 # FCFF - depreciation

When calculating FCFF from NI we add back interest but reduced for the taxes that would be paid.

Why doesn’t the same apply for depreciation?

Why don’t we reduce depreciation (or other non- cash charges) for the taxes that would be paid?

Isn’t depreciation also a sort of a ‘tax shield’?

depreciation provides a tax shield - yes, but it is NOT a real expense at all. It is a way the firm progressively reduces the assets on its balance sheet - but it is just an accounting expense.

So NI + Depreciation (in total) is the starting point for FCFF or FCFE for that matter.

Look at an Income Statement:

EBITDA

(Depreciation)

EBIT

(Interest expense)

EBT

(Taxes)

Net Income

Interest payment is a cash outflow, so the debtholders will receive our interest expense in total. Say 100 interest. However, they are tax deductible so we can save taxes for T%, say 40%. We save taxes for 40. The “net” cash outflow is 60 only which would be interest x (1-T). I say “net” because I pay 100 but save 40, so it would be like I just paid 60 on interests. The FCFF calculation uses the “net” cash outflow.

Non-cash charges like depreciation are not cash outflows, they only generate tax savings. Hence, they are added back enterely.

In the FCFF formula Interest add back is net of tax shield because the WACC formula uses cost of debt after taxes. Subtracting the tax shield reduces the FCFF, as not doing so would double count the interest tax shield in the valuation formula.

Harrogath: I dont think your explanation is the right way to look at this. As I understand, per your explanation the “net” cash outflow for the depreciation component (D) should be 0 outflow + D(t) tax shield = +D(t) to be added back.

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nope,

depreciation is added back irrespective of tax shield. harrogath is right.

cpk - I wasn’t saying that depreciation isn’t added back in full. It should be. My point was that, in my opinion, harrogath’s reasoning that depreciation tax shield is ignored because depreciation is non-cash is incorrect.

depreciation is NON cash.

This was an explanation posted a long time ago… which might be of help.

Interest Expense (1-T) is added back in the calculation of FCFF because the debt financing reduced your taxable income which amounted to a tax savings of Interest Expense (T). Adding back Interest Expense alone would ignore the cash flow savings generated by the debt, which reduces the overall “cost of debt.”

Depreciation is added back in full because it is a non-cash expense. You cannot add back Depreciation net of taxes because there was no cash flow payment of “depreciation.” The only cash flow related to depreciation expense would be the tax savings resulting from the reduction of taxable income, which are equal to Deprecation Expense x (T)…and you cannot add this back because it was never “subtracted.”

You should see now that the two expenses are, in fact, not treated different. The cash flow benefit of both expenses (Dep. Exp. x (T) AND Int. Exp. x (T)) are reflected in the FCFF figure. Interest Expense x (1-T) is added back because it represents the portion of the interest expense cash outflow going to compensate debt holders. Finally, the non cash depreciation is added back.

How is the cash flow benefit of both expenses reflected in the FCFF figure if the formula is subtracting the interest tax shield (and not the depreciation tax shield) in the FCFF computation? Hence the formula pretends that interest tax shield benefit is not derived, when it actually is (actual tax outflow is lower due to interest expense, and that is already reflected in the NI figure). This is consistent with using EBITx(1-T) as a starting point for FCFF computations.

Moreover, Interest Expense x (1-T) does not represent the portion of the interest expense cash outflow going to compensate debt holders. Debt holders receive interest payment in full and not net of the borrower’s tax shield.

that was an old post from a similar discussion in the past (and not posted by me), and I copied and pasted it here … But below is a possible explanation.

two things…

interest - you get a tax benefit to the extent of the interest tax shield - so int(t) goes to the government.

you paid the interest in full to the debt holders but the portion int * t is returned by the govt to you (tax shield). so you actually paid int(1-t) to the debt holders.

so you add that portion alone back.

Depreciation - though you took out an expense, and got a tax shield to the effect of dep * t - you never paid any depreciation at all. So add back full depreciation to the FCFF.

Note that in both cases the tax saving is already accounted in the Net Income number. D(t) tax shield is not added back because it is already captured in the net income as it is in the case of the Interest expense tax shield I(t).

