ESTIMATING THE EXPECTED COST OF EQUITY CAPITAL USING ANALYSTS CONSENSUS FORECASTS**

Transcription

1 EXPECTED COSTS OF EQUITY CAPITAL Holger Daske/Günther Gebhardt/Stefan Klein* ESTIMATING THE EXPECTED COST OF EQUITY CAPITAL USING ANALYSTS CONSENSUS FORECASTS** ABSTRACT In this study, we develop a technique for estimating a firm s expected cost of equity capital derived from its stock price and analysts consensus earnings forecasts. Our estimation method, which is based on the residual income valuation model, extends and refines currently available approaches by explicitly allowing daily estimation and using only publicly available information at that estimation date. We apply this technique to estimate the expected cost of equity capital at the market, industry and individual firm level, using historical German data from , and to examine firm characteristics that have been systematically related to these estimated return expectations. JEL-Classification: G12, G14, G31, M41. Keywords: Analyst Forecasts; Cost of Equity Capital; Equity Premium; Residual Income Valuation. 1 INTRODUCTION Sound estimates of the cost of capital are crucial for evaluating investments and for corporate valuation. Current state-of-the-art methods of estimating the cost of equity capital, such as the CAPM or the Fama and French Three-Factor Model, have not only produced disappointing results empirically (Fama and French (1997, 2004)). They are also ques- * Holger Daske (corresponding author), Assistent Professor, Günther Gebhardt, University Professor, and Stefan Klein, Research Assistant, Chair of Accounting and Auditing, Johann Wolfgang Goethe-Universität Frankfurt am Main, Mertonstr , D Frankfurt am Main, [email protected]. ** This paper forms part of the HARMONIA program. The research was in part conducted while Holger Daske was visiting researcher at Lancaster University. We thank Wolfgang Ballwieser (the editor), two anonymous reviewers, Peter Easton, Steve Penman, and the AK Finanzierungsrechnung of Schmalenbach-Gesellschaft für Betriebswirtschaft, workshop participants at Lancaster University, the EAA Annual Congress 2003, Seville, the Amsterdam-Nijenrode Accounting Research Workshop 2003, the EFMA Annual Meeting 2004, Basle and the AAA Annual Meeting 2004, Orlando for helpful comments. We gratefully acknowledge the financial contribution of the European Commission through the Human Potential Program, Contract HPRN-CT as well as of Arthur Andersen and Ernst & Young. We are grateful to Thomson Financial IBES for providing analysts earnings forecast data as part of a broad academic program to encourage earnings expectations research. 2

2 EXPECTED COSTS OF EQUITY CAPITAL tionable in that they use average realized returns instead of measures of expected returns for which the underlying theories on asset pricing call for. Recently, Claus and Thomas (2001), Gebhardt, Lee, and Swaminathan (2001) and Easton, Taylor, Shroff, and Sougiannis (2002) have proposed an alternative approach to estimating a firm s expected cost of equity capital that does not rely on realized returns. Their idea uses a model of corporate valuation to generate a market-implied cost of equity capital. These studies define this implied cost of equity capital as the internal rate of return that equates the current stock price of a firm to the present value of the market s expected future residual flows to common shareholders as approximated by observable financial analysts consensus forecasts. Gebhardt, Lee, and Swaminathan (2001) and Easton (2003) propose these estimates of implied cost of equity capital for application in investment decisions. However, both investors and firms should then be able to estimate their expected cost of equity capital at any date of their own choice. The approach taken in related papers allows estimation only at a specific point in time that is predetermined by the disclosure of financial results once a year (typically April or June). In addition, input variables that reflect information at different points in time have been matched to that estimation date. For example, Claus and Thomas (2001) use share prices and book values of equity as of December 31 but earnings forecasts as of April 30 of the following year, which means that information flows into the estimation as of December 31 which will be available only at the end of April. We extend previous approaches by applying the residual income valuation framework in a way that allows estimation on any day in the fiscal year, using only data concurrently and publicly available. We calculate the book value of equity at the estimation date by adding to last year s book value the intra-year profit accumulated until that date, utilizing the expected return on equity (ROE) of the next period implied in one-year-ahead analysts earnings forecasts. We also adjust that period s earnings forecast and use daily discounting (Actual/365) for discounting future residual income to the estimation date. We implement daily estimation both in the estimation method assuming long-term growth in terminal value estimation (method I; Gebhardt, Lee, and Swaminathan (2001)) and in the portfolio-approach estimating expected cost of equity capital and infinite growth simultaneously (method II; Easton, Taylor, Shroff, and Sougiannis (2002)). International evidence for market-implied cost of equity capital estimates is available only for the market risk premium (Claus and Thomas (2001)), but not at the industry or individual firm level. We estimate the expected cost of equity capital and risk premia at the market, industry, and individual firm level by using our method and German companies historical data from We also examine firm characteristics that have been systematically related to our estimates of expected returns. This research supplements prior findings in the U.S. for a major European financial market that has been characterized as distinct from the U.S. in its institutional setting (Franke, Gebhardt, and Krahnen (2002)). We find that during the period in Germany the average expected cost of equity capital under estimation method I (II) is 10% (11.2%), and the average expected market risk premium is 3.9% (5.2%). Under both methods, we observe a clear trend of a rising 3

3 H. DASKE/G. GEBHARDT/S. KLEIN market risk premium over time that has not been documented by the corresponding U.S. literature covering only periods before We also find significant industry effects, as the market assigns higher discount rates to the information technology and service sectors and lower rates to sectors such as utilities, real estate, or the food and beverage industries. At the firm level, we find reasonable results for individual companies and present the distribution of expected cost of equity capital estimates. When we examine the cross-sectional relation between expected risk premia and several firm characteristics, the book-to-market ratio and the industry category prove to be the most important factors. In a multifactor model, the traditional beta factor seems to be important only in the Fama and French (1992) Three-Factor Model context, but looses explanatory power as soon as we include additional factors. The paper is organized as follows: Section 2 presents our motivation for this new approach and explains our residual income based estimation procedures. In Section 3 we summarize the findings of our empirical analysis of the expected cost of equity capital and its determinants. Section 4 concludes. 2 CONCEPTS OF ESTIMATING THE EXPECTED COST OF EQUITY CAPITAL The cost of equity capital is the rate of return investors require for an equity investment in the firm. It represents the opportunity costs that could have been earned on alternative investments at an equivalent level of risk. Since investing is forward looking, the cost of capital represents investors expectations about (ex-ante) future returns, not (ex-post) realized returns on a particular project (e.g., Pratt (1998, 5); Penman (2004, )). However, in practical applications, realized returns have been used as best estimates for the unobservable expected returns, based on the assumption that in the long run we should get what we expect (Elton (1999)). But current studies describe these cost of capital estimates based on return realizations not only as unavoidably imprecise, but even conclude that the CAPM s empirical problems probably invalidate its use in applications (Fama and French (1997; 2004)). Despite these concerns, in practice the CAPM remains the most frequently used technique to estimate the required rate of return on equity capital (Graham and Harvey (2001); Aders and Hebertinger (2003)). The basic idea of the ex-ante cost of capital models is to use observable forward-looking data instead of historical return realizations (Claus and Thomas (2001); Gebhardt, Lee, and Swaminathan (2001)). The unobservable expected cost of equity capital is estimated from currently available analysts consensus forecasts about a firm s future income and its market price. Building on a model of corporate valuation, the expected cost of equity capital is estimated by equating the current stock price with the intrinsic value of the firm and by solving for the internal rate of return. In equilibrium, the same information is reflected in the stock price on the left side and in the consensus forecasts on the right side of the equation. Therefore, the implied rate of return reflects the cost of equity capital that the market applies to expected future cash flows of the firm (Mehra (2002)). 4

4 EXPECTED COSTS OF EQUITY CAPITAL This estimation procedure requires a model of corporate valuation. Typically, in neoclassical security valuation, we define a stock s intrinsic value as the present value of its expected future free cash flows to equity. Under the assumption that clean-surplus accounting holds in expectations, that is, all changes in book value net of cash flows to/from equity holders are included in earnings, the stock s value can alternatively be expressed in terms of book value of equity plus the present value of residual earnings under the residual income valuation model (RIV)1: E (1) p t = bvps t + t [eps t+τ- - r e bvps t+τ 1 ] τ=1 (1+r e)τ where: E t [ ] = Expectation based on information available at time t, p t = Price per share at time t, bvps t = Book value per share at time t, eps t = Earnings per share at time t, r e = Cost of equity capital. The RIV model expresses firm value in terms of accounting numbers instead of cash flows and has been preferred in estimating expected costs of equity capital 2. It has been shown to have higher accuracy empirically than do cash flow-oriented methods (DDM, DCF) (Penman and Sougiannis (1998), Frankel and Lee (1998), Francis, Olsson, and Oswald (2000)). Also, analysts earnings forecasts have been available for international data since 1987, but cash flow and dividend forecasts have become available only very recently 3. The implied cost of capital estimation procedure inverts the residual income valuation model. Under the assumptions of a flat term-structure of interest rates, it yields the expected costs of equity capital via the internal rate of return (IRR) 4. This nominal rate of return covers a period of one year (p.a.). Since value estimates obtained in any valuation model are sensitive to the choice of the long-term growth rates in terminal value, we apply two estimation procedures. Estimation method I uses economically plausible assumptions and can be applied to a single firm. Method II simultaneously estimates the expected cost of equity capital and the long-term growth rate, but can only be applied to a portfolio of firms. 1 The residual income valuation model is often labeled Edwards-Bell-Ohlson or EBO in the related U.S. literature and in Germany after Lücke (1958) (Copeland, Koller, and Murrin (2000, )); Penman (2004, )). 2 See Claus and Thomas (2001); Gebhardt, Lee, and Swaminathan (2001); Easton, Taylor, Shroff, and Sougiannis (2002). The RIV is also used in value-based management and is particularly well-known under the label Economic Value Added (EVA ) by Stern Stewart & Co., see, e.g., Ehrbar (1998), Young and O Byrne (2001). 3 See Thomson Financial (2003), Glossary IBES Summary History. 4 For a discussion of this assumption and the possibility to incorporate the term-structure of interest rates, see Claus and Thomas (2001, ). 5

