Cap value

Hi all - if Q4 LIBOR is 8,6% but cap is 8% on 100m principal, then Q4 payoff is 150,000

what time value discount to use for the PV of the Q4 payoff please. 1 year i.e payoff at end of quarter or 270days at start of quarter please

I do not believe there is a time value discount - the payoffs are assumed to occur at the end of the quarter (in the real world you wouldnt know what Q4 Libor interest rate is going to be until it happens)