FCFF Calculation From EBITDA

CFA Level II Equities
#1

Hi All,

Please help me figure out why we don’t add back tax shield from interest expense in this FCFF equation.

It seems like if we account for the depreciation tax shield by adding Depr*Tax, then we should also do the same for interest expense by adding Int*Tax.

FCFF = EBITDA(1-t) + Depr*Tax - FCInv - WCInv

Other forums suggest that depreciation is non-cash while interest expense is an actual outflow, but this doesn’t seem to answer the question because we are talking about the tax shield benefits created, regardless of the nature of the expense.

Thanks so much!

#2

EBITDA(1-T) + DT = NI + Int(1-T) + D

EBITDA is before interest,

#3

Algebra:

NI = EBITDA − Dep’n − Int − Taxes

= EBITDA − Dep’n − Int − (EBITDA − Dep’n − Int)(Tax rate)

= (EBITDA − Dep’n − Int)(1 − Tax rate)

= EBITDA(1 − Tax rate) − Dep’n(1 − Tax rate) − Int(1 − Tax rate)

= EBITDA(1 − Tax rate) − Dep’n + Dep’n(Tax rate) − Int(1 − Tax rate)

So,

FCFF = NI + Dep’n + Int(1 − Tax rate) − FCInv – WCInv

= EBITDA(1 − Tax rate) − Dep’n + Dep’n(Tax rate) − Int(1 − Tax rate) + Dep’n + Int(1 − Tax rate) − FCInv – WCInv

= EBITDA(1 − Tax rate) + Dep’n(Tax rate) − FCInv – WCInv

#4

Ebitda is also before depreciation, so why add depreciation tax shield but not interest tax shield?

#5

Thanks, algebraically it makes sense and the numbers work out but is there a more conceptual or intuitive answer?

#6

Conceptually, you should just go back to the definition (or rather, the name) of FCFF - it represents the free cash flows available to the firm, i.e. to equity holders AND bond holders. So conceptually, this is the free cash flow, which is obtained before paying bond holders’ interest, so before having the right to the respective tax shield as well.

You would find that in FCFE, which is free cash flow to equity holders only (i.e. AFTER paying bond holders interest and/or principal), the tax shield from the interest expense is indeed included.

#7

It’s algebra, do the math and you will see.

Even though EBITDA is before depreciation, you are multiplying EBITDA by (1-T) and when you add Deprec to NI, you have:

NI + D = (EBITDA - I - D) (1-T) + D =

You want to add the full depreciation after already getting the tax deduction

DT + D(1-T) = D

Easiest way to see this is to start frm EBITDA, turn it to NI, and add back D… then cancel out the terms, which is what smagi showed you in his post.

#8

Thanks! This makes sense intuitively. Depreciation tax shield is benefits to both equity and debt holders, whereas interest tax shield only benefits the equity holders (i.e. the firm). Therefore, we don’t account for it in FCFF. We do, however, account for it in FCFE.