23-114 What should be the price of a $5,000,000 collar if the bank purchases a three-year 6 percent cap and sells a 5 percent floor,if the current (spot)rates are 6 percent?

Question

Quizplus · Accepted Answer

In a collar, the bank purchases a cap to limit the maximum interest rate and a floor to limit the minimum interest rate. In this case, the bank purchases a three-year 6 percent cap (which means if the interest rate goes above 6%, the cap will kick in and the bank will receive payments from the counterparty) and sells a 5 percent floor (which means if the interest rate goes below 5%, the counterparty will receive payments from the bank).

Since the current (spot) rates are 6%, the cap will not kick in and the floor will not be exercised, resulting in a net payment from the bank to the counterparty. To find the price of the collar, we need to calculate the present value of the net payment:

PV = ($5,000,000 x 5%) / (1+6%) + ($5,000,000 x 6%) / (1+6%)^2 = $259,259

Therefore, the price of the collar is $259,259, which means the bank will pay a net amount of $259,259 to the counterparty. Option C is the correct answer.

23-114 What Should Be the Price of a $5,000,000 Collar