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Cost of equity capital, control divergence, and institutions: the international evidence

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Abstract

This study investigates the governance role of a country’s legal and extra-legal institutions in explaining the variations in firms’ cost of equity capital induced by concentrated ownership structures from 21 countries. Using four implied cost of equity proxies, the results show that the large ownership-control divergence of the ultimate owner has a positive and significant impact on the firm’s cost of equity capital. The finding lends support to the entrenchment effect in that the concentrated ownership structure increases the firm’s external financing cost. Further analyses demonstrate that the higher equity cost induced by the ultimate ownership structure is significantly reduced by a country’s stronger legal and extra-legal institutions, highlighting the governance role played by a country’s institutions in reducing the firm’s external financing cost.

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Notes

  1. There is intriguing evidence showing that under certain circumstances, controlling shareholders are willing to expose themselves to greater monitoring through the adoption of self-bonding mechanisms, such as cross-listing in markets with a higher level of legal protection or employing high-quality auditors (Doidge et al. 2004; Fan and Wong 2005; Hail and Leuz 2009). A counter argument, therefore, suggests that controlling owners may be willing to supply greater disclosure and higher-quality information if doing so would be beneficial to them, which eventually translates to lower equity cost.

  2. We identify firm size, the standard deviation of monthly stock returns, the standard deviation of accounting return on total assets, analyst forecast bias, and discretionary accruals as underlying channels through which the concentrated ownership structure affects the cost of equity capital (see Sect. 6.2).

  3. La Porta et al. (1999) is the first and foremost study to investigate ultimate control by tracing the control chains of firms in 27 countries. Claessens et al. (2000) and Faccio and Lang (2002) document evidence on separation of ownership and control for 9 East Asian and 13 Western European countries, respectively. Lins (2003) studies the ultimate ownership structure of firms in 18 emerging markets. Finally, Cronqvist and Nilsson (2003) carry out a detailed analysis on ultimate ownership in Sweden.

  4. Guedhami and Mishra (2009) estimate the cost of equity for a sample of 1,207 firms from 9 Asian and 13 Western European countries in 1996 and find the implied cost of equity is significantly positively associated with the difference between the ultimate controlling shareholder’s control rights and ownership rights. However, as Claessens et al. (2002) suggest, it is critical to control for the cash flow rights in the model to disentangle the incentive alignment effect (a proxy of cash flow rights) and the entrenchment effect (a proxy of the ownership-control divergence) on the external capital cost. In addition, their results based on one year data from 1996 may not be representative.

  5. As an illustration, the excess control is the same for two firms if a firm A’s control and cash flow rights are 30 and 20 percents while a firm B’s are 50 and 40 percents, respectively. However, the divergence measures are 0.33 for the firm A and 0.20 for the firm B as they take into consideration the level of control in a firm.

  6. Hail and Leuz (2009) provide strong evidence that cross-listing on a U.S. stock exchange reduces firms’ cost of equity. The effects are larger for firms with weaker institutional structure as those firms attempt to “opt out” of the home country’s poor institutional framework. Doidge (2004) also confirms that cross-listing in the U.S. enhances the protection afforded to minority investors and reduces the private benefits of control.

  7. Guedhami and Mishra (2009) control for legal institutions in robustness tests by including the four traditional constructs derived from La Porta et al. (1998) and find the implied cost of equity is associated with Rule of Law and Quality of Disclosure Standard significantly negatively, but with Anti-Director Rights (Efficiency of Judicial System) significantly positively (insignificantly). In our study, we focus on the interaction effects between concentrated ownership structure and legal/extra-legal institutions to examine governance roles played by a country’s institutions on the equity costs.

  8. La Porta et al. (2006) provide three possible explanations to their results: (1) legal origin is a proxy for the effectiveness of private contracting as supported by securities laws, (2) investor protection through corporate law still matters but disclosure and liability standards are cleaner measures and (3) corporate and securities laws often rely on similar rules and these rules are essential for private investors to seek remedy for expropriation by corporate insiders.

  9. The index is computed as the arithmetic mean of six sub-indices which measure the strength of affirmative disclosure requirements from six perspectives: (1) prospectus, (2) insider’s compensation, (3) ownership by large shareholders, (4) inside ownership, (5) contracts outside the normal course of business and (6) transactions with related parties. Although prior studies generally support the prediction that disclosures directly influence the cost of equity capital on the firm-level (e.g., Botosan 1997; Botosan and Plumlee 2002; Hail 2002; Easley and O’Hara 2004), DISC_REQ is used as a proxy for investor protection in the country-level.

