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 FACULTY WORKING 
 PAPER NO. 953 
 
 An Analytical and Empirical Comparison of Alternative 
 Cost of Equity Capital Estimation Methods 
 
 Cheng F. Lee 
 Charles M. Linke 
 J. Kenton Zumwalt 
 
 College cf Commerce and Business ^dminis 
 Bureau of Economic and Business Research 
 University cf Illinois. Urbana-Chamoaign 
 
BEBR 
 
 FACULTY WORKING PAPER NO. 953 
 College of Commerce and Business Administration 
 University of Illinois at Urbana-Champaign 
 April 1983 
 
 An Analytical and Empirical Comparison of Alternative 
 Cost of Equity Capital Estimation Methods 
 
 Cheng F. Lee, Professor 
 Department of Finance 
 
 Charles M. Linke, Professor 
 Department of Finance 
 
 J. Kenton Zumwalt, Associate Professor 
 Department of Finance 
 
Abstract 
 Cost of equity capital estimation is an important issue for both 
 regulated and unregulated firms. There are several methods for estimating 
 the cost of equity capital, including: (1) discounted cash-flow methods; 
 (2) capital asset pricing model methods; (3) M&M's cross-sectional 
 method; and (4) integrated methods. This paper reviews the alternative 
 estimation methods and empirically compares three of the most frequently 
 used methods. The results indicate there are no consistent relationships 
 among the three methods analyzed and the results vary across different 
 industries. 
 
I. INTRODUCTION 
 
 Cost of equity capital estimation is one of the most important 
 issues in public utility regulation and in capital budgeting decisions. 
 The concept of the cost of capital presents no particular difficulty 
 under conditions of perfect certainty — the assumption on which most of 
 classical theory has been developed. It is simply the market rate of 
 interest. Under conditions of uncertainty, the cost of capital is no 
 longer directly observable and several methods have been developed to 
 estimate the cost of equity capital. These include: (1) the earnings 
 yield method, (2) the discounted cash-flow (DCF) model, (3) the capital 
 asset pricing model (CAPM) method; (4) M&M's [13] cross-sectional esti- 
 mation method; and (5) integrated methods. The integrated method com- 
 bines the CAPM with M&M's proposition III in estimating the cost of equity 
 capital. Most recently Glenn and Litzenberger [3] have integrated M&M's 
 cross-sectional method and the CAPM method to propose "an interindustry 
 approach for cost of capital estimation." 
 
 The main purposes of this paper are to review the alternative cost 
 of equity capital estimation methods and to empirically compare three 
 of the most frequently used methods. Possible biases related to the 
 application of the CAPM for different industries will also be discussed. 
 In the second section, alternative cost of equity capital estimation 
 methods will be reviewed. In the third section empirical data from both 
 the utility industry and three non-utility industries will be used to 
 estimate empirically the cost of capital using the three most popular 
 alternative methods. Finally, some guidelines for choosing amonp, the 
 alternative cost of capital estimation methods are established in accor- 
 dance with a compromise of theory and practice. 
 
-2- 
 
 II. ALTERNATIVE COST OF EQUITY CAPITAL ESTIMATION METHODS: A REVIEW 
 There are two basic approaches for estimating the cost of equity 
 capital — the discounted cash flow method which is based on the firm's 
 operating and financial characteristics, and the capital asset pricing 
 model method which is based on the relationship between a firm's expected 
 returns and the returns of a market index. There are several alternative 
 specifications under each of these two basic approaches, and each par- 
 ticular specification has its own set of underlying assumptions. This 
 section develops the different models, summarizes the assumptions of each 
 model, and describes the estimation problems associated with each model. 
 
 Discounted Cash Flow Methods 
 
 The discounted cash flow (DCF) method assumes the market price of 
 
 an asset, here a common stock, is equal to the present value of expected 
 
 future cash flows to the suppliers of equity capital, the stockholders. 
 
 Since cash flows to stockholders come in the form of dividends, the 
 
 DCF model is 
 
 D D D 
 P n = — + 1 —~ + . . . + = (1) 
 
 u i + k a + k r (1 + K )" 
 
 e e e 
 
 or 
 
 00 d 
 
 P n = E (2) 
 
 t 
 
 u t=i a + k r 
 
 e 
 where P n is the current observable market price of the stock, D , ..., D ot 
 
 are the expected future (unobservable) dividends, and k is the rate of 
 
 return necessary to equate expected dividends to the share price and, 
 
 hence, is the required rate of return or cost of equity capital. Obviously, 
 
 the crucial problem is the estimation of future dividends and several 
 
-3- 
 
 alternative specifications have been developed in attempting to simplify 
 the estimation problem. 
 
 The earnings-price ratio or earnings yield model simplifies the 
 dividend estimation problem by assuming a 100% dividend payout and no 
 growth in earnings. In this model dividends equal earnings and the 
 earnings constitute a perpetuity. That is: 
 
 E E E °° 
 
 1 + k (1 + k ) z (1 + k ) 
 e e e 
 
 which may be simplified to: 
 
 e 
 or 
 
 k e = f- . " (5) 
 
 
 
 Here, k is the return required on a perpetuity and is the inverse of 
 the familiar price-earnings ratio reported in the financial press. The 
 major problems associated with using the earnings yield as a cost of 
 equity capital measure are the omission of possible earnings growth and 
 dividend policy considerations. It should also be noted that the P/E 
 ratio reported in the financial press is generally based on historical 
 earnings, not expected earnings. 
 
