bchadwick

You are actually comparing (in this case) 2 coupns to 2 coupns.
as you know the fixed side doesn’t reset, so you need to find the value of all the future pmts discounted at the given rates.
for the floating rate you do the same thing only you are multiplying the notional by the libor rate and then discounting it by the same libor rate which gives you a value of 1.
for example:
suppose we are at a reset date and the current 180 day libor is 5%
The floater pmt would now be .05(180/360) of the notional in 180 days or .025. now, to discount that back to the present you would divide by .05(180/360) or .025.
.025 / .025 = 1
It’s easier just to add the 1 to the amount that is left untill the next reset date instead of going through this each time the floater changes.Hope that makes sense.