This question assumes that the floating side will be equal to par on reset dates. However, if you discount the floating payments at the HIBOR rate, you do not get par. Therefore, you get a different answer. What is the appropriate methodology in that case?
Cooper Industries (Cooper) is the pay-fixed counterparty in an interest rate swap. The swap is based on a notional value of $2,000,000, and Cooper receives a floating rate based on the 6-month Hong Kong Interbank Offered Rate (HIBOR). Cooper pays a fixed rate of 7% semiannually. A swap payment has just been made. The swap has a remaining life of 18 months, with pay dates at 6, 12, and 18 months. Continuously compounded spot HIBOR rates are shown in the table below. 6-month HIBOR 6.5% 12-month HIBOR 6.8% 18-month HIBOR 7.5% 24-month HIBOR 7.7%
The value of the swap to Cooper is closest to: a. $0. b. $6,346. c. $17,093. d. $72,486.
Answer
The fixed payments made by Cooper are (0.07 / 2) x $2,000,000 = $70,000.
The present value of the fixed payments . ($70,000e-(0.0650.5)) +($70,000e-(0.0681))+ [($70,000 + $2,000,000) * e-(0.075*1.5)] = $67,762 + $65,398 + $1,849,747 = $1,982,907 The value of the floating rate payments received by Cooper at the payment date is the value of the notional principal, or $2,000,000. Recall that a swap payment has just been made. The value of the swap to Cooper is ($2,000,000 — $1,982,907) = $17,093. (See Book 3, Topic 29)