Windfall profits created by Free Cash-Flow Valuation

Mr. Drs. C.B.A. Spil RA(1)


In company valuation, free cash-flow discounting is predominant now, at least theoretically. This is in large part due to the excellent book ¨Valuation¨ by Copeland, Koller and Murrin(2). They elaborated in much more detail the thoughts of Rappaport(3).

It is not a well-known fact however that, compared with other cash-flow discounting methods, valuation outcome by free cash-flow, is generally different and tends to be lower.

As a basis for comparison the ¨cash is king¨ criterion, is used. This is applied by calculating the refinancing cash-flow of a supposed investor buying a target company at a price equal to the outcome of free cash-flow valuation. This comparison of refinance valuation and free cash-flow valuation makes sense in case of valuation for acquisition purposes. By realizing an acquisition, these differences become apparent both from the cash-flow and from the accounting point of view. Both theory and practice tend to ignore these differences so we call them windfall profits and/or losses.

The present article explains why there are almost always windfall profits and/or losses. It presents three basic reasons influencing these windfall profits or losses on buyer's refinancing cash-flow.

1. Interest on debt discounted at WACC (Weighted Average Cost of Capital).

2. WACC calculation biased by different capital structures

3. Biased treatment of positive interest in debt-low target companies.

Free cash-flow valuation tends to under-valuate companies compared to refinancing cash-flow of buyer thus mostly giving windfall profits to buyers.

The combined result of these three effects are presented in the following table (details in appendix 1). The different columns indicate increasing equity levels of an identical target company with only differences in capital structure. This defined as net worth being a percentage of equity+interest bearing debt.
Equity % target cie. 29% 43% 57% 71% 86% 100% 114%
REFINANCE VALUE 986 1037 1094 1144 1198 1251 1304
FREE CASH-FLOW VALUE 1133 1016 951 920 915 926 926

2. Interest on debt discounted at WACC

Normally cash available for an investor without infringement on operations of the target company is defined as:

+net profit after tax

+depreciation -investments

+continuing value.

This cash-flow is also available and necessary for an investor refinancing the purchase of a company to cover his debt service normally through equity and loans.

For the sake of uncomplicated financial arithmetic, a very simplified company is introduced in the form of an entity generating an everlasting profit after tax of 100 with zero growth, zero investments, zero depreciation, (10) interest cost at a rate before tax of 10% and with equity of 1000. Free cash-flow discount rate is calculated at 10% after tax; a supposed buyer pays the same 10% to his financing partners financing being done with equity and loans.

Supposing a statutory marginal tax rate of 35%, this gives the

following target company in figures:
Income Statement Balance  Sheet
Ebit(Earnings Before) 

(Interest Tax)

164 Fixed assets 500 Net worth 1000
Interest -10 Stock 500 Debt 10% 100 
Taxes -54 Debtors 300 Creditors 200
Net Profit 100 Total 1300 Total 1300


With discount rates set at 10% and assuming a realizable continuing value of 1000, our simplified example comes close to a bullet loan and would be valued at 1000 in all financial markets. Supposing an investor buys the target company at 1000 and interest costs of this debt service happens to be 10%, then cash is king implies in this case refinancing cash-flow matches value. With the available cash-flow from the target company, refinancing requirements are exactly met. Now let us compare this refinance valuation with free cash-flow valuation.

By assuming f.0 increase in working capital, free cash-flow theory adds (simplified) the following components to refinancing cash-flow:

+ 6,5 net interest(interest on interest bearing debt minus tax)

- 100 interest bearing debt.

+ 6,5*10 continuing value difference end year 10.

With discount rates in both valuation methods set to be equal at 10% and time horizon set at 10 years, the difference between financing cash-flow in the above-mentioned example and free cash-flow valuation is:

+ present value of net interest (6,5 N1..N10) 39.94

- interest bearing debt -100

+ continuing value difference (6,5*10 N10) 25.06

The difference in valuation thus results in: - 35.00

The free cash-flow value of the company therefore is 965. An investor buying the target company at 965 would make a profit of 35 in refinancing if his refinancing discount rate was 10%. So in this example free cash-flow valuation generates an additional windfall refinancing profit for the shareholders of buyer on top of discount rate requirements.

This difference of 35 is equal to the statutory tax rate over net interest and multiplied by the discount rate used. More generally, under constant EBIT (growth)conditions and given identical discount rates, the difference between free cash-flow valuation and refinancing cash-flow valuation is related to the statutory tax rate, net interest and discount rate as follows.

Deducting refinancing from free cash-flow valuations taking their respective (growing) perpetuities:

.free cash-flow perpetuity (1-t)*(EBIT-I)+I)/(W-g)- I/i

.refinancing perpetuity (1-t)*(EBIT-I) /(W-g),

gives the exact difference I*(1-t)/(W-g)-I/i.

W = Discount rate; in valuation normally called WACC

I = Interest charges before tax paid by target company

i = pre tax rate on interest bearing debt target company

t = marginal tax rate of target company, usually statutory rate

EBIT= earnings before interest and taxes

g = growth rate of EBIT.

In words this difference means net interest divided by WACC minus growth rate from which gross debt deducted.

