Why does FCF calculation ignore interest?

Haven't looked at finance in a while, so apologies if I sound dumb, but when calculating FCF using EBIT, you multiply EBIT by (1-Tax). My question is, by doing this, aren't you ignoring the fact that interest is tax deductible?

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Interest is only excluded from the equation when calculating FCF to the firm (FCFF), since FCFF is attributed to both debt and equity holders. When calculating FCF to equity (FCFE), you start with Net Income where interest payments are taken into account.

When performing a DCF using FCFF, the WACC will implicitly account for the tax-deductible nature of debt because you are taking the after-tax cost of debt and not the cost of debt itself.

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