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\begin{document}

             \author[1]{Prof. S. K.  Mitra}

             \affil[1]{  Institute of Management Technology, Nagpur, India}

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\date{\small \em Received: 22 September 2011 Accepted: 17 October 2011 Published: 28 October 2011}

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\begin{abstract}
        


The paper compares classic WACC valuation method with equity cash flow and capital cash flow methods. As WACC method always use market values of debt and equity to determine weights, the method can give erroneous results whenever there are mismatches in the market valuation of debt. The tax-shield benefits are related to the actual interest amount that is based on the book value and therefore, the WACC computation method need to account tax shield benefits using book values. The paper used an example to compare valuation of a project using various valuation methods and found that the net present value obtained using modified version of the WACC, that used book value of debt to account tax shield, was comparable to other methods.

\end{abstract}


\keywords{Cash Flow Discounting, Cost of Capital, Net Present Value, WACC}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
o assess the value of a project or business, a number of cash flow valuation methods are used. The most common method to value the business is to determine free cash flow to the business and discount the cash flows by weighted average cost of capital (WACC). Though the method is quite popular and used since mid of last century, the method do not accurately measure effects of interest tax shields benefits whenever market value of debt differs substantially from its book value and therefore valuing of a project using the classic WACC method is not always correct. This distortion is apparent when the same project is valued using other valuation methods.\par
The accuracy of ascertaining discounting rate is important as a small change in this single estimate alters the Net present Value (NPV) measure of the project in a significant manner. The use of classic WACC formula may often present an optimistic NPV and consequently lead to a wrong investment decision. In this paper the WACC method of valuing cash flows is compared with the method of valuing a project from cash flow accruing to equity holders and capital cash flow (CCF) method proposed by Rubeck  {\ref (2002)}. It was found that a minor adjustment in WACC computation method will make valuation using all the methods identical. 
\section[{II.}]{II.} 
\section[{WACC}]{WACC}\par
From the seminal contribution of \hyperref[b6]{Modigliani and Miller (1958)}, finance theory has accepted that a project's cash-flows should be discounted at a rate that reflects the project's risk characteristics. Whenever a Author : Institute of Management Technology, Nagpur, India. ( Telephone : +917122805000 Email : skmitra@imtnag.ac.in) company's equity structure consists of both equity and debt, the appropriate discounting rate is weighted average cost of capital (WACC).\par
WACC method is the most popular approach used to value a project by discounting its unlevered cash flows using a weighted average after tax cost of capital. It is assumed that the project is fully financed by equity and therefore tax liability is estimated on earning before interest payment. The net asset value (NPV) for a constant perpetual cash flow of the project is measured as follows:\par
1 (  {\ref 1})n t t t wacc FCF NPV I r = = ? + 
\section[{?}]{?}\par
Where FCF is free cash flow, I is the initial investment from the project and rwacc is the weighted average cost of capital.\par
When the project is financed with both debt and equity, the interest expense qualifies for tax exemption and reduces effective cost of debt. The benefit of tax shield is incorporated in the discounting rate by multiplying a factor (1-tax rate) to the cost debt. The effective cost of debt after tax is thus reduced to account for tax benefit available for interest expense. The usual formula to estimate WACC is given below:\par
.\par
. \hyperref[b0]{(1 )}. According to the formula, the weighted average cost of capital embodies the relative proportion of debt and equity supplied by investors at the respective required rates of return. The cost of debt capital depends on a company's outstanding interest bearing debt. Since interest expense qualifies for a tax deduction, the formula captures the cost of debt at the company's effective tax rate. The WACC approach incorporates all financing considerations in a single discount rate and simplifies decision making.\par
In the formula, market values of equity and debt are taken instead of their book values. The market value of the company's equity can be obtained from stock price quotes. The market value of debt capital can be estimated by considering cash flow accruing to debt holders and the market interest rate.  
\section[{CASH FLOW MEASURES}]{CASH FLOW MEASURES}\par
In the paper following three cash flow estimates are discussed: ? Free Cash Flow ? Cash flow to Equity ? Capital Cash Flows a) Free Cash Flow\par
The value of a business is equal to the discounted value of future cash flows. The free cash flows (FCF) to the business equal the cash flow generated by the project during its life less capital invested in the business. The free cash flow of the firm includes the cash flows available to all investors -equity holders and bond holders. Thus free cash flow is independent of capital structure of the business.\par