  10. The index is measured as the average over the disclosure requirement index, the liability standard index and the public enforcement index. In addition to the prospectus disclosure requirements, SEC_REG encompasses the level of burden of proof required by the investors in recovering losses from the issuers, directors, distributors and accountants due to misleading statements in the prospectus as well as the power of the securities market supervisor in issuing rules, investigating violations and giving sanctions.

  11. Prior studies suggest that the models have methodological limitations and suffer from substantial measurement error due to noisy analyst forecasts (e.g., Hail and Leuz 2009; Easton and Monahan 2005; Guay et al. 2005). We gauge the sensitivity of our results to these assumptions and limitations.

  12. For individual cost of capital proxies, N is computed after deleting 1% extreme observations of all firm-level attributes (except for SIZE which uses natural logarithm) and of that particular proxy. This sample size is used in the sensitivity analyses of the main model in testing different equity proxies. Except otherwise stated, all remaining statistics are based on r AVG which has the final sample of 8,868 firm-year observations.

  13. Ireland is excluded in this study due to the problem in downloading the monthly exchange rate which is required to convert the I/B/E/S data from Euro to Irish Punt after Euro adoption in January 1999. For France, Germany, Italy, Switzerland, and United Kingdom, data are as of 1996. For Portugal and Spain, data are as of 1997. For Norway and Sweden, data are as of 1998. Finally, for Australia, Belgium, Finland, and Ireland, data are as of 1999.

  14. In the country-by-country analysis (unreported), DIV and CASH have the correct signs in 14 and 12 countries, respectively. In addition, seven countries have the expected signs for both variables and they include Austria, Malaysia, Norway, Portugal, Sweden, Taiwan, and the United Kingdom. On the contrary, there are two countries (Hong Kong and Korea) with both signs incorrect. Overall, our results are consistent with prior studies that investigate the effects of corporate governance on the cost of debt capital in a cross-country setting. For example, Boubakri and Ghouma (2010) find that the wedge between voting rights and cash flow rights is positively associated with bond yield-spreads and negatively associated with bond ratings.

  15. Hail and Leuz (2009) recently examine the role of institutional characteristics in the cost of capital effects of cross-listing using DISC_REQ as one of the partitioning variables. They find that the decline in cost of equity capital is greater for firms from countries with weaker institutional structures as cross-listings are means to elude the home country’s poor institutional framework. Though the interpretations differ, their results and ours should be in accord as firms with poor investor protection have higher cost of equity capital and the improvements of those firms (that is, the reduction in cost of capital) in migrating from a deficient to an efficient governance system are indeed larger.

  16. In unreported results, significant difference in DIV (at the 5% level) is found between the high and low MKT_COMP sub-samples. Nevertheless, no significant difference in DIV is documented between sub-samples partitioned by other variables.

  17. Nevertheless, the coefficients for INSTITUTION become negative (except for disclosure requirements) when the institutional variables are added without the interaction terms between ownership variables and legal protection variables. The ownership variables remain significant with expected signs.

  18. Again, while MKT_COMP has the opposite sign, the result (unreported) vanishes when the extra-legal institution is added without the interaction terms.

  19. This short-hand valuation is widely used in current finance literature in the international context (e.g., Errunza and Miller 2000; Lombardo and Pagano 2002). Since Bekaert and Harvey (2000) show that dividend yields also reflect differences in growth expectations, the 1-year ahead percentage change in analyst earnings per share forecast (g Forecasts ) is added to control for the variations in earnings growth.

  20. The U.S. one-month Treasury bill rates are the Fama risk free rates taken from the Wharton Research Data Services (WRDS). The global market returns, the global value and growth portfolio returns are downloaded (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data.library.html). Only 15 of the countries in the sample have the value and growth portfolios returns available hence observations of Indonesia, Korea, Portugal, Philippines, Taiwan and Thailand are excluded from this sensitivity analysis. The estimation is based upon the rolling regressions of 60 monthly excess returns (with 36 monthly returns as a minimum) on the global market premium and the value-growth premium as the second explanatory return portfolios since Fama and French (1998) suggest a two-factor intertemporal capital asset pricing model (ICAPM) better explains the value premium in country and global returns than the international capital asset pricing model.

