Simple FCFF concept I'm really struggling with.

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cleverCFA

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Not being able to figure this out is really bothering me. I’m trying to understand the FCFF concept of adding back the Int*(1 – t). I don’t get the derivation of the (1- t) part.
FCFF = NI + NCC + Int*(1 – t) – FCInv – WCInv
Free cash flow is meant to be the cash flow available to shareholders and creditors. So I’m trying to figure out this formula using an example.
I own an ice cream van and sell ice creams. I buy $100 of ice cream inventory and sell them for $230. My van has depreciated by $20 during the year and I need to pay $10 in interest for a loan on my van. My tax rate is 40%. I have no FCInv or WCInv.
So, the breakdown is as follows:
$130 (EBITDA) - ($230 of sales minus $100 of cost of good sold)
-$20 depreciation
= $110 (EBIT)
-$10 Interest
= $100 (EBT)
-$40 tax
= $60 Net Income
So now I want to calculate FCFF, the cash available to shareholders and creditors. If I think of it without the formula, I take $130 in my hand at the end of the day minus what I paid in taxes to the government. So according to me my shareholders and creditors should have $130 - $40 = $90 available between them.
But according to the formula, it should be
FCFF = NI + NCC + Int*(1 – t) – FCInv – WCInv
= 60 + 20 + 10 (1 – 0.4) – 0 – 0 = $86
What simple concept am I not understanding here. Is it because the creditors will need to pay $4 in tax on the interest that I paid them? So its $90 - $4 = $86.
Sorry if this is a simple concept but I’m just not understanding the formula.
 
FCFF is all cash that is available to the suppliers of capital after expenses etc from normal business operations. A interest payment is payable to the capital providers..i.e. the creditors and lenders. Therefore we need to add back the after tax deduction to arrive at a complete figure for FCFF.
Hope this helps.
 
Hey pokhim,
Thanks for the reply. Unfortunately it’s stil not getting through. Your explanation is similar to what I’m reading in the Schweser and CFAI and there’s just something that isn’t ticking.
Are you able to use my example to help it get through?
At the end of my ice cream sales run I’ve got $130 in CASH in my pocket. All I got to do now is pay taxes of $40 and the rest of the cash after that ($90) is there to be split amongst the shareholder and bondholders (the Free Cash Flow to Firm). So why is it only $86 according to the FCFF equation? What is this $4? Is it $4 of tax the bondholders need to pay in tax on the $10 interest they’ve earned from me (a second/final round of taxation)? What is it I’m not understanding?
Apologies for being so thick but not understanding this is really irritating me. It’s Saturday night and I just can’t move on without understanding this.
btw - congrats on finishing first pass! It’s still a painful journey ahead but we’re getting there!
 
cleverCFA wrote:
Not being able to figure this out is really bothering me. I’m trying to understand the FCFF concept of adding back the Int*(1 – t). I don’t get the derivation of the (1- t) part.
FCFF = NI + NCC + Int*(1 – t) – FCInv – WCInv
Free cash flow is meant to be the cash flow available to shareholders and creditors. So I’m trying to figure out this formula using an example.
I own an ice cream van and sell ice creams. I buy $100 of ice cream inventory and sell them for $230. My van has depreciated by $20 during the year and I need to pay $10 in interest for a loan on my van. My tax rate is 40%. I have no FCInv or WCInv.
So, the breakdown is as follows:
$130 (EBITDA) - ($230 of sales minus $100 of cost of good sold)
-$20 depreciation
= $110 (EBIT)
-$10 Interest
= $100 (EBT)
-$40 tax
= $60 Net Income
So now I want to calculate FCFF, the cash available to shareholders and creditors. If I think of it without the formula, I take $130 in my hand at the end of the day minus what I paid in taxes to the government. So according to me my shareholders and creditors should have $130 - $40 = $90 available between them.
But according to the formula, it should be
FCFF = NI + NCC + Int*(1 – t) – FCInv – WCInv
= 60 + 20 + 10 (1 – 0.4) – 0 – 0 = $86
What simple concept am I not understanding here. Is it because the creditors will need to pay $4 in tax on the interest that I paid them? So its $90 - $4 = $86.
Sorry if this is a simple concept but I’m just not understanding the formula.
Click to expand...
FCFF is the cash flow that is available to the firm BEFORE anything gets paid to your creditors or shareholders.
You have a $10 dollar interest expense in your exam… if you decide to not pay your $10 dollar interest expense you will have to pay tax on that income. Previously, that interest expense was tax deductible. This is the equivalent to:
EBIT $110
Interest Expense $0
EBT $110
Tax Expense $44
Net Income $66
^You see above, Net Income is $66 which is higher by 10(1-.4) than your previous Net Income of $60. This represents the FCFF = NI + Int*(1 – t) part of the Free Cash Flow problem. Net Income without any payments to creditors or shareholders yet.
 
