I am still confused about the seemingly inconsistent treatment of depreciation (adding back the full amount) and interest payments (adding back only interest payments X (1-t). There are many discussions of this, but none of them really answer the question, which is probably why the topic keeps coming up. They discuss the problem conceptually, but don’t actually show how the NUMBERS work out. Examples of discussions (which have NOT answered the question) are: 1.) https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91347702 2.) https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9934289 So I thought I’d ask this question using actual numbers, simultaneously tracking the INCOME STATEMENT and the ACTUAL CASH FLOWS. To make this really easy, I assume WCInv and FCInv are both 0. I also assume net new borrowing is 0 for the purpose of FCFE. Please show me where my understanding is wrong. There must be a mistake here, or else the FCFF and FCFE definitions being used would be wrong, which is (presumably) not the case). If you can use the actual example below, instead of saying something general like “depreciation is not a cash flow, while interest payments are a cash flow”, that would be very much appreciated. I know it’s possible to do well by just memorizing the formulas, and I am sure I will do fine, as I’ve memorized them, but understanding it would make it easier to retain it or re-learn its in the future. REVENUE: $1,000 COGS: $200 _____________________ GROSS PROFIT: $800 (cash is also 800 at this point) SG&A: $150 ______: $650 (cash is also 650 at this point, assuming SG&A was all paid in cash, let’s assume that) —>Not sure what this line on the income statement is called, but in any case, you have $650 ____________________________ DEPRECIATION: $50 EBIT: $600 (cash is $650 at this point, as depreciation is not an actual cash outflow) ________________ INTEREST PAYMENT: $60 PRE-TAX EARNINGS: $540 (free cash flow to the FIRM is still $650, as all of the interest payment goes to investors in the firm, meanwhile FCFE is $590, as none of the interest payment is available to equity holders) ___________________________ TAX payment (at 40%): $216 Net Income: $324 (FCFF is $434 ($650-$216). Meanwhile FCFE is $374 ($590-$216) However, the formulas for CFA Level II don’t yield the final cash values that I get for FCFF (though interestingly for FCFE it is consistent). Again, to make this really easy, I assumed WCInv and FCInv are both 0. I also assume net new borrowing is 0 for the purpose of FCFE. The FCFF would yield NI + NCC + interest payments (1-tax) - FCInv - WCInv = $324 + $50 + $60 (1-0.4) - 0 - 0 = $410 (as opposed to $434 as calculated above) And the FCFE formula would yield NI + NCC + net borrowing - FCInv - WCInv = $324 + $50 + 0 - 0 - 0 = $374 (this is consistent, interestingly) Again, I would really, really appreciate it if you use numbers in your answers, and don’t skip steps. Basically every answer I’ve seen to this question appears to skip steps, use shorthand, and gloss over how the numbers actually work out.
I could be wrong but here is my best guess at this (Someone else please chime in if you can)
So in the formula for FCFF you have NI + NNC + Interest Payments (1-tax) - FCInv - WCInv as you noted.
Interest Payments (1-tax) would only add back 60% of the interest that was paid, which would be $36. Since we paid $60 in interest but only added back $36 of it, we seem to be missing $24.
Interestingly enough, this $24 we are missing from the interest also seems to be missing from your FCFF calculation and income statement exercise. I _ THINK _ (Take with a grain of salt) that this is because firms get a tax shield on the interest payments, and only truly pay the after-tax cost of debt. So I think you should increase your Net Income by $24 due to the interest tax shield, which would make your two calculations tie out.
Then, when you do FCFE=FCFF - Int(1-t) + Net Borrowing, you get $398 as your FCFE
Checking is with FCFE=NI + NCC + Net Borrowing - FCinv- WCinv, you would get $398 as well.
I could be completely wrong, but I made it tie somehow…
I could be wrong but here is my best guess at this (Someone else please chime in if you can)
So in the formula for FCFF you have NI + NNC + Interest Payments (1-tax) - FCInv - WCInv as you noted.
Interest Payments (1-tax) would only add back 60% of the interest that was paid, which would be $36. Since we paid $60 in interest but only added back $36 of it, we seem to be missing $24.
Interestingly enough, this $24 we are missing from the interest also seems to be missing from your FCFF calculation and income statement exercise. I _ THINK _ (Take with a grain of salt) that this is because firms get a tax shield on the interest payments, and only truly pay the after-tax cost of debt. So I think you should increase your Net Income by $24 due to the interest tax shield, which would make your two calculations tie out.
Then, when you do FCFE=FCFF - Int(1-t) + Net Borrowing, you get $398 as your FCFE
Checking is with FCFE=NI + NCC + Net Borrowing - FCinv- WCinv, you would get $398 as well.
I could be completely wrong, but I made it tie somehow…
AnalystDude123 is right.
OP, you calculated the tax payment using Earnings before taxes (US$ 540), however you should have used US$ 600 as “Earnings before taxes”. So the tax payment is higher in US$ 24 and the FCFF arrives to US$ 410.
If FCFF does not deduct interest payment as a cash outflow, then do not also consider the tax shield gained from the supposed interest payment. Remember that FCFF is a measure of cash for valuation purposes, not just cash balance. This means that FCFF is commonly discounted at the WACC rate of the company to find the value of the firm. Also remember that WACC rate is already adjusted for interest payment tax shield, so we must not double count the effect (in the wacc rate and in the FCFF). FCFF does not consider interest payment nor the tax shield gained from it.