5 H. DASKE/G. GEBHARDT/S. KLEIN 2.1 METHOD I: ASSUMING LONG-TERM GROWTH Our estimation method I is a modification of the approach of Gebhardt, Lee, and Swaminathan (2001). For the practical implementation of the residual income model, we divide the infinite forecast horizon into three stages: (a) the explicit forecast period, (b) the fading period, and (c) the terminal value: feps' t (2) p t = E (bvps' t ) + [ (1+r e days (t, fiscal year end 1) ) ] bvps' t (1+r e days (t, fiscal year end 1) ) n= n=6 feps t,n r + e bvps t,n-1 (1+r e days (t, fiscal year end n) ) 365 (FROE t,n r + e ) bvps t,n-1 (1+r e days (t, fiscal year end n) ) 365 (FROE t,12 r + e ) bvps t,11 r e (1+r e days (t, fiscal year end 11) ) 365 where: E(. ) = Expectation based on information available at time t, p t = Price per share at estimation date t, bvps ' t = Adjusted book value per share at estimation date t, bvps t,n = Expected book value per share for the n-th full fiscal year after t at estimation date t, feps ' t = Adjusted forecasted earnings per share for current fiscal year at estimation date t, feps t,n = Forecasted earnings per share for the n-th full fiscal year after t at estimation date t, FROE t,n = Forecasted (book-) return on equity for the n-th full fiscal year at estimation date t, r e = Cost of equity capital, days (t, year (n)) = Number of days between estimation date t and n-th full fiscal year s end. (a) The explicit forecast period covers the next five financial years of detailed analysts consensus earnings forecasts, the maximum future period for which historical data is available on IBES. We utilize the median EPS forecasts in IBES as consensus earnings estimates. We require consensus earnings forecasts for at least the next three financial years following the estimation date. If there are fewer than five future years of forecast data, but instead there is a consensus estimate of the long-term growth 6

6 EXPECTED COSTS OF EQUITY CAPITAL rate of earnings applying to the period from the last detailed EPS-forecast until year 5 (Gordon and Gordon (1997, 53); Thomson Financial (2003, 13)), we estimate the missing forecasts for fiscal years 4 and/or 5 as feps t,n+1 = feps t,n (1+ g t IBES ). If a consensus growth rate is not available, we approximate these forecasts by applying an estimated growth rate of earnings implicit in the previous period forecasts, calculated as the mean absolute change in earnings5: (3) feps t,4 = feps t,3 + (feps t,3 feps t,1 ) 2 feps t,5 = feps t,4 + (feps t,4 feps t,1 ) 3 The earnings forecasts, the assumption of a constant dividend payout-ratio, and the current book value of equity allow us to calculate expected future book values of equity and also the expected residual income for the next five future periods, starting from the estimation date 6 : (4) E t (RI n ) = feps t,n r e bvps t,n-1 where: E t (RI n ) = Expected residual income per share for n-th full fiscal year at estimation date t. (b) During the fading period, we calculate forecasted earnings by utilizing the return on equity (ROE). Starting from the ROE at the end of explicit forecast period 5 (FROE t,5 ), we then assume that the ROE fades in a straight line in the following years to the expected target ROE of the industry in period 12 (TROE). Accordingly, we calculate the expected earnings for fiscal years 6 to 12 as: (5) feps t,n = [FROE t,5 +((n-5)/7) (TROE FROE t,5 )] bvps t,n-1, n = 6,,12 TROE = Target ROE. This method implies that due to the dynamics of market competition, no individual firm is able to earn abnormal profits beyond a certain period of time and will be tending towards their industry peers. Absent a database which collects analyst expectations beyond period 5, we determine the target ROE of the various industries as in Gebhardt, Lee, and Swaminathan (2001). We group all firms into the various industry peers as in Fama and French (1997) and then calculate the median ROEs over the past five years for each group as proxy for the expected ROE. 5 Gebhardt, Lee, and Swaminathan (2001) use the mean percentage change (as opposed to the absolute change) in earnings. Such an approach has severe disadvantages (e.g., a hockey-stick-effect). 6 The clean-surplus relation in equation (4) assumes that dividends are paid at the fiscal year-end. In German practice, dividends are usually paid out once a year, immediately after the annual shareholders meeting, see, e.g., Heiden (2002, 5-10). 7

7 H. DASKE/G. GEBHARDT/S. KLEIN (c) We estimate the terminal value after year 12 by computing the present value of residual income in period 12, which we assume is earned as constant rent in perpetuity and implies that any growth in earnings after year 12 is value neutral (Gebhardt, Lee, and Swaminathan (2001, 142))7. Alternatively, other studies assume a moderate growth rate of residual income METHOD II: SIMULTANEOUS ESTIMATION OF EXPECTED COST OF EQUITY CAPITAL AND LONG-TERM GROWTH Our estimation method II is a modification of the Easton, Taylor, Shroff, and Sougiannis (2002) approach that requires no explicit assumptions about the long-term growth. We simultaneously estimate the expected cost of equity capital and the growth rate of residual income in a regression framework. This approach can be applied only to a portfolio of stocks, but not to individual firms. Under estimation method II, the infinite forecast horizon is covered in only one single stage. Under the traditional single-stage perpetuity method using the Gordon (1962) growth formula, we compute the present value of all future residual income as the residual income of the next period divided by the cost of equity capital minus the growth rate of residual income: (6) p t = bvps t + feps t+1 r e bvps t r e g ri where: g ri = Infinite growth rate of residual income. However, this specification ignores the information available about the forecasted analysts consensus estimates of the following periods. Therefore, under method II, we cumulate projected earnings over the period of four future years as aggregate earnings 9. When computing aggregate earnings over a period of several fiscal years, we must assume that dividends are reinvested in the firm at the expected cost of equity capital to determine the earnings from those reinvestments 10 : 7 The assumption of value neutrality from period 12 also implies that all firms will have reached that stage equally in period 12, independent of the current stage in their business cycle. Yet firms in mature industries could reach this stage in earlier periods and young growth firms in periods later than 12 which would imply that our cost of capital estimates may be biased upwards (downwards) for mature (growth) firms. However, Gebhardt, Lee, and Swaminathan (2001) show for an estimation procedure similar to ours that their estimates are not sensitive to the choice of the length of the fading period and the corresponding start of the terminal value calculations. 8 Claus and Thomas (2001, 1640) assume abnormal earnings grow at an expected inflation rate. 9 Similar to the aggregation of quarterly earnings to fiscal year earnings, earnings of several financial years can be aggregated to, e.g., a four-year aggregate earnings figure, see Easton, Harris, and Ohlson (1992, ) and Easton, Taylor, Shroff, and Sougiannis (2002, 660). 10 We assume that the reinvestments are value neutral and dividend payments are due at the fiscal year end. 8

8 EXPECTED COSTS OF EQUITY CAPITAL (7) X t c = feps ' t + feps t,2 + feps t,3 + feps t,4 + feps ' t,p days (fiscal year end date 1, P ) + dps t+1 [( 1 + r e) 365-1] days (fiscal year end date 2, P ) + dps t+2 [( 1 + r e) 365-1] + dps t+3 [( 1 + r e days (fiscal year end date 3, P ) ) 365-1] + dps t+4 [( 1 + r e days (fiscal year end date 4, P ) ) 365-1] where: X t c = Aggregate earnings over four years (including interest on reinvested dividends), dps t = Dividends per share at time t, P = End of four year estimation window starting at estimation date t, feps t,p = Adjusted forecasted earnings per share for the period from fiscal year end 4 until the four-year estimation window end date P at estimation date t. In formula (8) a future period is not one year, but a four-year period. We then estimate the fundamental value of a firm using a four-year aggregate earnings approach as: (8) p t = bvps t + X c t [( 1 + r e)4 1] bvps t. ( 1 + r e)4 ( 1 + gri )4 This equation can be applied to a single firm, but it cannot be solved for the two unknown variables to be estimated (r e and g ri ). This problem is addressed by adding similar firms to a portfolio which therefore increases the number of equations. By assuming a linear relation between the cost of equity capital and price to book ratio, after rearranging 11 we obtain the following regression function: c X j,t p (9) = α + β bvps j,t ( j,t bvps j,t ) + ε j,t where: c X j,t = Aggregate four year earnings of firm j at time t, bvps j,t = Book value per share of firm j at time t, p j,t = Price per share of firm j at time t, ε j,t = Error term of the linear regression, and α = ( 1 + g ri ) 4 1, and β = ( 1 + r e ) 4 ( 1 + g ri ) For further details, see Easton, Taylor, Shroff, and Sougiannis (2002, ). 9

