The Role of Private Information Precision In Determining ... - CiteSeerX

The Role of Private Information Precision In Determining Cost of Equity Capital Christine A. Botosan* Associate Professor of Accounting C. Roland Christensen Faculty Fellow Email: [email protected] Marlene A. Plumlee* Assistant Professor of Accounting Email: [email protected] Yuan Xie* Doctoral Student in Accounting Email: [email protected]

*David Eccles School of Business University of Utah Salt Lake City, UT 84112 Current draft: April 2003

The authors gratefully acknowledge the financial support of the David Eccles School of Business and the contribution of I/B/E/S Inc. for providing earnings per share forecast data, available through the Institutional Brokers Estimate System. These data have been provided as part of a broad academic program to encourage earnings expectations research. We also wish to thank David Plumlee for his helpful comments.

Abstract. Studies that examine the association between voluntary public disclosure and cost of equity capital typically conclude that greater voluntary disclosure is associated with a lower cost of equity capital. However, these studies fail to account for the potential affect of enhanced public disclosure on investors’ private information sets and the possible affect of private information on cost of equity capital, which has been suggested in prior theoretical research. In this study, we examine the association between the quality of private information and cost of equity capital (after controlling for market beta, earnings growth, firm size, book-to-price and the quality of public information). We find that (1) cost of equity capital is increasing in the precision of private information and (2) cost of equity capital is decreasing in the precision of public information (after controlling for the precision of private information). We also document that the precision of private and public information are highly correlated, consistent with private and public information precision acting as complements. The association between the precision of private and public information combined with their offsetting effects on cost of equity capital suggest that a manager must consider the relationship between the precision of private and public information when determining her firm’s optimal corporate reporting strategy. In fact, we find no combined net benefit to the average sample firm from greater information precision.

Key Words: Private information, cost of capital, public information, risk. Data Availability: Data are available from public sources.

Prior empirical research that examines the association between voluntary public disclosure and cost of equity capital generally concludes that greater voluntary disclosure is associated with a lower cost of equity capital.1 Based on these findings managers may reasonably infer that, provided production, dissemination, and proprietary costs of disclosure do not outweigh the equity benefit, greater voluntary public disclosure is desirable. However, this ignores the possible impact of enhanced public disclosure on investors’ private information sets and the potential impact of private information on cost of equity capital. Theoretical research suggests that private information may increase, decrease or have no effect on the cost of equity capital but, to date, few empirical studies attempt to investigate this question.2 We examine the association between the quality of private information and cost of equity capital, after controlling for market beta, earnings growth, firm size, book-to-price and the quality of public information. We employ separate empirical proxies for the precision of individual analysts’ private and public information sets, to capture the quality of private and public information, respectively.3 Our proxy for the cost of equity capital is the internal rate of return that equates current stock price to analysts’ forecasts of future dividends and target prices.4 We find that cost of equity capital is increasing in the precision of private information. In addition, consistent with prior research examining the association between voluntary disclosure and cost of equity capital, we document a negative association between cost of equity capital and the precision of public information. Finally, we confirm that our cost of equity capital estimates are increasing in market beta, expected long-term growth in earnings, and book-to-price and decreasing in firm size, as predicted by theory. The positive association between the precision of private information and cost of equity capital we document has implications for managers and academics interested in the impact of corporate financial reporting strategy on cost of equity capital. This is because theory demonstrates and prior empirical

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research concludes that private and public information are not independent.5 Indeed, we document a significant positive correlation between the precision of private and public information, consistent with private and public information precision acting as complements not substitutes. Taken together, these findings are significant for managers. The association between the precision of private and public information combined with their offsetting effects on cost of equity capital implies that a manager must consider the relationship between the precision of private and public information when determining her firm’s optimal corporate reporting strategy. In fact, we document that the magnitude of the reduction in cost of equity capital arising from more precise public information is entirely offset by the magnitude of the increase in cost of equity capital arising from more precise private information. That is, we find no combined net benefit to the average sample firm from greater information precision. Our findings also have implications for academics interested in examining the association between voluntary disclosure and cost of equity capital. Our results indicate that failing to control for private information in an examination of the association between voluntary disclosure and cost of equity capital can lead to a correlated omitted variable specification error. The severity of the correlated omitted variable bias that results is such that one might conclude that voluntary disclosure has a weak or nonexistent role in explaining cross-sectional variation in cost of equity capital when, in fact, this is not the case. The study most related to our research is Easley, Hvidkjaer, and O’Hara (EHO) (2002). EHO examine the association between average realized returns (their proxy for cost of equity capital) and the probability of information-based trading (PIN) (their proxy for private information), after controlling for market beta, firm size and book-to-price. While EHO document a strong positive association between PIN and averaged realized returns, none of the coefficients on their other risk proxies is consistent with expectations, suggesting that their dependent variable may not be a reliable proxy for cost of equity capital. Moreover, EHO do not control for cross-sectional differences in public information in their analysis.

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Our study builds on the EHO study in several respects. First, we employ a proxy for cost of equity capital that, as documented in Botosan and Plumlee (BP) (2003), is robustly and predictably related to risk. BP assess the empirical validity of several alternative methods of estimating cost of equity and conclude that the approach we employ yields estimates whose association with risk measures (market risk, leverage, information risk, firm size, and growth) are consistent with theoretical predictions.6 Although our sample is drawn from a more recent period than the sample examined in BP, we document results consistent with theirs. Second, we examine the association between private information and cost of equity capital after controlling for public information. The remainder of our paper is organized as follows. Section 1 develops our hypotheses with reference to applicable prior research. Our research design and the empirical proxies employed in our analyses are described in Section 2. Section 3 outlines our sample selection procedures and presents descriptive statistics pertaining to our sample. The results of our analyses are found in Section 4, and Section 5 concludes the paper and offers suggestions for future research.

1.