 A second DCF specification is the dividend growth model . In this 
 model the dividends in equation (1) are assumed to follow a particular 
 pattern. A pattern frequently used by institutional investors involves 
 dividing the expected dividend stream into three periods based on dif- 
 ferent growth expectations. This results in: 
 
-4- 
 
 m D (1 + g ) t n D(l + g ) t_m » Dd + g-)*" 11 
 P Q = E-2 i- + i JS L_ + E _S L_ (6) 
 
 t-1 (1 + k ) L t=m+l (1 + k ) t=n+l (1 + k ) c 
 e e e 
 
 where g. is the expected growth in dividends for the first m years, 
 g_ is the expected growth for the second n years and g,, is the growth 
 rate assumed to be constant in perpetuity. Using this specification, 
 
 the dividends can easily be estimated for the first two terms and the 
 
 D n+1 
 last term approaches. r With this information and the 
 
 k e" 8 3 
 
 current market price, the expected rate of return can be calculated. 
 
 A similar growth model developed by the Wells Fargo Bank includes 
 estimation of dividends and earnings for the next five years, the ex- 
 pected earnings growth rate and payout ratio for the sixth year, the 
 time when a constant growth rate is expected, the amount of the constant 
 growth rate, and the expected payout ratio when the firm reaches its 
 constant growth. Using this information, dividends are estimated up to 
 the time the firm is expected to achieve its constant growth; the value 
 of the constant growth term is determined; then the expected dividends 
 and constant growth value is used with the current price to determine 
 the stock's expected return. 
 
 Probably the most widely used specification of equation (1) is: 
 
 °° D n (l + g) t 
 P = I -2 . (7) 
 
 u t=i (i + k r 
 
 e 
 The crucial assumptions for this model are that the dividend growth rate, 
 
 g, will be constant forever and that k is greater than g. This model also 
 
 e 
 
 generally assumes a firm's earnings are growing at the rate g and that the 
 payout ratio and P/E ratio are constant. This allows the model to be 
 simplified to: 
 
-5- 
 
 D l 
 
 P o = IT^T (8) 
 
 or 
 
 D l 
 k - jr + g (9) 
 
 
 
 where D is the expected dividend, P_ is the current stock price, and 
 g is the expected growth in earnings /dividends. 
 
 The obvious difficulty faced in applying any DCF model involves the 
 estimation of future dividends or the expected growth rate(s) in future 
 dividends. Whether the analyst is using a specification such as the 
 Wells Fargo model which requires actual dividend estimates for a number 
 of years or a specification such as the constant growth model which re- 
 quires an estimate of the constant growth term, assumptions must be made 
 regarding the general economic outlook and the outlook for the markets 
 in which the firm competes. 
 
 M&M's Cross-Sectional Model 
 
 M&M's proposition 2 deals with the cost of capital determination. 
 In their 1966 AER article, they extended their proposition 1 with taxes 
 and growth potential and proposed a cross-sectional cost of capital model 
 Following M&M [14], proposition 1 (with taxes but without growth) can 
 be defined as 
 
 V = V + xD (10) 
 
 J-j u 
 
 where V T and V are market values for the levered and the unlevered 
 
 L u 
 
 firm, respectively; x is the marginal tax rate and D is the total debt 
 of the firm. By allowing for growth potential, M&M [13] suggest a cross- 
 sectional model to estimate the cost of capital as 
 
-6- 
 
 V L " TD 1 X(l - t) AA , ,,„ N 
 
 — IT" =a 0l +a l A - + Q 2 "A + U (11) 
 
 where X is the expected earnings, A is total assets, and AA/A is the 
 
 average growth rate. X is generally not observable and the current 
 
 earnings are used to replace the expected earnings. M&M suggest the 
 
 proxy error problem arising from the use of X instead of X may be 
 
 alleviated by using, 
 
 m 
 Y = E r.Z. + W (12) 
 
 i-1 X X 
 
 where Y = , and the Z.'s refer to a firm's size, growth, debt, 
 
 A 1 
 
 preferred stock, and dividends. If the estimated Y is used to replace 
 
 xYl - t) 
 
 : , then the inverse of the estimated a n is the estimated cost of 
 
 A 1 
 
 capital. This model assumes all firms used in estimating equation 11 
 belong to a single business risk class. The cost of capital estimated 
 by this procedure is an industry cost of capital estimate. This concept 
 and method were extended by Litzenberger and Rao [10, 11] and Higgins [6]. 
 
 Capital Asset Pricing Model 
 
 The Sharpe [19]-Lintner [8] Capital Pricing Model CAPM predicts 
 the relationship between betas and risk premiums to be: 
 
 E(r.) = E(r )6., (13) 
 
 J m 3 
 
 where E(r.) and E(r ) are the expected excess rates of return above the risk- 
 
 J m 
 
 less rate of interest for the j-th security and the market portfolio, respec- 
 tively, and 6. is the beta of the j-th security as measured against the true 
 market portfolio of all assets. The model assumes risk averse investors 
 with homogeneous expectations, existence of a riskless asset, marketability 
 of all assets and the absence of transactions costs and taxes. 
 
-7- 
 
 When short selling of securities is limited, the relationship be- 
 tween risk premiums and betas becomes: 
 
 E(r ) = E(r m )6 j + E(r z )(l - S ), (14) 
 
 where E(r ) is the risk premium associated with the minimum variance 
 z 
 
 zero beta portfolio. 
 