9 H. DASKE/G. GEBHARDT/S. KLEIN The regression coefficients α and β represent the average expected cost of equity capital and the average infinite growth rate of residual income for the firms included in the portfolio, and determine a combination of r e and gri: (10) gri = 4 (1+α) 1 r e = 4 (β+(1+gri)4 ) 1 When solving for the regression-function, a circularity problem exists, because the solution to be found (r e ) is also needed as an input parameter into the regression through equation (7). We resolve this issue by using an iterative process. Starting from an initial arbitrary value of r e = 12%, we find a first solution of r e running the regression, which then enters into a second-stage regression as starting value. We repeat this procedure until the difference between starting value and solution converges to zero. 2.3 DAILY ESTIMATION PROCEDURE Both investors and firms 12 must continuously evaluate potential investment opportunities. Thus, it is crucial to be able to estimate the expected cost of equity capital potentially at any date using input-variables which consistently reflect only currently available information at that estimation date. Prior studies usually do not follow these requirements. (1) Availability of input-variables: Easton, Taylor, Shroff, and Sougiannis (2002) perform their estimation at December 31 only for firms with fiscal years that go by the calendar year. They use the book value of equity, although this number becomes available (even to insiders in the company) only later in the next fiscal year. Such information is available in retrospect to a researcher, but not contemporaneously to a practitioner. Also, few decisions will be taken around New Year s Eve. (2) Information consistent matching of input-variables: The input variables which have been used in the residual income valuation frameworks often reflect the level of information at different points in time. Claus and Thomas (2001) use share prices and book values of equity as of December 31, but forecasts as of April 30 of the following year. Gebhardt, Lee, and Swaminathan (2001) use share prices and forecasts as of June 30, but book values as of December 31. This match implies that information which will be available only at the end of April or June of the following year flows into the estimation as of December 31. (3) Estimation yearly/monthly : All previous studies calculate the rate of return only once a year at a specific predetermined date (April /June /December ). Lee, 12 Firms generally have fixed capital budgeting procedures in which they, typically once a year, determine the cost of capital they will charge on their new investments. Since these dates vary across firms, just as do their fiscal year-end dates, it is essential for practical implementation of the concept to have the flexibility to calculate the expected rates of return at any date of the firm s choice. 13 See Claus and Thomas (2001, ). 14 See Gebhardt, Lee, and Swaminathan (2001, 145). 15 See Easton, Taylor, Shroff, and Sougiannis (2002, 664). 10

10 EXPECTED COSTS OF EQUITY CAPITAL Myers, and Swaminathan (1999) use a residual income valuation model to estimate the monthly intrinsic value of a firm. To match the input variables that reflect the currently available information at the estimation date, we adjust accounting data which refer to the fiscal year-end dates (book value of equity, earnings forecasts). We compute a virtual book value of equity at the intrayear estimation date t (bvps' t ) under the assumption that book value of equity is growing steadily over the fiscal year, and calculate the bvps' t as 16 : (11) bvps' t = bvps 0 (1+FROE 1 ) days (t, fiscal year end date 1) 365 where: bvps 0 = Book value per share at the previous fiscal year end date 0. Into this calculation flows the expected ROE for the next as yet unpublished financial year (FROE 1 ) which we use to calculate the interest compound up to that estimation date. We calculate the expected ROE by using the most recent explicit analyst consensus earnings forecast that apply to that current fiscal year end: (12) FROE 1 = feps 1 bvps 0 Adding compound interest to the last fiscal-year book value of equity (bvps 0 ) is our proxy for the earnings realized from last fiscal year-end up to the estimation date. This method in turn implies that we must calculate the expected earnings from estimation date to the next fiscal year-end by using the definition of earnings as a change in shareholders equity (e.g., Coenenberg (2003, 6-8)): (13) feps' t = feps 1 [bvps' t bvps 0 ] According to formula (13), the earnings estimate feps' t then forms the basis for calculating the first residual income number in the explicit forecast period E t [RI 1 ] in equation (2). Projected residual incomes of the following periods (2, 3, 4, 5) refer to full fiscal years and are discounted to the estimation date under the daily conventions. So far, the underlying premise is that all analyst forecasts refer to future fiscal year-end dates ( future estimators ). However, there are also cases in which the estimator for the first future period (FY1) refers to a past date ( historical estimator ). This situation can occur when the fiscal year-end date has already passed, but the annual report has not yet been published. In such a case, the first earnings estimator in IBES applies to that past fiscal year-end date. If the first estimator is a historical estimator and refers to the past, the starting input bvps 0 is not available yet and must be calculated via the clean surplus relation using the most recently published book value of equity bvps -1, the payout-ratio 16 For daily discounting we use the act/365 convention, which is standard in the financial industry internationally. It computes the actual number of days between the two dates and divides this number by 365. See, e.g., Harter, Franke, Hogrefe, and Seger (1993, 290); Eller (2001, 3-28); Pratt (1998, 31). 11

11 H. DASKE/G. GEBHARDT/S. KLEIN and the earnings forecast for FY1. Since this calculation results in a loss of one earnings estimator, the maximum number of explicit forecasts in the detailed planning period is reduced to four years. In this case, we extend the fading period by one additional year. We implement daily estimation in the Easton, Taylor, Shroff, and Sougiannis (2002) approach by which we are also able to include firms with different fiscal year-ends in the portfolio. The original study includes only December fiscal year-end firms. As in method I, we calculate a starting book value of equity for each firm at the estimation date. Since we keep constant the length of earnings aggregation over a four-year window (from starting, estimation date t to ending date P ), we must also perform a similar adjustment at the ending date P for the calculation of aggregate earnings, again by assuming the dividends are paid out at the fiscal year-end dates. In the case of a future estimator, we calculate the projected last earnings forecast we use as: days (fiscal year end date 4, P ) (14) feps' p = bvps 4 [(1+ FROE 5 ) 365 1] To include the maximum number of detailed analyst consensus forecasts available, we use a four-year window, as in the original Easton, Taylor, Shroff, and Sougiannis (2002) study. In case not all the necessary future earnings estimates are available, we approximate these forecasts by applying the consensus earnings long-term growth rate estimates or an artificial growth rate of earnings implicit in the available previous period earnings forecasts, respectively, as under method I (see equation (3)). The appendix presents the calculation of the expected cost of equity capital and the risk premium for DaimlerChrysler (DCX) as of August 7, 2003, under method I (Appendix A) and for a portfolio of companies in the European automobile industry under method II (Appendix B). The calculation reflects the situation of the future first estimator, since the annual report for the last fiscal year 2002 has already been published, and the first forecast FY1 refers to the fiscal year ending December 31, The procedure yields an expected cost of equity capital (risk premium) of 12.91% (8.57%) for DaimlerChrysler under method I and of an expected cost of equity capital of 10.92% and an infinite growth in residual income of 3.92% for the European automobile industry under method II. 3 RESULTS FOR GERMAN COMPANIES We apply our estimation procedures to a large sample of German listed firms, using data over the period 1989 to We report two sets of results under both estimation methods I and II: expected cost of equity capital and risk premia at the market, industry, and firm level; and the relations between expected risk premia and various firm characteristics. 12

12 EXPECTED COSTS OF EQUITY CAPITAL 3.1 DATA Table 1 lists the input variables for our estimations and their data sources. We use the IBES Summary History File Version 2.0 as of January 2003 for monthly analysts consensus earnings forecasts, the number of shares outstanding, and stock prices. We obtain the book value of equity, payout ratio, industry classification, and the industry target ROE from Thomson Financial Analytics Worldscope. Our proxy for the risk-free rate is the ten-year REX return collected from Datastream. Table 1: Definition of Variables and Data Sources Input Variable Description in Database Symbol Forecasted EPS IBES Median EPS Estimate feps t+n Long-term growth LTG IBES Long Term Growth g ltg Book value of equity WORLDSCOPE Total Common Equity BV t No. of shares outstanding BVE per share IBES Shares Outstanding (in millions) Payout ratio WORLDSCOPE Div Payout Ratio k Share price IBES Price p t bvps t Target-ROE Median of Industry ROE over the past five years FROE t,12 Industry WORLDSCOPE SIC Code Estimation Date Estimation date, one per month t Risk free rate of return DATASTREAM REX BOND SUB INDEX CURRENT, 10 YRS r f Data availability in IBES on analyst forecast data limits our analysis to the period from January 1989 to December Table 2: Sample Selection Description No. Percent IBES data set 69, % Shares outstanding data missing (594) 0.85% Share price data missing (690) 0.99% Accounting data missing (10,019) 14.36% Target ROE data missing (814) 1.17% At least three future EPS-estimators or two future EPS-estimators and long-term growth (24,963) 35.77% Stacked forecasts (3,295) 4.72% Insolvency estimates (517) 0.74% Final Dataset 28, % 13

