Financial Leverage and Cost of Equity

Sanjoy Sircar For a typical stock investor, the returns from holding a stock is accrued through dividends and price appreciation, or capital gains. If we assume that the typical stock investor is risk averse, then the expected return on a stock must equal the risk free rate p[us a risk premium commensurate with the degree of risk assumed by the investor. In modern finance literature, the risk borne by the stock investor holding a well diversified portfolio is referred to as systematic or market risk. The risk premium expected to be earned by the investor is a result of the operating or business risk of the firm as well as the additional financial risk imposed on the stockholder in the presence of debt in the capital structure of the firm. The objective of this note is to demonstrate a method to estimate the degree of incremental risk imposed on the shareholder of a firm with debt in its capital structure and measure the impact on the firm’s cost of equity capital, Financial Leverage and Risk Any business investment subjects its shareholders to the operating rik inherent in the business in which the assets are being invested which we call operating risk . The business risk is determined by various factors which influence the variability in a firm’s sales and overall profitability. Operating leverage is a measure that can be used a surrogate of business risk . We characterize operating leverage as a firm’s variability in operating income due to change in sales. Let us take the hypothetical example of two firms A and B : Firm A Firm A Firm B Firm B 2004 2005 2004 2005 Sales 100 50 100 50 Variable Cost 30 15 50 25 Fixed Cost 40 40 20 20 EBIT 30 -5 30 5 As we can see, both the firms’ sales have been negatively affected in 2005 compared to 2004, but Firm A’s operating income is more adversely impacted by the presence of a grater proportion of fixed costs in its total cost structure. In a similar situation where sales of both the firm’s double, Firm A’s gains will be proportionately more than that of Firm B. This additional variability of Firm A’s operating earnings due to a change in its sales is the result of business risk that is borne by the shareholders of the firm. He impact of business risk can be due to the industry structure, choice of technology and degree of automation, efforts to achieve minimum economies of scale etc.

When firms raise funds by issuing debt securities, the fixed amount of interest payments (implicitly) guaranteed to bondholders ahead of any dividends payable to shareholders impose an additional risk to shareholders of firms with debt in their capital structure (levered firms) as opposed to (unlevered ) firms with no debt in their capital structure. Let us look at two firms to examine the impact of debt in the capital structure on shareholder returns: Levered Levered Unlevered Unlevered Y 2004 2005 2004 2005 EBIT 100 50 100 50 Interest 30 30 0 0 EBT 70 20 100 50 Taxes at 30 percent

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Net Income 49 14 70 35 While a 50 percent reduction in the operating profits of the unlevered firm results in a proportionate loss to the net income available to shareholders, for the levered firm a 50 percent reduction sales results in a 71 percent decline in net income available to investors. This additional variability in earnings is a source of risk to stockholders and is a result of financial leverage which is imposed upon stockholders due to the presence of debt in the firm’s capital structure. Please note that if the interest payments were a fixed percentage of the firm’s operating earnings that were allowed to rise and fall in level with the firm’s operating income (EBIT) then the returns to the shareholders of the levered and unlevered firm will be affected in the same proportion as the change in the firms operating profits and thus not impose an additional risk to the levered firm’s shareholders. As shareholders are entitled to residual earnings, the presence of debt and the resulting fixed charge on operating income to bondholders forces the stockholders of levered firms to assume a disproportionately higher degree of risk compared to that of the shareholders of the unlevered firm. If we look at the expected return on a stock as Expected return = Risk free rate +Risk premium, Then we can now decompose the risk premium according to the source of uncertainty, that is, Expected return = Risk free rate + Business Risk premium + Financial Risk premium . As per our previous discussion, the shareholders of the unlevered firms would receive compensation only for the business risk while the shareholders of the

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levered firm will be compensated through a total risk premium paid a risk premium for both the business and financial risk assumed by them. The Capital Asset Pricing Model (CAPM) provides a methodology of measuring these risk premia and estimating the impact of financial leverage on expected returns. The Effect of Financial Leverage on Beta Though CAPM is an idealized representation of the manner in which efficient capital markets price securities and thereby determine expected returns, it is universally applied in practice to model the trade off between risk and expected returns. So we can use CAPM to examine the impact of financial leverage on shareholder expected returns or from the firm’s perspective, the cost of equity capital. In CAPM, systematic or market risk is the only risk relevant in the pricing of securities or their expected returns . Systematic risk is measured by beta which measures the co-movement of a firm’s stock returns with that of the market ( in practice a broad based value weighted index ). CAPM explain a stock’s expected returns as Re = Rf + Risk premium or Re = Rf + ( RM – Rf ) β This basic CAPM relationship is known as the Security Market Line (SML), where the stock’s expected return is the risk free rate plus a risk premium. He risk premium applicable to each stock is a function of the degree of (systematic) riskiness of the stock as represented by beta and the average reward per unit earned by stock investors which is represented by the expression RM – Rf , or market risk premium. For an unlevered firm, the beta is simply a representation of its business risk. In such cases, we characterize the beta as the unlevered beta or βU. For a firm with debt in its capital structure, the systematic risk, beta consists of an element of business risk as well as financial risk, which we represent as β L , or levered beta . he betas published by various financial service organizations reflects both the business and financial risks affecting the overall risk level to the stockholder. If we consider the Balance Sheet of a firm with debt in its capital structure, the liabilities side ( sources of long term funds ) represents a portfolio comprisjng the debt and equity of the firm. The Asset side represents the firm’s application of funds and the total riskiness of the firm’s investment in assets is shared by both the bondholders and equity shareholders, though not in proportion ot the capital invested by each party. Typically the stockholder’s bear a greater proportion of