 Recently, Litzenberger, Ramaswamy and Sosin [9] [LRS] discussed the 
 possible estimation bias associated with the specification of the CAPM. 
 One important source of bias results from using the traditional CAPM 
 instead of the after-tax version of the CAPM. The after-tax version 
 of the CAPM may be written as : 
 
 E(r.) = E(r )6. + E(r')(l - 6.) + E(r.)(d. - S.d ), (15) 
 
 3 ™ 3 z 3 n Jjm 
 
 where E(r f ) is the risk premium of a zero beta portfolio with a zero 
 dividend yield, E(r, ) is the expected return on a hedged portfolio with 
 
 a zero beta and a dividend yield of unity, and d. is the dividend vield. 
 
 3 
 
 Comparing this more generalized cost of equity capital model with the 
 traditional model of equation (13) shows that the traditional CAPM has 
 three possible biases; (1) a risk free rate bias and (2) a dividend yield 
 bias and, (3) a beta bias. 
 
 The alternative CAPM specifications as in equations (13) , (14) and 
 (15) do not explicitly consider the impact of growth on the cost of equity 
 capital estimation. Fewings [1975] and Gordon and Gould [1978] indicate 
 that systematic risk is a positive function of the growth rate of cor- 
 porate earnings. However, Myers and Turnbuli [1977] suggest systematic 
 risk is negatively related to beta. Senbet and Thompson [1982] review 
 
-8- 
 
 the controversy and conclude that the relationship between growth and 
 systematic risk "depends on the way in which the response of cash flows 
 to unanticipated changes in the economy changes with g." 
 
 Myers [15], using real option theory, argued that the estimated 
 beta in terms of the traditional CAPM is a positive function of the 
 proportion of the stock's value accounted for by growth in the M&M sense, 
 That is, if the market value of a growth firm can be decomposed into a 
 perpetual component and a growth component, the hurdle rate obtained 
 from the traditional CAPM will be an overestimate of the correct rate 
 for any firm having valuable growth opportunities. 
 
 Integrated Models 
 
 The DCF and CAPM methods of cost of equity capital estimation have 
 been used in determining the required rates of return in the electric 
 utility industry. The DCF model of share valuation in partial equilib- 
 rium emphasizes corporate characteristics such as growth while risk is 
 consigned to a black box. The CAPM, on the other hand, provides a gen- 
 eral equilibrium risk and return model in which everything else is con- 
 signed to a black box, hence, some integrations of the alternative cost 
 of capital estimation methods have been made. 
 
 One method of combining M&M's formulation with the CAPM involves 
 using the CAPM to allow for different levels of risk instead of assuming 
 equivalent risk classes. As shown in Copeland and Weston [1, p. 293], 
 M&M's after-tax cost of equity model is; 
 
 k = p + (p - k,)(l - t )(B/S) (16) 
 
 e d c 
 
-9- 
 
 where p is the unlevered cost of equity, k, is the cost of debt, t 
 
 d c 
 
 is the corporate tax rate, and B/S is the ratio of the market value of 
 
 debt to the market value of equity. Substituting 
 
 E (R ) — R 
 
 P-E(R)-R f +— H. £<r a) (17) 
 
 m 
 
 into equation (16) gives 
 
 . D E( V " R f (r T a ) + m " f (r T a ) (1 - t )#, (18) 
 
 k = R_ + Lm u o Lm u c S' 
 
 e f a m 
 
 m 
 
 where R c is the risk free rate, E(R ) is the expected market return, 
 t m 
 
 a and a are the standard deviations of the expected returns of the 
 m u 
 
 market and the unlevered firm, and r T is the correlation between the 
 
 Lm 
 
 returns of the levered firm and the market. Other symbols are as pre- 
 viously defined. 
 
 In a recent study, Glenn and Litzenberger [3] used the multiperiod 
 certainty growth model of M&M in combination with the single period 
 capital asset pricing model. They combined a modified M&M model; 
 
 D(X ) (tt - K.) 
 
 V = 3-=— -4- T — J J— x (19) 
 
 JO K. ' ;}1 K. j K J 
 
 with the traditional Sharpe-Lintner CAPM; 
 
 K. = R + [E(R ) - R f ]3., (20) 
 
 3 r n r 3 
 
 to get; 
 
 K «u? 
 
 |e(x : 
 
 v j0 " R f " !E(R .' " R f ]B 
 
 _ .- - , . (21) 
 
 Here, V._ is the current market value of the j-th firm's equity, E(X ) 
 
 is the expected earnings to equity for the j-th firm in year 1, I 
 
 is 
 
-10- 
 
 the j-th firm's equity investment expenditure in year 1, it is the 
 expected rate of return on equity investment for the j-th firm, T. is 
 the number of years into the future that positive NPV investment oppor- 
 tunities are expected to be available, K. is the j-th firms required 
 
 rate of return on equity, R r is the risk free rate, E(R ) is the ex- 
 
 i m 
 
 pected return of the market index, and 6. is the j-th firm's beta. 
 Equation 21 was used to estimate the market risk premium for a particular 
 industry; then this estimated risk premium is used with equation 13 to 
 determine the cost of equity capital for a particular firm. 
 
 IV. THE EMPIRICAL RESULTS 
 
 The main purposes of this section are: (i) to investigate the rela- 
 
 E 
 tionships among the cost of capitals obtained from — , k and R. as indi- 
 cated in equations (5), (9) and (13) respectively. 'In addition, the 
 empirical results are classified into (i) utility industry and (ii) non- 
 utility industries. This classification is used to determine how the 
 dividend yield and grow the potential effects can affect alternative cost 
 of capital estimations. 
 
