Question

An FI has purchased a $207 million cap of 9 percent at a premium of 0.60 percent of face value. A $207 million floor of 4.7 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 3.7 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 3.7 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 3.7 percent

c.Net savings if interest rates rise to 11 percent

Net savings if they fall to 3.7 percent

Answer 1

a).
If interest rates rise to 10 percent, cap purchasers receive = $207 million x 0.01 = $2,070,000.
Premium for purchasing the cap = 0.0060 x $207 million = $1,242,000.

The net savings = $2,070,000 - $1,242,000 = $828,000.

b).
Cost of floor= 0.65% x $207 million = $1,345,500.
Total cost = $1,345,500 + $1,242,000 = $2,587,500.
If interest rates rise to 11 percent,
Cap purchasers receive= 0.02 x $207 million = $4,140,000.

Net Savings = $4,140,000 - $2,587,500 = $1,552,500.

If interest rates fall to 3.7 percent,

Floor purchaser receive = 0.01 x $207 million = $2,070,000.

Net savings = $2,070,000 - $2,587,500= -$517,500.

c). If the FI sells the floor, it receives = $1,345,500 - $1,242,000 =$103,500.

Net savings when rates increases to 11% = $4,140,000 + $103,500 = $4,243,500.

Net savings (loss) when rates decline to 3.7% = $-2,070,000 + $103,500 = -$1,966,500.

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