Hypotheses Development and Literature Review Our predictions rest on research from two different streams of literature. The first stream of

literature considers the impact of private information on cost of equity capital. The second considers the association between the quantity and quality of investors’ private and public information sets. These literatures do not always draw a clear distinction between the quantity (or existence) of information and the quality (or precision) of information. Our interest is in the precision of information. However, our discussion of prior research also includes literature that deals explicitly with the quantity or existence of information, as well as literature that makes no clear distinction. In so doing, we assume that theoretical and empirical research examining the quantity of information has implications for the precision of information as well, particularly since empirical studies often measure the quantity of

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information but interpret the result as a proxy for disclosure quality or precision. In addition, in many empirical settings quantity and quality are not separable information attributes. 1.1

Association Between Private Information and Cost of Equity Capital Few studies explicitly model the association between private information and cost of equity capital.

Two exceptions are Wang (1993) and Easley, Hvidkjaer, and O’Hara (EHO) (2002). Wang (1993) concludes that the association between private information and cost of equity capital is indeterminate. In Wang’s model the presence of traders with superior information yields two opposing effects on cost of equity capital. The premium uninformed investors demand to compensate for the risk of trading against an informed trader is mitigated by a reduction in information risk since trading by informed investors makes prices more informative. EHO employ a rational expectations equilibrium asset-pricing example to demonstrate that the existence of private information generates expected excess returns to some assets. In addition, they conclude that when private information is made public excess returns decline. Empirical research examining the association between private information and cost of equity capital is similarly limited in quantity and tends to be indirect in nature. For example, Brennan and Subrahmanyam (1996) and Amihud (2000) examine how the slope of the relationship between trade volume and price changes (a proxy for illiquidity) affects asset returns. Both studies provide evidence consistent with a positive association between cost of equity capital and illiquidity. A direct linkage between the slope variable and private information is not established in the literature, however, leaving the interpretation of these results open to debate. EHO (2002) address this issue by employing a measure from the market microstructure literature intended to capture the probability of information-based trading (PIN). The authors regress PIN, firm size, book-to-price, and market beta on average realized returns. While they document a strong positive association between PIN and averaged realized returns, none of the coefficients on the other risk proxies is consistent with theoretical predictions. Specifically, the coefficient on market beta in EHO’s regression equation is negative or insignificant, depending on the statistical test applied, the coefficient on firm size is positive, and the coefficient on book-to-price is insignificant. In contrast, theory suggests a positive

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coefficient on market beta, a negative coefficient on firm size, and a positive coefficient on book-to-price. The unexpected results EHO document on all the risk proxies they examine except the PIN measure suggests that their dependent variable may not be a reliable proxy for cost of equity capital. In addition, EHO examine the association between private information and cost of equity capital without controlling for the documented association between public information and cost of equity capital. Brown, Finn and Hillegeist (2001) document a negative association between PIN and AIMR disclosure scores. Accordingly, EHO’s analysis may be subject to a correlated omitted variable bias. In summary, neither theoretical nor extant empirical evidence yields a directional prediction regarding the association between the precision of private information and cost of equity capital, although theory suggests the two are related. Accordingly, our first hypothesis states H1: There is an association between the precision of private information and the cost of equity capital. 1.2

Association Between Private and Public Information Existing analytical research supports a variety of conclusions regarding the association between

private and public information. One stream of literature suggests that private and public information are substitutes. For example, Verrecchia (1982) shows that conditionally independent private and public information signals can act as substitutes. Diamond (1985), Bushman (1991), Lundholm (1991), and Alles and Lundholm (1993) extend this finding to other settings. In contrast, another branch of this literature suggests that private and public information are complements. For example, Lundholm (1988) demonstrates that private and public information act as complements when the error in the signals is sufficiently correlated. Kim and Verrecchia (1994) show that if private information usefulness is a function of the public information signal, public disclosure provides a source of private information to traders able to process public information into private information. In addition to the research discussed above, which suggests that the existence of public information may preempt private information acquisition or encourage it, several theoretical studies examine the association between the precision of private and public information. Kim and Verreccchia’s (1991) model

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suggests that more informed investors increase the precision of their private information to a greater extent than less informed investors in response to an increase in the precision of public information, suggesting a complementary effect. McNichols and Trueman (1994) extend this finding to short-horizon investors acquiring private information in anticipation of a public information release. They conclude that in such settings investors are motivated to acquire more precise private information when they anticipate a more precise public information announcement. Clearly the theoretical literature discussed above does not support a directional prediction regarding the association between the quantity and/or precision of investors’ private and public information sets. Existing empirical analysis, which might shed some light on the issue, is characterized by mixed results, however. Consistent with a substitution effect, several studies document reductions in bid-ask spreads coincident with improved disclosure of specific items of information such as oil and gas reserve disclosures (Raman and Tripathy (1993)), segment disclosures (Greenstein and Sami (1994)), and the disclosure of management forecasts (Coller and Yohn (1997)). Welker (1995) finds that firms scoring higher in terms of the disclosure rankings produced by the Association for Investment Management and Research (AIMR) have lower bid-ask spreads. Brown, Finn, and Hillegeist (2001) find that higher AIMR disclosure scores are associated with a lower probability of informed trading. In contrast, evidence presented in other studies suggests the two are complements. Lee, Bucklow, and Ready (1994) document an increase in the bid-ask spread shortly before, after and during earnings announcements. Barron, Byard, and Kim (2002) examine changes in the precision of analysts’ private and public information sets around earnings announcements and find that the precision of private information increases immediately after a public earnings announcement. Venkataraman (2000) examines the effect of a change in segment disclosure requirements on the precision of analysts’ public and private information sets and documents a positive correlation between the change in the precision of private and public information around the adoption of the new disclosure standard.

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As discussed above, existing theory implies an association exists between the precision of private and public information. At the same time, neither theory nor extant empirical evidence supports a hypothesis regarding the direction of the association. Accordingly, our second hypothesis states: H2: There is an association between the precision of private and public information.

2.