  21. This study mainly uses firm-level estimates of the cost of equity. However, prior studies argue that the firm-specific estimates derived from the valuation models using analysts’ forecasts can be biased and contain substantial measurement errors due to analysts’ optimistic tendency and the assumptions for estimating future growth rates (Easton 2007; Easton and Sommers 2007). For the reason, we additionally estimate cost of equity capital at portfolio-level to avoid bias or measurement errors. In addition, portfolio-level estimation enables researchers to empirically measure long-term growth rates rather than assume the rates (Easton et al. 2002; Easton 2007; Easton and Sommers 2007). At first, we simply estimate portfolio-level cost of equity capital by taking an average of the estimated cost of equity capital by portfolio (Easton 2007). Next, we estimate the following equation to obtain the implied cost of equity capital (r) (Easton et al. 2002; Easton 2007; Easton and Sommers 2007):

    $$ \frac{{eps_{jt + 1} }}{{bps_{jt} }} = \gamma_{0} + \gamma_{1} \frac{{P_{jt} }}{{bps_{jt} }} + \mu_{jt} $$

    where r o = g and r 1 = r − g. As a result of estimating the above regression model for portfolios of stock j = 1, 2, …, J, we get the portfolio-level cost of equity capital (r) and the average rate of change in abnormal growth in earnings (g) simultaneously (Easton and Sommers 2007). Although the results are not tabulated, we find that there is still a significantly positive association between the ownership-control divergence and the cost of equity capital. The authors are indebted to an anonymous referee for the helpful comment on this issue.

  22. Data is taken from the Journal of Financial Economics and is available only for Asian corporations. A firm is classified as an affiliate if it is at least 20 % controlled by the owner of the business group.

  23. On the other hand, the variations in the demand for external capital are expected to have vital impact on the results if the reverse causality in the hypothesis is true. That is, firms with modest capital requirements should be less likely to form groups than those firms with immense capital requirements and facing comparable external financing costs. External Capital Need and Financial Constraint are used to capture the extent to which a firm is financially constrained. Although these tests provide no direct evidence that the reverse causality is invalid, they essentially demonstrate that the inclusion of additional variables do not alter the major findings of this study.

  24. The score is a 90-point index created by rating a company’s annual report for the inclusion or omission of 90 accounting items. CIFAR (1993) reports data for the fiscal year 1991. Data is not available for Hong Kong, Indonesia, Taiwan, Thailand and Switzerland hence only 16 countries are included in this sensitivity. Due to data limitation, the sample in this analysis consists of only 364 firms and just 1,283 firm-year observations. Francis et al. (2005) show that disclosure policies can mitigate information asymmetry and significantly reduce both the cost of debt and equity around the world. Firm-level disclosures are included to test if the original results still hold.

  25. This study matches 13 years of financial data with ownership variables taken from 1996 to 1999 based upon the assumption that ownership structure changes slowly and can reasonably be treated as exogenous in the sample period. To address the possible effects of data misalignment, the sample is split into pre- and post-1996 periods with 1996 data included in both samples as majority of the observations (14 out of 21 countries) are gathered in that particular year. Unreported results show that the phenomenon remains the same in both periods. These results are opposite to the view that ownership structure is endogenous and firms change the ownership structure precisely because of concern over high cost of equity capital. Last of all, untabulated analyses show that the main model remains unchanged when each of the four cost of equity estimates are used instead.

  26. First, we include firm size (SIZE) as it captures a firm’s information environment or asymmetric information (Gebhardt et al. 2001; Gode and Mohanram 2003). Claessens et al. (2000) find that the separation of ownership and control rights is more pronounced in small firms, and thus SIZE is likely to be a channel between the ownership-control divergence and the cost of equity capital. Second, we include stock return volatility (RETVAR), which is widely used as a proxy for firm risk regarding information environment or information uncertainty in prior literature (Core et al. 1999; Gebhardt et al. 2001; Jiang et al. 2005; Hail and Leuz 2006; Zhang 2006). RETVAR can be regarded as a channel because it is related to the ownership-control divergence which aggravates information environment (Malkiel 1997; Gebhardt et al. 2001; Hail and Leuz 2006). Third, we introduce the standard deviation of accounting return on total assets (ROAVAR) to capture firm risk regarding operating performance which is affected by the ownership-control divergence (Beaver et al. 1970; Core et al. 1999; Gebhardt et al. 2001; Gode and Mohanram 2003). We consider ROAVAR to be a channel between the ownership-control divergence and the cost of equity capital. The fourth one is analyst forecast bias (FBIAS) because it is expected to be positively associated with the cost of equity estimates (Hail and Leuz 2006; Barth et al. 1999; Gode and Mohanram 2003). Since the discrepancy (DIV) between voting rights and cash flows rights is expected to induce such information asymmetry in a firm, FBIAS can be a channel through which the ownership-control divergence influences the cost of equity capital. The fifth channel variable that we introduce is the absolute value of discretionary accruals (|DACC|), which are estimated from the performance adjusted modified Jones (1991) model (Kothari et al. 2005). |DACC| represents the degree of managerial discretion in choosing accounting policy and is commonly used as a proxy for information asymmetry or information risk (Haw et al. 2004; Aboody et al. 2005; Francis et al. 2008). Since information asymmetry is expected to increase in discretionary accruals (Aboody et al. 2005) and |DACC| is an increasing function of the divergence between control and cash flow rights (Haw et al. 2004), |DACC| is likely to serve as an important channel through which the ownership-control divergence affects the cost of equity capital.