The simplest route to measure free cash flow to the firm is to use information available in the income statement of the firm. From the earning before interest and tax (EBIT) the non cash expense of depreciation is added, taxes are deducted and net cash flows on account of new investments in assets and working capital are also deducted. 
\section[{FCF = EBIT (1 -tax rate) + Depreciation -Capital Expenditure -Î?" Working Capital}]{FCF = EBIT (1 -tax rate) + Depreciation -Capital Expenditure -Î?" Working Capital}\par
In the above formula, payments to debt holders are not considered; therefore the estimate is a measure of for unlevered cash flow. Since leverage is not accounted, the tax benefits because of interest payments are also excluded. It is therefore necessary to consider the tax benefits on interest tax shields in the discounting rate.\par
The discount rate for FCF need to represent rates of return required by both equity holders and bond holders blended together. It is a single estimate of opportunity cost of capital for the whole business. 
\section[{b) Capital Cash Flows}]{b) Capital Cash Flows}\par
In capital cash flow (CCF) method, the cash flow includes the cash available to all capital providers, including the interest tax shields. The interest tax shields decrease taxable income; decrease taxes and thereby increase after-tax cash flows. Thus capital cash flows is equal to the total cash flows available to both equity holders and bond holders including interest tax shield benefits accruing to equity holders.\par
Capital Cash Flow = Free Cash Flow + Interest Tax Shield Since tax shield benefits are included in the cash flow estimates, the taxes are not again counted in the denominator. The discount rate to value Capital Cash Flows (CCF) is a before-tax weighted average rate.\par
.\par
. The Free Cash Flow and Capital Cash Flow methods treat interest tax shields differently. In the first method, the tax shield is considered in the discounting rate rwacc and in the second case it is included in the cash flow. As per \hyperref[b7]{Ruback (2002)}, when debt is forecasted in dollar amounts or when capital structure changes over time, the CCF method is easier to use as the interest tax shields are a part of the cash flows. In the method, the expected return from the asset depends on the risk involved in the asset and therefore it is independent of changes in the capital structure. Consequently, the discount rate for the capital cash flows need not be re-estimated every period.\par
Ruback (2002) also showed that under certain assumption, the before tax WACC depends only on the market-wide parameters for the risk-free rate, the risk premium and on the unlevered asset beta.\par
( )risk free unlevered p wacc beforetax r r R ? = +\par
Where p R is the risk premium and unlevered ? is unlevered asset beta of the firm.\par
In the formula the market values of equity and debt are not required for estimating the discounting rate. This reduces the complexity of estimating WACC for every period. Though Ruback's method of measuring discount rate apparently does not depend on capital structure of the company and need not be estimated afresh as capital structure changes, the main implementation problem is to find out future values of risk premium. 
\section[{c) Cash flow to Equity}]{c) Cash flow to Equity}\par
In some instances financial cash flow statements are prepared from two points of view: 1. The total investment point of view and 2. The owner's point of view.\par
The WACC and CCF method values the project from total investment point of view. However, it is also sometimes useful to analyze a project by constructing the cash flow statements from different points of view to establish whether the parties involved will find it worthwhile to execute the project. Cash flow to equity method value the business from the perspective of equity holders claims in the cash flows. cash flow to the firm measures the cash flow available to all investors but In the method, the suitable discount rate is shareholders required rate of return (r e ) and not r wacc .\par
IV. 
\section[{PROBLEMS ASSOCIATED WITH WACC}]{PROBLEMS ASSOCIATED WITH WACC}\par
According to theory, companies should value a project using a discount rate determined by the risk characteristics of the project. Discounting the cash flows at the firm's weighted average cost of capital (WACC) is the most popular but the method is sometimes inappropriate if the project differs in terms of its riskness from the rest of the firm's assets. Thus WACC need to be calculated separately for each project. A survey carried out by \hyperref[b0]{Bierman (1993)} in the top 100 firms of the Fortune 500 found that 93\% of the responding firms use a constant company-wide WACC to value projects and only 35\% used division-level discount rates. \hyperref[b3]{Graham and Harvey (2001)} reported that a large majority of firms use a common company-wide discount rate to value a project independently of the risk characteristics of the project. Another survey carried out by \hyperref[b4]{Kruger et al (2011)} found that performing capital-budgeting using a unique firm-level WACC is common.\par
Additionally, risks involved in project cash flows are not always amenable to be measured with a constant discounting rate. The discounting rate r wacc changes when debt to equity ratio of the firm changes on year to year basis. \hyperref[b5]{Miles \& Ezzel (1980)} showed that the WACC will yield correct valuations if the leverage ratio of the firm remains constant through time. WACC method is suitable as long as the firm maintains a constant leverage ratio. For project that need subsequent additional investment in future, maintaining constant debt to equity ratio is difficult.\par