 The Electric Utility Industry Results 
 
 Table 1 presents the means and standard deviations for three esti- 
 mates of the cost of equity capital for the electric utility industry; 
 
 D l 
 E/F, k = -— + p and R. = R^ + £ . (R - R c ). As can be seen, the 5-year 
 e P Q j f j m t 
 
 average E/P ratio increases every year, from a low of .0517 in 1966 to 
 .116 7 in 1976. This increase emerged as a result of both increased 
 earnings per share and a lower price per dollar of earnings. The esti- 
 mate of Gordon's k is always greater than the E/P ratio. Indeed, it 
 
-11- 
 
 is more than double the E/P ratio in six of the years when the total 
 growth rate proxy was over ten percent. Further, because the payout 
 ratio is high in the electric utility industry relative to other indus- 
 tries, the D/P term in the model is near the E/P ratio for the electric 
 utility industry. (The payout ratio averaged 67.5% for the ten year 
 period). The systematic risk coefficient, beta, varied from a low of 
 
 .6250 in 1968 to a high of .7852 in 1976. The excess return on the 
 
 2 
 market portfolio was assumed to be 8.278% over the years of the study. 
 
 Changes in beta and the risk free rate caused the required return of 
 the CAPM approach to vary from a low of .1010 in 1971 to a high of .1313 
 in 1974. This measure of the cost of equity was always greater than 
 the E/P ratio but was smaller than the estimates of Gordon's Model in 
 all but the first two years. 
 
 These results which suggest that the CAPM may underestimate the 
 cost of equity capital in the utility industry can be explained by ex- 
 amining equation (15). If equation (15) instead of equation (13) is 
 the correct specification for estimating a firm's cost of equity capital, 
 
 then the signs of both E(r')(l - 3.) and E(r, )(d. - 6dm) can be used to 
 
 2 J h 3 j 
 
 determine whether the bias upward or downward. For firms in the electric 
 utility industry betas are typically less than 1.0 and d. is generally 
 larger than 6. dm. Thus, both terms in equation (15) are positive, 
 and the cost of equity capital obtained from equation (13) is under- 
 estimated. 
 
 Table 2 presents the correlations amons the three measures for the 
 electric utility industry. As can be seen, there are differences in 
 
-12- 
 
 the relationships when comparing the E/P ratio with the other two mea- 
 sures, k and R. For example, the E/P ratio is not significantly 
 related to the DCF model, k , while the E/P ratio is significantly 
 related to the CAPM measure, R. in five of the ten years. 
 
 The Industrial Firms Results 
 
 Table 3 presents the cost of equity estimates for the Textile, 
 Chemical, and Retail Store Industries. The E/P ratio generally in- 
 creases over time in all three industries. For the 1967-1976 period, 
 the Chemical Industry exhibited the lowest E/P ratio and all three in- 
 dustries' E/P ratios were lower than that of the electric utility indus- 
 try in every year. The k measure of Gordon's Model increased over time 
 for the Textile Industry but decreased and then increased for the 
 Chemical and Retail Store Industries. In the first seven years the 
 Textile Industry exhibited the lowest k and the Chemical Industry had 
 the lowest k in the later years. The electric utility industry exhib- 
 ited the highest k in seven of the ten years for which utility data 
 were available. The cost of equity estimate using the CAPM shows the 
 utility industry having the lowest R in every year. The Chemical 
 Industry's Rs are less than those of the Textile and Retail Store 
 Industries in ten of the thirteen years. 
 
 Correlation results for the Textile Industry are presented in Table 
 
 4. As can be seen the E/P ratio is significantly related to the k 
 
 e 
 
 measure in eight of the years. However, the E/P ratio is not signifi- 
 cantly related to systematic risk in any year, k is significantly 
 
 related to R. in five years. 
 
 J 
 
-13- 
 
 Table 5 shows the Chemical Industry results. Unlike earlier re- 
 sults, the E/P ratio is unrelated to both k and R. Also, no correla- 
 
 e 
 
 tion is present between the k measure and the R. measure. Table 6 
 
 e j 
 
 shows the Retail Stores Industry results. The E/P ratio is related to 
 
 k in five of the years, but is not related to R in any year. Again, 
 
 there is an absence of correlation between k and R.. 
 
 e J 
 
 Among the four industries there is little relationship between the 
 DCF and CAPM measures. There were no significant relationships in the 
 Chemical and Retail Stores Industries; there were tx^o (of ten) signifi- 
 cant relationships in the utility industry and five (of thirteen) sig- 
 nificant relationships in the Textile Industry. 
 
 These correlation coefficients among three alternative cost of cost 
 of capital estimates indicates that different cost of capital estimates 
 do not give the same rankings for firms in an industry. In addition, 
 the correlation coefficient structure is unstable over time, giving some 
 empirical support for Haley and Schall's [4] analytical arguments on 
 "problems with the concept of the cost of capital." 
 
 The correlation coefficient between k and R. can be analytically 
 analyzed as follows. 
 
