Calculating FCFF from EBITDA

[cindylaurel]

Could some bright soul help me understand why the formula for FCFF from EBITDA requires adding the depreciation tax shield when EBITDA is by definition before any charge for depreciation has been subtracted? It seems counterintuitive to me.

 

[Harrogath]

It is not much straightforward, you must follow the formula and realize that a portion of depreciation is not eliminated when calculating FCFF from EBITDA.
NI = (EBITDA - Dep - Int)*(1 - tax rate)
Open the formula to:
NI = EBITDA*(1 - tax rate) - Dep*(1 - tax rate) - Int*(1 - tax rate)
Now calculate FCFF from NI:
FCFF = NI + Dep + Int*(1 - tax rate) - FCInv - WCInv
Replace NI with the ebitda derivation:
FCFF = EBITDA*(1-t) - Dep*(1-t) + Dep + Int*(1-t) - Int*(1-t) - FCInv - WCInv
Interests cancel each other and factorize Dep like ” -Dep*(1-t-1) = -Dep*(-t) = Dep*(t) “
FCFF = EBITDA*(1 - tax rate) + Dep*(tax rate) - FCInv - WCInv
The intuitive explanation comes from the side that depreciation reduces taxable income so you save some moeny in tax expense. That money saving is the Dep*(tax rate), therefore you add it to FCFF.
Hope this helps.

 

[Yayyywork]

Depreciation is a non cash charge, but it does reduce your tax bill which does effect cash. With EBITDA you do not need to add depr back in, but you do need to account for the cash savings via the taxes.