equating the present value of the fixed-rate payments to that of the floating-rate payments.   Valuing a Swap Once the swap transaction is completed, changes in market interest rates will change the payments of the floating-rate side of the swap. The value of an interest rate swap is the difference between the present value of the payments of the two sides of the swap. The 3-month LIBOR forward rates from the current Eurodollar CD futures contracts are used to (1) cal- culate the floating-rate payments and (2) determine the discount factors at which to calculate the present value of the payments.   To illustrate this, consider the 3-year swap used to demonstrate how to calculate the swap rate. Suppose that one year later, interest rates change as shown in Columns (4) and (6) in Exhibit 12.7. In Column (4) shows the current 3-month LIBOR. In Column (5) are the Eurodollar CD futures price for each period. These rates are used to compute the forward rates in Column (6). Note that the interest rates have increased one year later since the rates in Exhibit 12.7 are greater than those in Exhibit 12.2. As in Exhibit 12.2, the current 3-month LIBOR and the forward rates are used to compute the floating-rate payments. These pay- ments are shown in Column (8) of Exhibit 12.7. In Exhibit 12.8, the forward discount factor is computed for each period. The calculation is the same as in Exhibit 12.4 to obtain the for- ward discount factor for each period. The forward discount factor for each period is shown in the last column of Exhibit 12.8. In Exhibit 12.9 the forward discount factor (from Exhibit 12.8) and the floating-rate payments (from Exhibit 12.7) are shown. The fixed-rate payments need not be recomputed. They are the payments shown in Col- umn (8) of Exhibit 12.3. These are fixed-rate payments for the swap rate of 4.9875% and are reproduced in Exhibit 12.9. Now the two payment streams must be discounted using the new forward discount factors. As shown at the bottom of Exhibit 12.9, the two present values are as follows:   Present value of floating-rate payments $11,459,495 Presentvalueoffixed-ratepayments $9,473,390     The two present values are not equal and therefore for one party the value of the swap increased and for the other party the value of the swap decreased. Lets look at which party gained and which party lost. The fixed-rate payer will receive the floating-rate payments. And these payments have a present value of $11,459,495. The present value of the payments that must be made by the fixed-rate payer is $9,473,390. Thus, the swap has a positive value for the fixed-rate payer