Research Design and Empirical Proxies

2.1

Hypothesis Tests and Empirical Model To test our first hypothesis we estimate the following regression equation. We expect the

coefficient on RPRIVATE (γ6) to positive (negative) if cost of equity capital is increasing (decreasing) in the precision of private information. rit = α 0 + γ 1 BETAit + γ 2 GROWit + γ 3 LMKVLit + γ 4 BPit + γ 5 RPUBLICit + γ 6 RPRIVATEit + ε it (1)

Where:

rit = equity risk premium (i.e. cost of equity capital less the risk free rate) for firm i, year t. BETAit = market model beta for firm i, year t. GROWit = expected long-term growth in earnings for firm i, year t. LMKVLit = log of market value of common equity for firm i, year t. BPit = book-to-price for firm i, year t. RPUBLICit = fractional rank of public information precision for firm i, year t. RPRIVATEit = fraction rank of private information precision for firm i, year t.

The procedures we employ in estimating the variables listed above are described in detail below. We include market beta, growth, firm size, book-to-price, and the precision of public information in our model to control for sources of risk that could confound our analysis and to validate our proxy for cost of equity capital. The Capital Asset Pricing Model indicates that cost of equity capital is increasing in market beta.7 Accordingly, we expect the coefficient on BETA to be significantly positive. Beaver, Kettler and Scholes (1970) argue that abnormal earnings streams derived from growth opportunities are more risky because they are subject to erosion as competition enters the market. This suggests a positive association between expected long-term earnings growth and cost of equity capital. Berk (1995) argues that, unless the empirical model for expected returns includes all risk factors, a negative association

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between firm size and expected returns should be observed as market value is inversely associated with risk in general. Accordingly, we expect the coefficient on firm size (measured by the market value of equity) to be negative. Moreover, Berk (1995) argues that book-to-price inversely proxies for firm size and, consequently, we expect the coefficient on BP to be positive. Finally, a relatively large body of research suggests that greater public disclosure is associated with a lower cost of equity capital through greater liquidity or reduced estimation risk.8 Thus, we expect the coefficient on RPUBLIC to be negative. To test our second hypothesis we examine the correlation between our measures of the precision of public information (RPUBLIC) and the precision of private information (RPRIVATE). If the precision of public information acts as a substitute (complement) for the precision of private information, we expect to observe a negative (positive) correlation between RPUBLIC and RPRIVATE. 2.2

Empirical Proxies

2.2.1

Cost of Equity Capital (rDIVPREM) The dependent variable in regression equation (1) is the expected risk premium, or cost of equity

capital net of the risk free rate of interest. Following Botosan and Plumlee (BP) (2002 and 2003) we estimate the expected risk premium via the target price method. This method employs the short-horizon form of the dividend discount formula given in equation (2). In this form of the dividend discount formula, the infinite series of future cash flows is truncated at the end of year 5 by a forecasted terminal value. 5

P0 = ∑ ( 1 + rDIV )−t E0 [ d t ] + ( 1 + rDIV )−5 E0 (P5 )

(2)

t =1

Where: Pt rDIV

= price at time t=0 or t=5. = estimated cost of equity capital. E0 (o ) = the expectations operator.

dt

= dividends per share, t=1 to 5.

The data and procedures we employ in estimating rDIV mirror those employed by BP. Dividend forecasts for the current fiscal year (i.e., t=1), the following fiscal year (i.e., t=2), the long run (i.e., t=5), and maximum and minimum long-run target price estimates are collected from forecasts published by

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Value Line during the third quarter of the calendar year. These data are collected from the Value Line database available in machine-readable form.

Value Line does not provide dividend forecasts for years 3 and 4. Accordingly, we assume a straight-line rate of growth in dividends from year 2 to year 5, and interpolate between these years to generate dividend forecasts for years 3 and 4. Forecasted target price is the 25th percentile of Value Line’s forecasted long-run price range.9 Current stock price (P0) equals the stock price reported on CRSP on the

Value Line publication date or closest date thereafter within 3 days of publication. We use the values for P0, E0[P5] and the E0[dt]’s (t=1 to 5) in a numerical approximation program to identify the annual firm-specific rDIV that equates the right and left-hand sides of the equation to within a $0.005 difference between the actual- and fitted-value of P0. rDIVPREM equals rDIV less the risk free rate of interest.10 The 5-year Treasury Constant Maturity Rate as of the end of the month in which the expected cost of equity capital estimates are determined is employed for the risk free rate of interest. The primary assumption underlying the target price method of estimating cost of equity capital is that analysts’ forecasts of future dividends and target prices accord with those of market participants. To the extent this assumption is violated, the link between current stock price and analysts’ forecasts of future cash flows is shaken and the link between the resulting estimates of cost of equity capital and the underlying construct is weakened, mitigating against finding results.

2.2.2

Market Beta (BETA) Market beta is estimated using the market model with a minimum of 30 out of 60 monthly returns

and a market index return equal to the value weighted NYSE/AMEX return. We obtain the data to estimate BETA from CRSP. The estimation period for BETA ends on June 30th of the year rDIVPREM is estimated.

2.2.3

Long-term Growth in Earnings (GROW) Our estimate of long-term growth in earnings is the 3-5 year annual rate of change in expected

earnings included in the Value Line database.

2.2.4

Firm Size (LMKVL)

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Our proxy for firm size is the market value of equity. We estimate market value of equity by multiplying the number of common shares outstanding by stock price at the quarter-end immediately prior to June 30th of the year rDIVPREM is estimated. We draw these data from the quarterly Compustat tape. If these data are unavailable, we substitute the market value of the firm reported on CRSP as of June 30th of the Value Line publication year. Market value of equity is stated in millions of dollars. We use a natural log transformation of the data to mitigate skewness in the distribution of market value of equity.

2.2.3

Book-to-Price (BP) We compute book-to-price by scaling the common equity of the firm by the market value of equity.

Both the numerator and the denominator of the ratio are measured at the quarter-end immediately prior to June 30th of the year rDIVPREM is estimated. We collect these data from the quarterly Compustat tape. If these data are unavailable, we substitute data for the fiscal year-end immediately prior to June 30th of the year rDIVPREM is estimated. These data are collected from the annual Compustat tape.

