The Reconciling Role of Earnings in Equity Valuation

Transcription

1 The Reconciling Role of Earnings in Equity Valuation Bixia Xu Assistant Professor School of Business Wilfrid Laurier University Waterloo, Ontario, N2L 3C5 (519) ext. 2659; Fax: (519) ; FIRST DRAFT: PLEASE DO NOT QUOTE WITHOUT PERMISSION FROM THE AUTHOR I thank Dr. S. Ryan for his insightful comments on this paper in AAA

2 The Reconciling Role of Earnings in Equity Valuation ABSTRACT: This study develops a theoretical model to alternatively describe the role of earnings in equity valuation under the current GAAP. The model defines a reconciling role for earnings (i.e., reconcile the book value of equity to the true value of equity), and posits that this reconciling role depends on the nature of the measurement error in book value. Empirical results based on 46,999 firm-year observations from the period of strongly support the proposed reconciling role. This study contributes to the literature by providing a way to comprehensively understand the differential associations between market values and earnings identified by prior studies, and by providing an explanation for the mixed evidence regarding the capitalization of negative earnings. Keywords: measurement error in book value; reconciling role of earnings; earnings response coefficient; investment in intangible assets; operational failure. Data Availability: Data are available from public sources identified in the text. I. INTRODUCTION The capital market research in the accounting literature considers earnings as a major fundamental value driver (e.g., Easton and Harris, 1991), whereas earnings are not well defined economically. Prior studies, no matter treating earnings as a separate explanatory variable or interacting earnings with other explanatory variables, assume earnings to proxy for a specific economic phenomenon (e.g., unexpected future abnormal cash flows), thus, assigning earnings a valuation role as an independent value driver. No research has related the role of earnings in equity valuation to the measurement error in book value except for a theoretical statement by Scott (2000). Scott (2000) states that accounting earnings gain a role in equity valuation only in an imperfect and incomplete market, where book value cannot be measured based on future cash flows without error. This statement implies the dependence of the role of 2

3 earnings in equity valuation on the measurement error in book value. Penman (1996) motivates the current study through his examination of the articulation of price-earnings (P/E) ratio and market-to-book ratio (P/B). He argues and finds evidence that P/B=P/E*E/B (E/B is the ratio of earnings over end-of-period book value) serves as a reconciliation of P/E and P/B, given one of them. His study provides a way to jointly understand the signals by P/E and P/B through E/B. Building on Scott and Penman, I propose a theoretical model to alternatively understand the role of earnings in equity valuation. Unlike the models in prior studies, this model relates the role of earnings in equity valuation to the measurement error in book value, and defines earnings a reconciling role. That is, when book value of equity, which serves as the very basic representation of firm value, is biased with respect to the true value of equity, earnings play a role to reconcile book value to the true value. Such reconciling role in fact depends on the nature of the measurement error in book value. Specifically, the model posits that: i) when book value is biased downward with respect to the true value of equity, earnings reconcile book value up to the true value, leaving a positive earnings response coefficient (ERC) to positive earnings but a negative ERC to negative earnings; ii) when book value is biased upward, earnings reconcile book value down to the true value, leaving a negative ERC to positive earnings but a positive ERC to negative earnings. Empirical results base on 46,999 observations from the period of strongly support this reconciling role. In addition, they reveal a more pronounced reconciling role in the case where book value is biased downward for both positive and negative earnings. The current study focuses on the reconciling function of earnings in equity valuation. However, the possible economic implications of this reconciling role are also explored in the model section. The current study is also motivated to explain the mixed evidence on the capitalization of negative earnings. Based on broad samples, prior studies under the topic of equity valuation find a significant negative association between negative earnings and market value (e.g., Collins et al., 1999). A negative ERC of negative earnings implies that higher negative earnings are associated with higher market values, which is economically contradictory to both discounted future dividend valuation model in finance and the welldemonstrated conceptual association between dividends and earnings in accounting (e.g., 3

