FCFF calculation why use Int(1-T)

CFA Level II
#1

Hi

I have a question about FCFF calculation. Why add Interest(1-T) instead of interest for FCFF.

Let say EBIT= $1000, interest= = $100, tax rate = 30%

Then Net Income = (1000-100)-300=700

FCFF is by definition cash flow available for bondholders. Since 300 will be paid for tax, shouldn’t the available cash flow for bondholders equal 700+100=800 instead of 700+100(1-0.3)=770?

#2

FCFF is by definition residual cash flow available for both bond and stock holders and tax decreases an interest burden given that an interest expense deducts tax base and reduces tax outflows, thus more cash is avail to firm.

#3

You gotta start with the right Net Income:

  • EBIT = $1,000
  • Interest expense = $100
  • EBT = $900
  • Tax rate = 30%
  • Tax = $900(0.30) = $270
  • Net income = $900-$270 = $630

Or,

  • EBT = $900
  • Net income = $900(1-30%) = $900(0.70) = $630

Also, FCFF is cash not needed for operations, so therefore available to be distributed to both bondholders and equity investors.

Plugging and chugging (ignoring NCC, FCInv and WCInv):

  • FCFF = NI + Int(1-t)
  • FCFF = $630 + $100*0.70 = $630 + $70 = $700

But your real question is, Why Int(1-t) and not Int?

The reason is in the first bullets above, where deducting interest before calculating the taxes let you pay $30 less tax. So, pretend it’s a $30 refund from the tax authority. That fact that your business pays interest means:

  • Negative $100 interest
  • Positive $30 tax “refund” (actually just a conceptual tax shield)

Starting from NI, FCFF adds the negative $100 back in for the obvious reason you note (to show it’s available to be paid to bondholders). FCFF also subtracts the positive $30 “refund”. It nicely parallel. But the other reason is that WACC incorporates the tax shield.

  • Firm value = FCFF/(WACC-g)
  • For a firm funded half debt and half equity, WACC = 50%×(interest rate)(1-t) + 50%®

So you don’t want to count your tax shield twice.