13 H. DASKE/G. GEBHARDT/S. KLEIN The initial number of 69,785 monthly earnings forecast observations in IBES on German companies is reduced for the following reasons: (1) Financial data missing after merging databases on shares outstanding, share price, accounting data, and target ROE results in a loss of 17.37% of total observations. (2) The market s consensus earnings forecasts are a key determinant of our estimation procedure. To ensure that our inputs really measure market expectations over the relevant forecast horizon, we require that each observation either have at least consensus EPS forecasts for the next three periods (out of a theoretically maximum of five periods available in IBES) or consensus EPS forecasts for the next two periods and a long-term growth rate (LTG, applying to periods three to five). In our view, this choice represents the best tradeoff between extracting market expectations on the one hand and a representative sample size, including also smaller, less covered firms, on the other. We lost another 35.77% of the initial observations for which we had only FY1 or FY1 and FY2 forecasts. (3) We minimize data errors by deleting forecast data of questionable quality which includes stacked forecasts (4.72%) and insolvency forecasts (0.74%). a. Stacked forecasts: According to 325(1) HGB, annual reports should be available within nine months after the end of the fiscal year. Accordingly, we delete all forecasts which refer to a fiscal year-end longer than nine months ago and which most probably have not been updated by the database. b. Insolvency forecasts: In some special cases, analysts estimate losses that could result in a negative book value of equity in a future period. Such losses would lead to the firm s insolvency if no additional equity capital were provided. We delete such observations as not representative. It is also important to note that IBES requires that analysts report their earnings estimates for German companies according to the DVFA/SG rules, not according to local or international GAAP, under which the companies report their results (Thomson Financial (2003)) 17. Further, Worldscope adjusts the reported book value of equity numbers to make them comparable internationally 18. Therefore, when we apply our residual-income based estimation framework, we must assume that analysts have prepared their earnings forecasts according to the clean-surplus principle, and that the Worldscope adjustments have not introduced any (further) violations. In Table 2 we summarize our sample selection procedure. Our final sample consists of 28,893 observations pooled across all estimation months. Since we estimate the expected cost of equity capital and risk premia monthly, our data set is comparable in size with the previous U.S. studies 19. The total number of firms per month in our sample varies from around 100 in 1989 to around 350 in 2002, as the number of listings in Germany increased considerably over the last decade For the concept of DVFA/SG core earnings, see Busse v. Colbe et al. (2000). 18 See the Glossary on Thomson Financial Worldscope (2002). 19 Gebhardt, Lee, and Swaminathan (2001) use 18,615, Claus and Thomas (2001) use 33,389 and Easton, Taylor, Shroff, and Sougiannis (2002) use 26,561 total observations in their analysis. 20 See DAI-Factbook (2002, 03-8-b). 14

14 EXPECTED COSTS OF EQUITY CAPITAL 3.2 EXPECTED COST OF CAPITAL AND RISK PREMIA We estimate the expected cost of equity capital and risk premia at the market, industry, and firm levels. Even in the traditional CAPM context aggregation at the market level can be useful for identifying the implied market risk premium. Instead, the industry and individual firm level estimates can be seen as substitutes of the traditional approaches MARKET LEVEL Under method I, we calculate the equally weighted mean of all estimates per firm of the cost of equity capital and risk premium monthly. Under method II, we pool all observations in a portfolio per month and estimate the corresponding market cost of equity capital, the risk premium, and the infinite growth rate of residual income, using the regression from regression equation (9). Table 3: Expected Cost of Equity Capital and Risk Premia Market Level Number of observations N Risk-free rate r f Cost of Equity Capital r e Risk Premium r e - r f Growthrate g RI r e - g RI Method Year I II I II I II II II % 7.9% 10.7% 0.9% 3.6% 7.3% 3.4% % 7.4% 10.5% -1.5% 1.6% 8.2% 2.3% ,125 1, % 7.8% 8.2% -0.8% -0.4% 5.1% 3.1% ,530 1, % 8.2% 8.3% 0.2% 0.3% 4.2% 4.0% ,588 1, % 7.8% 7.9% 1.5% 1.6% 4.5% 3.4% ,618 1, % 7.6% 8.1% 1.1% 1.5% 4.0% 4.1% ,862 1, % 8.4% 9.3% 2.0% 2.9% 4.4% 4.9% ,038 1, % 9.1% 9.0% 3.5% 3.4% 3.8% 5.2% ,220 2, % 8.9% 9.0% 3.8% 3.9% 5.2% 3.8% ,576 2, % 9.9% 11.7% 5.6% 7.3% 9.2% 2.5% ,021 2, % 11.6% 15.6% 7.4% 11.4% 13.9% 1.7% ,219 3, % 11.6% 22.1% 6.4% 16.8% 21.2% 0.9% ,306 3, % 15.6% 14.8% 11.0% 10.2% 12.1% 2.7% ,383 3, % 17.5% 12.3% 13.0% 7.9% 8.0% 4.3% All 28,893 27, % 10.0% 11.2% 3.9% 5.2% 7.9% 3.3% 15

15 H. DASKE/G. GEBHARDT/S. KLEIN Table 3 reports the mean monthly expected cost of equity capital and risk premia in Germany under methods I and II, summarized as averages per year. Pooled over our total sample period, the average expected cost of equity capital in Germany is 10% under method I and 11.2% under method II. The average expected market risk premium is 3.9% (5.2%) under method I (II). Under both methods, over time we observe a clear trend of rising expected market-risk premia. Particularly interesting is the increase in the expected market cost of equity capital and risk premia that starts in Excluding the periods from 1999 to 2002, the average market-risk premium is significantly lower at only 1.6% (2.6%). This result is similar to Claus and Thomas (2001), who report an average expected market-risk premium of 2.02% for Germany from 1988 to 1997 using a comparable approach. With respect to the discussion on the equity premium puzzle (e.g., Mehra and Prescott (1985), Claus and Thomas (2001), Fama and French (2002)), our ex-ante risk premia are within the range of evidence reported for the magnitude of expost realized premia in Germany (Ballwieser (2002, 739) or Drukarczyk (2003, 366)). Starting from a low number of observations and estimates of comparatively high volatility and low average risk premia from the beginning of our sample period until 1991, the number of firms increases substantially over the next years and reflects the overall market reasonably well. In the following years, we see an increasing trend of expected risk premia over time, independent of the method applied. The expected market-risk premium rises from around zero at the end of the 80 s to around 13% (8%) under method I (II) at the end of We observe a sharp increase at the end of our estimation period, a phase in which stock market participants appear to be euphoric about expected returns of their investments. Table 3 also documents high growth expectations, as average expected growth of residual income exceeds 10% under method II for the years This finding is in part attributable to the increasing number of newly listed growth companies during that period. Altogether, the set of listed firms in Germany increased substantially during the 90 s, particularly at the end of the 90 s, when predominantly young, risky firms entered the set of firms that empirically determine the German market. Thus, rising expected market premia of investors appear to be more logical than exceptional. Related U.S. studies that cover sample periods ending before 1999 do not document this rising trend in market expectations about future returns 21. This finding contradicts the Stulz (1999) argument that increased globalization causes the equity premia to decline in financial markets globally. Our results show increasing risk premia required by investors for providing funds to German companies during the 90 s. Since cost of capital reflects the opportunity costs of alternative investment of similar risk elsewhere, this trend could also mirror better investment opportunities in the global market place. When we compare the results of the two estimation procedures, Table 3 best shows the influence of assuming (method I) instead of estimating long-term growth simultane- 21 The sample periods of Gebhardt, Lee, and Swaminathan (2001), Claus and Thomas (2001) and Easton, Taylor, Shroff, and Sougiannis (2002) end in 1995, 1998 and

16 EXPECTED COSTS OF EQUITY CAPITAL ously (method II). In years with high estimated implied growth rates, the differences between the two resulting costs of capital are greater than in years with low implied growth rates. We see that method II always provides higher expected return estimates than method I. This result appears because method II estimates high implied growth rates in periods when earnings estimates in the detailed planning period are optimistic relative to the stock price. In such a scenario, the intercept of method II, regression (9), and its corresponding implied long-term growth rate in regression (10) move upwards, which means that the very optimistic forecasts are projected to the future. According to equation (10), higher long-term growth rates then transform, ceteris paribus, to higher cost of capital estimates. However, under method I, optimistic forecasts in the detailed planning period are not projected to the future. Instead, earnings are assumed to move back to lower longrun levels during the fading period, which transforms into lower implied cost of capital estimates. Altogether, method I, with the restrictive assumption of no future growth after period 12, gives a lower bound of cost of capital estimates, and method II transforms high short-term earnings growth into high long-term growth and thus potentially overstates implied cost of capital estimates INDUSTRY LEVEL At the industry level, we do not have enough observations for an analysis of each of the 168 month and 20 industry combinations. To generate results which are not driven by individual firms, we require a minimum of ten firms per month, per industry, for estimation. To make method I and II more comparable, we calculate our industry results under method I for the same set of firms by averaging all method I s individual estimations. Table 4: Expected Cost of Equity Capital and Risk Premia Industry Level Number of observations N Cost of Equity Capital re Risk Premium re - rf Ranking of Industries Method Industry I II I II I II I II Utilities % 8.5 % -0.5 % 1.9 % 1 7 Banking % 8.6 % 0.9 % 1.9 % 2 8 Food & Beverages % 6.8 % 1.5 % 0.1 % 3 1 Real Estate % 8.7 % 1.8 % 2.1 % 4 9 Insurance % 12.6 % 2.2 % 5.9 % 5 15 Retail & Wholesale 3,604 3, % 10.3 % 3.6 % 3.7 % 6 10 Construction % 8.2 % 4.2 % 1.6 % 7 6 Consumer Goods % 8.1 % 4.4 % 1.4 % 8 4 Construction Material 1,319 1, % 8.1 % 4.5 % 1.4 % 9 3 Machinery 2,862 2, % 10.4 % 4.8 % 3.8 %