2.2.4

Precision of Public Information (RPUBLIC) and Private Information (RPRIVATE) Our proxies for the precision of public and private information, which capture the precision of

analysts’ public and private information sets, are drawn from Barron, Kim, Lim, and Stevens (BKLS) (1998). Accordingly, we draw inferences about the characteristics of investors’ information sets by focusing on financial analysts. If the characteristics of analysts’ information sets differ from those of investors our proxies represent a noisy measure of the underlying construct we seek to capture. While this measurement error may mitigate against finding results, we do not expect it to induce bias. BKLS assume the following: (1) analysts observe a signal common to all analysts (i.e. the public signal); (2) each analyst also observes a signal unique to the individual analyst (i.e. the private signal); (3) analysts’ forecasts of earnings are unbiased and are based only on their public and private signals; and (4) the precision of private information is similar across analysts. Barron, Byard and Kim (2002) conduct extensive analyses to investigate the sensitivity of their results to violations of these assumptions with no impact on their conclusions. Venkataraman (2000) conducts similar analyses, also with no impact on his conclusions. Moreover, the measures developed by

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BKLS are employed in a number of prior empirical studies including Barron, Kile, and O’Keefe (1999), Venkataraman (2000), Botosan and Harris (2000), Barron, Byard, and Kim (2001), Byard (2001), and Byard and Shaw (2002). Accordingly, we believe that the assumptions described above are sufficiently descriptive to render the BKLS measures useful in empirical research. BKLS demonstrate that, given their assumptions, observable attributes of analysts’ forecasts can be employed to estimate the precision of the analysts’ public and private information sets. Equation (3) below is the BKLS formula for the precision of analysts’ public information and equation (4) is the BKLS formula for the precision of analysts’ private information.

D   SE −  N  PUBLIC = 2   D  SE − N  + D     PRIVATE =

Where:

(3)

D   D  SE − N  + D    

(4)

2

SE = expected squared error in the mean forecast.

= (Fit − Ait )

2

D = expected forecast dispersion. 2

=

1 N ∑ (Fit − Fijt ) N − 1 i =1

N = number of forecasts. Fit = mean forecast for firm i, quarter t. Ait = actual earnings for firm i, quarter t. Fijt = analyst j’s forecast of earnings for firm i, quarter t. We estimate SE, D, and N using analysts’ most recent one-quarter-ahead forecasts of quarterly earnings. Forecast and actual earnings data are collected from IBES. A minimum of three individual analysts must provide forecasts of earnings for a given firm-quarter for that firm-quarter to be included in our sample. Quarterly values of PUBLIC and PRIVATE are averaged across the four quarters preceding the third quarter of the calendar year rDIVPREM is estimated to obtain an average level of precision of public

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and private information for the firm during the year. Since PUBLIC and PRIVATE are, in theory, the inverse of the variance of analysts’ public and private information signals, non-negative values of PUBLIC and PRIVATE are not well-defined. Accordingly we limit our analyses to non-negative values of PUBLIC and PRIVATE. Prior research shows and our empirical analysis confirms that PUBLIC and PRIVATE are highly skewed. Accordingly, we employ the within year fractional rank of PUBLIC (denoted RPUBLIC) and the fractional rank of PRIVATE (denoted RPRIVATE) in our analyses. Our primary analysis focuses on PRIVATE. However, BKLS discuss how the PRIVATE and PUBLIC measures can be combined to create a measure referred to as consensus (CONSENSUS). We employ CONSENSUS in supplementary analysis of the relative association between private and public information precision and cost of equity capital. CONSENSUS is computed by taking the ratio of common precision to total precision (see equation (5) below). CONSENSUS it =

PUBLICit PUBLICit + PRIVATEit

(5)

Finally, we construct a variable intended to capture the extent to which the precision of private information exceeds the precision of public information for a given firm in a given year. This variable, denoted RDIFF, is computed by taking the difference between a given firm’s rank of PRIVATE and its rank of PUBLIC (see equation (6) below). RDIFFit = RPRIVATEit − RPUBLICit

(6)

3.

Sample Selection and Descriptive Statistics

3.1

Sample Selection

A total of 3,718 firm-year observations from 1993 through 2001 are included in our analysis. Observations are included in our sample if there is sufficient data from Value Line, IBES, Compustat and

CRSP to estimate the variables described above. The number of observations varies year-by-year and

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increases across time. 1993 contributes the fewest number of observations to the sample (143) and 2000 contributes the most (619). 3.2

Descriptive Statistics

Table 1 provides descriptive statistics pertaining to our cost of capital estimates and independent variables. We compute our descriptive statistics using all observations in our sample pooled across the years 1993-2001. The mean (median) value of our estimate of the risk premium (rDIVPREM) is 5.6% (4.3%). In comparison, Botosan and Plumlee (2003) employ a sample spanning the years 1983 through 1993 and estimate a mean (median) value for rDIVPREM of 6.4% (5.7%). Mean (median) BETA for our sample is approximately 1.07 (1.01). These data indicate that our average sample firm is relatively risky, whereas our median sample firm presents a level of market risk similar to that of the market portfolio. Mean (median) expected long-term growth in earnings (GROW) is 17.1% (14.5%). These growth statistics are similar, albeit higher, than the 15.1% mean and 13.7% median long-term growth in IBES earnings documented by Gode and Mohanram (2002) for an earlier time period. Mean MKVL is $8225.7 million; the median is $2286.0 million, which indicates a sample populated by relatively large firms and a skewed distribution. Mean (median) book-to-price (BP) equals 0.45 (0.39). This indicates that firms trading at a substantial premium above book value characterize our sample. In absolute terms, PUBLIC and PRIVATE do not lend themselves to meaningful interpretation. However, consistent with prior research (e.g., Barron, Byard, and Kim (BBK) (2002)) the distribution of PUBLIC and PRIVATE are highly skewed with large standard deviations. The magnitude of PUBLIC and PRIVATE may not be directly comparable between studies, however. This is because prior research generally scales SE and D by the absolute value of actual EPS (or by stock price at the beginning of the year) before using the data in the computation of precision. We use unscaled SE and D in our computations for two reasons. First, the BKLS model makes no provision for scaling SE and D. Second, prior empirical research that scales SE and D concludes that using unscaled SE and D in the computations produces consistent results (BBK (2002)).