4 Ohlson 1995), as they both imply a positive association between market value and earnings. Such contradiction warrants an examination of the capitalization of negative earnings. Hence, Hayn (1995), for the first time, explores the valuation role of earnings in the case of loss firms. She finds the price response to a reported loss depends on the likelihood of exercising the abandonment option. This price response is more pronounced when such likelihood is relatively smaller. However, she finds a positive ERC for loss firms, regardless the level of the proposed likelihood. Building on Hayn, Joos and Plesko (2004) find ERC for loss firms is positive when the likelihood of loss reversal (i.e., return to profitability) in the next period is high, but negative when such likelihood is low. 1 The two studies explain the capitalization of negative earnings from similar points of view of economics. Unfortunately, they provide inconclusive evidence regarding the sign of ERC. Unlike the two studies, Collins et al. (1999) examine the same phenomenon but from an econometric point of view. They argue and provide evidence that the anomalous ERC for loss firms is caused by the omission of book value of equity in the simple earnings capitalization model. The ERC for loss firms is negative when book value is omitted in this model, but becomes positive when book value is added. In fact, they treat book value as an omitted related variable without realizing that the role of earnings in equity valuation inherently depends on the existence of book value, as proposed by the current study. The above-mentioned studies do not link the role of negative earnings in equity valuation with the measurement error in book value. However, making such a linkage can lead to a clear understanding of this role. As stated before, the sign of the ERC of negative earnings can be explained by the reconciling role of earnings. According to this reconciling role, when book value is biased downward, negative earnings are positively valued (i.e., negative ERC) because they bear a function to reconcile book value up to the true value, while, when book value is biased upward, negative earnings are negatively valued (i.e., positive ERC) because they bear a function to reconcile book value down to the true value. The current study contributes to the literature in two ways. First, it establishes a 1 Joos and Plesko find a negative and significant ERC for loss firms with low likelihood of loss reversal from the raw data but a negative and insignificant ERC from the ranking analysis. 4

5 theoretical model to alternatively describe the role of earnings in equity valuation. In this model, the role of earnings simply depends on the nature of the measurement error in book value. Therefore, the model provides a way to comprehensively understand the cross-sectional differential associations between market value and earnings identified by prior studies (e.g., Easton and Zmijewski, 1989; Collins and Kothari, 1989; Hyan, 1995; and Burgstahler and Dichev, 1997) through summarizing factors that contribute to these differential associations into one measure: the measurement error in book value. For example, Collins and Kothari (1989) find growth and earnings persistence have positive effects on the magnitude of ERC. Indeed, these factors can positively cause the difference between book value and the true value of equity. In the framework of the reconciling role, high growth and earnings persistence can lead to a high measurement error in book value and, then to a high reconciling role of earnings. Therefore, future research should explore how these factors determine the measurement error in book value. Such exploration may provide insight into the accounting for book value of equity. Second, the current study extends studies of Hayn (1995), and Joos and Plesko (2004) by suggesting from a measurement point of view that the sign of the ERC of loss firms can be comprehensively determined by the nature of the measurement error in book value. From an economic point of view, the current study suggests that negative earnings can represent either investments in intangibles or operational failure; accordingly, the sign of ERC is negative when negative earnings represent investments in intangibles but positive when they represent operational failure. Moreover, the current study finds that the sign reversal by adding book value into the simple earnings capitalization model identified by Collins et al. (1999) do not exist when negative earnings have a function to reconcile book value up to the true value of equity, thus complementing Collins et al. by suggesting that it is not only the omission of book value but also the nature of the measurement error in book value that cause the negative ERC of negative earnings. In the following section, I present the theoretical model, followed by the research design in Section three. Section four provides the discussions of empirical results, followed by the summaries and concludes in Section five. 5

6 II. MODEL Perfect and Complete Market Assumption The discounted cash flow valuation model in finance specifies firm value as a function of the present values of future expected cash flows in an infinite period. When the market is perfect and complete, i.e., firm future cash flows and the risk-adjusted rate of return are publicly known with certainty or the probabilities of states of nature are publicly known with certainty, firm values of both end-of-period and beginning-of-period can be calculated without error (Scott 2000). Under this ideal condition, the true value of equity can be completely recognized on the balance sheet, i.e., y jt = BV jt (M1) Where y is the true value of equity; BV is the recognized value of equity in accounting books; subscripts j and t represent firm j and time t, respectively. In this case, net income can be well defined economically as the difference in firm value between end-of-period and beginning-of-period, i.e., NI jt = BV jt BV jt-1 (E1) Where NI is the economic net income; other variables are defined as before. M1 and E1imply three perfect positive correlations (i.e., the correlation coefficients are equal to one): the correlation between y and BV; the correlation between change in BV and NI; and the correlation between change in y and NI. Drawn from those correlations, change in y can be specified as below:?y jt = y jt -y jt-1 = BV jt BV jt-1 = NI jt (M2) Where?y jt represents the change in y jt ; other variables are defined as before. It is obvious that book value and net income are redundant, suggesting that there is no valuation role attached to net income when the market is prefect and complete. BV 6