17 H. DASKE/G. GEBHARDT/S. KLEIN Table 4: Expected Cost of Equity Capital and Risk Premia Industry Level Number of observations N Cost of Equity Capital re Risk Premium re - rf Ranking of Industries Method Industry I II I II I II I II Communications % 8.2 % 4.8 % 1.5 % 11 5 Health % 7.5 % 5.5 % 0.9 % 12 2 Chemicals % 11.1 % 6.1 % 4.5 % Automobiles % 11.8 % 6.4 % 5.2 % Electrical Equipment % 13.3 % 6.8 % 6.7 % Textiles % 10.8 % 7.4 % 4.1 % Recreation % 18.7 % 9.4 % 12.0 % Trading % 21.3 % 10.4 % 14.6 % Business Services 2,453 2, % 22.5 % 13.4 % 15.9 % Computers % 18.0 % 15.7 % 11.4 % Table 4 presents the implied cost of equity capital and risk premia for 20 industry group classifications as in Fama and French (1997) utilizing the primary SIC classifications in Worldscope. The industries with the lowest expected risk premia are traditional low-risk sectors such as Utilities (-0.5%; 1.9%), Real Estate (1.8%; 2.1%) or Food and Beverages (1.5%; 0.1%), but also Banking (0.9%; 1.9%) and Insurance (2.2%; 5.9%). Investors demand the highest implied risk premia for the Information Technology and Service sectors, including Computers (15.7%; 11.4%), Business Services (13.4%; 15.9%), and Trading (10.4%; 14.6%). The last two columns in Table 4 present the rankings of expected rates of return per industry for each estimation method. The rank correlation between the two methods is FIRM LEVEL Table 5 reports the distribution parameters of the expected cost of equity capital and risk premia at the firm level. Since method II is only applicable for a portfolio of stocks, we estimate each observation on the (next higher) industry level and present the distribution of these estimates that apply to each firm included in that industry portfolio (a total of 1,187 monthly regressions). 18

18 EXPECTED COSTS OF EQUITY CAPITAL Table 5: Expected Cost of Equity Capital and Risk Premia Firm Level Cost of Equity Capital (r e) Risk Premium (r e - r f ) Method I Method II Method I Method II Mean 11.07% 11.27% 5.53% 4.62% Median 9.49% 10.09% 3.99% 3.44% 5% Quantil 4.32% 5.63% -2.35% -1.03% 95% Quantil 23.17% 19.18% 18.55% 12.52% No No.< %<0 (0%) (0%) (17.2%) (12.05%) Without a benchmark against which to compare our estimates, given that even average realized returns do not necessarily reflect expected returns even over the long run (Miller (1977), Elton (1999)), we focus on the percentage of cases with either negative expected cost of equity capital or negative risk premia. Such estimates are difficult to reconcile with traditional capital market theory 22. In our sample, the number of observations with a negative cost of equity capital estimate is zero, but the percentage of firms with negative expected risk premia is 17.2% (12.05%) of the full sample under method I (II). Guay, Kothari, and Shu (2003) report a comparable percentage of negative risk premium firms using the Fama and French (1992) Three-Factor Model (Guay, Kothari, and Shu (2003, 13)). 3.3 DETERMINANTS OF EXPECTED RISK PREMIA Next, we analyze determinants of expected risk premia. The cross-sectional relation between our estimates and the various firm characteristics that affect such estimates is interesting for two reasons. First, systematic relations between implied estimates and variables that have been found in prior literature to capture the riskiness of firm could rationalize or justify this new measure. Second, financial managers are interested in understanding the market perception of risk and which of their firm s characteristics affect their cost of equity capital. Since we are interested in the determinants at the individual firm level, we can only use method I in this section. We concentrate on the risk premia and the 22 In decision-theory, a negative risk premium can be explained by risk-seeking investors willing to pay for taking on additional risk (e.g., Tversky and Fox (2000, 93-96)). In capital market theory and a CAPM context, a negative risk premium can be reconciled with a negative beta of a stock (e.g., Ross, Westerfield, and Jaffe (2002, )). 19

19 H. DASKE/G. GEBHARDT/S. KLEIN following explanatory variables (also Gebhardt, Lee, and Swaminathan (2001) and Gode and Mohanram (2003))23: (A) SYSTEMATIC AND UNSYSTEMATIC RISK The CAPM beta factor plays a central role in capital market theory and valuation practice (e.g., Ross, Westerfield, and Jaffe (2002, ); Brealey and Myers (2003, )). The CAPM predicts a positive linear association between a firm s measure of systematic risk (beta) and its expected risk premium. As is common in the literature, we estimate the beta of each stock based on a five-year rolling regression, using monthly returns with the value-weighted Composite DAX (CDAX) index as the market proxy 24. Prior studies find a positive relation between a stock s volatility as measure for unsystematic risk and its future returns (Malkiel (1997)). We measure volatility as annualized standard deviation from the previous year s daily discrete stock returns, assuming 250 trading days in a year (e.g., Steiner and Bruns (2000, 57-59)). (15) Vola i = 1 n 1 t=1 250 (ri,t E [r i ]) where: Vola i = Volatility of stock i, n = Number of returns (250), r i,t = Discrete daily returns of stock i at date t, E [r i ] = Mean of discrete daily stock returns over the past 250 trading days. (B) FINANCIAL LEVERAGE According to financial theory (Modigliani and Miller (1958)), a firm s cost of equity capital should be an increasing function of the debt-to-equity ratio. Empirically, Fama and French (1992) find a positive relation between market leverage and realized stock returns. We use the ratio of long-term debt to the market value of equity at fiscal yearend as a measure of leverage. (C) INFORMATION ENVIRONMENT Corporate disclosures and additional information created by financial intermediaries can lower the information asymmetry between a firm and its investors, and thus lower the 23 We do not analyze aspects of corporate disclosure or regulation, see Hail (2002); Hail and Leuz (2003) for such an analysis. 24 We require at least 24 data-points (monthly returns) for estimation. The CDAX includes about 750 listed stocks traded on the official market. 20

20 EXPECTED COSTS OF EQUITY CAPITAL risk premium required (Diamond and Verrecchia (1991)). Although empirical research has applied many kinds of proxies for measuring the information environment, these variables are often highly correlated (Gode and Mohanram (2003)). We hypothesize that the risk premium is lower for firms with more analysts following or of larger size. Therefore, we use the number of analysts following a firm and firm size (log market capitalization of equity) as proxies for the information environment. (D) EARNINGS VOLATILITY One rationale for earnings management taking the form of smoothing income over time is the notion that firms with stable and increasing earnings trends will have lower risk premia over time (e.g., Ronen and Sadan (1981, 7-8) for an overview). In fact, recent research finds a valuation premium for such firms (Barth, Elliott and Finn (1999)). We measure earnings variability as the standard deviation of one-year ahead analysts earnings forecasts by IBES. (E) STOCK MARKET ANOMALIES Increasingly, empirical studies document variables that have no explicit foundation in theory, but which have been shown to be statistically associated with realized returns (Elton and Gruber (1995) for an overview). The book-to-market ratio (B/M) is among the most prominent of those variables and is included in the Fama and French (1992) Three- Factor Model. These authors show that high B/M firms earn higher returns ex-post than do low B/M firms. La Porta (1996) shows that firms with high (low) long-term earnings growth expectations earn lower (higher) subsequent-year returns. We examine whether we can also find such anomalies in expected returns. (F) INDUSTRY MEMBERSHIP Firms in a specific industry share similar business risks and often, similar accounting choices. Estimations of the cost of equity capital using realized returns have often been performed at the industry, rather than at the individual firm level. Gebhardt, Lee, and Swaminathan (2001) find that industry effects explain much of the cross-sectional variation in expected risk premia. We control for industry effects by including the average industry expected risk premium of the previous year. (G) TIME Absent a theoretical background, but given the obvious (increasing) trend of expected risk premia in Table 3, in our pooled regressions we control for time by including a yearly count variable, beginning in 1989 (=1) and ending in 2002 (=14). 21

21 H. DASKE/G. GEBHARDT/S. KLEIN Table 6 (Panel A): Description of Variables Variable RP CoC Rex Beta Vola DM No ln_size Std_FEPS1 BM LTG Description (Source) Risk premium computed using Estimation method I Cost of equity capital computed using Estimation method I Return of the risk-free rate r f as proxied by the yield on the REX-Index Five-year rolling over market beta, monthly returns, against CDAX-Market Index (Datastream) Standard deviation of the previous years daily returns, measured over 250 trading days (Datastream) Ratio of long-term debt to market capitalization (Worldscope, Datastream) Number of analyst following (IBES) Natural Log of firm size in millions (IBES) Dispersion of one-year-ahead analysts earnings per share forecasts (IBES) Book to market value of equity (Worldscope, IBES) Consensus long-term growth earnings estimate (IBES) RP_Lag Previous year s risk premium of the firm s industry (based on estimation using method I) Time Count variable, from 1989 (=1) to 2002 (=14). Table 6 (Panel B): Descriptive Statistics for Expected Risk Premia and Firm Characteristics Variable N Mean StDev Min Q1 Median Q3 Max RP 2, % 5.68% -4.60% 0.74% 3.56% 7.43% 28.74% CoC 2, % 5.09% 2.58% 6.96% 9.21% 12.49% 33.42% Rex 2, % 1.36% 3.73% 4.64% 5.20% 6.35% 9.06% Beta 1, Vola 1, DM 2, No 2, ln_size 2, Std_FEPS1 2, BM 2, LTG 1, RP_Lag 2, % 4.53% -3.88% 1.38% 3.65% 7.36% 16.93% 22

22 EXPECTED COSTS OF EQUITY CAPITAL Table 6 (Panel C): Spearman-Correlations for Expected Risk Premia and Firm Characteristics RP CoC Rex Beta Vola DM No ln_ size Std_ FEPS1 LTG BM RP_ Lag Time RP CoC Rex Beta Vola DM No ln_ size Std_ FEPS LTG BM RP_ Lag Time Table 6, Panel A, describes all variables and their data sources. We winsorize each variable by the top and bottom 1% observations. Panel B presents the mean, standard deviation, and the range of the dependent and explanatory variables. Panel C displays nonparametric Spearman rank correlations between these variables UNIVARIATE RESULTS The signs of all correlations in Table 6, Panel C, are in line with expectations. Risk premia are negatively correlated with the information environment variables (number of analysts following a firm and firm size), but positively correlated with all other variables. The beta factor from the CAPM is not highly correlated with any of the other explanatory variables. The rank correlation with the implied risk premium is very low. 23