  27. To obtain discretionary accruals (DACC), we cross-sectionally estimate the following performance adjusted modified Jones (1991) model for a two-digit Standard Industrial Classification (SIC) industry for each sample year across 21 sample countries:

    \( TA_{it} = \beta_{0} + \beta_{1} \left( {1/ASSETS_{it - 1} } \right) + \beta_{2} \left( {\Updelta SALES_{it} - \Updelta AR_{it} } \right) + \beta_{3} PPE_{it} + \beta_{4} ROA_{it} + \varepsilon_{it} , \)where TA it is the change in non-cash current assets minus the change in current liabilities excluding the current portion of long-term debt, minus depreciation and amortization, ASSETS it−1 is lagged total assets, ∆SALES it is change in sales, ∆AR it is change in accounts receivable, PPE it is net property, plant and equipment, and ROA it is return on assets (Haw et al. 2004; Kothari et al. 2005). All the variables in the model are scaled by ASSETS it−1. Following Haw et al. (2004), we assume the industrial characteristics to be homogeneous across the sample countries because some factors that may affect normal accruals vary significantly across industries rather than across countries. On the other hand, ROA it is included in the estimation of discretionary accruals to control for the measurement errors which are correlated with firm performance (Dechow et al. 1995; Kasznik 1999; Kothari et al. 2005). Due to lack of data, we measure 6,370 firm-year observations of the discretionary accruals.

  28. Since our study uses firm risk variables, such as stock return variation (RETVAR) in the main analyses, we introduce firm beta (BETA) only in the sensitivity analyses for several reasons. According to Hail and Leuz (2006), it is necessary to use world market portfolio in estimating BETA if the capital markets are integrated across countries but not easy to choose the appropriate market portfolio. In addition, some prior studies document that future stock returns in emerging markets are often negatively or insignificantly related with beta estimates (Harvey 1995; Erb et al. 1996; Hail and Leuz 2006).

  29. Hail and Leuz (2006) point out that there is some concern about using MTB in the regression analyses of the cost of equity capital because it is not clear how the combinations of the factors such as growth opportunities, accounting conservatism, or perceived risk, represented by MTB, will affect the cost of equity capital (Gode and Mohanram 2003). For this reason, this study controls for MTB in the sensitivity tests rather than in the main analyses. According to prior empirical studies, the cost of equity capital is expected to be negatively associated with MTB (Fama and French 1992, 1993). Due to lack of data, we measure 7,039 and 7,164 firm-year observations of BETA and MTB, respectively.

  30. Although we control for the effects of the indirect channels of the divergence, we should be cautious in interpreting the results because there is no clear and objective way to identify those channels without having a comprehensive theoretical model in literature. Thus, it is unclear whether the positive coefficient on DIV is due to the direct effects of the ownership-control divergence or the effects of omitted unidentified channels in our regression models.

  31. Though +10 months is somewhat arbitrary, Hail and Leuz (2006) show that all analyses remain qualitatively similar when +7 months is used. To adjust for the time misalignment between financial data and forecasts data, Hail and Leuz (2006) discount +10 months price to the beginning of the fiscal year by the inputted cost of capital, that is, (1 + r)−(10/12). The results are virtually indifferent with or without the adjustment.

  32. On January 1, 1999, eleven of the countries in the European Economic and Monetary Union (EMU) decided to give up their own currencies and adopted the Euro currency. Among the Euro-in countries, Austria, Belgium, Finland, France, Germany, Italy, Portugal and Spain are included in the sample. The I/B/E/S data of these 8 countries are in legacy currency before the Euro adoption but are in Euro after the participation. An adjustment is made to correct this currency misalignment by converting the price and earnings forecasts data after January 1999 to the legacy currency based on the monthly exchange rate obtained from I/B/E/S. By performing the currency conversion, all stock price and earnings forecasts have consistent currency over the entire sample period.

