Question

An FI has purchased a $202 million cap of 9 percent at a premium of 0.75 percent of face value. A $202 million floor of 4.2 percent is also available at a premium of .80 percent of face value. a. If interest rates rise to 10 percent, what is the amount received by the FI? What are the net savings after deducting the premium? b. If the FI also purchases a floor, what are the net savings if interest rates rise to 11 percent? What are the net savings if interest rates fall to 3.2 percent? (Negative amounts should be indicated by a minus sign.) c. If, instead, the FI sells (writes) the floor, what are the net savings if interest rates rise to 11 percent? What if they fall to 3.2 percent?

Answer 1

Amount, A = $ 202 million; Cap rate = K1 = 9%; Premium, C = 0.75%; FLoor rate = K2 = 4.2%; Floor premium, P = 0.80%

Part a.

If interest rates rise to I = 10 percent, the amount received by the FI = max (I - K1, 0) x A = max (10% - 9%, 0) x 202 = 1% x 202 = $ 2.02 million = $ 2,020,000

The net savings after deducting the premium = Amount received by FI - premium paid = 2,020,000 - C x A = 2,020,000 - 0.75% x 202,000,000 = $ 505,000

Part b.

If the FI also purchases a floor, the net savings if interest rates rise to I = 11 percent wil be = max (I - K1, 0) x A - C x A - P x A = max (11% - 9%, 0) x 202 - 0.75% x 202 - 0.80% x 202 = $ 0.909 million = $ 909,000

The net savings if interest rates fall to I = 3.2 percent = = max (K2 - I, 0) x A - C x A - P x A = max (4.2% - 3.2%, 0) x 202 - 0.75% x 202 - 0.80% x 202 = $ - 1.111 million = - $ 1,111,000

Part c.

If, instead, the FI sells (writes) the floor, the net savings if interest rates rise to I = 11 percent will be = P x A - max (K2 - I, 0) x A - C x A + Max (I - K1, 0) x A = 0.80% x 202 - max (4.2% - 11%, 0) x 202 - 0.75% x 202 + max (11% - 9%, 0) x 202 = $ 4.141 million = $ 4,141,000

If they fall to I = 3.2 percent then = P x A - max (K2 - I, 0) x A - C x A = 0.80% x 202 - max (4.2% - 3.2%, 0) x 202 - 0.75% x 202 = - $ 1.919 million = - $ 1,919,000

Hence, final answers are:

A	amount received	2,020,000
	Net savings	505,000
B	Net savings if interest rates rise to 11 percent	909,000
	Net savings if interest rates fall to 3 percent	-1,111,000
C	Net savings if interest rates rise to 11 percent Net savings if interest rates fall to 3 percent	4,141,000 -1,919,000