23 H. DASKE/G. GEBHARDT/S. KLEIN To reduce measurement errors (e.g., Gujarati (2003, )) we pool observations as of March of each year25, form five equally sized portfolios (quintiles) based on each firm characteristic, and calculate the mean and median expected risk premium for the firms in each portfolio. We then test for the differences in risk premia across the two extreme portfolios, Q1 and Q5 (parametric t-test, nonparametric Wilcoxon Z-test) and across the portfolios using ANOVA F-tests. Table 7 presents the results. The relation between beta and vola and the expected risk premium is not monotonically increasing from the lowest to the largest portfolio of beta or vola. For beta, the difference between the largest portfolio Q5 and the lowest portfolio Q1 is significant only at the 10% level, using the t-test, but the nonparametric test and the ANOVA are not significant. In the case of vola, the mean (median) difference from Q5 to the Q1 is highly statistically significant with 2.19% (1.31%), as are the ANOVA F-Statistics, across the five portfolios. Except for the long-term growth variable, all other explanatory variables in Table 7 show continuously decreasing or increasing expected risk premia across the different portfolio levels. These results are in line with our expectations. The test statistics are significant. The size variable turns out to have the highest negative impact on expected returns, since the mean (median) difference in expected returns between the largest (Q5) and smallest (Q1) firm portfolios amounts to -6.08% (-4.74%). For the industry risk premium of the previous period (5.55%), the book-to-market ratio (5.71%), and the time variable (9.58%), the mean differences in expected cost of equity capital between the largest and smallest magnitude of independent variable portfolios (Q5-Q1) are particularly high, as are the related test statistics and significance levels. These univariate results appear to be even stronger than those in Gebhardt, Lee, and Swaminathan (2001). 25 We choose the month of March each year for several reasons: First, the maximum number of observations per month in our sample is available in March. Second, most of the financial results for the majority of firms with a fiscal year-end in December 31 are already available at that date. Thus, more future estimators for the FY1 are available, in which case we gain an additional earnings forecast relative to the historical estimator. Third, it is important to include each firm only once in the sample for this analysis. This requirement would be violated by a monthly analysis. 24

24 EXPECTED COSTS OF EQUITY CAPITAL Table 7: Expected Risk Premia and Firm Characteristics: Univariate Analysis Smallest Largest t-stats/ ANOVA Ranked by: Q1 Q2 Q3 Q4 Q5 Q5-Q1 Z-Stats F-Stats Beta Mean Exp. Risk Premium 3.66% 4.04% 3.99% 4.45% 4.52% 0.86% 2.66* 1.43 Median Exp. Risk Premium 2.88% 2.74% 3.28% 2.92% 3.00% 0.12% Vola Mean Exp. Risk Premium 3.70% 5.46% 4.64% 4.22% 5.89% 2.19% 5.85*** 9.22*** Median Exp. Risk Premium 2.93% 3.88% 3.21% 3.25% 4.24% 1.31% 4.30*** DM Mean Exp. Risk Premium 3.32% 4.10% 4.74% 5.47% 7.31% 3.99% 12.29*** 34.71*** Median Exp. Risk Premium 2.11% 2.97% 3.81% 4.32% 6.66% 4.55% 11.09*** No Mean Exp. Risk Premium 5.88% 5.65% 5.19% 4.10% 3.07% -2.81% -8.89*** 22.40*** Median Exp. Risk Premium 4.31% 4.55% 4.17% 3.26% 2.61% -1.70% -5.86*** ln_size Mean Exp. Risk Premium 8.37% 5.98% 4.35% 2.81% 2.29% -6.08% *** *** Median Exp. Risk Premium 6.92% 5.23% 3.70% 2.21% 2.17% -4.74% *** Std_FEPS1 Mean Exp. Risk Premium 3.93% 4.02% 4.43% 5.25% 5.37% 1.44% 4.31*** 7.29*** Median Exp. Risk Premium 2.91% 3.06% 3.61% 4.06% 3.95% 1.04% 3.15*** LTG Mean Exp. Risk Premium 2.61% 2.14% 2.08% 2.78% 2.74% 0.13% Median Exp. Risk Premium 1.95% 1.33% 1.44% 2.10% 2.53% 0.58% BM Mean Exp. Risk Premium 2.60% 2.91% 3.74% 5.75% 8.31% 5.71% 19.07*** *** Median Exp. Risk Premium 1.56% 2.10% 3.07% 4.44% 7.04% 5.48% 15.69*** RP_Lag Mean Exp. Risk Premium 2.04% 3.75% 4.76% 6.26% 7.59% 5.55% 17.62*** 80.35*** Median Exp. Risk Premium 1.28% 2.99% 3.93% 5.11% 5.95% 4.67% 14.98*** Time Mean Exp. Risk Premium 0.14% 2.20% 4.29% 6.67% 9.72% 9.58% 23.31*** *** Median Exp. Risk Premium -0.28% 1.93% 3.90% 6.24% 8.57% 8.85% 25.68*** ***, **, * Significantly different from zero at significance levels of 0.01, 0.05, and 0.10 respectively. 25

25 H. DASKE/G. GEBHARDT/S. KLEIN MULTIVARIATE RESULTS We use two different approaches to analyze the multivariate relation between the implied risk premia and the various firm characteristics. In our pooled cross-sectional regressions in Table 8, Panel A, we apply linear GLS regressions and use clustering of the firm s residuals to control for autocorrelation in the cost of capital estimates. For our standardized yearly cross-sectional regressions in Table 8, Panel B, we report mean coefficients and R 2s, with t-statistics based on the standard error of the yearly coefficient estimates (Fama and McBeth (1973)) 26. Because we standardize the variables to a mean of zero and a standard deviation of one in the second approach, this step allows us to measure the relative influence of each explanatory variable on the dependent variable (Gujarati (2003, 174); Gebhardt, Lee, and Swaminathan (2001, 164)). Each panel of Table 8 reports results for four different model specifications. Model 1 in Panel A and B is based on the variables in the Fama and French (1992) Three- Factor Model. The explanatory power of the pooled regression version is relatively high (41.84%), but lower than the standardized Fama and McBeth (1973) approach with 50.53%. All three independent variables (beta, size, book-to-market ratio) are highly significant and their signs are in the directions predicted. A comparison of the coefficients in the standardized regressions in Panel B shows that the variation of the book-to-market ratio has the highest impact on the variation of expected returns (0.54), followed by the size variable with a regression coefficient of Beta is the least important variable in this model (0.095). Model 2 includes all independent variables, except the number of analyst following and the debt-to-market ratio. The former variable is highly correlated with size (0.67) and the latter with the book-to-market ratio (0.62), respectively (Table 6, Panel C ). The overall explanatory power of the model is similar in both panels (77% compared to 72.03%). All variables except the systematic and unsystematic risk measures, and the standard deviation of analysts earnings forecasts, are highly significant. The influence of the lagged industry risk premium variable is remarkable: in the pooled regression in Panel A, an increase of the industry risk premium by 100 basis points would lead, on average, to an increase of the firm s expected risk premium of 53 basis points. This result confirms the conclusion of Gebhardt, Lee, and Swaminathan (2001), that industry membership should be an important characteristic in cost of capital estimation (p. 138). Model 3 replaces the highly correlated variables and includes the number of analyst following instead of size, and the debt-to-market ratio as an alternative for the book-tomarket ratio. The explanatory power in both regressions declines noticeably, but is still above 50%. The change in variables causes the vola variable to be statistically significant at the 5% level, but only in the pooled regression case. 26 Fama and McBeth (1973)-type regressions with adjustments for autocorrelation (Abarbanell and Bernard (2000, 228), and Newey and West (1987) yield comparable results. 26

26 EXPECTED COSTS OF EQUITY CAPITAL Table 8: Expected Risk Premia and Firm Characteristics: Multivariate Analysis BETA LN_SIZE BM VOLA STD_FEPS1 NO LTG DM RP_LAG TIM E ADJ-R2 HYP OTHESES O O Panel A: Pooled Regressions (1) *** *** *** *** 41.84% (6.07) (5.20) (-8.29) (12.61) (2) *** *** *** *** *** *** 77.00% (-4.81) (0.18) (-2.38) (12.81) (0.85) (-0.56) (2.79) (11.60) (4.78) (3) ** ** *** *** *** *** 67.20% (-2.60) (-1.15) (2.32) (-1.57) (-4.44) (1.45) (7.98) (10.26) (2.60) (4) *** * *** 73.50% (-1.59) (-0.68) (-1.62) (8.89) (-0.86) (1.49) (1.83) (23.53) Panel B: Standardized Yearly Cross-Sectional Regressions (1) *** *** *** 50.53% (1.44) (3.02) (-2.85) (7.23) (2) *** *** *** 72.03% (-1.36) (-0.05) (-1.24) (8.75) (0.90) (1.30) (4.61) (17.84) (3) ** *** *** 52.95% (-1.00) (-1.58) (1.38) (0.95) (-0.49) (1.99) (4.80) (14.88) (4) * *** *** *** 71.35% (-1.87) (-0.13) (-0.89) (8.34) (0.42) (3.68) (0.46) (17.02) ***, **, * Significantly different from zero at significance levels of 0.01, 0.05, and 0.10 respectively. 27