 P(R ,K e .) «p[7 f + 3 (7 -7 f ),f- + g ] 
 
 J J 3 
 
 = [Cov(£ -2-) + Cov(e.,g.)]/(cr8)[o ] 
 
 J P .! J J K 
 
 P. 
 Cov(S.,g.) is generally positive. The sign of o is dependent 
 
 Empirically it is found that Cov(3., — ) is generally negative and 
 
 UP 
 
 ccn whether [Cov(S.,- — ) + Cov(E.,g.)] is positive or negative. If 
 
 D 
 [Cov(2., — ) + Cov(6.,g.)] approaches zero, then the relationship 
 
 •' *i J J 
 
-14- 
 
 between R. and k . will be trivial. Graphically the relationship 
 
 3 ej 
 
 between k . and R. can be indicated in figure 1 
 ej 3 
 
 Cost of Equity 
 Capital 
 
 Figure 1 
 
 If k holds, then the cost of equity capital obtained from the DCF 
 
 2 
 method is unrelated to the beta estimates; if k holds, then the DCF 
 
 e ' 
 
 cost of equity capital estimate is negatively related to the beta esti- 
 
 3 
 mate; if k holds, then the DCF cost of equity capital is positively 
 
 related to the beta estimate. Since k is one of the major components 
 
 of weighted cost of capital, and therefore, the weighted cost of capital 
 
 is not necessarily unrelated to beta as suggested by Weston [25] and 
 
 Rubenstein [19]. 
 
 V. Summary and Concluding Remarks 
 
 In this study, alternative costs of equity capital are reviewed 
 and three widely used estimation methods were compared. Empirical re- 
 sults of these alternative cost of equity capital measures for the 
 electric utility, the textile, the chemical, and the Retail Stores 
 industries show wide differences in both the average industry values 
 and standard deviations of the measures. Not only are there wide 
 
-In- 
 differences across industries, but there are also wide differences over 
 time within each industry. 
 
 Besides the differences in means and standard deviations, there 
 were no consistent relationships among the three cost of equity esti- 
 mation methods. These results indicate that firms must be cognizant 
 of the different assumptions inherent in the different models. Growth 
 rate biases associated with applying the CAPM to estimate the cost of 
 equity capital for different industries must be explored in future 
 research. 
 
-16- 
 
 Footnotes 
 
 1 See Sharpe [1981], pp. 381-82. 
 
 2 
 This value is the expected excess return derived by Merton's 
 
 [1980] Model #1. The value is higher than the historical NYSE excess 
 
 return of 8.150% reported by Merton but lower than the 8.8% reported by 
 
 Ibbotson and Sinquefield for the S&P 500 [1977]. 
 
-17- 
 
 Ref erences 
 
 1. Copeland, T. E. and F. J. Weston, Financial Theory and Corporate 
 
 Policy , Add i son-Wesley (1979). 
 
 2. Friend, I., and M. Blume (1975), "The Demand for Risky Assets," 
 
 The American Economic Review (December 1975), pp. 900-922. 
 
 3. Fewigs, D. R. (1975), "The Impact of Corporate Growth on Risk of 
 
 Common Stocks," Journal of Finance , 30, pp. 525-531. 
 
 4. Glenn, D. W. , and R. H. Litzenberger (1979), "An Interindustry 
 
 Approach to the Econometric Cost of Capital Estimation," 
 Research In Finance , JAI Press (1979), pp. 53-75. 
 
 5. Gordon, M. J. and L. I. Gould (1978), "The Cost of Equity Capital: 
 
 A Reconsideration," Journal of Finance , 23, pp. 849-861. 
 
 6. Gordon, M., (1962), "The Savings, Investment and Valuation of a 
 
 Corporation," Review of Economics and Statistics (February 
 1962), pp. 37-51. 
 
 7. Kaley, C. W. and L. D. Schall (1978), "Problems With the Concept 
 
 of the Cost of Capital," Journal of Financial and Quantitative 
 Analysis (December 1978), pp. 847-870. 
 
 8. Higgins, R. C, "Growth, Dividend Policy and Capital Costs in the 
 
 Electric Utility Industry," Journal of Finance (December 
 1974), pp. 1189-1201. 
 
 9. Ibbotson, R. G. and R. A. Sinquefield (1977), "Stocks, Bonds, Bills, 
 
 and Inflations: The Past (1926-1976) and the Future (1977- 
 2000), The Financial Analysts Research Foundation , reprinted 
 in Readings in Investment edited by J. C. Francis, C. F. Lee, 
 and D. E. Farrar, McGraw-Hill Book Company, pp. 723-829. 
 
 10. Lintner, J., "The Cost of Capital and Optimal Financing of Corporate 
 
 Growth," Journal of Finance , (May 1963), pp. 292-310. 
 
 11. Litzenberger, R. , K. Ramaswamy and H. Sosin, "On the CAPM Approach 
 
 to the Estimation of a Public Utility's Cost of Equity Capital," 
 The Journal of Finance (May 1980), pp. 369-83. 
 
 12. Litzenberger, R. H. and C. V. Rao, "Estimates of the Marginal 
 
 Rate of Time Preference and Average Risk Aversion of Investors 
 in Electric Utility Shares: 1960-66," Bell Journal of 
 Economics and Management Sciences , II, 1 (Spring 1971), 265-277. 
 
 13. Litzenberger, R. H. and C. V. Rao, "Portfolio Theory and Industry 
 
 Estimates of the Cost of Capital," Journal of Financial and 
 Quantitative Analysis , VII, 2 (March 1972), 1443-1462. 
 
-18- 
 
 14. Merton, R. C. (1980), "On Estimating the Expected Return on the 
 
 Market," Journal of Financial Economics (December 1980), 
 pp. 323-361. 
 
