while calculating the fcff both depreciation and interest are tax deductible then why do we add after tax amount of only interest (whereas entire depreciation) to Net Income

It would seem to me the tax benefits because of the interest payment are available to the capital providers hence entire interest payment should be added back.

the one possible explanation that occurs to me is that tax effect has already been accounted for during the calculation of the WACC (there the debt capital required return is multiplied by (1-taxrate))

Because depreciation is a non cash charge, but interest expense is an actual cash outlfow

does it make a difference? tax benefits are available to the capital providers so why only after tax amount is added back?

The tax benefits from Interest expenses in FCFF are not in the cash flows but in the WACC.

I understand FCFF best by starting from After tax operating income and adding back depreciation, and subtracting reinvestment needs ( capex and change in non cash WC). In FCFF you act like as if you have paid taxes on the operating income ( not the actual taxes you paid) and hence you start with after tax operating income. As Mosstastic said rightly, Depreciation is non-cash expense, so its not an actual cash flow and hence added back.

The other way as given in the curriculim is you start with Net income and when you add back the after tax interest income, you reach after tax operating Income and then you subtract the Net capex and change in WC to get FCFF. So, you can see that the tax savings are not reflected in FCFF equation. Its there in WACC