27 H. DASKE/G. GEBHARDT/S. KLEIN Model 4 reconstructs Gebhardt, Lee, and Swaminathan s (2001) model with the highest explanatory power in our German setting. The model gains an adjusted R 2 of 73,50%/71,35% which is even higher than in the original study. The variables B/M, LTG, and RP_lag have the same significance as in Gebhardt, Lee, and Swaminathan (2001). However, the variation in short-term analysts earnings forecasts is of minor importance in our study. In addition, leverage and firm size appear to be more important in the German capital market. To sum up, the historical beta, vola, and the variation in short-term analysts earnings forecasts do not contribute much to the explanation of expected risk premia. Beta looses explanatory power as soon as we add more variables to the Three-Factor Model. The variables most important for explaining the variation of expected risk premia are the lagged industry risk premium and the book-to-market ratio. Although industry effects evidently reflect the common operating and financial risks faced by firms in the same business, several competing explanations have been put forward for the book-to-market ratio. When analyzing realized returns, Fama and French (1998) find that high book-to-market firms ( value stocks ) have historically earned higher risk adjusted returns than low book-to-market firms ( growth stocks ). This Value versus Growth anomaly has been interpreted as either representing mispricing or, alternatively, as some underlying risk that is not adequately captured by traditional asset pricing models and is reflected by the book-to-market ratio (e.g., La Porta, Lakonishok, Shleifer, and Vishny (1997)). The significant relationship we find for expected returns could represent the same reasons. Either investors expect high returns, since they anticipate mispricing to persist in the future, or, alternatively, they expect high book-to-market firms to earn high returns to compensate for underlying risk DISCUSSION Sound estimates of the cost of capital are crucial for the evaluation of investments and for corporate valuation. Companies must know what the opportunity costs of their investors are. When maximizing shareholder value, they should further understand how they can lower their cost of capital. Thus, we discuss the key advantages and disadvantages of the new approach for the application in investment practice 28 : A major argument supporting the implied cost of capital approach is its consistency with asset pricing theory, calling for measures of expected returns whereas traditional estima- 27 Wallmeier (2004) argues that the significant relation between book-to-market and expected returns could be due to the estimation procedure based on the residual income model. He shows that the expected costs of equity capital are a function of the book-to-market ratio as expected in period 12 (when assuming full payout). However, we regress our cost of capital estimates on the current book-to-market ratio, and we do not assume full payout, in which case we cannot derive a linear relationship in period See Daske and Gebhardt (2006) for a discussion of the applicability of these methods in corporate valuations. See also Gebhardt, Lee, and Swaminathan (2001, ) and Guay, Kothari, and Shu (2003). 28

28 EXPECTED COSTS OF EQUITY CAPITAL tion procedures have generally used realized returns instead. The new approach derives its estimates from the forward-looking market data currently available. It bypasses the crucial implementation issues inherent in the traditional CAPM approach, for which there are so far no convincing solutions. The advantage of not relying on historical returns is especially relevant to newly listed companies or firms that experience a major structural change, such as an M&A or a restructuring activity. For such firms, information in historical returns is even less useful for projections than it is for other firms. The communication process between firms and their investors could be enhanced by discussing the underlying reasons for diverging expectations on the required returns of new investment, if the implied cost of equity capital estimates derived from current market data do not correspond to the benchmarks used internally. One disadvantage of the new concept for the application in capital budgeting decisions that is common to all market-oriented approaches is that the project must have the same systematic risk as the firm for which the cost of capital was calculated. If this is not the case, the expected cost of capital could be determined by using listed pure-play firms of comparable risk. Further, the concept results in only one discount rate to be applied at all future periods. It does not incorporate time-varying discount rates. However, under the assumption of a constant risk premium over time (Claus and Thomas (2001, )), it is possible to incorporate the term-structure of risk-free rates of return. Another key issue to be considered is data availability and quality. The concept naturally applies only to listed companies covered by financial analysts. The question for covered firms then is how well do the consensus earnings projections reflect the true market expectations of future earnings on which the stock price formation is built. Forecast data used for estimation is based on sell-side, not on buy-side, financial analysts who are actually trading. Both groups of analysts might have different incentives when they form their earnings expectations. Further, it is well documented that analysts earnings forecasts are subject to bias and timeliness problems which might affect the accuracy of cost of capital estimates. 29 While these issues in analyst forecasts are well known, only very recent research has tried to adjust for such biases when estimating implied cost of capital (Guay, Kothari, and Shu (2003)). In Germany, analysts earnings forecasts are formed according to the joint guidelines of the German financial analysts society, Deutsche Vereinigung für Finanzanalyse (DVFA), and the Schmalenbach-Gesellschaft für Betriebswirtschaft (SG). These guidelines are designed 29 Such problems include the optimistic bias of analysts across the financial year (e.g., Brown (1993)), their tendency to be guided by companies towards achievable results at the financial year end (e.g., Matsumoto (2002)), and their sluggishness to react to changes in information in stock prices (e.g., Abarbanell (1991)). For reviews of the financial analyst literature, see, e.g., Kothari (2001); Healy/Palepu (2001). 29

29 H. DASKE/G. GEBHARDT/S. KLEIN to bring about more consistency in earnings forecasts among companies preparing their financial reports according to different sets of accounting standards (HGB, IAS/IFRS or US GAAP)30. How well analysts cope with the more than 100 adjustments proposed under DVFA/SG earnings, and whether the ex-ante clean-surplus requirement of residual income valuation is fully met when analysts prepare forecasts of earnings and book values under DVFA/SG, remains an open question. When we apply the residual income model based estimation procedures across different accounting standards, the effects of different measurement rules should reverse over the full forecast horizon of a firm s lifetime. But, given the multistage forecast procedures based on the next five available earnings forecasts, the effects of accounting rules may not be adequately balanced in the fading or terminal value period, and could lead to an estimation bias. 31 However, it is difficult, if not impossible, to quantify or correct for these effects on real-world companies forecasted earnings and book values of equity. For example, under a conservative accounting regime, due to accelerated depreciation a company may have a depressed book value of equity and earnings in an early stage of its business cycle. However, due to the reversal of these accruals in a later stage of its business cycle, this effect would lead to overstated earnings and book values. Thus, methods I and II implicitly assume that any potential downward (upward) biases of the book value of equity due to conservatism (optimism) will be balanced fully by corresponding higher (lower) analysts earnings projections in the detailed planning period. 4 CONCLUSIONS In this study, we present an alternative, prospective method of estimating investors required rates of return. This concept does not rely on realized returns to estimate a firm s cost of equity capital, but instead depends on market expectations which are reflected in stock price and consensus forecasts of analysts. We present a procedure that allows the estimation of expected cost of equity capital at any date of choice, which is essential for applying the new concepts in practice. Our analysis of the history of expected returns in the period shows that the new estimation procedures based on the residual income model generally have yielded reasonable results in the past. Because the data needed is readily available from the various information sources, the new concept has the potential to complement or even replace methods that use realized returns in the near future. 30 See Busse v. Colbe et al. (2000, 3-5). The option to choose among local (HGB) or International accounting standards (IAS/IFRS or US GAAP) was legalized in 1998 in Germany after the introduction of 292a HGB in German company law. 31 For a theoretical analysis of the effects conservatism on residual income valuation, see Zhang (2000). 30

30 EXPECTED COSTS OF EQUITY CAPITAL REFERENCES Abarbanell, Jeffery S. (1991), Do Analysts Earnings Forecasts Incorporate Information in Prior Stock Price Changes?, Journal of Accounting and Economics 14, Abarbanell, Jeffery S. and Victor L. Bernard (2000), Is the U.S. stock market myopic?, Journal of Accounting Research 38, Aders, Christian and Martin Hebertinger (2003), Value Based Management, Shareholder-Value-Konzepte in Ballwieser, Wolfgang, Peter Wesner, and KPMG (eds.), Shareholder-Value-Konzepte Eine Untersuchung der DAX100-Unternehmen, Frankfurt a. M.: KPMG. Ballwieser, Wolfgang (2002), Der Kalkulationszinsfuß in der Unternehmensbewertung: Komponenten und Ermittlungsprobleme, Die Wirtschaftsprüfung 55, Barth, Mary E., John A. Elliott, and Mark W. Finn (1999), Market Rewards Associated with Patterns of Increasing Earnings, Journal of Accounting Research 37, Brealey, Richard A. and Stewart C. Myers (2003), Principles of Corporate Finance, 7 th international edition, Boston et al.: Mc Graw-Hill. Brown, Lawrence D. (1993), Earnings Forecasting Research: Its Implications for Capital Market Research, International Journal of Forecasting 9, Busse von Colbe, Walther, Winfried Becker, Helmut Berndt, Klaus M. Geiger, Hermann Haase, Friedrich Schellmoser, Günter Schmitt, Thomas Seeberg, and Klaus v. Wysocki (eds.) (2000), Ergebnis je Aktie nach DVFA/SG: Gemeinsame Empfehlung der DVFA und der Schmalenbach-Gesellschaft zur Ermittlung eines von Sondereinflüssen bereinigten Jahresergebnisses je Aktie, 3 rd edition, Stuttgart: Schäffer-Poeschel. Claus, James and Jacob Thomas (2001), Equity Premia as Low as Three Percent? Evidence from Analysts Earnings Forecasts for Domestic and International Stock Markets, Journal of Finance LVI, Coenenberg, Adolf G. (2003), Jahresabschluss und Jahresabschlussanalyse, 19 th edition, Stuttgart: Schäffer-Poeschel. Copeland, Tom, Tim Koller, and Jack Murrin (2000), Valuation Measuring and Managing the Value of Companies, 3 rd edition, New York et al.: John Wiley & Sons. Daske, Holger and Günther Gebhardt (2006), Zukunftsorientierte Bestimmung von Kapitalkosten für die Unternehmensbewertung, in zfbf (forthcoming). DAI-Factbook (2002), Deutsches Aktieninstitut, Frankfurt a. M. DAI. Diamond, Douglas W. and Robert E. Verrecchia (1991), Disclosure, Liquidity, and the Cost of Capital, Journal of Finance XLVI, Drukarczyk, Jochen (2003), Unternehmensbewertung, 4 th edition, München: Vahlen. Easton, Peter (2003), Recent research in accounting and finance that has had, and will have, a significant effect on the practice of valuation, Presentation held at the Amsterdam-Nyrode Accounting Research Workshop Easton, Peter D., Trevor S. Harris, and James A. Ohlson (1992), Aggregate accounting earnings can explain most of security returns, Journal of Accounting and Economics 15, Easton, Peter, Gary Taylor, Pervin Shroff, and Theodore Sougiannis (2002), Using Forecasts of Earnings to Simultaneously Estimate Growth and the Rate of Return on Equity Investment, Journal of Accounting Research 40, Ehrbar, Al (1998), EVA: the real key to creating wealth, New York et al.: John Wiley & Sons. Eller, Roland (2001), Modernes Bondmanagement, 2 nd edition, Wiesbaden: Gabler. Elton, Edwin J. (1999), Expected Return, Realized Return and Asset Pricing Tests, Journal of Finance LIV, Elton, Edwin and Martin Gruber (1995), Modern Portfolio Theory and Investment Analysis, 5 th edition, New York et al.: John Wiley & Sons. Fama, Eugene F. and Kenneth R. French (1992), The Cross-section of Expected Stock Returns, Journal of Finance 47,