 15. Miller, M. H. and F. Modigliani (1966), "Some Estimates of the Cost 
 
 of Capital to the Utility Industry, 1954-57," American 
 Economic Review (June 1966), pp. 333-391. 
 
 16. Modigliani, F., and M. H. Miller (1963), "Corporate Income Tax and 
 
 the Cost of Capital: A Correction," American Economic Review , 
 53, pp. 433-443. 
 
 17. Myers, S. C. (1977), "The Relationship Between Real and Financial 
 
 Measures of Risk and Return," in Risk and Return in Finance , 
 Vol. 1, edited by Friend and Bicksler, pp. 49-80. 
 
 18. Myers, S. C. and S. M. Turnbull (1977), "Capital Budgeting and 
 
 Capital Asset Pricing Model: Good News and Bad News," 
 Journal of Finance , 32, pp. 321-333. 
 
 19. Rubinstein, M. E. (1973), "A Mean-Variance Synthesis of Corporate 
 
 Financial Theory," Journal of Finance , 28, pp. 167-187. 
 
 20. Senbet, L. W. and H. E. Thompson, "Growth and Risk," Journal of 
 
 Financial and Quantitative Analysis , (September 1982), pp. 
 331-340. 
 
 21. Sharpe, W. F., Investments , 2nd ed. Prentice Hall, Inc., Englewood 
 
 Cliffs, New Jersey, 1981. 
 
 22. , "Capital Asset Prices: A Theory of Market Equilibrium 
 
 Under Conditions of Risk," Journal of Finance , (September 
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 23. Van Home, J. C. (1983), Financial Management and Policy , Prentice- 
 
 Hall: Englewood Cliffs, New Jersey. 
 
 24. Vasicek, 0. A. (1973), "A Note on Using Cross-Sectional Information 
 
 in Bayesian Estimation of Security Beta," The Journal of Finance , 
 35, pp. 883-896. 
 
 25. Weston, J. F. (1973), "Investment Decision Using the Capital Asset 
 
 Pricing Model," Financial Management (Spring 1973), pp. 25-33. 
 
 26. Weston, J. F. and E. F. Brigham (1981), Managerial Finance , seventh 
 
 edition, The Dryden Press, Hinsdale, Illinois. 
 
 M/E/247 
 
Table 1 
 
 Means and Standard Deviations for 
 Three Estimates of the Cost of Equity for the 
 Electric Utility Industry 
 (Standard Deviations in Parentheses) 
 
 Year 
 
 E/P 
 
 k 
 e 
 
 R. 
 -1 
 
 .0558 
 
 .1033 
 
 .1054 
 
 (.0077) 
 
 (.0169) 
 
 (.0140) 
 
 .0589 
 
 .1119 
 
 .1063 
 
 (.0077) 
 
 (.0186) 
 
 (.0149) 
 
 .0663 
 
 .1340 
 
 .1209 
 
 (.0088) 
 
 (.0225) 
 
 (.0140) 
 
 .0713 
 
 .1451 
 
 .1252 
 
 (.0092) 
 
 (.0283) 
 
 (.0143) 
 
 .0752 
 
 .1576 
 
 .1010 
 
 (.0090) 
 
 (.0330) 
 
 (.0133) 
 
 .0788 
 
 .1657 
 
 .1034 
 
 (.0091) 
 
 (.0354) 
 
 (.0152) 
 
 .0880 
 
 .1891 
 
 .1285 
 
 (.0088) 
 
 (.0395) 
 
 (.0157) 
 
 .1031 
 
 .2381 
 
 .1313 
 
 (.0119) 
 
 (.0566) 
 
 (.0156) 
 
 .1115 
 
 .2009 
 
 .1258 
 
 (.0146) 
 
 (.0388) 
 
 (.0163) 
 
 .1167 
 
 .1905 
 
 .1202 
 
 (.0166) 
 
 (.0350) 
 
 (.0159) 
 
 1967 
 
 1968 
 
 1969 
 
 1970 
 
 1971 
 
 1972 
 
 1973 
 
 1974 
 
 1975 
 
 1976 
 
Table 2 
 
 Correlations Among the Three 
 Cost of Equity Capital Measures 
 (Electric Utility Industry) 
 
 1967 
 1968 
 1969 
 1970 
 
 1971 
 1972 
 1973 
 1974 
 1975 
 1976 
 
 E/P 
 
 E/P 
 
 k 
 
 e 
 
 vs 
 
 vs 
 
 vs 
 
 k 
 
 e 
 
 R. 
 
 Jl 
 
 b. 
 
 •.057° 
 
 -.016 
 
 .064 
 
 .030 
 
 -.222 
 
 -.018 
 
 .132 
 
 -.254** 
 
 -.144 
 
 .079 
 
 -.441* 
 
 -.094 
 
 .007 
 
 -.378* 
 
 .012 
 
 .045 
 
 -.386* 
 
 .131 
 
 .091 
 
 -.382* 
 
 .158 
 
 .166 
 
 -.248 
 
 .102 
 
 .003 
 
 .095 
 
 .291** 
 
 .173 
 
 .222 
 
 .290** 
 
 *Significant at the .01 level 
 **Significant at the .05 level 
 
Table 3 
 
 Means and Standard Deviations for Three Estimates 
 of the Cost of Equity Capital 
 
 Textiles (n=14) 
 
 Chemicals (n=21) 
 
 Retail Stores (n=14) 
 
