Financial Leverage, The Capital Asset Pricing Model and The Cost of Equity Capital

Size: px

Start display at page:

Download "Financial Leverage, The Capital Asset Pricing Model and The Cost of Equity Capital"

Delilah Glenn
5 years ago
Views:

1 Harvard Business School Rev. October 1, 1980 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital A stock s expected return, its dividend yield plus expected price appreciation, is related to risk. Risk averse investors must be compensated with higher expected returns for bearing risk. One source of risk is the financial risk incurred by shareholders in a firm which has debt in its capital structure. The objective of this note is to delineate a methodology for measuring the risk associated with financial leverage and estimating its impact on the cost of equity capital. Financial everage and Risk The presence of debt in a firm s capital structure has an impact on the risk borne by its shareholders. In the absence of debt, shareholders are subjected only to basic business or operating risk. This business risk is determined by factors such as the volatility of a firm s sales and its level of operating leverage. As compensation for incurring business risk, investors require a premium in excess of the return they could earn on a riskless security such as a Treasury bill. Thus, in the absence of financial leverage a stock s expected return can be thought of as the risk free rate plus a premium for business risk. The addition of debt to a firm s capital structure increases the risk borne by its shareholders. One source of additional risk is the increased risk of financial distress (e.g., bankruptcy). A second source is the effect of financial leverage on the volatility of shareholder s returns. The fixed obligations associated with debt amplify the variations in a firm s operating cash flows. The result is a more volatile stream of shareholder returns. For investors to hold the shares of firms with debt in their capital structures they must be compensated for the additional risk generated by financial leverage. The additional risk premium associated with the presence of debt in a firm s capital structure is the financial risk premium. Therefore, the expected return on a firm s stock can be thought of as the risk free rate plus a premium for risk. xpected Return = risk free rate + risk premium The risk premium consists of a premium for business risk and a premium for financial risk. xpected Return = risk free rate + business risk premium + financial risk premium This note was prepared as a basis for class discussion. Copyright 1980 by the President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call , write Harvard Business School Publishing, Boston, MA 02163, or go to No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the permission of Harvard Business School. This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar

2 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital This relation can be expressed in symbols. + BRP + FRP Thus, the expected return on a firm s stock can be decomposed into three components. These components are (1) the return on a riskless security, R F, (2) a premium reflecting the firm s basic business (or operating) risk in the absence of financial leverage, BRP, and (3) a premium for the additional risk created by the existence of debt in a firm s capital structure, FRP. This relationship is illustrated graphically in xhibit 1. The Capital Asset Pricing Model provides a methodology for measuring these risk premia and estimating the impact of financial leverage on expected returns. The ffect of Financial everage on Beta CAPM is an idealized representation of the manner in which capital markets price securities and thereby determine expected returns. 1 Since CAPM models the risk/expected return trade-off in the capital markets, it can be used to examine the impact of financial leverage on expected returns. In CAPM systematic (or market related) risk is the only risk relevant in the pricing of securities and the determination of expected returns. Systematic risk is measured by beta (β). CAPM provides a measure of a stock s risk premium employing beta which facilitates the estimation of the stock s expected return. In general, + risk premium If CAPM correctly describes market behavior, + (R M ) 1 For a more complete description of CAPM see Diversification, the Capital Asset Pricing Model and the Cost of quity Capital, Intercollegiate Case Clearing House, Soldiers Field, Boston, MA This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar 2016.

3 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital xhibit 1 The Relationship Between a Firm s Financial everage and the xpected Return on Its Stock xpected return on the Firm s Stock R F } } } financial risk premium business premium risk free rate The Firm s Ratio of Debt to quity D A stock s expected return is equal to the risk free rate, R F, plus a premium for risk. With CAPM the risk premium is β times the return on the market, R M, minus the risk free rate. This basic CAPM expression is known as the Security Market ine, the SM. If a firm has no debt in its capital structure, the stock s risk premium consists solely of a business risk premium. The stock s beta therefore reflects the systematic risk inherent in its basic business operations. With no financial leverage, this beta is its unlevered beta, β. This unlevered beta is the beta the stock would have if the firm had no debt in its capital structure. The presence of debt in a firm s capital structure results in additional risk. The systematic risk inherent in the firm s basic business operations is amplified by financial leverage. With financial leverage, the beta on a firm s stock reflects both business and financial risk. This beta is called a levered beta, β. mploying a levered beta in the CAPM expression, the SM measures both the business risk premium and the financial risk premium. The beta published by various investment advisory services reflects both the business and financial risk experienced during the time period over which the beta was determined. nder the assumptions of CAPM there is a simple relationship between levered and unlevered betas. Alternatively, β = β [1 + (1 - t) D ] β = β [ 1+ ( 1 t) D ] A stock s levered beta is equal to its unlevered beta multiplied by a factor which includes the firm s ratio of debt to equity, D/, and its tax rate, t. The tax rate appears in the equations because of This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar

