FCFF and multiple ways to calculate it

CFA Level II
#1

hello,

Does anyone have an easy way to remember the 4 different formulas? I find it really hard to understand intuitively b/c I do not know at *which point* on the income statement I am trying to go from point A to point B.

For instance, calculating FCFF using EBITDA vs EBIT

FCFF = [EBITDA x (1-tax)] + (dep x tax) - FCInv - WCInv

vs

FCFF = [EBIT x (1-tax)] + Dep - FCInv - WCInv

Why in the first instance (EBITDA), I have to add back only the tax shield, but when using EBIT, I must add back the entire depreciation? At which line item on the income statement is the starting point to work backwards from? or is using the income statement a poor way to explain this logically?

Please help!

#2

This is simple algebra:

Substituting EBITDA = EBIT + dep into the first equation:

= [(EBIT + dep) x (1-tax)] + (dep x tax) - FCInv - WCInv

= EBIT x (1 - tax) + dep (1 -tax) + (dep x tax) - FCInv - WCInv

= EBIT x (1-tax) + dep - FCInv - WCInv

I believe all the formulas can be reconciled to one another by algebra, so the key is to remember only one formula and understand the relations between the various terms (ie EBITDA = EBIT + dep in this example).

#3

Because you deduct taxes from depreciation expense, but depreciation expense itself is a non-cash expense.

Working from the bottom up, remove taxes from EBIT, then add back the non-cash expense (depreciation).