7 (change in BV) alone can fully explain y (change in y). However, it is also implied that when the market is imperfect and incomplete, book value and net income may be no longer redundant; consequently, net income gains a valuation role (Scott 2000). Relaxing the Perfect and Complete Market Assumption An imperfect and incomplete market is the most likely case in reality. When the market is imperfect and incomplete, future cash flows, risk-adjusted rate of return and probabilities of states of nature cannot be known with certainty. In such a situation, a true value-based accounting system is not operational. Instead, a historical cost-based accounting system with conservatism evolves. In such a system, the true value of equity cannot be completely recognized in book value, and the change in such true value cannot be fully recognized in earnings, i.e., both book value and earnings contain measurement errors. Consequently, all above-described relationships cannot hold simultaneously. The true value of equity (y) and its change has to be re-specified as below: y jt = BV jt +γ (M3)?y jt =?BV jt +η (M4) Where BV represents the recognized true value of equity in accounting books under the current GAAP (i.e., book value of equity);?bv represents the change in BV ; γ (η) represents the difference between the true value of equity (true change) and recognized true value of equity (recognized change), i.e., the measurement error in book value (the change in book value). The incomplete recognition of the true value of equity reflects an incomplete expectation of future cash flows in valuation models that specify firm value as a function of future expected cash flows. Given the fact that earnings can proxy for unexpected future cash flows, I argue that earnings in fact play a reconciling role in equity valuation. That is, they reconcile book value of equity toward the true value of equity when the true value of equity is incompletely recognized. In other words, when the true value of equity is under-recognized, earnings proxy for positive unexpected future cash flows, and reconcile book value up toward the true value; in contrast, when the true value of equity 7

8 is over-recognized, earnings proxy for negative unexpected future cash flows, and reconcile book value down toward the true value. Assuming earnings cannot fully mitigate the measurement error in book value, as they also contain measurement errors due to the biases in the accounting system, M3 and M4 can be transferred into below: y jt = a 0 + a 1 BV jt + a 2 NI jt + e (M5)?y jt = a 0 + a 1?BV jt + a 2?NI jt + e (M6) Where NI is the earnings in accounting books under the current GAAP;?NI is the change in NI ; e is the error term. Other variables are defined as before. Therefore, when the true value of equity is under-recognized in M5, a 2 NI must be positive in order to reconcile book value up to y, implying that when the true value of equity is over-recognized, a 2 NI must be negative in order to reconcile book value down to y. For a 2 NI to be positive, either of the following conditions must hold: Alternatively Earnings > 0 and a 2 > 0 Earnings < 0 and a 2 < 0 (C1) (C2) For a 2 NI to be negative, either of the following conditions must hold: Alternatively Earnings > 0 and a 2 < 0 Earnings < 0 and a 2 > 0 (C3) (C4) a 2 is called earnings response coefficient (ERC) in the accounting literature. C1 through C4 also apply to M6. Re-arranging M5 and M6 with these conditions generates four predictions for the sign of ERC in both price-earnings and return-earnings specifications, as described below: 8