4 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital the tax deductibility of interest payments. Therefore, a stock s beta (and its expected return) increases as its debt ratio increases. The increase in beta reflects the additional systematic risk generated by financial leverage. The resulting increase in expected return reflects the increase in the financial risk premium required by investors as compensation for additional risk. These results can be employed to estimate the impact on expected return of a change in a firm s capital structure. The approach is illustrated in xhibit 2. Assuming the firm currently employs debt in its capital structure, its observed beta will be the levered beta associated with its current ratio of debt to equity. The beta which the stock would have if it changed its debt ratio can be estimated by a two step procedure. The first step involves unlevering the stock s beta. Given its current debt ratio, D/, its tax rate, t, and its current beta, β, its unlevered beta, β can be calculated from the equation presented above. The second step consists of re-levering the stock s beta to reflect a change in capital structure. Given β the tax rate, t, and the new, hypothetical debt ratio, D/, the other equation presented above can be used to calculate the stock s new leveraged beta, β. This levered beta is an estimate of the beta the stock would have if it changed its debt ratio to that employed in the second stage of the procedure. The resulting estimate of beta can then be plugged into the familar CAPM expression presented earlier, the Security Market ine, to estimate the stock s expected return associated with the proposed debt ratio. An example of levering and unlevering General lectric s beta and expected return is presented in xhibit 3. A reduction in G s ratio of debt to equity from approximately.33 to.11 would result in a decrease in its beta from 1.24 to The reduction in financial risk would result in a reduction in the financial risk premium required by investors. Therefore the estimated expected return on G s stock falls from about 17% to roughly 16%. Similarly, an increase in G s debt ratio would increase its beta and expected return. 4 This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar 2016.

5 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital xhibit 2 The Relationship of xpected Return and Financial everage with CAPM Definitions = the stock s expected return. R M = the expected return on the market. t = the firm s tax rate. D = the firm s ratio of debt to equity. β = the (levered) beta on the stock of a firm with D > 0. β = the (unlevered) beta on the stock of the same firm if D = 0. CAPM quations: The Security Market ine, thesm +β( RM R F ) β = evering Beta β [1+ (1 t) D ] nlevering Beta β β = [1+ (1 t) D ] To stimate the Impact of a Change in Capital Structure Step 1. stimate the nlevered Beta Given: current D, current estimated β, and t nlever the Beta by Solving: β = [1 + (1 t) D ] β Step 2. stimate the evered Beta Associated with the new D Given: current β from Step 1, the new D, and t ever the Beta by Solving: β = β [ 1+ ( 1 t) D ] The estimated beta for the new debt ratio is then used in the SM equation to estimate the expected return associated with the new D. This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar

6 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital xhibit 3 Sample Analysis of the Impact on xpected Return of Financial everage with CAPM, General lectric Company Assumptions: R M = 15% R F = 7% t =.50 G s current D =.33 current β G = 1.24 nlevering G s Beta: β G = β G [ 1+ ( 1 t) D ] = 124. [ 1+ (. 50)(. 33)] = 1.06 CAPM quations: β = everingbeta β [1+ (1 t) D ] The Security Market ine, SM R = R + β ( R R ) S F G M F xample: Proposed D = 1.00 β G = 1.06 [1 + (.50)(1.0)]= 1.59 = 7% (15% 7%) = 19.72% Summary Results: Debt Ratio G s Beta G s xpected Return, currently, D = % unlevered, D = % proposed, D = % proposed, D = % 6 This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar 2016.