Yes that’s what I was going to reply! You have to add back the interest expense net of the interest tax shield ($6 in you example).
 
^ Exactly.
The payments of interest go to your bondholders. You are trying to calculate the free cash before this payment has been made, hence the reason you would add back the interest amount to NI.
 
pokhim wrote:
^ Exactly.
The payments of interest go to your shareholders and bondholders.
Click to expand...
Interest payments don’t go to your shareholders…
 
Nice, edit. I was still able to quote it before you corrected it
 
DaSh 1s wrote:
FCFF is the cash flow that is available to the firm BEFORE anything gets paid to your creditors or shareholders.
You have a $10 dollar interest expense in your exam… if you decide to not pay your $10 dollar interest expense you will have to pay tax on that income. Previously, that interest expense was tax deductible. This is the equivalent to:
EBIT $110
Interest Expense $0
EBT $110
Tax Expense $44
Net Income $66
^You see above, Net Income is $66 which is higher by 10(1-.4) than your previous Net Income of $60. This represents the FCFF = NI + Int*(1 – t) part of the Free Cash Flow problem. Net Income without any payments to creditors or shareholders yet.
Click to expand...
pokhim wrote:
^ Exactly.
The payments of interest go to your shareholders and bondholders.
Click to expand...
I wholeheartedly disagree with this. No offense, so I apologize if I’m stepping on some nerves.
FCFF is the cash available to the firm after accounting for operating expenses and CapEx.
DaSh 1s wrote:
You have a $10 dollar interest expense in your exam… if you decide to not pay your $10 dollar interest expense you will have to pay tax on that income.
Click to expand...
Not even sure what this means - if I decide not to pay the $10 interest expense, for all intents and purposes, I have defaulted. Uncle Sam doesn’t reward you for NOT paying your dues.
cleverCFA: There’s no mathematical reason behind this adjustment of after-tax interest expense to FCFF. You’re forgetting the golden rule… if something seems fishy at L2, it must be real fishy. All the adjustments in the CFAI material are shown using GAAP. Then, there’s a separate discussion on what you’d do under IFRS. Most people who simply glance over this aren’t going to realize what they’re missing out, come exam day :).
In valuation, we care about operating cash flows. FCFF is no different. Interest-bearing debt, just like cash and equivalents, is nonoperating. GAAP classifies interest expense as CFO, so we must back it out - so we’re really making an adjustment to CFO, not so much to FCFF. Uncle Sam took a cut which we don’t care about since it doesn’t belong to us. Hence, the adjustment [Int * (1 - T)].
Now, let’s step into the wonderful world where both GAAP and IFRS coexist. If some Asian nation decided to classify interest expense (i.e. interest paid) as CFF, there would be no adjustment to CFO when calculating FCFF.
Be careful on the exam - uttely important to recognize if we’re dealing with GAAP vs. IFRS and how interest expense (and other items) are classified.
FCFE: Assuming you’re using CFO, the [Int * (1 - T)] adjustment is not required because that portion doesn’t belong to the shareholders. Just like (Int * T) in the above discussion didn’t belong to the entire firm - it belonged to Uncle Sam. If you’re using FCFF to arrive at FCFE, you’d subtract [Int * (1 - T)] under two circumstances:
  1. If you’re a GAAP firm.
  2. If you’re an IFRS firm and you decided to classify interest expense as CFO.
Hope this helps.
 