Maybe I was right by mentioning the tax shield, but I assumed the FCFF would increase the $434 because the shield would be added. What is the right way to look at the shield?
The approach:
FCFF = NI + NNC + Interest Payments (1-tax) - FCInv - WCInv
Is called “the indirect method” to arrive at FCFF. So, if you start from NI, you add back interest expense after tax. If calculate FCFF using “the direct method” which starts from sales (like the OP’s example), then you don’t deduct interest expense as a cash outflow and don’t assume the tax shield of this interest expense, thus you pay more taxes.
Whatever the method you apply, be sure to do it correctly.
Harrogath, Not sure I’m following. 1.) you said "OP, you calculated the tax payment using Earnings before taxes (US$ 540), however you should have used US$ 600 as “Earnings before taxes”. Isn’t interest excluded entirely from interest payments, such that “earnings before taxes” would be $540? Isn’t the $60 of interest entirely untaxed, by virtue of being removed subtract the income sheet before the taxation line? 2.) Even if, contrary to my understand, $600 is the amount that should be taxed, then that would make the income sheet look like this:
INTEREST PAYMENT: $60
PRE-TAX EARNINGS: $540 (free cash flow to the FIRM is still $650, as all of the interest payment goes to investors in the firm, meanwhile FCFE is $590, as none of the interest payment is available to equity holders)
___________________________
TAX payment (at 40%): $216 --> $240 (assuming $600 is the taxable amount)
Net Income: $324 $360 (assuming the right number is $600 - $240) FCFF is $434 410($650-$240). Meanwhile FCFE is $374 $350($590-$240)
As you can see, the numbers still don’t add up. How would you make the number work?
AnalystDude123, if I increase by $24, that gets me to $348. That doesn’t match either FCFF or FCFE, as I calculated them. How do the numbers work? The point of this thread isn’t to apply the formulas “correctly”. I can already do that and get the right answer on the test. I want to understand why they work so that it is intuitive. So far, I can’t make any of these numbers add up. What would be super awesome is if someone could copy and paste my income sheet, along with the cash flow annotations in parentheses, and then edit it, explain where it’s wrong.
REVENUE: $1,000
COGS: $200
_____________________
GROSS PROFIT: $800 (cash is also 800 at this point) _ Correct _
SG&A: $150
______: $650 (cash is also 650 at this point, assuming SG&A was all paid in cash, let’s assume that) Agree
—>Not sure what this line on the income statement is called, but in any case, you have $650 (EBITDA)
____________________________
DEPRECIATION: $50
EBIT: $600 (cash is $650 at this point, as depreciation is not an actual cash outflow) Correct
________________
INTEREST PAYMENT: $60
PRE-TAX EARNINGS: $540 (free cash flow to the FIRM is still $650, as all of the interest payment goes to investors in the firm, meanwhile FCFE is $590, as none of the interest payment is available to equity holders) _ Excellent _
___________________________
TAX payment (at 40%): $216 (Wrong for FCFF and right for FCFE)
_ FCFF is a special measure of cash because its purpose is to calculate firm value. In other words, the analyst forecasts the FCFF for the following years, assume a terminal value and discount to present this stream of cash flows using the WACC rate. This discount rate assumes interest expense tax shield in its build up: _
WACC = We*Re + Wd*Rd*(1-t), where Wd is the weight of company capital in debt (commonly interest bearing debt), Rd is the weighted average of interest rates on all debts the company holds, and (1-t) is the interest expense tax shield (save in taxes due to increased expense in form of interest to debtholders).
Thus, as you can see, if FCFF assumed interest expense tax shield in its calculation (216 tax instead of 240 tax), by the moment the analyst finds the Present Value of the FCFF stream (firm value), the resulting number will double count the interest expense tax shield: in the FCFF and in the discount rate (WACC). The Firm Value would be overvalued in this case, because you assumed a higher FCFF than true.
Your FCFE calculation is right, so don’t continue worry about it.
Now you know why the FCFF formula in the Curriculum adds back interest expense after tax and not just interest expense 
Hope this helps.
@Harrogarth:
Ok that explanation mostly makes sense, and is the most helpful thing, I’ve seen so far, so thank you for that. Still unclear to me, though, are the following:
1.) If I make the tax payment $24 (240 instead of 216) that makes NI 300, right?
2.) so then, is the appropriate FCFF $300 + 50 + 60(1-0.4) - 0 - 0 = 386? That still doesn’t agree with the $434 I calculated. How come?
I agree, FCFE seems to be less of a problem for me 
You are welcome my friend.
Nope, NI is a measure independent of FCFF. As I explained in my previous post, FCFF is a “special” measure of cash. It can be calculated using the direct method or the indirect method.
The Income Statement is built independently of anything else. NI indeed considers interest expense, thus also its tax shield. In short, NI uses 216 income tax.
Hope this helps!
Oh I see. Do you have a link to what the direct method for calculating FCFF, and ending up with the same number as the indirect method, would be?
Your own P&L example was the direct method of calculating FCFF
The indirect method is using the book formula FCFF= NI + NNC + Interest Payments (1-tax) - FCInv - WCInv