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In contrast, CONSENSUS is amenable to interpretation and comparison across studies. Our descriptive statistics indicate that, on average, the precision of public information accounts for approximately 62% of total precision. For our median firm the relevant statistic is 68%. Relative to the statistics presented by BBK, our mean value is very close to the value of 63%, whereas our median value is less than BBK’s median of 83.3% RDIFF is computed for each firm-year by taking the rank of private precision (RPRIVATE) and deducting the rank of public precision (RPUBLIC). The mean value of the difference in ranks is zero. The median value is –0.005, indicating a slightly higher precision of public information relative to private information precision at the median.

Insert Table 1 here.

4.

Empirical Results

4.1

Rank Correlation Among Risk Premium and Independent Variables

Table 2 presents correlation statistics among our estimates of the risk premium and our independent variables. To mitigate the impact of outlying observations we examine the Spearman correlation coefficients. The values reported in Table 2 represent the average across the nine years included in our sample of the year-by-year correlation coefficients. The values reported in parentheses are the number of years, out of the nine sample years, that the correlation between the variables is significantly positive/negative. Table 2 documents a positive correlation between rDIVPREM and BETA, GROW, and BP and a negative correlation with LMKVL and RPUBLIC. These results are consistent with cost of equity capital increasing in market beta, expected long-term growth in earnings and book-to-price and decreasing in firm size and the precision of public information. In each case the year-by-year correlations are statistically significant in the anticipated direction in the majority of years. The correlation between rDIVPREM and RPRIVATE is not statistically significant. However, RPRIVATE is highly correlated with 15

firm size, book-to-price, and RPUBLIC highlighting the need to examine our first hypothesis in a multivariate setting. The mean of the year-by-year correlation coefficients between rDIVPREM and CONSENSUS is -0.075 and are significantly negative in four of nine years. This provides some evidence that, as the precision of public information accounts for a greater proportion of total precision, cost of equity capital declines. The correlation between rDIVPREM and RDIFF is significantly positive in six of the nine years included in our sample period. This suggests that when the precision of private information exceeds the precision of public information by a larger amount cost of equity capital is higher. We test hypothesis two by examining the correlation between RPUBLIC and RPRIVATE. If the precisions of public and private information are substitutes (complements) the correlation between these two variables will be negative (positive). We document a strong positive correlation between RPUBLIC and RPRIVATE. The correlation coefficient is 0.765, and is significantly positive in each of the nine years we examine. Accordingly, we conclude that the precision of public information and the precision of private information are complements. As noted earlier, this finding is consistent with conclusions drawn by Lee et al. (1994), Barron, Byard and Kim (2002) and Venkataraman (2000). In summary these results provide support for the following conclusions. First, rDIVPREM performs well in capturing cross-sectional variation in risk. Second, there is little evidence in support of our first hypotheses. However, given the strong correlation between RPRIVATE and several of our control variables it is important to examine the association between RPRIVATE and cost of equity capital in a multivariate setting. Finally, the precisions of public and private information act as complements, not substitutes.

Insert Table 2 here. 4.2

Regression of rDIVPREM Estimates on BETA, GROW, LMKVL, and BP

To provide additional evidence regarding the validity of rDIVPREM prior to proceeding with our hypothesis test of H1, we estimate a regression model that limits the explanatory variables to the risk

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proxies included in our analysis as control variables except that we do not include RPUBLIC in the analysis at this point, due to the high correlation between RPRIVATE and RPUBLIC. The parameter values reported in Table 3 are the average parameter values from year-by-year regressions with Fama-MacBeth t-statistics shown in parentheses. The association between cost of equity capital and each of market beta, earnings growth, firm size and book-to-price is highly significant and consistent with the relationship predicted by theory. These findings agree with those of Botosan and Plumlee (2003) in their analysis of alternative methods of estimating cost of equity capital. Accordingly, we conclude that rDIVPREM is a reliable estimate of the cost of equity capital.


Regression of rDIVPREM Estimates on Control Variables and Information Precision

Table 4 presents the results of estimating regression equation (1). The parameter values reported in the table are the average parameter values from year-by-year regressions with Fama-MacBeth t-statistics shown in parentheses. The results indicate that the association between rDIVPREM and the control variables is unaffected by the addition of RPUBLIC and RPRIVATE to the model. The average coefficient on RPUBLIC is –0.020, statistically significant at a 1% level, which is consistent with prior research that documents a negative association between disclosure and cost of equity capital. The average coefficient on RPRIVATE is 0.025, also statistically significant at a 1% level. This provides support for our first hypothesis. The sign of the coefficient implies that greater precision of private information is associated with a higher cost of equity capital. In supplementary analysis not reported in Table 4 we conduct an F-test to determine if γ6 + γ5 = 0. The purpose of this test is to determine, on average, the magnitude of the combined effect on cost of equity capital of greater precision in public and private information. The test fails to reject the null hypothesis that the coefficients are equal. Accordingly, we conclude that on average, the two effects offset one another.

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To highlight the importance of adequately controlling for both public and private precision of information when examining the association between disclosure quality and cost of equity capital we estimate reduced forms of regression equation (1) in which RPUBLIC and RPRIVATE are included separately in the analysis. The results are much weaker in both alternative specifications. The second model, which incorporates RPUBLIC but not RPRIVATE, provides no support for the hypothesis that cost of equity capital and the precision of public information are related. The results of the third model, which includes RPRIVATE but not RPUBLIC, suggests a positive association between the precision of private information and cost of equity capital, although the results are weaker than those documented in the first model. The strong positive correlation between RPUBLIC and RPRIVATE combined with the opposing and yet significant associations between cost of equity capital and RPUBLIC and RPRIVATE results in a severe correlated omitted variables bias in the latter two models. Consequently, erroneous conclusions could result if researchers fail to control for public (private) information when assessing the association between private (public) information and the cost of equity capital.

