Computing FCFF from EBIT. Tax shield issue

Calculation of FCFF from EBIT. Tax shield issue

Introduction

Free Cash Flow to the Firm (FCFF) from earnings before interests and taxes (EBIT) defined in CFA Curriculum[1] as:

FCFF_a = EBIT * (1-tax rate) + Non-Cash Charges (Depreciation) - Working Capital investments - Fixed capital investments,

Or rewriting in a short way using abbreviations:

                                       FCFF_­a = EBIT * (1-tax rate) + NCC – WCI – FCI                        [1]

This formula is quite popular in practise. However, students usually get confused by the absence of the ctax shield. They think tax shield, which is [interest expenses * tax rate], should be added back to calculate FCFF because most companies deduct interest expenses in calculating taxes.  However, computing FCFF by using the formula [1] is quite logical for the calculation of company’s value using after-tax weighted average cost of capital (WACC_a) as a discount rate.

Let’s take a closer look at the formula and FCFF concept.

Explanation

Theoretically speaking, FCFF could be defined as the firm cash flow after subtracting operating expenses, working capital investments and fixed capital investments. The exact reading of this definition gives us the following formula for FCFF:

                                        FCFF_b = EBIT – Taxes + NCC – WCI - FCI                              [2]

By having Taxes = EBT * tax rate, which is = (EBIT – Interest expenses) * tax rate, the formula [2] could be further developed as:

FCFF_b = EBIT – (EBIT – Interest expenses) * tax rate + NCC – WCI – FC  
= EBIT – EBIT * tax rate + Interest expenses * tax rate + NCC –WCI - FCI
                = EBIT * (1 – tax rate) + NCC – WCI – FCI + Interest expenses * tax rate    [3]

Thus, by following the definition for FCFFb we have the tax shield term in the equation. This is exactly what students would want to see based on the intuitive feeling on tax shield idea. Although, in practise it is more common to see FCFF_a rather than FCFF_b, my opinion is that both ways are appropriate from the calculation of company value standpoint.

Next table summarizes that formula [1] differs from [3] by the amount of Interest expenses * tax rate.

Column A (practical alternative)[2]	Column B (theoretical alternative)
FCFFa	FCFFb
EBIT – EBIT * tax rate + NCC – WCI – FCI    = FCFFa	EBIT – EBIT * tax rate + NCC – WCI – FCI + Interest expenses * tax rate    = FCFFb
Thus, FCFFa less than FCFFb by Interest expenses * tax rate

Company value estimation by discounted cash flow method

The purpose of calculating FCFF is to estimate the value of the company, by discounting forecasted FCFF by the average cost of capital (debt and equity). Taking into consideration FCFF calculated in the column B (theoretical one), we would discount FCFF_b by the average cost of capital calculated as:

WACC_b = Cost of debt * Debt/Assets + cost of equity * Equity/Assets

Here, we are not using after tax cost of debt because the adjustment for the tax amount has been done on the stage of calculating FCFF_b. 

However, it is common to calculate the average cost of capital on the after tax basis:

WACC_a = Cost of debt * (1 – tax rate) * Debt/Assets + cost of equity * Equity/Assets

Which is less than WACC_b by the amount of Cost of debt * tax rate * Debt/Assets, which is an interest rate * tax rate *Debt/Assets.  Where interest rate * Debt/Assets is the Interest expenses expressed in terms of percentage from Assets (Interest rate * Debt/Assets = Interest expenses / Assets). These are the same Interest expenses we used in calculating of FCFF and the tax shield term.

Column A (practical alternative)	Column B (theoretical alternative)
WACCa	WACCb
WACCa =    cost of debt * Debt/Assets + cost of equity * Equity/Assets - cost of debt * tax rate * Debt/Assets	WACCb =    cost of debt * Debt/Assets + cost of equity * Equity/Assets
Thus, WACCa less than WACCb by Interest rate * Debt/Assets * tax rate

Now we have the tax shield term shown up in the calculation of both FCFF and WACC. This helps us to understand the difference between A and B ways to calculate firm's value. Next table summarizes the result. 

