Question

An FI has purchased a $201 million cap of 8 percent at a premium of 0.70 percent of face value. A $201 million floor of 4.1 percent is also available at a premium of .75 percent of face value.

a. If interest rates rise to 9 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 10 percent? What are the net savings if interest rates fall to 3.1 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 10 percent? What if they fall to 3.1 percent? (Negative amounts should be indicated by a minus sign.)

Answer 1

Ans.

a)

Amount received = Face value * (Market interest rate - cap rate)

Amount received = $201,000,000 * (9% - 8%)  

Amount received = $2,010,000.

Net savings = Amount received - Premium amount.

Premium amount = Face value * premium %.

Premium amount = $201,000,000 * 0.70%  

Premium amount = $1,407,000.

Net savings = $2,010,000 - $1,407,000

Net savings = $603,000

b)

When a floor is purchased and interest rates rise, payoff will be zero as the payoff will generate when interest rates fall below the specified rate.

Net savings if interest rates rise

The payoff is zero and the premium paid is a loss.

Premium paid = Face value * premium %.

Premium paid = $201,000,000 * 0.75%

Premium paid = $1,507,500.

Net savings = -$1,507,500

Net savings if interest rates fall

Amount received = Face value * (Floor rate - Market interest rate)

Amount received = $201,000,000 * (4.1% - 3.1%)  

Amount received = $2,010,000.

Premium paid = Face value * premium %.

Premium paid = $201,000,000 * 0.75%

Premium paid = $1,507,500.

Net savings = $2,010,000 - $1,507,500

Net savings = $502,500

c)

Net savings if interest rates rise

The payoff and net savings to the seller of a floor will be exactly opposite of the payoff and net profits to the buyer of a floor. That is, the buyer's profit is the seller's loss and the buyer's loss is the seller's profit.

Net savings = $1,507,500

Net savings if interest rates fall

Net savings = -$502,500