Question

An FI has purchased a $214 million cap of 9 percent at a premium of 0.75 percent of face value. A $214 million floor of 5.4 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 4.4 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 4.4 percent? (Negative amounts should be indicated by a minus sign.)

	a. Amount received Net savings b. Net savings if interest rates rise to 11 percent Net savings if interest rates fall to 3 percent c. Net savings if interest rates rise to 11 percent Net savings if they fall to 3 percent

Answer 1

a). Premium for purchasing the cap = 0.0075 x $214 million = $1,605,000.

If interest rates rise to 10 percent, cap purchasers receive $214 million x 0.01 = $2,140,000.

The net savings = $2,140,000 - $1,605,000 = $535,000.

b). If the FI also purchases the floor:

Premium = 0.0080 x $214 million = $1,712,000,

Total Premium = $1,712,000 + $1,605,000 = $3,317,000.

If interest rates rise to 11 percent,

Cap purchasers receive 0.02 x $214m = $4,280,000,

Net Savings = $4,280,000 - $3,317,000 = $963,000

If interest rates fall to 4.4 percent,

Floor purchaser receive 0.01 x $214 million = $2,140,000,

Net savings = $2,140,000 - $3,317,000 = -$1,177,000.

c). If the FI sells the floor, it receives net $1,712,000 minus the cost of the cap of $1,605,000

= +$107,000.

If interest rates rise to 11 percent,

Cap purchasers receive 0.02 x $214m = $4,280,000.

Net savings = $4,280,000 + $107,000 = $4,387,000.

If interest rates fall to 4.4 percent,

Floor purchasers receive 0.01 x $214 million = $2,140,000.

Net savings to the FI = $-2,140,000 + 107,000 = -$2,033,000.