A FI buys a $500 million cap of 7 percent at a premium of 0.75 percent of face value. In addition,it sells $500 million floor of 3 percent at a premium of 0.70 percent of face value.
If interest rates fall to 2.5% what is the net profit of the FI?

Question

Quizplus · Accepted Answer

To calculate the net profit, we need to calculate the gains and losses from the cap and floor options.

For the cap option:

Premium paid = 0.75% of $500 million = $3.75 million
Strike rate = 7%
Current rate = 2.5%
Notional amount = $500 million

The gains from the cap option = Notional amount * (Current rate - Strike rate)
= $500 million * (2.5% - 7%) = -$17.5 million

However, the premium paid is a sunk cost and needs to be subtracted from the gains to calculate the net profit. Therefore, the net profit from the cap option = -$17.5 million - $3.75 million = -$21.25 million

For the floor option:

Premium received = 0.70% of $500 million = $3.5 million
Strike rate = 3%
Current rate = 2.5%
Notional amount = $500 million

The gains from the floor option = Notional amount * (Strike rate - Current rate)
= $500 million * (3% - 2.5%) = $2.5 million

The premium received is a revenue and needs to be added to the gains to calculate the net profit. Therefore, the net profit from the floor option = $2.5 million + $3.5 million = $6 million

Therefore, the total net profit for the FI is = -$21.25 million + $6 million = -$15.25 million, which is closest to option A) -$2,750,000.

A FI Buys a $500 Million Cap of 7 Percent