Mr. Drs. C.B.A. Spil RA^{(1)}
1. INTRODUCTION
In company valuation, free cashflow 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 wellknown fact however that, compared with other cashflow
discounting methods, valuation outcome by free cashflow, 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 cashflow of a supposed
investor buying a target company at a price equal to the outcome of free
cashflow valuation. This comparison of refinance valuation and free cashflow
valuation makes sense in case of valuation for acquisition purposes. By
realizing an acquisition, these differences become apparent both from the
cashflow 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 cashflow.
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 debtlow target companies.
Free cashflow valuation tends to undervaluate companies compared to refinancing cashflow 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 CASHFLOW 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 cashflow 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 cashflow 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 cashflow
matches value. With the available cashflow from the target company, refinancing
requirements are exactly met. Now let us compare this refinance valuation
with free cashflow valuation.
By assuming f.0 increase in working capital, free cashflow theory adds
(simplified) the following components to refinancing cashflow:
+ 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 cashflow in the abovementioned example and free cashflow valuation is:
+ present value of net interest (6,5 N_{1}..N_{10}) 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 cashflow 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 cashflow
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 cashflow valuation and refinancing cashflow valuation is
related to the statutory tax rate, net interest and discount rate as follows.
Deducting refinancing from free cashflow valuations taking their respective (growing) perpetuities:
.free cashflow perpetuity (1t)*(EBITI)+I)/(Wg) I/i
.refinancing perpetuity (1t)*(EBITI) /(Wg),
gives the exact difference I*(1t)/(Wg)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 cashflow valuation tends to be lower than refinance
valuation. The basic reason being that WACC normally exceeds interest on
debt.
The recommended free cashflow WACC formula (simplified) is:
WACC = i(1t)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 interestbearing debt
V = market value of target company where V = B+S
k = marketdetermined 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*(1t)/(Wg)I/i explained before, can be rewritten
as I*((1t)/(Wg)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 WesternEurope.
The statement that the difference tends to become negative and thus
creates windfall profits for buyers buying at free cashflow 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 cashflow 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 standalone and consolidated
values. Free cashflow 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 cashflow 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 noninterest
bearing liabilities such as creditor liabilities and so on. This requires
a lot of nonverifiable judgments. Basically the amount of noninterest
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 noninterest bearing
liabilities. The resulting WACC therefore is lower as the weight of equity
decreases.
4. Biased treatment of positive interest in debtlow
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 lowdebt industry, in most cases,
finance their acquisition partly by debt. In all those cases by definition,
refinancing WACC is lower than free cashflow WACC (100% equity). Thus
refinance valuation is higher than free cashflow valuation. So there are
always windfall profits for buyers in these industries buying at free cashflow
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 cashflow 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 cashflow WACC remain identical with column 2 while net profit is increasing. Therefore free cashflow 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 cashflow 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 cashflow 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. 

5. Conclusions
Point 1, "the impact on free cashflow valuation of loan deduction calculated before, interest after tax", is mostly not recognized.
Point 2, "interest on debt discounted at WACC" is wellknown. Academic theory however in this point is quite contradictory. Practicians obscure this point which can be very misleading.
Point 3, "the impact on free cashflow valuation of positive interest results in debtlow 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 cashflow 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% interestbearing debt, 30%
noninterestbearing debt. The above mentioned conditions are more or less
actual in the Netherlands around mid 1998.
Free cashflow 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 WACCg%  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 CASHFLOW WACCg%  6.5%  7.5%  8.5%  9.5%  10.5%  11.5%  11.5%^{(6)} 
FREE CASHFLOW 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 cashflow valuation there gives 1131 and refinance valuation 986. So left to column 2 with higher capital structure then 29% buying at free cashflow valuation, implies windfall losses for buyer.
At the right of column 2 with lower capital structure buying at free cashflow 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 cashflow valuation minus refinance valuation as a result. Interest cost assumed as having positive figures.
The formula used is explained on page 3: I*((1t)/(Wg)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.
NOTES
1. Manager of Finiconsult B.V., independent consultancy for corporate finance.
2. ISBN 0471086274, John Wiley 1994, paperback edition
3. Alfred Rappaport, Creating Shareholder Value
The Free Press ISBN 0029257204.
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 cashflow and refinance valuation in this column.