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the risk in terms of an adverse impact on firm earnings due to the residual nature of cash flows available to stockholders. So if we characterize the total risk of the firm in terms of its unlevered beta ( or asset beta as it is sometimes called ) then the portfolio of the long term sources of funds will have a total risk which is a weighted average of the risk borne by each class of investors, that is, bondholders and stockholders in proportion to their investment of capital in the firm. Hat is βU = βD * D / V + βL * E/V where V = D+E βU is the beta of the unlevered firm ( representing total business risk ), βD and β L represent the systematic risk of the firm’s debt and equity respectively. D/ V and E/V measure the proportion of capital invested in total capital of the firm by each class of stakeholders. Assuming βD equal to zero ( as the systematic risk of bondholders is quite negligible unless the firm is in financial distress due to the priority in payment enjoyed by bondholders over stockholders ), we have βU = βL * E/V or βL = V / E * βU

A stock’s levered beta is an increasing function of its debt equity ratio. As the level of debt in the total capital increases, the stockholders are subjected to an increasing degree of (systematic ) financial risk which is reflected by the increase in beta. The resulting increase in expected returns is simply a reflection of the additional risk premium demanded by risk averse stockholders as compensation for bearing additional risk. This results can be employed to estimate the impact of a change in a firm’s capital structure on its cost of equity capital. He approach is illustrated in Exhibit 1. For a firm employing debt in its current capital structure, its observable ( publicly available ) beta is composed of both business and financial risk – that is levered beta. The beta which the stock would have if it changed its debt ratio can be estimated through a two step procedure. The first step involves unlevering the stock’s beta. Given the firm’s current debt ratio, and its current βL, the firm’s unlevered beta βU can be calculated from the equation presented above. The second step involves relevering the stock’s beta to reflect a change in capital structure. Given the βU computed in the previous step, we can use the same equation in reverse to incorporate the new debt equity ratio and re-compute the firm’s βL , the new leveraged beta of the firm under the hypothetical capital structure.

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The newly computed levered beta , βL is an estimate of the beta the firm’s stock would have had if it had changed its capital structure in the hypothetical fashion. The new beta can now be plugged into the familiar CAPM expression, the Security Market Line to estimate the stock’s expected return associated with the new debt ratio. An example of unlevering and relevering the beta for Tata Motors is presented in Exhibit 2. Application to Corporate Finance CAPM facilitates the examination of a stock’s expected return to the riskiness represented by the firm’s business risk (represented by its asset structure) and financial risk ( capital structure). A firm’s cost of equity capital is simply the expected rate of return on the firm’s stock. If the firm cannot at least expect to earn at least Re on the equity financed portion of its investments, the firm is better off not reinvesting any profits and paying out its entire distributable earning to its shareholders as dividends. CAPM can be used by corporate financial mangers to obtain an estimate of the firm’s stockholders’ expected rates of return from investing in the firm’s equity and examine the impact of any change on expected returns due to change in the firm’s capital structure. A firm’s cost of equity capital is by definition the expected return on its stock. Since the basic CAPM, expression, the Security market Line, links expected returns to riskiness borne by the equity investors, it can be also used to estimate the equity cost of capital. Hence, the CAPM concepts and techniques relating expected returns and financial leverage can also be applied in the context of estimating equity cost of capital from the corporate perspective.

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Exhibit 1 The Relationship of Expected Return and Financial Leverage with CAPM CAPM Equations : The Security Market Line (SML ): Re = Rf + (RM – Rf )β (Re) Levering Beta : βL = βU V/E Unlevering Beta: βU = βL *E/V Notation Definitions: Re = Stock’s expected returns RM = expected return on the market E/V = the firm’s ratio of equity to total value ( based on market value where V = value of debt + value of equity ) ΒL = the levered beta on a firm’s stock with D/E > 0 βU = the unlevered beta on a firm’s stock with D/E = 0 Estimating the Impact of a Change in Capital Structure Step 1 :Estimate the unlevered beta Given, current D/E and D/V and current βL ( either estimated or obtained from publicly available sources ) Unlever the beta by solving βU = βL * E/V Step 2 :Re-Lever the beta in line with the new Debt Equity Ratio Given βU from Step 1 and the new D/E or E/V ( where V = D +E ) Levewr the beta by using βL = βU * V/ E Use the re-levered beta estimated in Step 2 in the SML equation to obtain the new estimate of the expected rate of return consequent upon a change in financial leverage.

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Exhibit 2 Sample Analysis of the Impact on Expected Return of Financial Leverage with CAPM for Tata Motors Limited. Assumptions : Rf = 6 %; Market Risk Premium (RM – Rf ) : 9% Current B LTata Motors :1.17 (Source:National Stock Exchange ) Tata Motor’s Current Equity : Rs. 31883 crores ( Source:National Stock Exchange ) Tata Motor’s Book Value of Debt : Rs. 2495.42 crores (Source:Tata Motor’s Annual Report) E/V for Tata Motors: :31883 / (31883+2495.42) : 0.93 CAPM Equations : Levering Beta : Security Market Line βL = βU V/E Re = Rf + (RM – Rf )β Proposed E/V ratio : 60 % 1.17 = βU (1/0.93) So βU = 1.09 At the proposed E/V ratio, re-lever the beta as follows: βL = 1.09 * ( 1/0.60) = 1.82 So estimated cost of equity capital : Re = Rf + (RM – Rf )β; 6 + 1.82*9 = 22.38% E/V Tata Motor’s BL Tata Motor’s Expected Return Currently 0.93 1.17 17.53% Unlevered 1 1.09 15.81% Proposed 0.60 1.82 22.38%

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