Our simplified example covered a case where I=10, t=35%, i=10%, W=10% and g=0%.

Now we explain why free cash-flow valuation tends to be lower than refinance valuation. The basic reason being that WACC normally exceeds interest on debt.

The recommended free cash-flow WACC formula (simplified) is:

WACC = i(1-t)B/V +kS/V where

i = pre tax rate on interest bearing debt

t = marginal tax rate of target company, usually statutory rate

B = market value of interest-bearing debt

V = market value of target company where V = B+S

k = market-determined opportunity cost of equity capital

S = market value of equity

Usually opportunity cost of equity capital(k) is determined by a risk free interest rate + a market risk premium.

The difference formula I*(1-t)/(W-g)-I/i explained before, can be rewritten as I*((1-t)/(W-g)-1/i). By integrating the formula for WACC into this formula, a table can be computed in which this difference is related to various realistic interest, growth, tax rates and market risk premiums.

As shown in the table in appendix 2, for realistic interest(6%) and growth(0%=inflation), this difference is negative for all relevant ranges of tax rates and market risk premiums considered normal in USA and Western-Europe.

The statement that the difference tends to become negative and thus creates windfall profits for buyers buying at free cash-flow valuations, is especially true in slow growing companies, in industries with high equity rates and/or high market risks premiums and in countries where tax rates are high. The reason clearly is that in these cases the opportunity cost of capital is higher than interest on debt.

It might be objected however that using the same WACC for both valuation methods is unrealistic. In the following paragraph's it will be argued that this statement is basically true but at the same time enhances the argument that buying at free cash-flow valuation creates more often windfall profits than losses.

3. WACC calculation biased through different capital structures

Rappaport(4) defines the difference in WACC between buyer and seller as a difference in stand-alone and consolidated values. Free cash-flow theory tradition on WACC as further developed by Copeland cs however, emphasizes in WACC the capital structure of the target company.

In conformity with recommendations by Copeland(5), weights B, k, and S used in the free cash-flow WACC formula, are established by using a capital structure oriented to the target company. This capital structure includes all debt and equity components and excludes all non-interest bearing liabilities such as creditor liabilities and so on. This requires a lot of non-verifiable judgments. Basically the amount of non-interest bearing debt in any company is a financing decision causing shifts between interest and some other profit and loss account detail.

The refinancing WACC would also use gearing assumptions but oriented to the capital structure of buyer or, in case of valuation for an unknown buyer, using industry capital structure. The real capital structure in standard financial analysis, most commonly includes also non-interest bearing liabilities. The resulting WACC therefore is lower as the weight of equity decreases.

4. Biased treatment of positive interest in debt-low target companies

There are quite a few companies in service industries, software, all industries with prepayments (maintenance, publishers, construction), where there is no or little need for debt. In some cases also even no equity is needed either. Buyers in the same low-debt industry, in most cases, finance their acquisition partly by debt. In all those cases by definition, refinancing WACC is lower than free cash-flow WACC (100% equity). Thus refinance valuation is higher than free cash-flow valuation. So there are always windfall profits for buyers in these industries buying at free cash-flow valuations. This case is an extension of the previous argument in paragraph 3 and is illustrated in the second column of the table beneath(100%).

There are also quite a lot of companies where for the above mentioned or different reasons, liquidity surplus being part of operations and thus structural is predominant. This results in positive interest results without there being excess liquidity unrelated to operations. This case strongly enhances windfall profits for buyers buying at free cash-flow valuations. The reason is the definition of NOPLAT (Net Operating Profit Less Adjusted Taxes) . NOPLAT = EBIT - Adjusted Taxes(Taxes adjusted for tax on interest). So in column 3 in the table beneath both NOPLAT and free cash-flow WACC remain identical with column 2 while net profit is increasing. Therefore free cash-flow valuation remains stable in both columns.

This case is illustrated in the third column beneath(114%).
Both cases can be most effectively demonstrated with the original simplified example slightly adapted to realistic weights and interest rates (details in appendix 1). 

Consider the table to the right with calculating results for: 

- 100% equity, zero debt, zero interest results. 

- 114% equity, zero debt, positive interest results 

Look what happens with free cash-flow valuations compared to refinance valuations in the last four rows where WACC's and valuation results (perpetuities) appear. 

Windfall profits increase for buyers buying against free cash-flow valuation and refinancing with debt as indicated in appendix 1. 

These windfall profits are further strengthened if some profit growth is supposed in target company and therefore interest results increase during the planning period. 

Equity % target cie 100% 114%
EQUITY 700 800
EBIT(Earnings Before Interest Tax) 164 164
TAXES -57 -60
NET PROFIT 107 111
NOPLAT(Net Operating Profit Less Adj.Tax) 107 107
REFINANCE WACC-g% 8.5% 8.5%
FREE CASH-FLOW WACC-g% 11.5% 11.5%

5. Conclusions

Point 1, "the impact on free cash-flow valuation of loan deduction calculated before, interest after tax", is mostly not recognized.

Point 2, "interest on debt discounted at WACC" is well-known. Academic theory however in this point is quite contradictory. Practicians obscure this point which can be very misleading.

