Question 15 (4 marks) A financial institution has entered into an interest rate

Question

Question 15 (4 marks) A financial institution has entered into an interest rate swap with company X. Under the terms of the swa it receives 5% per annum and pays six-month LIBOR on a principal of $10 million for 5 years. Payment are made every six months. Suppose that the company X defaults on the eighth payment date (end of yea 4), when the interest rate with semi-annual compounding is 4% per annum for all maturities. Assume that six-month LIBOR was 3.5% per annum halfway through year 4 (year 3.5). What is the loss to the financial institution? (4 marks)

Explanation / Answer

At the end of year 3 the financial institution was due to receive $250,000 (=0.5X 5%% of $10 million) and pay $175,000 (0.5X 3.5% of $10 million). The immediate loss is therefore $75,000. To value the remaining swap we assume than forward rates are realized. All forward rates are 4% per annum. The remaining cash flows are therefore valued on the assumption that the floating payment is (0.5X 0.04 X 10,000,000) = $200,000  and the net payment that would be received is 250,000-200,000 = 50,000. The total cost of default is therefore the cost of foregoing the following cash flows:

4 year:             $75,000 -CF0

4.5 year:          $50,000 - CF1

5 year:             $50,000 - CF2

Present value of this loss (Disc rate = 2%) = 172078

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