4.3.1 Econometric Issues As documented in Table 2 the correlation between RPUBLIC and RPRIVATE is high at 0.765. This raises the concern that multicollinearity may be an issue in our regression analysis. To address this issue we examine condition indices and find that the magnitude of the condition indices indicates the presence of multicollinearity arising from the correlation between RPUBPLIC and RPRIVATE variables. As discussed in Kennedy (1998), in the presence of multicollinearity, the OLS estimator is still the best linear unbiased estimate of the parameter and the R2 of the model is unaffected. The primary undesirable consequence of multicollinearity is a loss of statistical power since in the presence of multicollinearity the variances of the afflicted parameter estimates are large. This makes it more difficult to reject the null hypothesis. The variances are large because the OLS procedure uses only variation unique to RPUBLIC in calculating the OLS estimate of the coefficient on RPUBLIC and uses only

18

variation unique to RPRIVATE in calculating the OLS estimate of the coefficient on RPRIVATE. The variation common to RPUBLIC and RPRIVATE is ignored, except in computing the R2. The impact is as if the regression equation is estimated with a small sample size. Both Kennedy (1998) and Fox (1997) state that the practical implications of collinearity are not obvious. Fox states (pg. 338), “The standard errors of the regression estimates are the bottom line: If these estimates are sufficiently precise, then the degree of collinearity is irrelevant; if the estimates are insufficiently precise, then knowing that the culprit is collinearity is of use only if the study can be redesigned to decrease the correlations among the X’s.” Kennedy concurs citing the rule of thumb – don’t worry about multicollinearity if the t-statistics are all greater than 2. Our t-statistics are generally greater than 2.0 in our year-by-year regressions and in a regression employing all of our data pooled across time. Kennedy (1998) also discusses the option of dropping a variable as we have done in estimating the reduced forms of our regression equation. However, Kennedy cautions against this move because if the true coefficient of the dropped variable is not zero, eliminating the variable from the model creates a correlated omitted variable specification error. Indeed Dreze (1983, pg. 296) states, “setting a coefficient equal to zero because it is estimated with poor precision amounts to elevating ignorance to arrogance.” Accordingly, while we recognize that collinearity exists in our data we conclude that the existence of collinearity does not have practical implications in our setting for two reasons. First, collinearity is hypothesized to exist based on the theoretical research that underlies hypothesis one. Accordingly, knowing that collinearity is present is of little use since the ability to redesign the study to decrease the correlation between RPUBLIC and RPRIVATE is limited by the theoretical existence of a relationship between the two. Second, even in the presence of collinearity, our results are highly statistically significant, indicating that the estimates are sufficiently precise to support the conclusions we draw. Our primary results are based on estimating regression equation (1) year-by-year. The coefficients reported in our tables are the mean values of the coefficients across the nine years of our sample. We compute our t-statistics based on the mean and standard error of the year-by-year coefficients (Fama and MacBeth (1973)). This procedure is employed to mitigate the potential effect of cross-sectional

19

correlation on our test statistics, since the presence of cross-sectional correlation in known to inflate tstatistics obtained from when the regression is estimated with data pooled across years. At the same time, this approach places stringent demands on our data, since only nine years of data are available to estimate the mean value and standard error of the annual parameter estimates. Even so, our results are highly statistically significant. Finally, we check for the presence of influential data points in our regression analysis using Cook’s D statistic. One influential data point is detected and is eliminated from all analyses. After eliminating this data point, no further influential data points are identified by Cook’s D.


Supplementary Analyses

To provide evidence pertaining to the association between the relative impact of public and private information precision on cost of equity capital, we estimate two alternative specifications of regression equation (1) that employ variables derived from linear combinations of the PUBLIC and PRIVATE variables. Since the theoretical research we rely upon in the development of our hypotheses do not speak to the association between variables defined by linear combinations of public and private information precision, we do not specify the expected sign of the coefficients on these variables, and we conduct two-tailed tests of statistical significance. The first model we present in Table 5 replaces RPUBLIC and RPRIVATE with CONSENSUS, defined as the precision of public information relative to total precision. Our results indicate that the larger the proportion of total precision attributable to public precision, the lower the cost of equity capital. (The mean coefficient on CONSENSUS is –0.016 and is significant at a 1% level.) The second model we present in Table 5 replaces RPUBLIC and RPRIVATE with RDIFF. RDIFF is the difference between the rank of private precision (RPRIVATE) and the rank of public precision (RPUBLIC). We find that the coefficient on RDIFF is positive and significant at a significance level of 1%. This result suggests that when the precision of private information exceeds the precision of public information, cost of equity capital is higher.

20

Insert Table 5 here.

5.

Conclusion and Suggestions for Future Research

Using separate empirical proxies for the precision of individual analysts’ public and private information sets and a proxy for cost of equity capital shown to be related to risk, we examine the association between the precision of private information and cost of equity capital. We find that cost of equity capital is increasing in the precision of private information. We also find that the precisions of public and private information are strongly positively correlated, suggesting that they act as complements. Finally, we demonstrate the importance of including both measures of precision in an analysis of the association between information precision and cost of equity capital. The results we present have implications for individuals in the business community concerned with the design of optimal corporate reporting strategies. The positive correlation between the precisions of public and private information combined with the offsetting effect of each on cost of equity capital, illustrates the interdependency of managers’ corporate reporting choices. The interdependency of these choices significantly increases the complexity of identifying an optimal corporate reporting strategy. On the one hand, increasing the precision of the public information produced by a firm may benefit the firm by reducing its cost of equity capital. On the other hand, an increase in the precision of public information may lead to an increase in the precision of private information, which has a detrimental effect on cost of equity capital. Accordingly, managers cannot make decisions regarding their optimal corporate reporting strategy without considering the implications of their public reporting choices for investors’ private information sets. This result echoes the conclusion in Botosan and Plumlee (2002) that public disclosure could have unintended consequences that lead to an increase in cost of equity capital the impact of which may or may not be offset by the reduction in cost of equity capital enjoyed via public disclosure. Our results also have implications for academicians interested in empirically testing the association between voluntary disclosure and cost of equity capital. Our results demonstrate that the high correlation between public and private information combined with the significant role both metrics play in explaining