Column A (practical alternative)	Column B (theoretical alternative)
Firm Valuea	Firm Valueb
∑ FCFFa / WACCa	∑ FCFFb / WACCb
Here, by calculating Firm Valuea we subtract Interest expenses * tax rate in the numerator, and interest rate * Debt/Assets * tax rate in the denominator, which conceptually gives the same result as the Firm Valueb  [3]

Calculation of Free Cash Flow to the Equity holders (FCFE)

Further, if we want to calculate Free Cash Flow to the Equity holders (FCFE) starting from the Free Cash Flow to the Firm (FCFF) step from the practical point of view, it would be suggested subtracting after-tax interest expenses and adding Net borrowing component:

FCFE_a =  FCFF_a – Interest expenses * (1 – tax rate) + Net borrowing

However, from a itheoretical point of view (column B), we would adjust our FCFF_b by subtracting whole interest expenses and add Net borrowing component to reflect the amount of cash left to the providers of equity capital, which gives us FCFE_b.

Column A (practical alternative)	Column B (theoretical alternative)
FCFEa	FCFEb
FCFFa - Interest Expenses * (1- tax rate) + Net borrowing = FCFEa	FCFFb - Interest Expenses + Net borrowing = FCFEb

By making some rearrangement in the formulas [1] and [3] will show us that FCFE_a and FCFE_b are equal.

Indeed, let's take a look at FCFE_a:

FCFE_a = FCFF_a - Interest Expenses * (1- tax rate) + Net borrowing

Substitute FCFF_a from the formula [1]:

FCFE_a = EBIT * (1-tax rate) + NCC – WCI – FCI - Interest Expenses * (1- tax rate) + Net borrowing =

= (EBIT – Interest expenses) * (1 – tax rate) + NCC – WCI – FCI + Net borrowing   [4]

Now let's take a look at FCFE_b:

FCFE_b = FCFF_b  - Interest Expenses + Net borrowing

Substitute FCFF_b from the formula [3]:

FCFE_b =  EBIT * (1 – tax rate) + NCC – WCI – FCI + Interest expenses * tax rate - Interest Expenses + Net borrowing =

= EBIT * (1 – tax rate) + NCC – WCI – FCI - Interest expenses * (1 - tax rate) + Net borrowing =

= (EBIT – Interest expenses) * (1 – tax rate) + NCC – WCI – FCI + Net borrowing     [5]

Thus, we have right sides of [4] and [5] are equal which means left sides are equal as well: 

FCFE_a = FCFE_b

This gives us no difference in calculating Equity Value of the company either by practical or theoretical alternative. We just need to use the cost of equity as the discount rate.  

Which one to use - FCFF_a or FCFF_b? 
When we think about the value of the company as of the price one party actually pays after all negotiations have been completed, the method to estimate the value of the company should be chosen in favour of the party. The selling party probably would try to use a method that gives higher estimation. The buying party - could choose smaller estimation. Eventually, analyst would use a number of methods to come up with a reasonable estimation, such as finding similar publicly-traded companies and using multiples to compare; or finding information on recent transactions for similar companies. 

Conclusion

Calculation of FCFF should be consistent with further calculation of WACC in order to estimate proper company’s value. If we use after-tax cost of debt in the WACC rate, then we should use after-tax interest expenses in the calculation of FCFF (variant A). Or, if we use WACC without adjusting cost of debt, then FCFF with adding tax shield term would be appropriate (variant B).

As to the calculation of FCFE starting from FCFF, both ways of calculation FCFF give exactly the same result for value of FCFE.

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[1] Institute, CFA. Level II 2012 Volume 4 Equity, 6th Edition. Pearson Learning Solutions, p. 298

[2] The reference on "practical" and "theoretical" alternatives is done to simplify the discussion so it will be easier to distinguish between A and B way of calculation in the text

[3] Both values are not mathematically equal, and they should not be, because these are two different ways to estimate the value