# Why do we add back Interest Expense (1-t) in FCFF?

Hello,

I know this question has been asked many times, I’ve reviewed all answers, but my confusion has remained the same. I know FCF = *Cash* flow available to debt and equity holders.

I am genuinely confused on why I would add back interest expense. Moreover, I know the concept of tax shield, but I want to know how it is adapted in this context. I do however understand why we add back depreciaiton.

I usually try to solve these problems by applying generic examples, but I will apply one now and show you where i’m confused:

Assume: Interest = 800,000; Depreciation = 2,000; Tax Rate = 10% … This would mean we have a tax shield for interest of 80,000 and tax shield for depreciation of 200. Now FCF says I have to add back Int(1-t); so I am adding back 720,000 worth of Interest.

1. Why did I add back 720,000 and not 800,000? It is as if the tax shield hurts a debt holder as the company’s value becomes less after we include the tax shield

2. When projecting, Is Interest Payable included in the NWC equation? In FCF we have to include the change in NWC, so if we see an increase in Interest Payable, do we add include that as well or would it be double counting to include it as an interest expense and in the NWC? Also what happens if in our projections Interest payable decreases?

3. If we do add back Interest(1-t), what happens to the WACC we use to discount? Do we still do Wd*(Cost of debt)(1-t) or do we only use Wd*(Cost of debt) portion?

4. Why dont we account for the tax shield that depreciation creates?

Thank you, I am genuinely and utterly confused …

You’ll understand this much better if you do the work yourself: create a simple income statement, balance sheet, and cash flow statement and see what happens.

I’ll get you going. You start your company with \$100 in cash and \$100 in equity, no liabilities.

• You borrow \$100 @ 5% interest for 10 years
• You buy a delivery truck with that \$100
• You’ll depreciate that truck over 5 years, straight line, with zero salvage value
• You buy \$50 of inventory for cash
• You have sales of \$90
• All sales are for cash
• COGS is \$40
• Wages are \$10
• The income tax rate is 30%
• You have no other expenses

Let’s see your income statement for year 1, balance sheet for the end of year 1, cash flow statement for year 1, FCFF and FCFE for year 1.

Don’t worry about making mistakes; we’ll correct them for you. What’s important is that you do the work. It will solidify your understanding.

I’ll give a more intuitive answer than Magician. Whether or not you add back after-tax interest expense (i.e. Int x (1-t)) depends on where you start from. The key is that FCFF is available to both creditors and owners, so it must be calculated on a “before interest” basis.

If you start from Net Income, you are starting from a number that is AFTER after-tax interest expense has been deducted. So, to get to a value that is AVAILABLE to both debt and equity, we must move to a number that is BEFORE interest expense (because Interest Expense represents a cash flow paid out ot creditors). Remember that Interest is deducted before taxes are calculated, so the net effect of a dollar of additional interest expense is to decrease net income by \$1 (1-t).

Likewise, if we start from CFO, remember that the first item in CFO is Net Income. So refer to the previous paragraph.

If we are starting from EBIT or EBITDA, we are starting from a number that is BEFORE Interest Expense is deducted. So no adding back of Interest Expense is needed.

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You said the answer (available for debtor). the intensest expense is the cash paid on loan to lenders. FCFF required the net income (cash inflow) before we deduct any amount to the financing activities.

Hello S2000magician! Thank you so much for setting this example up, my apologies on the late response, I have been sick for a few days. Here are my results:

Balance Sheet Y0:

Assets: Liabilities:

Cash 50 Loan: 100 Truck 100 Inventory 50 Equity: Deposit: 100

Income Statement Y1:

Sales 90 COGS 40 Gross Profit = 50 Salary Exp: 10 EBITD = 40 Depreciation 20 EBIT = 20 Interest = 5 EBT = 15 Tax = 4.5 Net Profit = 10.5

Balance Sheet Y1:

Assets: Liabilities:

Cash 120.5 Loan: 100 Truck 80 Inventory 10 Equity: Deposit: 100 R/E 10.5

Cash Flow Statement Y1:

CFO:

CFI CFF Beginning Cash 50 Net Cash from Activities 70.5 Ending Cash Balance 120.5

FCFF: 20(1-0.3) + 20 + 40 => 74.5

FCFE: 10.5 + 20 + 40 => 70.5

I hope I did it correctly.