21

cross-section variation in cost of equity capital induces a correlated omitted variable bias when the role of public (private) information is examined in the absence of a control for private (public) information. The severity of the correlated omitted variable bias is such that one might erroneously conclude that public (or private) information has only a weak or nonexistent role in explaining cross-sectional variation in cost of equity capital. Our results indicate that the effect of greater precision of public and private information on cost of equity capital are offsetting, for the average firm included in our sample. Future research could be undertaken to determine whether the magnitude of the combined effect on cost of equity capital of greater precision in public and private information is positive (or negative) for certain types of firms. A model developed by Zhang (2001) may provide the theoretical basis for such a study. Zhang (2001) develops a model in which the amount of public and private information produced is determined endogenously. Unique to Zhang’s model is the conclusion that in the cross-section, cost of equity capital could be positively or negatively related to the level of public and/or private information. In Zhang’s model the direction of the association is conditional on firm characteristics including earnings volatility, variability of liquidity shocks facing investors, the cost of producing private information, and the cost of disclosure to the firm. Future research could examine the extent to which the Zhang’s model is descriptive by investigating samples constructed to ensure certain pre-identified firm characteristics dominate the sample. The results of such a study could aid managers in identifying optimal corporate reporting strategies by providing them with a better understanding of the implications for their firm of the interdependency of public and private information precision.

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Table 1. Descriptive statistics pertaining to estimated risk premium and independent variables for the sample of 3,718 firm/year observations with sufficient data to compute all variables listed. Variableb rDIVPREM BETA GROW MKVL BP PUBLIC PRIVATE CONSENSUS RDIFF a

Mean 0.056 1.068 0.171 8225.7 0.448 21301.5 28207.8 0.622 0.00

q1 0.009 0.723 0.110 904.5 0.247 547.9 139.7 0.375 -0.118

Median 0.043 1.009 0.145 2286.02 0.388 2728.2 1336.4 0.680 -0.005

q3 0.087 1.332 0.200 6016.8 0.576 11128.8 10540.9 0.898 0.111

Std. Dev. 0.068 0.523 0.114 24839.7 0.334 105510.2 163378.8 0.294 0.202

The sample consists of 3,718 firm/year observations from 1993-2001. rDIVPREM= the estimated risk premium based on the target price method (BP 2003). BETA = capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW = Value Line forecasts of long-range (3-5 year) earnings growth. MKVL = the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP = book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. PUBLIC = the precision of analysts’ public information set, based on the BKLS method. PRIVATE = the precision of analysts’ private information set, based on the BKLS method. CONSENSUS = PUBLIC/ (PUBLIC+PRIVATE). RDIFF = RPRIVATE - RPUBLIC. b

23

Table 2. Rank correlations among risk premium and the independent variables. a

Variableb BETA

rDIVPREM 0.158 (5/0)

BETA 1.000

GROW

GROW

0.151 (6/1)

0.285 (9/0)

1.000

LMKVL

-0.248 (0/8)

-0.002 (3/0)

-0.038 (1/1)

1.000

BP

0.248 (7/0)

-0.037 (0/4)

-0.128 (0/9)

-0.416 (0/9)

1.000

RPUBLIC

-0.105 (0/5)

0.079 (5/0)

0.024 (4/0)

0.270 (9/0)

-0.381 (0/9)

1.000

RPRIVATE

-0.027 (0/0)

0.052 (3/0)

-0.022 (1/0)

0.212 (9/0)

-0.256 (0/9)

0.765 (9/0)

1.000

CONSENSUS

-0.075 (0/4)

-0.003 (1/0)

0.039 (2/0)

-0.015 (0/1)

-0.030 (0/3)

-0.071 (0/6)

-0.654 (0/9)

1.000

RDIFF

0.112 (6/0)

-0.038 (1/1)

-0.065 (0/4)

-0.083 (0/5)

0.183 (8/0)

-0.341 (0/9)

0.343 (9/0)

-0.851 (0/9)

LMKVL

BP

a

RPUBLIC

RPRIVATE

CONSENSUS

Above are the means of annual Spearman correlation coefficients from 1993-2001. The sample contains 3,718 firm/year observations from 1993-2001. The numbers in parentheses are the number of years (out of nine) that the annual correlation coefficient is significantly positive/negative. b rDIVPREM= the estimated risk premium based on the target price method (BP 2003). BETA = capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW = Value Line forecasts of long-range (3-5 year) earnings growth. MKVL = the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP = book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. PUBLIC = the precision of analysts’ public information set, based on the BKLS method. PRIVATE = the precision of analysts’ private information set, based on the BKLS method. CONSENSUS = PUBLIC/ (PUBLIC+PRIVATE). RDIFF = RPRIVATE - RPUBLIC.

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Table 3. Summary of nine annual cross-sectional regressions from 1993-2001.a Model: rDIVPREM it = γ 0 + γ 1 BETAit + γ 2 GROWit + γ 3 LMKVLit + γ 4 BPit + ε it b BETA (+)

GROW (+)

LMKVL (-)

BP (+)

Avg. Adj. R2

Prediction

Intercept (?)

Coefficient (t-statistic)

0.067 (4.16) **

0.016 (5.76)**

0.075 (4.24)**

-0.007 (-4.03)**

0.040 (5.32)**

15.4 %

* Significant at 5%, ** Significant at 1%. T-tests are one-tailed when a directional prediction is made and two-tailed otherwise. a Table values are mean parameter estimates from nine year-by-year regressions. Fama-MacBeth t-statistics in parentheses. The sample contains 3,718 firm/year observations, ranging from 142 firms in 1993 to 619 firms in 2000. b rDIVPREM= the estimated risk premium based on the target price method (BP 2003). BETA = capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW = Value Line forecasts of long-range (3-5 year) earnings growth. MKVL = the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP = book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated.

