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value of a swap, we will see how to calculate the swap rate. This will require an explanation of how the present value of any cash flow


in an interest rate swap is computed. Given the floating-rate payments and the present value of the floating-rate payments, the swap rate can be deter- mined by using the principle that the swap rate is the fixed rate that will make the present value of the fixed-rate payments equal to the present value of the floating-rate payments. Finally, we will see how the value of swap is determined after the inception of a swap.   Calculating the Floating-Rate Payments For the first floating-rate payment, the amount is known. For all subse- quent payments, the floating-rate payment depends on the value of the reference rate when the floating rate is determined. To illustrate the issues associated with calculating the floating-rate payment, we will assume that   ■ a swap starts today, January 1 of year 1(swap settlement date) ■ the floating-rate payments are made quarterly based on "actual/360" ■ the reference rate is 3-month LIBOR ■ the notional amount of the swap is $100 million ■ the term of the swap is three years   The quarterly floating-rate payments are based on an "actual/360" day count convention. Recall that this convention means that 360 days are assumed in a year and that in computing the interest for the quarter, the actual number of days in the quarter is used. The floating-rate pay- ment is set at the beginning of the quarter but paid at the end of the quar- ter-that is, the floating-rate payments are made in arrears. Suppose that today 3-month LIBOR is 4.05%. Lets look at what the fixed-rate payer will receive on March 31 of year 1-the date when the first quarterly swap payment is made. There is no uncertainty about what the floating-rate payment will be. In general, the floating-rate payment is determined as follows:   no.ofdaysinperiod ----------------------------------------------------- 360     In our illustration, assuming a non-leap year, the number of days from January 1 of year 1 to March 31 of year 1 (the first quarter) is 90. If 3- month LIBOR is 4.05%, then the fixed-rate payer will receive a floating- rate payment on March 31 of year 1 equal to:   $100,000,000´0.0405 ´--9----0--- 360 = $1,012,500