  33. As the Indonesian inflation rates of 1992–1996 are missing from Datastream, they are replaced by the data from the Statistical Yearbook 1997.

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Acknowledgments

We appreciate the useful comments and suggestions of C.-F. Lee (Editor), anonymous reviewer, Joseph Fan, Larry Lang, T.J. Wong, and of participants at the 2010 European Accounting Association Annual Conference (Istanbul, Turkey), 2008 National Taiwan University International Conference on Finance (Taipei, Taiwan), and research seminars at the Chinese University of Hong Kong and the University of Macau. Professor Wu gratefully acknowledges the financial support from the Chinese University of Hong Kong through the Direct Allocation Grant (Project ID: 4057004).

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Appendix: Cost of equity models

Appendix: Cost of equity models

1.1 Definitions and model descriptions

Below are the four cost of equity models stated in the form of a pricing equation and the model specific assumptions.

1.1.1 Notation

P t :

Price per share at date t

bv t :

Book value of equity per share at date t

bv t+τ :

Expected book value of equity per share at date t + τ

dps t+τ :

Expected dividend per share at date t + τ

eps t+τ :

Expected earnings per share at date t + τ

g, g st, g lt :

Expected perpetual, short-term and long-term growth rate, respectively

r CT, r GLS, r OJ, r PEG :

Implied cost of equity capital of Claus and Thomas (2001), Gebhardt et al. (2001), Ohlson and Juettner-Nauroth (2005) and Easton (2004), respectively

1.1.2 Claus and Thomas (2001)

$$ P_{t} = bv_{t} + \mathop \sum \limits_{\tau = 1}^{T} \frac{{\left( {eps_{t + \tau } - r_{CT} \cdot bv_{t + \tau - 1} } \right)}}{{\left( {1 + r_{CT} } \right)^{\tau } }} + \frac{{\left( {eps_{t + T} - r_{CT} \cdot bv_{t + T - 1} } \right)\left( {1 + g} \right)}}{{\left( {r_{CT} - g} \right)\left( {1 + r_{CT} } \right)^{T} }} $$

This model is an abnormal earnings model. The pricing equation shows that the current stock price equals the current book value of equity plus the present value of future expected abnormal earnings. Future abnormal earnings are proxies for economic profits and are computed by deducting a charge of equity capital from expected earnings. The model assumes an explicit forecast period of 5 years (T = 5) hence uses a stream of five expected earnings per share forecasts. Beyond year 5, all future earnings are assumed to grow perpetually at g, which is proxied by the country-specific 1-year ahead realized annual inflation rate.

1.1.3 Gebhardt et al. (2001)

$$ P_{t} = bv_{t} + \mathop \sum \limits_{\tau = 1}^{T - 1} \frac{{\left( {eps_{t + \tau } - r_{GLS} \cdot bv_{t + \tau - 1} } \right)}}{{\left( {1 + r_{GLS} } \right)^{\tau } }} + \frac{{\left( {eps_{t + T} - r_{GLS} \cdot bv_{t + T - 1} } \right)}}{{r_{GLS} \left( {1 + r_{GLS} } \right)^{T - 1} }} $$

This model is an abnormal earnings model. The pricing equation shows that the current stock price equals the current book value of equity plus the present value of future expected abnormal earnings. It specifies a forecast period of 12 years (T = 12). It first forecasts earnings explicitly for 3 years and then forecasts implicitly by mean reverting the period t + 3 firm return on equity to the industry-specific median return on equity. The mean reversion attempts to capture the long-term erosion of abnormal earnings over time. It further assumes that any growth in earnings past year 12 is value neutral hence all future abnormal earnings thereafter are assumed to be constant.

1.1.4 Ohlson and Juettner-Nauroth (2005)

$$ P_{t} = \frac{{eps_{t + 1} }}{{r_{OJ} }} \cdot \frac{{\left( {g_{st} + r_{OJ} \cdot dps_{t + 1} /eps_{t + 1} - g_{lt} } \right)}}{{\left( {r_{OJ} - g_{lt} } \right)}} $$

This model relates share price to expected earnings per share 1-year ahead, the expected dividends per share 1-year ahead, the short-term growth and long-term growth in expected earnings and the cost of equity capital. It assumes that the present value of dividends per share affects share price though the dividend policy is irrelevant. Following the approach of Gode and Mohanram (2003), g st is proxied by the average of the growth in expected earnings between period t + 1 and t + 2 and the explicit 5-year growth forecast. The model also assumes positive growth in expected earnings so as to generate a solution. g lt mirrors the growth rate of the overall economy and is proxied by the country-specific 1-year ahead realized annual inflation rate.

