Do you know which formula they used to get the right answer. The formula I had in mind was:
Value To Payer = SumZ * (SFR new - SFR old) * (days/360) * Notional Principal.
The question is:
Two parties enter into a 2-year fixed-for-floating interest rate swap with semiannual payments. The floating-rate payments are based on LIBOR. The 180-, 360-, 540-, and 720-day annualized LIBOR rates and present value factors are: Present value factor Rate 180-day LIBOR 5.0% 0.9756 360-day LIBOR 6.0% 0.9434 540-day LIBOR 6.5% 0.9112 720-day LIBOR 7.0% 0.8772
SWAP Rate = 0.0331 * (360/180) = 6.62%
After 180 days, the swap is marked-to-market when the 180-, 360-, and 540- day annualized LIBOR rates are 4.5%, 5%, and 6%, respectively. The present value factors, respectively, are 0.9780, 0.9524, and 0.9174. What is the market value of the swap per $1 notional principal, and which of the two counterparties (the fixed-rate payer or the fixed-rate receiver) would make the payment to mark the swap to market?
Value of fixed-rate side (per $ of notional principal) = [$0.0331 * (0.9780+0.9524+0.9174)] + ($1.00 * 0.9174) = $1.01166
The market value of the floating-rate side is 1.0000 because we’re at a payment date. The market value of the swap per of notional principal to the receive-fixed (and pay-floating) side is $1.01166 – $1.0000 = $0.01166. As the swap is marked to market, the pay-fixed swap holder makes a payment of $0.01166 to the receive-fixed holder for each $1 of notional principal.