Free Cash Flow to the Firm
Debt service cost is felt by equity owners and debt holders but neutral to the firm. Taxation does not care for cash flow, it is levied on tax law specific accounting profit, not even reporting profit, which tends to treat most interest charges (not all and not uniformly either) as a deductible cost. Thus you make an adjustment to your WACC as you said. However, interest charge does not need to be uniform during the life of the debt. Unless you do your WACC adjustment for every period and apply a different WACC for each (you should always at least justify not doing so anyway), you will end up with a inflated cash flow and higher discount rates.