31 H. DASKE/G. GEBHARDT/S. KLEIN Fama, Eugene F. and Kenneth R. French (1997), Industry costs of equity, Journal of Financial Economics 43, Fama, Eugene F. and Kenneth R. French (1998), Value versus Growth: International Evidence, Journal of Finance 53, Fama, Eugene F. and Kenneth R. French (2002), The Equity Premium, Journal of Finance LVII, Fama, Eugene F. and Kenneth R. French (2004), The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Perspectives 18, Fama, Eugene F. and James McBeth (1973), Risk, Return, and Equilibrium, Journal of Political Economy 81, Francis, Jennifer, Per Olsson, and Dennis R. Oswald (2000), Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Estimates, Journal of Accounting Research 38, Franke, Günter, Günther Gebhardt, and Jan Pieter Krahnen (eds.) (2002), German Financial Markets and Institutions: Selected Studies, sbr Special Issue Frankel, Richard and Charles M.C. Lee (1998), Accounting valuation, market expectation, and cross-sectional stock returns, Journal of Accounting and Economics 25, Gebhardt, William R., Charles M.C. Lee, and Bhaskaran Swaminathan (2001), Toward an Implied Cost of Capital, Journal of Accounting Research 39, Gode, Dan and Partha Mohanram (2003), Inferring the Cost of Capital Using the Ohlson-Juettner Model, Review of Accounting Studies 8, Gordon, Joseph R. and Myron Gordon (1997), The Finite Horizon Expected Return Model, Financial Analysts Journal May/June 1997, Graham, John R. and Campbell R. Harvey (2001), The theory and practice of corporate finance: evidence from the field, Journal of Financial Economics 60, Guay, Wayne, S.P. Kothari, and Susan Shu (2003), Properties of Implied Cost of Capital Using Analysts Forecasts, Working Paper , July 2003, MIT Sloan School of Management. Gujarati, Damodar N. (2003), Basic Econometrics, 4 th edition, Boston et al.: Mc Graw-Hill. Hail, Luzi (2002), The impact of voluntary corporate disclosures on the ex-ante cost of capital for Swiss firms, European Accounting Review 14, Hail, Luzi and Christian Leuz (2003), International Differences in Cost of Capital: Do Legal Institutions and Security Regulations Matter?, Working Paper, July 2003, University of Pennsylvania. Harter, Winfried, Jörg Franke, Jürgen Hogrefe, and Rolf Seger (1993), Wertpapiere in Theorie und Praxis, 4 th edition, Stuttgart: Deutscher Sparkassenverlag. Healy, Paul M. and Krishna G. Palepu (2001), Information asymmetry, corporate disclosure, and the capital markets: A review of the empirical disclosure literature, Journal of Accounting and Economics 31, Heiden, Stefan (2002), Kursreaktionen auf Dividendenankündigungen, Wiesbaden: Gabler. Kothari, S.P. (2001), Capital Markets Research in Accounting, Journal of Accounting and Economics 31, La Porta, Rafael (1996), Expectations and the Cross-Section of Security Returns, Journal of Finance 51, La Porta, Rafael, Joseph Lakonishok, Andrei Shleifer, and Robert Vishny (1997), Good News for Value Stocks: Further Evidence on Market Efficiency, Journal of Finance 52, Lee, Charles M., James Myers, and Bhaskaran Swaminathan (1999), What is the Intrinsic Value of the Dow?, Journal of Finance LVI, Lücke, Wolfgang (1955), Investitionsrechnungen auf Grundlage von Ausgaben oder Kosten?, Zeitschrift für handelswissenschaftliche Forschung 7, Malkiel, Burton G. (1997), Risk and Return Revisited, Journal of Portfolio Management 23, Matsumoto, Dawn (2002), Management s Incentives to Avoid Negative Earnings Surprises, Accounting Review 77,

32 EXPECTED COSTS OF EQUITY CAPITAL Mehra, Rajnish (2002), The Equity Premium Puzzle, in Pickford, James (eds.), Mastering Investments, 1st editon, London: Financial Times - Prentice Hall. Mehra, Rajnish and Edward Prescott (1985), The Equity Premium A Puzzle, Journal of Monetary Economics 15, Miller, Edward M. (1977), Risk, Uncertainty, and Divergence of Option, Journal of Finance 32, Modigliani, Franco and Merton Miller (1958), The Cost of Capital, Corporation Finance, and the Theory of Investment, American Economic Review XLVIII, Newey, Whitney K. and Kenneth D. West (1987), A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica 55, Penman, Stephen H. (2004), Financial Statement Analysis & Security Valuation, 2 nd edition, Hoboken et al.: John Wiley & Sons. Penman, Stephen H. and Theodore Sougiannis (1998), A Comparison of Dividend, Cash Flow, and Earnings Approaches to Equity Valuation, Contemporary Accounting Research 15, Pratt, Shannon P. (1998), Cost of Capital Estimation and Applications, New York et al.: John Wiley & Sons. Ronen, Joshua and Simcha Sadan (1981), Smoothing Income Numbers, New York et al.: Addison-Wesley. Ross, Stephen A., Randolph W. Westerfield, and Jeffrey F. Jaffe (2002), Corporate Finance, 6 th international edition, Boston et al.: Mc Graw-Hill. Steiner, Manfred and Christian Bruns (2000), Wertpapiermanagement, 7 th edition, Stuttgart: Schäffer-Poeschel. Stulz, René M. (1999), Globalization, corporate finance, and the cost of capital, Journal of Applied Corporate Finance 12, Thomson Financial (2002), Glossary Worldscope. Thomson Financial (2003), Glossary I/B/E/S Summary History Version 2.0. Tversky, Amos, Craig R. Fox (2000), Weighting Risk and Uncertainty, in: Kahneman, Daniel and Amos Tversky (eds.), Choices, values, and frames, Cambridge: Cambridge University Press, Wallmeier, Martin (2004), Residualgewinnmodell und Restwertannahme, Möglichkeiten und Grenzen der Kapitalkostenbestimmung auf der Grundlage von Analystenprognosen, Vortrag auf der 66. Tagung des VHB in Graz, 4. Juni Young, David S. and Stephen F. O Byrne (2001), EVA and value-based management: a practical guide to implementation, New York et al.: Mc Graw-Hill. Zhang, Xiao-Jun (2000), Conservative accounting and equity valuation, Journal of Accounting and Economics 29, APPENDIX APPENDIX A: ESTIMATING THE EXPECTED COST OF EQUITY CAPITAL FOR DAIMLERCHRYSLER ASSUMING LONG-TERM GROWTH This appendix provides as an example the calculation of the expected cost of equity capital and risk premium for DaimlerChrysler (DCX) as of August 7, We obtain key input parameters from last year s annual report as of December 31, 2002; analysts median EPS and DPS forecast for the next four years from Bloomberg; and the target ROE for the automobile industry of 13.5%, which we calculate as the median over the past five years. To compute the expected cost of equity capital, we adjust the implied discount rate in the residual income valuation model until the fundamental price of the model is equal to the current market price. This iteration is done using the MS Excel Solver function. The process yields a current expected cost of equity capital of 12.91%. 33

33 H. DASKE/G. GEBHARDT/S. KLEIN 34

34 EXPECTED COSTS OF EQUITY CAPITAL APPENDIX B: ESTIMATING THE EXPECTED COST OF EQUITY CAPITAL AND LONG-TERM GROWTH SIMULTANEOUSLY IN AN INDUSTRY-PORTFOLIO OF STOCKS This appendix demonstrates the simultaneous estimation of the expected cost of equity capital and the risk premium for the European automobile industry as of August 7, We obtain key input parameters from last year s annual reports, and analysts median EPS and DPS forecast for the next four years from Bloomberg. We estimate the expected cost of equity capital through a linear regression of the ratio of aggregate earnings-to-book value on the ratio of price-to-book value. The process yields a current expected cost of equity capital of 10.92% and a growth in residual income of 3.92%. 35

35 H. DASKE/G. GEBHARDT/S. KLEIN 36

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