25

Table 4. Summary of nine annual cross-sectional regressions from 1993-2001.a Model: rDIVPREM it = γ 0 + γ 1 BETAit + γ 2 GROWit + γ 3 LMKVLit + γ 4 BPit + γ 5 RPUBLICit + γ 6 RPRIVATEit + ε it b Intercept

BETA

GROW

LMKVL

BP

RPUBLIC

RPRIVATE

Prediction

(?)

(+)

(+)

(-)

(+)

(-)

(?)


0.063 (4.28)**

0.016 (5.77)**

0.078 (4.76)**

-0.007 (-4.12)**

0.039 (5.23)**

-0.020 (-3.88)**

0.025 (4.30)**


0.066 (6.15)**

0.016 (5.88)**

0.075 (4.24)**

-0.007 (-4.00)**

0.040 (5.19)**

-0.000 (-0.118)


0.062 (4.18)**

0.016 (5.60)**

0.077 (4.56)**

-0.007 (-4.15)**

0.042 (5.80)**

Avg. Adj. R2 15.7%

15.3%

0.011 (2.56)*

15.5%

* Significant at 5%, ** Significant at 1%. T-tests are one-tailed when a directional prediction is made and two-tailed otherwise. a Table values are mean parameter estimates from nine year-by-year regressions. Fama-MacBeth t-statistics in parentheses. The sample contains 3,718 firm/year observations, ranging from 142 firms in 1993 to 619 firms in 2000. b rDIVPREM= the estimated risk premium based on the target price method (BP 2003). BETA = capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW = Value Line forecasts of long-range (3-5 year) earnings growth. MKVL = the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP = book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. PUBLIC = the precision of analysts’ public information set, based on the BKLS method. PRIVATE = the precision of analysts’ private information set, based on the BKLS method.

26

Table 5. Summary of nine annual cross-sectional regressions from 1993-2001.a Model: rDIVPREM it = γ 0 + γ 1 BETAit + γ 2GROWit + γ 3 LMKVLit + γ 4 BPit + γ CONSENSUS( or RDIFF )it + ε it b 5

Intercept

BETA

GROW

LMKVL

BP

CONSENSUS

RDIFF

Prediction

(?)

(+)

(+)

(-)

(+)

(?)

(?)


0.077 (4.39)**

0.016 (5.59)**

0.078 (4.73)**

-0.007 (-4.15)**

0.040 (5.39)**

-0.016 (-3.98)**


0.066 (4.35)**

0.016 (5.77)**

0.078 (4.66)**

-0.007 (-4.10)**

0.038 (5.04)**

Avg. Adj. R2 15.7%

0.023 (4.56)**

15.7%

* Significant at 5%, ** Significant at 1%. T-tests are one-tailed when a directional prediction is made and two-tailed otherwise. a Table values are mean parameter estimates from nine year-by-year regressions. Fama-MacBeth t-statistics in parentheses. The sample contains 3,718 firm/year observations, ranging from 142 firms in 1993 to 619 firms in 2000. b rDIVPREM= the estimated risk premium based on the target price method (BP 2003). BETA = capital market beta estimated via the market model with a minimum of 30 monthly returns over the 60 months prior to June 30th of the year expected cost of equity capital is estimated using a value weighted NYSE/AMEX market index return. GROW = Value Line forecasts of long-range (3-5 year) earnings growth. MKVL = the market value of equity as of the most recent quarter prior to the date cost of equity is calculated, stated in millions of dollars. BP = book value of common equity scaled by the market value of common equity, both measured at the end of the most recent quarter prior to June 30th of the year cost of equity capital is estimated. PUBLIC = the precision of analysts’ public information set, based on the BKLS method. PRIVATE = the precision of analysts’ private information set, based on the BKLS method. CONSENSUS = PUBLIC/ (PUBLIC+PRIVATE). RDIFF = RPRIVATE - RPUBLIC.

27

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1

See for example, Botosan (1997), Botosan and Plumlee (2002), Frankel, McNichols and Wilson (1995),

Healy, Hutton and Palepu (1999), Lang and Lundholm (2000), Leuz and Verrecchia (2000), Marquardt and Wiedman (1998), and Welker (1995). 2

See for example, Admati (1985), Easley, Hvidkjaer, and O’Hara (2002), Easley and O’Hara (2000),

Grossman and Stiglitz (1980), Jones and Slezak (1999), and Wang (1993). 3

Our proxies are derived from Barron, Kim, Lim and Stevens (1998) and are employed in prior empirical

research including Barron, Byard and Kim (2002), Byard and Shaw (2002), and Venkataraman (2000). 4

The empirical validity of this estimate is assessed in Botosan and Plumlee (2003).

5

Existing research suggests public and private information may be substitutes or complements and that the

precision of private information may depend on the precision of public information. See for example, Alles and Lundholm (1993), Barron, Byard and Kim (2002), Bushman (1991), Byard and Shaw (2002), Diamond (1985), Indjejikian (1991), Kim and Verrecchia (1991), Kim and Verrecchia (1994), Lundholm (1988), Lundholm (1991), McNichols and Trueman (1994), Venkataraman (2000), and Verrecchia (1982). 6

Moreover, the association between the cost of capital estimates and risk is stble across alternative model

specifications and across time. 7

See Litner (1965), Mossin (1966) and Sharpe (1964).

8

See for example, Demsetz [1968], Klein and Bawa [1976], Copeland and Galai [1983], Glosten and

Milgrom [1985], Barry and Brown [1985], Amihud and Mendelson [1986], Coles and Loewenstein [1988], Diamond and Verrecchia [1991], Handa and Linn [1993], Coles, et al. [1995], and Clarkson, et al. [1996]. 9

BP examine the sensitivity of the association between the cost of capital estimates and risk to two

alternative points in the target price range (the 50th percentile and the minimum) and find their results are robust to both alternatives. We employ the 25th percentile because BP employ it in their primary analysis to adjust for an optimistic bias in analysts’ forecasts of target price. 10

Appropriate adjustments for fractions of years and the portion of the current fiscal-year dividend forecast

distributed to investors prior to the forecast date are made. These adjustments are described in detail in Botosan and Plumlee (2003).

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