1.1.5 Easton (2004)

$$ P_{t} = \frac{{\left( {eps_{t + 2} + r_{PEG} \cdot dps_{t + 1} - eps_{t + 1} } \right)}}{{r_{PEG}^{2} }} $$

This model emphasizes the role of short-term earnings forecasts in valuation. It assumes that price is determined by the abnormal earnings which is the expected earnings per share 2-year ahead plus earnings from re-invested dividends per share 1-year ahead minus the expected earnings per share 1-year ahead. In addition, the model assumes that the abnormal earnings is constant over time and constrains positive growth in expected earnings so as to obtain a solution.

1.2 Estimation procedures

The four models collectively require earnings forecasts of 3 years ahead (eps t+1, eps t+2 and eps t+3) and the expected 5-year earnings growth rate (g 5). All estimates are mean analyst consensus forecasts. Together with stock price (P t ), they are gathered from I/B/E/S using the native currency. To be included in the sample, an observation must have P t , eps t+1 and eps t+2 data and either eps t+3 or g 5. If eps t+3 is missing, it is assumed to be the 2-year ahead earnings forecast growing at the 5-year earnings growth rate, that is, eps t+3 = eps t+2 ×(1 + g 5). Any earnings forecasts beyond year 3 are generalized in the same way. On the other hand, g 5 can be proxied by computing a growth rate between the 2-year ahead and 3-year ahead earnings forecasts, that is, g 5 = (eps t+3eps t+2)/eps t+2. All negative earnings forecasts and growth rates are eliminated.

The financial data in the models are matched with the price and earnings forecasts taken +10 months after the fiscal year end, following Hail and Leuz (2006), to ensure that all financial information are available to investors and can be impounded into the model at the time of cost of equity estimation.Footnote 31 The book value of equity per share (bv t ) is computed as the total common equity divided by the number of common shares outstanding as of the fiscal year end, both of which are taken from Worldscope. Unlike I/B/E/S, Worldscope data applies Euro retroactively. Hence total common equity of the eight Euro-in countries can be extracted using the legacy currency throughout the sample period. Currency consistency is required in the cost of equity estimation as all price and analyst forecasts are either in the native currency or the legacy currency after the currency conversion.Footnote 32 For the expected book value of equity per share (bv t+τ ), clean surplus accounting is assumed, that is, bv t+τ  = bv t+τ1  +  eps t+τ  − dps t+τ . The expected dividend per share (dps t+τ ) is computed as a constant percentage of the expected earnings per share, that is, dps t+τ  = eps t+τ  ×  k t . Dividend payout ratio is obtained directly from Worldscope and k t is defined as the historic 3-year mean dividend payout ratio. If k t is missing or less than zero, it is replaced by the country-year median payout ratio.

Both g and g lt represent the perpetual or long-term growth rate in expected earnings. They are proxied by the country-specific 1-year ahead realized annual inflation rate, which are gathered from Datastream or the Statistical Yearbook.Footnote 33 Any negative inflation rates are substituted by the country-median inflation rates over the entire sample period. The rationale is that deflation is not expected to persist in the long-run, consequently a substitution is necessary.

Except for the Ohlson and Juettner-Nauroth (2005) model, there is no closed form solution provided to the equity valuation models. Each cost of equity proxy is therefore determined by an iterative numerical approximation which identifies an annual firm-specific discount rate that equates P t to the right hand side of the pricing equation. The iteration starts at zero and increments by 0.0001 and will discontinue either when the cost of equity proxy is accurate at two decimal places or when the proxy reaches a value of one. A maximum of one is set in the iteration procedure because any cost of equity estimate that is greater than 100 % seems irrational. To serve as a check over the iteration process, an inputted price is computed by placing the proxy back to the pricing equation and any proxy that results in greater than 1 % difference between P t and the inputted price is eliminated.

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Chu, T., Haw, IM., Lee, B.BH. et al. Cost of equity capital, control divergence, and institutions: the international evidence. Rev Quant Finan Acc 43, 483–527 (2014). https://doi.org/10.1007/s11156-013-0383-7

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