Hey Aether,
Your post is definitely the most helpful but I’m still confused about the Algebra used to to get the Int * (1-t).
I’m trying to work it out, and it feels like it’s on the tip of my head but I just can’t see the Algebra that was used to arrive at that figure. You’re saying it’s fishy as if we just need to accept it, is that right?
What I’m seeing is that we’re adding back in the interest component to get to CFO (the Int * 1 component). Also since paying interest would have shielded us from paying Int * t taxes, there is the other component of that equation Int * t. However, I’m failing to make that final hurdle to get + Int * (1 - t). It almost seems to me like it should be Int * (1 + t) (i.e. the interest that went to the bondholders plus the tax savings based on the shield).
I’m giving up and moving on. I’m just going to memorise the formulas and plug and chug without understanding. Hopefully it’ll be enough to get me through the exam.
 
You’re almost there: here’s a hint - go back to your very first post and recalculate the numbers assuming you did not have a loan, and thereby no interest to pay. So only thing you have is EBITDA, D&A, and Taxes.
If you still can’t get to it, I’ll post an explanation.
When I said it’s fishy, I meant the IFRS vs. GAAP stuff - the concept is straightforward once you recognize why the adjustments are being made.
 
To get to the free cash flow to the firm, you could try several ways:
1. For the given example you could start with EBIT since it represents cash flows to the firm ie both equity and debt holders. If you were to calculate it for equity holders then you would have started with earnings after interest and tax.
EBIT = 110 so EBAIT = 66 .. rememeber you need cash flow to the firm not to equityholders so you would not use interest.
Now add back depreciation and you will have 66+20= 86 since you net change in working capital and capex is 0 so 86 is you FCFF.
Now focusing on formula:
Lets say you start with EBIT= x and you substract interest payment Int from it, you end up with
EAIBT = x-Int
Your tax rate is t so NI= (x-Int)*(1-t)= y
Since you need cash flow to firm so you need add back the part of interest which is after tax ie int(1-t)
FCFF = y + int(1-t) + Dep + NWC+ Capex
Hope this helps.
 
Aether wrote:
You’re almost there: here’s a hint - go back to your very first post and recalculate the numbers assuming you did not have a loan, and thereby no interest to pay. So only thing you have is EBITDA, D&A, and Taxes.
Click to expand...
+1 .. this should makes sense now!
 
cleverCFA wrote:
So now I want to calculate FCFF, the cash available to shareholders and creditors. If I think of it without the formula, I take $130 in my hand at the end of the day minus what I paid in taxes to the government. So according to me my shareholders and creditors should have $130 - $40 = $90 available between them.
Click to expand...
Isnt this to do with the fact that every tax deductable expense comes with a tax shield benefit.
So in the portion that i have highlighted above …. if you go to the government saying that i have an EBITDA of $130 and no other expenses they would ask $52 as taxes from you and not just $40 as you have calculated (coz u know that u have more tax deductible expenses to account for).
But then u r yet to deduct two important expenses from your income …. Dep of $20 (non cash) and Interest of $10 (Cash).
Each of these two expenses have two components 1) the actual expense which moves out of the accounting statement and 2) the tax shield benefit that the firm gets since both these expenses are tax deductible.
In both the cases the expenses part goes to the benficiary and the tax shield benefits the corporate.
Since in case of Dep the corporate itself is the beneficiary both the components are added
But in case of Interest the expense part goes to the benficiaries (i.e. the lenders) but the corporate at the same time benefits from the tax shield (which is that missing $4)
The main issue in your way of understanding the problem is that you are arriving at the Tax number before taking into account all tax deductible expenses.
Once you do this …. that point onwards every further tax deductible expense needs to be accounted for along with the tax shield benefit that it will provide
 
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