7 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital The Decomposition of xpected Return into the Risk Free Rate, Business Risk Premium and Financial Risk Premium CAPM can be employed to decompose a stock s expected return into its basic components. This can be accomplished by combining the equation relating levered and unlevered beta and the basic CAPM expression, the SM. The general and CAPM versions of this decomposition are: xpected Return = risk free rate + business risk premium+ financial risk premium + β [R M R F ] + β (1 t) D [R M R F ] Alternatively, + β [R M R F ] + (β β ) [R M R F ] Thus, the expected return on a stock can be decomposed into (1) the risk free rate, (2) a business risk premium present with no debt in the firm s capital structure (i.e., D/ = 0), and (3) the additional risk premium created by the existence of debt in the capital structure. With no debt in a firm s capital structure, the expected return on its stock consists only of the first two components. The effects of financial leverage are captured entirely in the third component. With CAPM this third component, the financial risk premium, is simply the increase in its beta, β - β, caused by financial leverage, multiplied by the risk premium on the market as a whole, R M. Additional debt amplifies the systematic risk inherent in a firm s basic business operations and drives up the beta and expected return on its stock. The example presented in xhibit 4 demonstrates the use of these concepts to decompose the expected returns on two stocks, Procter & Gamble and Colgate-Palmolive. As one might suspect Colgate s business (or operating) risk is substantially greater than Procter & Gamble s. Colgate s unlevered beta is 1.01 versus.8 for P&G leading to a business risk premium of 8.08% for Colgate compared with 6.4% for P&G. Colgate s basic business risk is amplified by the higher level of debt in its capital structure resulting in a financial risk premium which is roughly one half of a percent more than P&G s. Thus, Colgate s overall risk premium, business risk premium plus financial risk premium, is substantially larger than P&G s. Consequently, Colgate s levered beta and the expected return on its stock reflect its higher level of business and financial risk relative to P&G. This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar

8 xhibit 4 Sample Decomposition of xpected Return, Procter & Gamble Company and Colgate-Palmolive Company nlevering Betas Procter & Gamble Colgate-Palmolive Debt Ratio: D =.25 D =.34 evered Beta: β PG =.90 β CP = 1.18 To unlever Beta: β = β [ 1+ ( 1 t) D ] nlevered Beta: β PG =.80 β CP = 1.01 xpected Return Calculation and Decomposition Assumptions: R M 15% R F = 7% t =.50 Definitions: BRP = business risk premium FRP = financial risk premium Procter & Gamble Colgate-Palmolive xpected Return Decomposition quation: R PG + β PG [R M ] + ( β PG - β PG )[R M ] R CP + β CP [R M ] + ( β CP - β CP )[R M ] Substituting Assumed Values: R PG = 7% +.80 [15% - 7%] + ( )[15% - 7%] R CP = 7% [15% - 7%] + ( )[15% - 7%] Results: 14.20% = 7% % +.80% 16.4% = 7% % % R PG + BRP PG + FRP PG R CP + BRP CP + FRP CP This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar 2016.

9 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital An example of the decomposition of the expected return on G s stock at different debt ratios is presented in xhibit 5. Note that changing the firm s debt ratio affects only its financial risk premium. As expected, the financial risk premium, the levered beta and the expected return on G s stock all increase with additional financial leverage. Application to Corporate Finance CAPM facilitates the examination of the impact of financial leverage on expected returns. It therefore has an important application to corporate finance. A firm s cost of equity capital, k, is the expected (or required) return on the firm s stock. If the firm cannot expect to earn at least k on the equity financed portion of its investments, funds should be returned to its shareholders who can earn k on other securities of the same risk level in the financial marketplace. CAPM can be used by financial managers to obtain an estimate of k and to examine the impact on k of financial leverage. A firm s cost of equity capital is by definition the expected return on its stock. Since the basic CAPM expression, the Security Market ine, yields estimates of expected returns, its can also be used to estimate costs of equity capital. Similarly, the CAPM concepts and techniques relating expected returns and financial leverage can be applied in examining the impact of financial leverage on the cost of equity capital. The results presented earlier can be applied directly simply by recognizing that, a stock s expected return is equal to k, its cost of equity capital. To apply these concepts requires as inputs the risk free rate, R F, the expected return on the market as a whole, R M, the stock s beta, its tax rate, t, and its ratio of debt to equity, D/. As with any CAPM application, R F can be estimated as the return on Treasury bills and R M as the expected return on the Standard and Poors Index of 500 stocks. Betas can be estimated by linear regression and are also published by various investment advisory services. The firm s tax rate, t, can be estimated easily from its financial statements. In estimating the debt ratio, the CAPM approach assumes that market values of debt and equity are employed. By definition market values reflect the current values of debt and equity. In contrast, book values represent values prevailing in the past when the securities were issued. In addition, betas are themselves market determined variables. Nevertheless, for convenience book value debt ratios are often used in practice. This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar

