FCFF from EBIT and EBITDA

I’m on my way to learning the eight different FCFF and FCFE formulas and for the time being I am not comfortable with the formulas that begin with EBIT and EBITDA. I searched the forum but did not find an answer. Below are my specific questions: FCFF = [EBIT x (1-tax rate)] + Dep - FCInv - WCInv I totally understand that you have to tax EBIT so that the cash flow to the firm must contain EBIT x (1-tax rate). Also, I see that you subtract FCInv and WCInv. The part that is not sitting well is that you add back all of the depreciation. Either way the FCFF figure is after tax so the depreciation should be after tax as well. Any pointers?

Depreciation is not actual cash flow so it has to be added back to get FCFF. It’s a noncash charge. The reason why you use EBIT is because you only want to capture cash charges, most of which occur in the Income Statement below EBIT. The one exception is depreciation which is captured above EBIT on the IS. That is why you add it back.

verse is right in his explanation. It might be helpful if you do the math: FCFF = [EBIT x (1-tax rate)] + DEP - FCInv - WCInv = = [(OPERATING CASH - DEP) (1-tax rate)] + DEP - FCInv - WCInv = = OPERATING CASH(1-tax rate) - DEP + DEP * tax + DEP - FCInv - WCInv. After you eliminate the DEP, you are left with the OPERATING CASH after tax + cash tax that was saved due to depreciation.

Thank you for the explanation. I realize that Depreciation occurs above EBIT and I understand that it must be added back. The issue here is with the order of that operation. The two options below do not result in the same figure and it seems to me that taking operating cash, taxing it and THEN adding DEP is wrong. Yes, you should add DEP, but in my understanding it should be done before you tax, otherwise, you are adding a credit that will not be taxed. [EBIT x (1-tax rate)] + DEP (EBIT + DEP) x (1-tax rate) Put another way, kyrylo’s example illustrates my point. In the worked out example above, you add back ‘DEP * tax’ not the full ‘DEP’ and that is my question. I must be missing something else. Care to give me some more suggestions? Thanks a lot.

When you multiply EBIT by (1-T) you are removing all taxes and providing an after tax figure; FCFF is an after tax figure. If you do the math it works out. Assuming that Dep is the only NCC you have with no Amortization: Then: EBIT= EBITDA - D (EBITDA - D)(1-T) + D is the first part of the equation excluding the FC and WC inv. (EBITDA - D)(1-T) + D = EBITDA - T(EBITDA) - D + DT + D The D’s (depreciation) cancel out and you are left with after tax EBITDA plus after tax depreciation: EBITDA(1-T) + DT So IF: EBITDDA(1-T) + DepT = EBIT(1-T) + Dep Then: [EBIT x (1-tax rate)] + DEP - FCInv - WCInv holds true

EBITDA just complicates things. Get to EBIT*(1-T) and then go from there

AndrewUNH Wrote: ------------------------------------------------------- > EBITDA just complicates things. Get to EBIT*(1-T) > and then go from there The reason why i’m using EBITDA above is because fullofquestions asked why we add back pre-tax depreciation. This is impossible to show without using EBITDA (without amortization)

yeah i get you, I’m just suggesting an easier alternative to the grand scheme of things

the easier alternative doesn’t answer his question

It was explained and ignored in the first response by verse. Depreciation is NOT cash. However, depreciation ALSO reduces your tax burden, which IS cash. So is there some type of “added credit” here? Yes! You need to (1) include the cash credit for reduction in taxes, Depr*t, and then (2) you also have to add back all of the depreciation that reduced earnings, which was not a real cash charge. EBIT*(1-t), contains the tax credit (1) since depreciation was taken out. Now we have to add back all of the Depreciation to earnings (2) since we removed it in the first place.

Good explanation SeesFA. I think of it like the firm is setting aside cash equal to depreciation, gets to avoid paying taxes on it, and and then adds it back to the after tax pile of cash.

Thank you very much for the full explanation verse214. I went through the calc superficially and it seems to work out. Thank you very much SeesFA, your explanation is the clearest (to me) since it is shorter and totally intuitive.

I follow a simpler approach that helps me remember only one formula (the original FCFF formula), rest is as follows, for CFO and FCFE the derivation from FCFF is very straightforward so may not need explanation. for EBIT - Just replace NI in original formula with EBIT(1-tax) - Int(1-tax) for EBITDA - Just replace NI in original formula with EBITDA(1-tax) - Int(1-tax) - DEP(1-tax) [DEP and NCC is same] If you follow the above approach and replace NI, you will get to the respective EBIT and EBITDA formula. What I replaced NI with is very obvious and intuitive, if you need proof or better understanding, then in a subsequent post I can provide the necessary explanation with a calculation.