 Year 
 
 E/P 
 
 k 
 e 
 
 R 
 
 E/P 
 
 k 
 e 
 
 R 
 
 E/P 
 
 k 
 
 e 
 
 R 
 
 1967 
 
 .050 
 (.022) 
 
 .076 
 (.067) 
 
 .142 
 (.029) 
 
 .033 
 (.019) 
 
 .150 
 (.037) 
 
 .156 
 (.02 ) 
 
 .041 
 (.022) 
 
 .138 
 (.059) 
 
 .128 
 (.021) 
 
 1968 
 
 .050 
 (.024) 
 
 .074 
 (.063) 
 
 .162 
 (.023) 
 
 .036 
 (.019) 
 
 .155 
 (.039) 
 
 .156 
 (.027) 
 
 .044 
 (.021) 
 
 .132 
 (.061) 
 
 .148 
 (.023) 
 
 1969 
 
 .053 
 (.023) 
 
 .071 
 (.070) 
 
 .179 
 (.020) 
 
 .041 
 (.022) 
 
 .151 
 (.036) 
 
 .161 
 (.020) 
 
 .050 
 (.022) 
 
 .123 
 (.055) 
 
 .165 
 (.020) 
 
 1970 
 
 .053 
 (.023) 
 
 .070 
 (.060) 
 
 .174 
 (.021) 
 
 .043 
 (.023) 
 
 .142 
 (.037) 
 
 .160 
 (.021) 
 
 .053 
 (.022) 
 
 .116 
 (.032) 
 
 .170 
 (.025) 
 
 1971 
 
 .047 
 (.022) 
 
 .077 
 (.037) 
 
 .159 
 (.018) 
 
 .041 
 (.021) 
 
 .131 
 (.031) 
 
 .140 
 (.023) 
 
 .050 
 (.019) 
 
 .103 
 (.035) 
 
 .153 
 (.026) 
 
 1972 
 
 .052 
 (.023) 
 
 .088 
 (.031) 
 
 .160 
 (.021) 
 
 .044 
 (.023) 
 
 .124 
 (.031) 
 
 .138 
 (.024) 
 
 .054 
 (.021) 
 
 .102 
 (.036) 
 
 .158 
 (.025) 
 
 1973 
 
 .076 
 (.023) 
 
 .100 
 (.040) 
 
 .188 
 (.021) 
 
 .055 
 (.030) 
 
 .102 
 (.026) 
 
 .169 
 (.023) 
 
 .069 
 (.028) 
 
 .103 
 (.037) 
 
 .195 
 (.027) 
 
 1974 
 
 .087 
 (.064) 
 
 .115 
 (.043) 
 
 .166 
 (.020) 
 
 .072 
 (.040) 
 
 .093 
 (.030) 
 
 .164 
 (.024) 
 
 .085 
 (.034) 
 
 .107 
 (.038) 
 
 .179 
 (.019) 
 
 1975 
 
 .087 
 (.061) 
 
 .111 
 (.043) 
 
 .157 
 (.028) 
 
 .080 
 (.046) 
 
 .100 
 (.040) 
 
 .150 
 (.014) 
 
 .096 
 (.041) 
 
 .115 
 (.031) 
 
 .172 
 (.017) 
 
 1976 
 
 .105 
 (.068) 
 
 .128 
 (.048) 
 
 .153 
 (.029) 
 
 .091 
 (.047) 
 
 .114 
 (.039) 
 
 .147 
 (.012) 
 
 .104 
 (.042) 
 
 .133 
 (.038) 
 
 .156 
 (.019) 
 
 1977 
 
 .089 
 (.118) 
 
 .144 
 
 (.049) 
 
 .156 
 (.028) 
 
 .103 
 (.046) 
 
 .125 
 (.042) 
 
 .148 
 (.013) 
 
 .111 
 (.042) 
 
 .147 
 (.054) 
 
 .159 
 (.021) 
 
 1978 
 
 .090 
 (.119) 
 
 .146 
 (.055) 
 
 .166 
 (.027) 
 
 .112 
 (.042) 
 
 .132 
 (.060) 
 
 .162 
 (.014) 
 
 .117 
 (.036) 
 
 .153 
 (.075) 
 
 .166 
 (.018) 
 
 1979 
 
 .084 
 (.138) 
 
 .134 
 
 (.051) 
 
 .209 
 (.031) 
 
 .114 
 (.029) 
 
 .131 
 (.067) 
 
 .193 
 (.018) 
 
 .116 
 (.034) 
 
 .154 
 (.083) 
 
 .204 
 (.023) 
 
Table 4 
 
 Correlations Among the Three 
 Cost of Equity Capital Measures 
 (Textiles) 
 
 1967 
 1968 
 1969 
 1970 
 1971 
 1972 
 1973 
 1974 
 1975 
 1976 
 1977 
 1978 
 1979 
 
 E/P 
 
 E/P 
 
 k 
 
 e 
 
 vs 
 
 vs 
 
 vs 
 
 k 
 
 e 
 
 R. 
 