10 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital xhibit 5 Sample Decomposition of xpected Return at Various Debt Ratios, General lectric Company From xhibit 3: Assumptions: Debt Ratio G s Beta R M = 15% currently, D =.33 β G = 1.24 R F = 7% unlevered, D = 0 β G = 1.06 t =.50 proposed, D =.11 β G = 1.12 proposed, D = 1.00 β G = 1.59 xpected Return Decomposition quation: R G + BRP G + FRP G R G + β G [R M ] + ( β G - β G ) [R M ] xample: Proposed D = 1.00 R G = 7% [15% - 7%] + ( )[15% - 7%] 19.72% = 7% % % Summary Results: Debt Ratio R G + BRP G + FRP G currently, D = % = 7% % % unlevered, D = % = 7% % + 0% proposed, D = % = 7% % +.48% proposed, D = % = 7% % % 10 This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar 2016.

11 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital To examine the relationship between the cost of equity capital and financial leverage, the estimated inputs are simply plugged into the equations presented earlier. The resulting expected returns are by definition costs of equity capital. The approach demonstrates that a firm s cost of equity is positively related to the level of debt in its capital structure and the increment to the cost of equity generated by financial leverage can be estimated in the manner described earlier. Conclusion The Capital Asset Pricing Model is based upon extremely simple and clearly unrealistic assumptions. mpirical studies demonstrate that, consistent with CAPM, there is a strong relationship between stock returns and risk as measured by beta. Studies also generally support the relationship between returns and financial leverage posited by CAPM. However, these studies are by no means conclusive in establishing the validity of CAPM. The application of CAPM is also limited by problems associated with the model s inputs. se of the model requires ad hoc estimates of several inputs and the betas employed are subject to substantial estimation errors. Thus, CAPM should not be viewed as a wholly reliable method of estimating the cost of equity and examining the impact of financial leverage. However, in view of the deficiencies in alternative approaches, CAPM represents a useful tool which managers may apply to an inherently difficult area of corporate finance. Finally, an alternative approach relating expected returns and financial leverage is outlined briefly in the appendix. This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar

12 Financial everage, The Capital Asset Pricing Model and The Cost of quity Capital Appendix The CAPM methodology described in the text of this note incorporates the implicit assumption that the firm s cost of debt is equal to the risk free rate. An alternative approach which relaxes this restrictive assumption is presented in this appendix. This more general approach examines the relationship between the cost of equity capital and financial leverage. This relationship expressed in cost of equity terms is: K = K + [ K - K D ] (1 - t) D where K is the levered cost of equity capital, K is the unlevered cost of equity, K D is the cost of debt, 2 t is the firm s tax rate and D/ its ratio of debt to equity. In this equation K is the cost of equity if the firm had no debt in its capital structure. Therefore, K reflects the risk free rate and a premium for business risk. The second term on the right hand side of the equation captures the impact of financial leverage the financial risk premium. With additional debt, the increase in the levered cost of equity is related to the difference between the unlevered cost of equity and the cost of debt. Solving for K, the equation becomes: K K K t D + ( 1 ) D = [ 1+ ( 1 t) D ] Thus, given estimates of K, K D, t and D/, the firm s unlevered cost of equity, K, can be calculated. To estimate the levered cost of equity associated with some new debt ratio, K, K D, t and the proposed D/ can be used as inputs in the previous equation. Therefore, this alternative approach can be employed in a manner analogous to that described in the text of this note. The equations can be manipulated to yield estimates of the cost of equity associated with various debt ratios and to decompose the cost of equity into its components. The advantage of this approach is that it is not tied exclusively to the assumptions of CAPM. Specifically, it avoids the assumption that the firm s cost of debt is the risk free rate. The advantage of the CAPM approach is the simple methodology it provides for levering and unlevering betas. 2 Note that the value for K D will change with the degree of leverage in the firm s capital structure. Thus the schedule of debt cost versus leverage must be known in order to estimate a new equity capital cost at a new debt ratio. 12 This document is authorized for use only in CCIIA CA's GRF MBA FT XIX MIM at Pontificia niversidad Catolica del Peru (CNTRM) from Sep 2015 to Mar 2016.

Harvard Business School Diversification, the Capital Asset Pricing Model, and the Cost of Equity Capital

Harvard Business School Diversification, the Capital Asset Pricing Model, and the Cost of Equity Capital Harvard Business School 9-276-183 Rev. November 10, 1993 Diversification, the Capital Asset Pricing Model, and the Cost of Equity Capital Risk as Variability in Return The rate of return an investor receives