Since FCFF starts from NI, you add back the net amounts of cash flows that flowed to the firm:

• Interest expense adjusted for tax saving because interest payment is a cash outflow.

• Depreciation in full because it is not a cash outflow.

1. you do not add back net amount of cash flows that flowed to firm; you would add back only the non-cash components (depreciation) and the flows to non-equity security holders (debt holders in this example). the other flows are captured in NI.

2. if

FCFF is cash available to ALL security holders:

a) cash available to equity = NI + depreciation

b) cash available to debt holders = interest (they get interest payment in full as we have agreed; the tax benefit is already included in NI and flows to equity, already captured in the cash available to equity above)

then:

FCFF (excluding capex and nwc adjustments) ought to be = a + b = NI + depreciation + interest

then why the interest tax shield adjustment?! loops back to the OP’s question

I reiterate that the interest tax shield adjustment is done only because it is captured in after-tax WACC and we want to avoid double counting

Everyone above has explained, intensively, but has not really answered your question; why is Interest x (1-Tax rate) added back but not Depreciation x (1-Tax rate)

Basically, it is because when we convert accounting numbers to cash flow, the net result is add back Interest x (1-Tax rate) and Depreciation

To illustrate:

1. Consider zero depreciation and zero Interest: the net income and cash flow will be (S-C)x(1-tax rate)

2. Consider zero depreciation (interest is existing): the net income and cash flow to equityholders (hence FCFE) is (S-C-I)x(1-tax rate). Because FCFF is an after-tax concept for both equity and debtholders, (S-C)x(1-tax rate) should be the cashflow for both debt and equity holders. add back Interestx(1-tax rate) to get from FCFE to FCFF.

3. Consider zero interest (existing depreciation). In accounting, when we get to the result S-C-D, in cashflow it is only S-C. We pay tax at (S-C-D)x tax rate. Hence the net income is (S-C-D)x(1-tax rate) [which is (S-C)x(1-tax rate)-Dx(1-tax rate)]. However, cash flow is at (S-C)-(S-C-D)xtax rate, [ultimately (S-C)x(1-tax rate)+DxTax rate]. To solve the difference between accounting and cash, D has to be added.

Conclusively, when interest and deprciation exists, to get from accounting numbers to cash flow, Depreciation and after-tax interest has to be added.

I find that it’s easiest to visualize this stuff if I put some numbers to it:

• Revenue: \$100, all cash
• Cash expenses: \$70
• Depreciation: \$10
• Tax rate: 30%

My net income is \$14 (= \$100 − \$70 − \$10 − \$6).

My cash flow from operations is \$24 (= \$100 − \$70 − \$6).

The difference is \$10 (= \$24 − \$14); that difference is depreciation.

This write-up is motivated by a heated discussion on the Analyst Forum (FCFF - depreciation), around several attempts to explain why when calculating the FCFF, we add back the after-tax Interest expense but when it comes to depreciation, we add it in full.

Hopefully, my explanation can finally put this matter to rest. Feel free to contact me if you need any clarifications or you wish to challenge my reasoning; any debates or comments will be highly welcomed.
—See Image attached—

The best way to understand this is to focus on the Total Cash Position available and NOT on accounting figures; and also recognize the differences in situations when cash actually flows in and out of the company and when cash is moved around within the company and still available to the company.
The confusion arises from the representation on the PnL Statement which portrays Depreciation to have a similar characteristic to Interest. The key take away is that interest is an item that generates actual external flows in two directions and we are only interested in the net effect; therefore we add back Interest (1-tax rate) = Interest (outflow to creditors) – Interest*tax rate (inflow from the government) [Remember, this already happened before we arrived at the NI, so we are reversing the events that is why the signs are counterintuitive]. With Depreciation, just picture it in your mind as if you deposited (hid) the depreciation expense in another internal cash account. After computing your net income, we are asked to calculate the total cash available on the firm accounts. What you simply do is: you add the cash in all your accounts, i.e. Net income in your PnL Account + Depreciation Expense in your other internal account.

This explains why we add depreciation in full and only the after-tax interest is added.

Best and Good Luck in the CFA exam.
Marcel Awasum