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 …

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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.

Simplify the complicated side; don't complify the simplicated side.

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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.

You keep using that word.  I do not think it means what you think it means.

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.

Things will workout

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:

Net Income                          10.5

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!

Hello S2000magician!

Howdy!

Thank you so much for setting this example up, my apologies on the late response, I have been sick for a few days.

I hope that you’re feeling better now.

Here are my results:

Let’s take a look at this.

Balance Sheet Y0:

Assets:                                                  Liabilities:

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

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

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

The income statement looks good.

Balance Sheet Y1:

Assets:                                                Liabilities:

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

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

Cash Flow Statement Y1:

CFO:

Net Income                          10.5

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.

You had investing and financing cash flows in year 1:

CFO:

Net Income                                   10.5
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

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

FCFE: 10.5 + 20 + 40               => 70.5

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.

Simplify the complicated side; don't complify the simplicated side.

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http://financialexamhelp123.com/

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.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

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?

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?

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.