# FCFF : FCInv versus Depreciation

Hi everyone, I would like to know why we seem to count two times the depreciation in the FCFF equation from EBIT and EBITDA. As an example, FCFF = EBITDA * (1- T) + Depreciation * T - WCInc - FCInv With FCInv = Change in gross PPE - Depreciation So Depreciation is counted in double, in EBITDA and add in FCInv… no ? Thank you very much

It shouldn’t be + depreciation * t, instead use -depreciation * (1-t).

But really most people just use EBIT * (1-t) -WCInv- FCInv (instead of breaking out depreciation from EBITDA when applying taxes)

FCFF as the name implies is a cash based metric, what would help is if we break down the formula

EBITDA * (1-T) = This piece of the equation represents the earnings net of any taxes incurred on said earnings, we use earnings excluding taxes (as we calculate the tax impact), depreciation (as it is a non cash expense) and amortization (as it is also a non cash expense).

Depreciation * T = This is the tax shield on the depreciation, while depreciation itself is not a cash expense, it does reduce the amount of income taxes owed during the period. Since the income taxes are a cash expense, calculated in the above formula does not include the tax shield, we need to calclate it here.

WCInv = Simple enough, this is the cash expenditure on working capital, usually calculated by the change in working capital year over year.

FCInv= Here we have the fixed capital investment (Change in PP&E - Depreciation) also known as ‘net additions’. The change in PP&E is made up of three components 1) additions 2) disposals and 3) depreciation during the period. Both additions and disposals impact cash flow where as depreciation does not, so in assessing any cash flows we would only want to look at net additions.

The reason why this formula is used instead of just net additions is because depreciation and YOY change in PP&E are usually readily available from the financial statements , where as net additions are not.

I hope that helped.

In this FCFF formula you started with EBITDA (1-T) and this item is already calculated before depreciation and net of tax. Full syntax “depreciation x T” means that you add back positive cash flow from use of a tax shield. FCInv are CAPEX outflows and thus mean deduction of remaining cash flow to equity and bond holders (unless it has positive prefix which would mean sales of equipment or divisions in such case). These two parts of formula have different meaning and there is no double counting. I’d recommend using of parentheses for each syntax.

Thank you for answering but it doesn’t really answer my question. Actually it confirms my doubt as Depreciation is contained in EBITDA and FCInv !! EBITDA = EBIT + Depreciation FCInv = Change in PPE - Depreciation So it is counted two times no ? FCFF = (EBIT + Depreciation) + (…) - (Change in PPE - Depreciation) FCFF = (EBIT + Depreciation) + (…) - Change in PPE + Depreciation I voluntary forgot about a lot of stuff in this equation

What i meant is that Depreciation is in EBITDA (so EBIT + Depreciation) and that it is also in FCInv (Change in PPE - Depreciation) Please forget about the part : “(Depreciation * T)”, i know the meaning of this

Actually EBITDA is earnings before interest, depreciation and amortization. So the correct formula would be EBITDA = EBIT - Depreciation.

Depreciation expense is not in the EBITDA if you meant this.

Exactly not than EBIT + Depreciation because i’ is already been deducted in EBIT. This is basic of accounting.

OP, I looped back and realized I made a mistake reading your first post that I think you might be making also.

FCInv as defined is the same as CapEx, it’s not net reinvestment (which would be a more intuitive definition, but that’s the way it is)

so re-writing your original formula as EBITDA * (1-t) + depreciation*t - WCInv - Capex might be clearer. ( also in this situation EBITDA * (1-t) + depreciation*t = EBIT (1-t) + depreciation)

this is ignoring all the little other things in each of these (earning in equity, cash from disposals etc. etc.)

Also the way it’s written it’s not double counted, it is ignored as a tax-deductible expense in EBITDA *(1-t) and then the tax implication is considered in depreciation*t, so that counting it once (the lack of cash expense plus the tax treatment equals one full depreciation).

It is not in FCInv, even if it is used to calculate it.

edit

Oh i think i got it thanks to your post… So FCInv = Capex = beginning PPE - ending PPE + depreciation However… Capex is supposed to be the money spent in asset by the company to pursue its activities… If for example there is an extraordinary sales in the company, the equation of FCInv remains the same but Capex doesn’t account for this sale. How do we account for an extraordinary asset sales/purchase in FCFF ?

FCInv = ending gros PPE - beginning gros PPE

or

FCinv = ending net PPE - beginning net PPE + depreciation - asset sales gain

also watch out on land item since it is not depreciated and may be the land value in PPE also in a sample.

All asset purchases within the period are contained in both formulas above.

Don’t you mean revaluation?

No. I mean on CAPEX - proceeds from sales of asset if it exists in period.

Higher (or lower if is subsequent measure) value of assets due to impact of taken revaluation is already contained in

higher (or lower) depreciation expense or in amount of gross value of asset if first equation is used.

A revaluation needs to be removed from the equation, it is a non-cash gain. Even if it’s reflected in the ending net PPE.

However, an asset sales gain is a cash inflow on the original book value, you do not subtract that from net income/operating income.

Hi Smart

Appreciate your opinion but would like if you can provide some backup. The link or source with such equation and revaluation metrics in FCInv equation.

Thank you.

FB