In WACC, the values of equity and debt are taken in terms of market values, not at their book values. As market values of both equity and debt constantly changes, the WACC measure also changes with change in market perceptions. In many instances, the cash flows are discounted at a constant WACC and all such cases the implicit assumption is that the leverage of the business remains constant throughout the evaluation period. But the assumption is erroneous as maintaining Should WACC be always measured on market Value? While estimating discounting rates for WACC and CCF methods, market values of equity and debt are used. In case of rwacc interest tax shields are incorporated in the discount rate in terms of market value of debt by application of the factor . On the other hand, the actual interest tax shield benefit is linked to actual interest paid that is related to the book value of debt. Thus interest tax shield need to be measured on book value and not on market value of debt. Whenever there is a valuation mismatch between book value and market value of debt, it is better to use book value of debt as interest tax shield is related to book value and not on market value. \hyperref[b1]{Fernandez (2003}\hyperref[b2]{Fernandez ( , 2010) )} argued that the WACC is the rate at which the Free Cash Flows need to be discounted for obtaining the identical result as in the valuation using Equity Cash Flows.\par
To obtain identical valuation using rwacc the formula to estimate the discounting rate need to be modified as follows: E mv and D mv are market values of debt and equity, D bv is the book value of debt and r actual is the interest rate payable on outstanding debt.\par
V. 
\section[{VALUATION EXAMPLE}]{VALUATION EXAMPLE}\par
So far three methods using free cash flows, capital cash flows and equity cash flows are discussed and all methods are found intuitively appealing! Let's now compare valuation using a simple numerical example.\par
The projected balance sheets and income statements of a hypothetical firm are given in table 1 and 2. The firm made an initial equity investment of \$5500 at the beginning of the project and all incremental investment in the business was raised from additional debt. The projected income statements gave estimates for the initial five years and it was assumed that the cash flows after the initial five years would grow at 5\% per year for perpetuity.\par
.\par
. The following cash flow estimates were made. ? Free Cash Flow ? Equity Cash Flow ? Debt Cash Flow ? Capital Cash Flow To arrive at free cash flow estimates, the PAT (unlevered) was calculated assuming no debt in the capital structure. From PAT (unlevered) depreciation is added back, additional investment in working capital and fixed assets are deducted. Equity cash flows were estimated considering actual leverage in capital structure. It was estimated from PAT adding depreciation and deducting additional investments.mv\par
Debt cash flow measures represented cash flows accrued to debt holders both in form of interest income and change in the principal component of debt. Whenever new debt was added to the capital of a firm, cash flows in hands of debt holders reduced. Capital cash flow was measured adding cash flows accrued to both shareholders and bond holders.  
\section[{VALUATION OF THE PROJECT}]{VALUATION OF THE PROJECT}\par
After ascertaining cash flows of the project in hands of different types of investors, the valuation of the project was done using following discounting rates. It was observed from table 7 that valuation using WACC (after tax) gave a different project valuation in comparison to other methods. To alleviate the difference of valuation using WACC (after tax) method, WACC (modified) was estimated using book values of debt and revised project valuation was given in table \hyperref[tab_5]{8}.  
\section[{CONCLUSION}]{CONCLUSION}\par
To value a business or project the post popular method is to use WACC as discounting rate. In its basic definition, WACC is the weighted average of the cost of capital coming from both the equity and the debt. of the firm and tax shield valuations linked to the divergence between book values and market values. In this paper disparity due to tax shield valuation when market valuation of firm's debt differs from its book value is addressed.\par
However, the practical implementation of WACC concept often poses problem due to changing leverage The net present value of a project using other methods was compared with the valuation using WACC method. It was observed that value of the project using WACC (modified) accounted tax shield benefits more accurately and produced result that were comparable to the results obtained from equity cash flow and capital cash flow methods.  
\section[{Global}]{Global}\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
     \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.3378205128205128\textwidth}P{0.2833333333333333\textwidth}P{0.21794871794871792\textwidth}P{0.010897435897435897\textwidth}}
Revisiting WACC\tabcellsep \tabcellsep \tabcellsep \\
wacc(modified) r\tabcellsep e E r D r mv debt mv + E +\tabcellsep bv actual D r mv D ?\tabcellsep T\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.85\textwidth}}
Cash Flow Statements\end{longtable} \par
 
