5*0.08*10000000 =

$400,000

Received net payment would be:

500,000-400,000 = $100,000. The total cost of default is therefore the cost of foregoing the following cash flows:

Year 3=$50,000

Year 3.5=$100,000

Year 4 = $100,000

Year 4.5 = $100,000

Year 5 = $100,000

Discounting these cash flows to year 3 at 4% per six months, the cost of default would be $413,000