@busprof: Thank you a lot for your feedback, it’s great to understand it this way using the BEFORE and AFTER approach and considering which formula you start with! Much appreciated for your response Sir.

@ Sami86: Thank you for your response! Much appreciated!

Howdy!

I hope that you’re feeling better now.

Let’s take a look at this.

The beginning balance sheet has only cash and equity; the loan and purchase of the truck and inventory occur in year 1. Thus:

Balance Sheet Y0:

Assets: Liabilities:

Cash: 100 Equity:

Paid-in Capital: 100

The income statement looks good.

Inventory is a current asset while the truck is a long-term asset; you should list Inventory before Truck.

Assets: Liabilities:

Cash: 120.5 Loan: 100 Inventory: 10 Truck: 80 Equity: Paid-in Capital: 100 R/E: 10.5

You had investing and financing cash flows in year 1:

CFO:

Net Income 10.5 Add: Depreciation 20 Subtract: Increase in Inventory (10)

Cash from Operations 20.5

CFI:

Truck (100)

Cash (used in) Investing (100)

CFF:

Loan 100

Cash from Financing 100

Net Cash from Activities 20.5 Beginning Cash Balance 100 Ending Cash Balance 120.5

Don’t use the formulae here; the idea is that you want to understand why the formulae are correct. Figure out, based on the cash flow statement, what FCFF and FCFE are, then confirm them with the formulae.

Hello Sir,

Thank you for correcting the mistakes I made. I understand now and I have corrected the three financial statements. Some follow up questions I have are:

1. After constructing the Income statement, we move onto the balance sheet. While filling in the balance sheet, do we leave cash account empty and do the cash flow statement first in order to derive proper cash value?

2. Is my FCFF correct now?

• FCFF = EBIT(1-t) + Depreciation - CapEx - Increase in Current Assets (only form of NWC we have here)
• FCFF = 20(1-0.3) + 20 - 100 - 10
• FCFF = -76

EBIT(1-t) = We want to keep the interest portion to embed creditors money but remove taxes as taxes are paid in cash (assuming no tax liability is created)

Depreciation is added back as it is a non cash expense

CapEx is deducted as it is paid through cash

Increase in Current Assets (inventory here) was paid through cash (\$50 worth) but we sold \$40 of it (evident through COGS) and it was received as cash as no receivables were accrued.

Correct?

Thank you

Bump for Mr Magician’s verification (:

You’re still using the formula to calculate FCFF. The idea was to verify that formula, so you have to calculate FCFF directly from the cash flows. Similarly for FCFE.

What cash came in during the year?

• Cash from customers: \$90
• Cash from the loan: \$100

What cash went out during the year?

• Cash to buy a truck: \$100
• Cash to buy inventory: \$50
• Cash to pay wages: \$10
• Cash to pay interest: \$5
• Cash to pay income taxes: \$4.50

Using these numbers, calculate FCFE. Then verify that the formula for FCFE gives you the correct number.

Hold off on FCFF till we know you have FCFE correct.

Okay, so FCFE is the amount of cash remaining to equity holders. Therefore, I will calculate it on that basis:

Cash from customers + Cash from loan - Cash to buy a truck - Cash to buy inventory - Cash to pay Wages - Cash to pay income taxes - Cash to pay Interest: => 90 + 100 - 100 - 50 - 10 - 4.50 - 5 => 20.50

*I understand why we add back cash from loan (I saw your post in 2013 after doing some research and realized that this cash can be used to give out dividends), but why do we not add it back to FCFF?

*Also, shouldn’t we add back depreciation?

The reasoning is that the firm will have to pay it back, so it’s not really theirs to do with as they please.

You may not like that reasoning, but you need to accept it; that’s just the way it is.

What do you mean by adding it _ back _?

