Question

An FI has purchased a $219 million cap of 9 percent at a premium of 0.60 percent of face value. A $219 million floor of 5.9 percent is also available at a premium of .65 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 4.9 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 4.9 percent? (Negative amounts should be indicated by a minus sign.)

Answer 1

a). Premium for purchasing the cap = Premium% * Face Value

= 0.0060 * $219,000,000 = $1,314,000

If interest rate rise to 10%, Cap Purchasers receive = Face Value * Change in Interest Rate

= $219,000,000 * (0.10 - 0.09) = $2,190,000

Net Savings = Amount Cap Purchasers Receive - Premium for purchasing the cap

= $2,190,000 - $1,314,000 = $876,000

b-1). Premium for purchasing the floor = Premium% * Face Value

= 0.0065 * $219,000,000 = $1,423,500

Total Premium = Premium for purchasing the cap + Premium for purchasing the floor

= $1,314,000 + $1,423,500 = $2,737,500

If interest rate rise to 11%, Cap Purchasers receive = Face Value * Change in Interest Rate

= $219,000,000 * (0.11 - 0.09) = $4,380,000

Net Savings = Amount Cap Purchasers Receive - Total Premium

= $4,380,000 - $2,737,500 = $1,642,500

b-2). If interest rate fall to 4.9%, Floor Purchasers receive = Face Value * Change in Interest Rate

= $219,000,000 * (0.059 - 0.049) = $2,190,000

Net Savings = Amount Floor Purchasers Receive - Total Premium

= $2,190,000 - $2,737,500 = -$547,500

c-1). Premium received for selling the floor = Premium% * Face Value

= 0.0065 * $219,000,000 = $1,423,500

Net Premium Received = Premium received for selling the floor - Premium for purchasing the cap

= $1,423,500 - $1,314,000 = $109,500

If interest rate rise to 11%, Cap Purchasers receive = Face Value * Change in Interest Rate

= $219,000,000 * (0.11 - 0.09) = $4,380,000

Net Savings = Amount Cap Purchasers Receive + Net Premium Received

= $4,380,000 + $109,500 = $4,489,500

c-2). If interest rate fall to 4.9%, Floor Purchasers receive = Face Value * Change in Interest Rate

= $219,000,000 * (0.059 - 0.049) = $2,190,000

Net Savings = Amount Floor Purchasers Receive + Net Premium Received

= $2,190,000 + $109,500 = $2,299,500