No, we do not include interest payments in free cashflow to firm neither in investment appraisal, because the discount factor used in the latter includes this cost already. And in FCF we don’t include it because we want to calculate the cashflow that is available to the company rather than equity holders.but we do include it in Free cashflow to equity.
My 2 cents, although John here will correct me if I’m wrong.
The reason for discounting in the first place is to account for the cost of money – if the interest payments were included in the cash flows it would mean that they were being accounted for twice!!