That suggests that we _ subtracted _ it earlier. Did we?

Mr. Magician - I have a follow up question on this example.

When we compute FCFF using the direct approach we get -74.5 while using the formula gives -76. The difference of 1.5 seems to be the tax savings on interest. Why is this ignored when computing the FCC using the formula.

Direct Method:

Direct Method Cash from Customers 90 Cash paid for Inventory 50 Cash to pay wages 10 Cash to pay interest 5 Cash to pay income tax 4.5 Cash from loan 100 Cash for Asset purchased 100 FCFF -74.5 FCFE 20.5

Using Formulas:

FCFF -76 FCFE 20.5

So my question - Why do we ignore the tax shield on interest while computing FCFF ?

If you’re getting −74.5 by one method and −76 by another, you’ve clearly done something wrong. FCFF is FCFF; the approach that you use to calculate it doesn’t matter.

Note that we do not ignore the tax shield on interest when computing FCFF. What we ignore is the interest itself: FCFF measures cash flow before interest is paid. And, of course, if you don’t pay interest, you don’t get any benefit from the interest tax shield.

I agree with the point conceptually (that FCFF is pre-levered cash flow and direct and indirect method should ideally result in the same answer).

However the number don’t seem to match (I have cross checked them). And the difference of 1.5 in FCFF is due to the lower tax amount paid due to the presence of interest in the income statement. If I remove interest, the numbers from the direct and indirect method match.

Secondly, your last statement throws me off a bit - (“if you don’t pay interest, you don’t get any benefit from the interest tax shield”). The company has paid interest and thus the tax liability is smaller because of that - and thats a fact. And we take that into account in the indirect approach also by adding back only interest (1-t) and not the complete interst. However in the direct approach we subtract the cash tax paid, due to which the numbers differ.

It isn’t that they should ideally result in the same answer. They _ must _ result in the same answer. If they don’t, rest assured that you’ve done something wrong.

That tells you that that is the correct approach.

You seem to be misunderstanding the relationship between FCFF and interest.

Nobody is disputing that the firm paid interest and thereby reduced its taxes.

The point is that paying interest is a _ use of _ FCFF. FCFF is calculated before the company pays interest and, therefore, before the company’s taxes are reduced because of it paying interest. Therefore, in the direct approach, you shouldn’t subtract the actual (after interest) taxes paid, you should subtract the taxes that would have been paid had the company not paid interest.

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I understand your question. Even I pondered on this question a lot when I was a student.

The difference is occurring because there is slight difference in the cash flow format and the formula calculation.

Many of us are not usually taught to match FCFF & FCFE using format and formula, that’s why we don’t notice this difference.

We always solve 2 different sums.

1. When we are solving Cash Flow using direct or indirect format, we are never required to match FCFF & FCFE, we are just required to match the cash flow.

2. When we are calculating FCFF & FCFE, we use formulas, we don’t have the time to solve entire cash flow by format.

If you notice, in the original income statement the tax paid (4.5) is charged on EBT (15 x 30% = 4.5) and you are using the same tax amount in cash flow statement. So when you are calculating FCFF using direct format you are considering tax charged on EBT

While in the FCFF formula we consider NOPAT which charges tax on EBIT (20 x 30%=6).

Hence both calculations are showing the difference of tax shield on interest (5 * 30% =1.5).

It will occur for FCFF but will not appear in FCFE (because it gets adjusted eventually). That’s why your FCFF is showing difference but FCFE is matching.

Now the question comes which is the correct approach. Considering fundamental logic of FCFF and FCFE calculation, I believe charging tax on EBIT which is done in the formula is more accurate ( my opinion completely).

If you want your FCFF & FCFE calculated by both methods to match, you should make the following changes in your cash flow direct format :

1. change ‘cash to pay income tax’ figure in your cash outflow from operations from 4.5 to 6 (so your FCFF matches -76)

2. Consider ‘tax shield on interest’ of 1.5 in your financing inflows (Revised FCFF and this adjustment will have nullifying effect eventually making FCFE to remain same as earlier)

Hope this solves your query … Cheers !