 JL 
 
 R__ 
 
 .128 
 
 .442 
 
 .193 
 
 .167 
 
 -.033 
 
 .249 
 
 .038 
 
 -.154 
 
 -.021 
 
 .313 
 
 -.109 
 
 .338 
 
 .374 
 
 .142 
 
 .443 
 
 .535** 
 
 .221 
 
 .518** 
 
 .532** 
 
 .226 
 
 .510 
 
 .545** 
 
 .184 
 
 .562** 
 
 .737* 
 
 .374 
 
 .399 
 
 .852* 
 
 .398 
 
 .641* 
 
 .816* 
 
 .460 
 
 .692* 
 
 .868* 
 
 .326 
 
 .409 
 
 .817* 
 
 .425 
 
 .542** 
 
 *Significant at the .01 level 
 **Signif icant at the .05 level 
 
Table 5 
 
 Correlations Among the Three 
 Cost of Equity Capital Measures 
 (Chemicals) 
 
 
 E/P 
 
 E/P 
 
 k 
 
 e 
 
 
 vs 
 
 vs 
 
 vs 
 
 Year 
 
 k 
 e 
 
 h. 
 
 R_ 
 
 1967 
 
 .176 
 
 -.066 
 
 .159 
 
 1968 
 
 .038 
 
 -.003 
 
 .270 
 
 1969 
 
 -.220 
 
 -.031 
 
 .170 
 
 1970 
 
 -.363 
 
 -.205 
 
 .238 
 
 1971 
 
 -.300 
 
 -.231 
 
 .160 
 
 1972 
 
 -.312 
 
 -.275 
 
 .422 
 
 1973 
 
 -.077 
 
 -.321 
 
 .251 
 
 1974 
 
 -.195 
 
 -.376 
 
 -.047 
 
 1975 
 
 -.032 
 
 -.109 
 
 -.206 
 
 1976 
 
 .060 
 
 -.136 
 
 .097 
 
 1977 
 
 .215 
 
 -.119 
 
 .124 
 
 1978 
 
 .154 
 
 -.065 
 
 .016 
 
 1979 
 
 .110 
 
 -.047 
 
 .095 
 
 *Significant at the .01 level 
 **Signif icant at the .05 level 
 
Table 6 
 
 Correlations Among the Three 
 Cost of Equity Capital Measures 
 (Retail Stores) 
 
 
 E/P 
 
 E/P 
 
 k 
 
 e 
 
 
 k 
 
 e 
 
 h 
 
 h. 
 
 1967 
 
 .458 
 
 -.033 
 
 .213 
 
 1968 
 
 .549** 
 
 .117 
 
 .197 
 
 1969 
 
 .439 
 
 -.001 
 
 .105 
 
 1970 
 
 .523** 
 
 -.178 
 
 -.494 
 
 1971 
 
 .017 
 
 -.160 
 
 -.379 
 
 1972 
 
 -.387 
 
 -.175 
 
 -.330 
 
 1973 
 
 -.460 
 
 -.222 
 
 -.073 
 
 1974 
 
 -.497 
 
 -.128 
 
 -.026 
 
 1975 
 
 -.432 
 
 -.266 
 
 .125 
 
 1976 
 
 .108 
 
 -.274 
 
 -.097 
 
 1977 
 
 .564** 
 
 -.206 
 
 -.124 
 
 1978 
 
 .619** 
 
 -.338 
 
 -.405 
 
 1979 
 
 .670* 
 
 -.243 
 
 -.400 
 
 *Significant at the .01 level 
 **Signif icant at the .05 level 
 
Table 7 
 Means and Standard Deviations of Beta 
 
 Year 
 
 Utilities 
 
 Textiles 
 
 Chemicals 
 
 Retail Stores 
 
 1967 
 
 .704 
 (.176) 
 
 1.152 
 (.355) 
 
 1.310 
 (.330) 
 
 .982 
 (.254) 
 
 1968 
 
 .625 
 (.178) 
 
 1.301 
 (.280) 
 
 1.288 
 (.243) 
 
 1.131 
 (.280) 
 
 1969 
 
 .640 
 (.168) 
 
 1.348 
 (.274) 
 
 1.244 
 (.255) 
 
 1.173 
 (.245) 
 
 1970 
 
 .730 
 (.171) 
 
 1.322 
 (.250) 
 
 1.145 
 (.284) 
 
 1.272 
 (.297) 
 
 1971 
 
 .656 
 (.160) 
 
 1.352 
 (.223) 
 
 1.130 
 (.294) 
 
 1.288 
 (.317) 
 
 1972 
 
 .673 
 (.182) 
 
 1.360 
 (.260) 
 
 1.091 
 (.275) 
 
 1.332 
 (.303) 
 
 1973 
 
 .705 
 (.188) 
 
 1.421 
 (.249) 
 
 1.169 
 (.292) 
 
 1.511 
 (.321) 
 
 1974 
 
 .656 
 (.188) 
 
 1.080 
 (.245) 
 
 1.052 
 (.169) 
 
 1.229 
 (.229) 
 
 1975 
 
 .762 
 (.196) 
 
 1.139 
 (.338) 
 
 1.057 
 (.151) 
 
 1.314 
 (.201) 
 
 1976 
 
 .785 
 (.191) 
 
 1.179 
 (.353) 
 
 1.108 
 (.158) 
 
 1.223 
 (.226) 
 
 1977 
 
 NA 
 
 1.193 
 (.336) 
 
 1.097 
 (.171) 
 
 1.231 
 (.250) 
 
 1973 
 
 NA 
 
 1.075 
 (.330) 
 
 1.018 
 (.228) 
 
 1.068 
 (.212) 
 
 1979 
 
 NA 
 
 1.342 
 
 (.375) 
 
 1.153 
 (.228) 
 
 1.287 
 
 (.274) 
 
HECKMAN l+J 
 BINDERY INC. |§| 
 
 JUN95 
 
 Bound -To -Picas? N.MANCHESTER 
 INDIANA 46962 '