Point 3, "the impact on free cash-flow valuation of positive interest results in debt-low target companies" is also widely disregarded.

As shown in appendix 1, the combined effect of all three points together is substantial. Practicians working with discounted cash-flow valuation should be well aware of these implications.

Appendix 1. Summary of combined effects in figures

It is supposed that actual risk free interest rate is 6%, interest rate on interest bearing debt (i) is 7%, growth rate(g) is 0%. With market risk rate at 5.5%, opportunity cost of equity(k) is 11.5%. Refinance capital structure is 40% equity, 30% interest-bearing debt, 30% non-interest-bearing debt. The above mentioned conditions are more or less actual in the Netherlands around mid 1998.

Free cash-flow capital structure would be as indicated in each column. The table shows valuation outcomes on a target company with identical operations, EBIT and NOPLAT, but slightly different net profit resulting only from different capital structures. Capital structure defined as net worth being a percentage of equity+interest bearing debt.
Equity % target cie. 29% 43% 57% 71% 86% 100% 114%
EQUITY 200 300 400 500 600 700 800
INTEREST BEARING DEBT 500 400 300 200 100 0 -100
EBIT(Earnings Before Interest Tax) 164 164 164 164 164 164 164
INTEREST RESULT -35 -28 -21 -14 -7 0 7
RESULT BEFORE TAX 129 136 143 150 157 164 171
TAXES -45 -48 -50 -53 -55 -57 -60
NET PROFIT 84 88 93 98 102 107 111
REFINANCE WACC-g% 8.5% 8.5% 8.5% 8.5% 8.5% 8.5% 8.5%
REFINANCE VALUE 986 1037 1094 1144 1198 1251 1304
NOPLAT(Net Operating Profit Less Adj.Tax) 107 107 107 107 107 107 107
FREE CASH-FLOW WACC-g% 6.5% 7.5% 8.5% 9.5% 10.5% 11.5% 11.5%(6)
FREE CASH-FLOW VALUE 1133 1016 951 920 915 926 926

The highest capital structure is found in column 2 (29% equity as a % of net worth + interest bearing debt). Free cash-flow valuation there gives 1131 and refinance valuation 986. So left to column 2 -with higher capital structure then 29%- buying at free cash-flow valuation, implies windfall losses for buyer.

At the right of column 2 -with lower capital structure- buying at free cash-flow valuations give windfall profits to buyers.

Changing g=0% into g=1%, changes the pivot column to column 3.

Appendix 2. Summary of loan deduction before, interest after tax.

This table gives -for interest(i =6%) and growth(g=0%)- in each cell a value by which interest costs in target company must be multiplied in order to get the difference in valuation outcome between free cash-flow valuation minus refinance valuation as a result. Interest cost assumed as having positive figures.

The formula used is explained on page 3: I*((1-t)/(W-g)-1/i).

In the table I(Interest Cost) is excluded.

Table with risk free interest at i=6%; growth at g=0% inflation).
interest i= 6.0% Mar ket risk 6% Mar ket  risk 4% Mar ket risk 2%
growth g= 0.0% 6 % 4 % 2 %
Tax(%) Equity% 0.29 0.43 0.57 0.71 0.29 0.43 0.57 0.71 0.29 0.43 0.57 0.71
0.30 -4.2 -5.5 -6.5 -7.2 -3.3 -4.4 -5.3 -6.1 -2.2 -3.1 -3.8 -4.4
0.35 -4.6 -5.9 -6.9 -7.7 -3.7 -4.9 -5.8 -6.6 -2.6 -3.5 -4.3 -5.0
0.40 -5.0 -6.3 -7.3 -8.1 -4.1 -5.3 -6.3 -7.1 -3.0 -4.0 -4.9 -5.6
0.45 -5.4 -6.8 -7.8 -8.6 -4.5 -5.8 -6.8 -7.6 -3.4 -4.5 -5.4 -6.2
0.50 -5.9 -7.3 -8.3 -9.0 -5.0 -6.3 -7.3 -8.1 -3.9 -5.1 -6.0 -6.8

This table implicitly supposes that the difference of i for risk free rates and normal interest rates(banking margins)for companies is 1%.

This table is most sensitive to changes in g, much less in i.

Increasing g=0% into g=1%, changes 2 negative values into positive ones. Further increasing g into 2%, changes a further 15 negative values into a total of 17 positive values.

Changes of i have some impact only after g has taken the level of this table to some positive values.


1. Manager of Finiconsult B.V., independent consultancy for corporate finance.

2. ISBN 0-471-08627-4, John Wiley 1994, paperback edition

3. Alfred Rappaport, Creating Shareholder Value

The Free Press ISBN 0-02-925720-4.

4. page 232 opus citatus

5. Page 249 etc. opus citatus

6. Interest bearing debt negative means liquidity here. Liquidity is normally presented as asset on the balance sheet. So in the WACC formula interest bearing debt is considered to be 0 and the weight for equity put at 100%. In the valuation formula also interest bearing debt is put at 0. At the same time NOPLAT remains stable.

It is the combined effect of these three elements together that creates sharply widening differences between free cash-flow and refinance valuation in this column.