# FCFF and FCFE Formulas - Too much tax?

Here are two alternate formulas presented in Schweser book 3 (pg. 191): FCFF = [EBIT x (1 - tax rate)] + Deprec - FC inv - WC inv FCFF = [EBITDA x (1 - tax rate)] + (Deprec x tax rate) - FC inc - WC inv It seems to me that these formulas charge too much for tax since we do not remove the amortization and other non cash expenses before applying the tax rate. The second formula only corrects this problem by adding back the “tax overcharge” on depreciation, but what about the other tax shields? If someone can make sense of this for me that would be great.

Remember [EBITDA-Depr] = EBIT Assume there is no Amortization expense. now apply the tax and do the expansion. EBIT*(1-T) + Depr = (EBITDA-Depr)*(1-T)+depr = EBITDA*(1-T) - Depr(1-t)+ Depr = Ebitda*(1-T) + depr*T

I realize that both of these formulas are consistent, my question is whether they are consistently wrong in the tax treatment. The original formula does not tax additional non-cash expenses like amortization, as the shields are embedded in the NI: FCFF = NI + NCC - FCinv - WCinv + after-tax interest expense If there is amortization or other non-cash charges, then we would be applying too much tax by using these two alternate formulas. Correct?

The best way to “prove” these formulas is to devise a simple example (\$100 in Sales, \$50 in expenses, \$5 depreciation, \$5 amortization etc.) and work through the formulas. They all work so I would not waste time trying to prove them wrong.

NI = (EBIT-int)*(1-tax) = EBIT*(1-tax) - int*(1-tax) Agreed: FCFF = NI + NCC - FCinv - WCinv + after-tax interest expense Substitute NI: FCFF = EBIT*(1-tax) - int*(1-tax) + NCC - FCinv - WCinv + after-tax interest expense = EBIT*(1-tax) + NCC - FCinv - WCinv “If there is amortization or other non-cash charges, then we would be applying too much tax by using these two alternate formulas.” No. If there is amortization, tax has to be applied as tax is cash. Thus, EBIT*(1-tax). However, amortization is not cash. So +NCC. Same concept when we do cash flow statement.

“If there is amortization, tax has to be applied as tax is cash. Thus, EBIT*(1-tax). However, amortization is not cash. So +NCC. Same concept when we do cash flow statement.” This makes no sense. Amortization is an expense that comes out before the tax is applied, and therefore acts as a tax shield. This is my entire point, look at this formula: FCFF = [EBITDA x (1 - tax rate)] + (Deprec x tax rate) - FC inc - WC inv In this case we tax the depreciation, amortization, and other expenses included in EBITDA. We fix this for depreciation by adding back the effects of the “extra tax,” but we do no such thing for amortization and other NCC’s.

1. There is no term called EBITD -> even if there is no Amortization - the term is called EBITDA. [Usually the term includes only Depreciation]. If there is amortization you would add back the T*Amortization as well.

“In this case we tax the depreciation, amortization, and other expenses included in EBITDA. We fix this for depreciation by adding back the effects of the “extra tax,” but we do no such thing for amortization and other NCC’s.” The CFAI Text specifically states that they assume depreciation is the only NCC in this case. if there were other NCC’s in your calc of EBITDA you would need to add back the extra tax included in the EBITDA(1-tax) portion of the formula. The exact formulas that are learned from the CFAI texts are by no means the final say in analysis. An analyst needs to think about what is included in the inputs and adjust/apply accordingly. Good job for thinking about what’s included, now apply it!

Thanks CP and FinNinja for confirming. Looks like a may need to look more at the CFAI texts instead of relying on Schweser.