\caption{\label{tab_1}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.0998220640569395\textwidth}P{0.21174377224199287\textwidth}P{0.2268683274021352\textwidth}P{0.31156583629893236\textwidth}}
Table\tabcellsep Cash Flow\tabcellsep Discounting Rate\tabcellsep Value\\
Table 4\tabcellsep Debt cash flow\tabcellsep Cost of debt\tabcellsep Market value of debt\\
Table 5\tabcellsep Equity cash flow\tabcellsep Cost of equity\tabcellsep Market value of equity\\
Table 6\tabcellsep Capital cash flow\tabcellsep WACC (before-tax)\tabcellsep Market value of project/firm\\
Table 7\tabcellsep Free cash flow\tabcellsep WACC (after-tax)\tabcellsep Market value of project/firm\end{longtable} \par
 
\caption{\label{tab_2}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.20247191011235954\textwidth}P{0.11078651685393258\textwidth}P{0.10314606741573033\textwidth}P{0.10314606741573033\textwidth}P{0.10887640449438202\textwidth}P{0.11078651685393258\textwidth}P{0.11078651685393258\textwidth}}
Year\tabcellsep 0\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\\
ECF\tabcellsep \tabcellsep -58.50\tabcellsep 577.20\tabcellsep 887.90\tabcellsep 1198.60\tabcellsep 1509.30\\
r e\tabcellsep 0\tabcellsep 18.89\%\tabcellsep 18.40\%\tabcellsep 18.20\%\tabcellsep 18.07\%\tabcellsep 18.01\%\\
Value of Equity\tabcellsep 7408\tabcellsep 8866\tabcellsep 9920\tabcellsep 10837\tabcellsep 11597\tabcellsep 12177\\
Debt\tabcellsep 6848\tabcellsep 7230\tabcellsep 7622\tabcellsep 8023\tabcellsep 8433\tabcellsep 8855\\
Value of Business\tabcellsep 14256\tabcellsep 16096\tabcellsep 17542\tabcellsep 18860\tabcellsep 20031\tabcellsep 21032\\
\tabcellsep \multicolumn{3}{l}{Table 6 : Valuation using CCF}\tabcellsep \tabcellsep \tabcellsep \\
Year\tabcellsep 0\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\\
CCF\tabcellsep \tabcellsep 106.50\tabcellsep 764.20\tabcellsep 1096.90\tabcellsep 1429.60\tabcellsep 1762.30\\
WACC (before tax)\tabcellsep \tabcellsep 13.66\%\tabcellsep 13.73\%\tabcellsep 13.77\%\tabcellsep 13.79\%\tabcellsep 13.80\%\\
Value of Business\tabcellsep 14256\tabcellsep 16096\tabcellsep 17542\tabcellsep 18860\tabcellsep 20031\tabcellsep 21032\\
Debt\tabcellsep 6848\tabcellsep 7230\tabcellsep 7622\tabcellsep 8023\tabcellsep 8433\tabcellsep 8855\\
Value of Equity\tabcellsep 7408\tabcellsep 8866\tabcellsep 9920\tabcellsep 10837\tabcellsep 11597\tabcellsep 12177\end{longtable} \par
 
\caption{\label{tab_3}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.22261904761904763\textwidth}P{0.056666666666666664\textwidth}P{0.10928571428571428\textwidth}P{0.11333333333333333\textwidth}P{0.11333333333333333\textwidth}P{0.11738095238095239\textwidth}P{0.11738095238095239\textwidth}}
Year\tabcellsep 0\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\\
ECF\tabcellsep \tabcellsep -47.50\tabcellsep 602.50\tabcellsep 927.50\tabcellsep 1252.50\tabcellsep 1577.50\\
WACC (after tax)\tabcellsep \tabcellsep 12.31\%\tabcellsep 12.47\%\tabcellsep 12.55\%\tabcellsep 12.60\%\tabcellsep 12.62\%\\
Value of Firm\tabcellsep 14803\tabcellsep 16673\tabcellsep 18150\tabcellsep 19501\tabcellsep 20704\tabcellsep 21740\\
Debt\tabcellsep 6848\tabcellsep 7230\tabcellsep 7622\tabcellsep 8023\tabcellsep 8433\tabcellsep 8855\\
Value of Equity\tabcellsep 7956\tabcellsep 9443\tabcellsep 10529\tabcellsep 11478\tabcellsep 12271\tabcellsep 12885\end{longtable} \par
 
\caption{\label{tab_4}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{P{0.22067307692307694\textwidth}P{0.05721153846153846\textwidth}P{0.11033653846153847\textwidth}P{0.11033653846153847\textwidth}P{0.11442307692307692\textwidth}P{0.11850961538461538\textwidth}P{0.11850961538461538\textwidth}}
Year\tabcellsep 0\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\\
ECF\tabcellsep \tabcellsep -47.50\tabcellsep 602.50\tabcellsep 927.50\tabcellsep 1252.50\tabcellsep 1577.50\\
WACC (modified)\tabcellsep \tabcellsep 12.58\%\tabcellsep 12.73\%\tabcellsep 12.80\%\tabcellsep 12.85\%\tabcellsep 12.88\%\\
Value of Firm\tabcellsep 14256\tabcellsep 16096\tabcellsep 17542\tabcellsep 18860\tabcellsep 20031\tabcellsep 21032\\
Debt\tabcellsep 6848\tabcellsep 7230\tabcellsep 7622\tabcellsep 8023\tabcellsep 8433\tabcellsep 8855\\
Value of Equity\tabcellsep 7408\tabcellsep 8866\tabcellsep 9920\tabcellsep 10837\tabcellsep 11597\tabcellsep 12177\end{longtable} \par
 
\caption{\label{tab_5}Table 8 :}\end{figure}
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\end{document}
