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Adding back interest tax shield to get FCFF

Hi guys, 

If you take a look at the formula for computing FCFF from EBITDA, 

FCFF = EBITDA (1-tax rate) + Depreciation (tax rate) - FCInv - WCInv

you would notice we add back the depreciation tax shield because that tax saving represents cash available to the company’s investors.

Why then, don’t we also add back the interest tax shield in this formula?

Regards,

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Interest is an actual cashflow, depreciation is not. We are only trying to measure cashflow here. All cash and noncash effects are included when doing EBITDA(1-T) so with noncash items like depreciation you want to reverse it out. 

No but when you calculate EBITDA (1-t), you deduct more taxes than are actually paid, because the amount gets reduced by the interest tax shield.