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 LIBOR/swap interest rate (with semiannual compounding) is 9% per annum for all maturities. What is the loss to the financial institution? Assume that six-month LIBOR was 8% per annum halfway through year 3. Use LIBOR discounting.

Answer 1

At the end of the 3rd the financial institution was to receive = $10 million *10% * 0.5 = 500,000

At the end of the 3rd the financial institution was to pay = $10 million *8% * 0.5 = 400,000

The immediate loss = 500,000 - 400,000 = 100,000

The remaining cash flows are valued on the assumption that the floating payment = 0.5 * 9% * 10 million = 450,000

The net payment that would be received = 500,000 - 450,000 = 50,000

Cost of the default = $279,376.285

		Present value @4.5%	Discounted cash flows
3 year	100,000	1	100000
3.5 year	50,000	0.956937799	47846.89
4 year	50,000	0.915729951	45786.4976
4.5 year	50,000	0.876296604	43814.8302
5 year	50,000	0.838561344	41928.0672
Present value			279376.285