Consider a bank that has entered into a five-year swap on a notational balance of $10,000,000 with a corporate customer who has agreed to pay a fixed payment of 10 percent in exchange for LIBOR.As of the fourth reset date,determine the price of the swap from the bank's point of view assuming that the fixed-rate side of the swap has increased to 11 percent.LIBOR is at 5 percent.
A)$909,090.91 gain.
B)$90,090.09 loss.
C)No loss or no gain since maturity has not arrived.
D)$90,090.09 gain.

Question

Quizplus · Accepted Answer

The bank has agreed to pay LIBOR and receive a fixed payment of 10 percent from the corporate customer. However, the fixed-rate side of the swap has now increased to 11 percent. This means the bank is paying more than it is receiving in the swap.

On the fourth reset date, the swap has a remaining life of 1 year. To value the swap, we need to determine the present value of the remaining fixed payments and the remaining floating payments.

Present value of remaining fixed payment = 10% * $10,000,000 * (1/1.05^4) = $7,974,448.68

Present value of remaining floating payment = LIBOR * $10,000,000 * (1/1.05^4) = $4,774,668.43

So, the net present value of the swap for the bank is:

-$7,974,448.68 + $4,774,668.43 = -$3,199,780.25

This means that the bank is losing money on the swap, and so the answer is B, a $90,090.09 loss.

Consider a Bank That Has Entered into a Five-Year Swap