9 Prediction 1: The sign of ERC is positive when the true value of equity is under-recognized & earnings > 0 the change in the true value of equity is under-recognized &?earnings > 0 Prediction 2: The sign of ERC is negative when the true value of equity is under-recognized & earnings < 0 the change in the true value of equity is under-recognized &?earnings < 0 Prediction 3: The sign of ERC is negative when the true value of equity is over-recognized & earnings > 0 the change in the true value of equity is over-recognized &?earnings > 0 Prediction 4: The sign of ERC is positive when the true value of equity is over-recognized & earnings < 0 the change in the true value of equity is over-recognized &?earnings < 0 These predictions reveal that the sign of ERC actually jointly depends on i) the completeness in the recognition of equity value and its change; and ii) the signs of earnings and earnings change. In addition, the model implies that a high level of unrecognized true value of equity is associated with a high level of reconciling role of earnings (i.e. a higher economic importance and statistical significance of earnings). Economics Related to the Predictions The four predictions are mathematically derived from the reconciling role of earnings. However, unlike the research in mathematics, econometric models or equations must represent economic relationships/associations. Therefore, in this part of the paper, I address the possible economic implications attached to each prediction. Prediction 1 represents a case where the true value of equity is under-recognized. Firms in this case may invest heavily in intangibles that generate future positive cash flow opportunities (e.g., Amir and Lev, 1996). Under the current conservative accounting system, such investments are expensed (e.g., expensing R&D expenditures), leading to an under-recognized book value. However, after expensing these investments, the firm is still able to generate positive earnings, which is a crucial positive signal about firm value. Therefore, higher positive earnings in this case proxy for higher unexpected positive 9

10 future cash flows, and then are associated with higher true values of equity. Hence, ERC should be positive. According to management consultants growth share matrix, firms in this case should belong to the stars category. Prediction 2 represents a case similar to that represented by Prediction 1. Unlike the case in Prediction 1, after expensing investments in intangibles, firms in this case are unable to generate positive current earnings but able to generate future positive earnings. Negative earnings in fact are mainly caused by expensing investments in intangibles. Therefore, higher investments in intangibles in this case can result in higher negative earnings that proxy for higher unexpected positive future cash flows. Hence, there exists a negative association between current negative earnings and the true value of equity. That is, ERC should be negative. According to the same growth share matrix, firms in this case should belong to the question marks category. Prediction 3 represents a case where the true value of equity is over-recognized. Firms in this case may make low investments in intangibles, which eventually departs the historical cost-based measures of assets from the value creation powers of these assets. Currently, the firm is still able to generate positive earnings. However, its earnings growth potential may be limited. It is difficult to attach an economic meaning to the predicted negative sign of ERC based on the proposed reconciling role for this case, as a negative ERC of positive earnings does not make a normal economic sense. The proposed negative sign can only be understood from the viewpoint of the reconciling role. According to the growth share matrix, firms in this case should belong to the cash cows category. Prediction 4 represents a case similar to that represented by Prediction 3. Different from the case in Prediction 3, firms in this case are unable to generate positive earnings. Therefore, different from the case in Prediction 2, negative earnings in this case do not proxy for investments in intangibles but surrogate for the failure of the firm to effectively and efficiently utilize its assets to create value, i.e., operational failure. If this is true, higher negative earnings are associated with lower true value of equity. Hence, ERC should be positive. According to the growth share matrix, firms in this case should belong to the dogs category. 10

11 III. RESEARCH DESIGN Data and Sample The sample firms are extracted from Compustat under three criteria: i) market value and required financial statement data are available for the period from 1992 to 2003 in Compustat; ii) positive book value; and iii) market value and required financial statement data are within the ranges of sample means plus three times standard deviations. Under those criteria, a sample of 46,999 firm-years for the period from is formed. 2 Descriptive statistics of the sample are presented in Table 1. Proxy For the Completeness in the Recognition of the True Value of Equity The current study argues that the role of earnings in equity valuation is reliant on the completeness in the recognition of the true value of equity in accounting books. The level of unrecognized true value of equity is unobservable since the true value of equity is unobservable in an imperfect and incomplete market. Based on the current GAAP and R&D literature which shows a positive association between market value and R&D expenditures, I argue that expensing investments in intangibles under the current GAAP contributes to the incomplete recognition of the true value of equity. In general, a high level of investments in intangibles leads to a high level of unrecognized true value of equity. Therefore, I use R&D intensity (i.e., R&D expenditures over sales) to proxy for the level of unrecognized true value of equity. Sample firm-years are accordingly ranked in an ascending manner based on R&D intensity, and divided into two groups. The high R&D group includes firm-years with R&D intensity higher than the sample median (.21). The low R&D group includes firm-years with R&D intensity lower than the median. Portfolio Formation In order to test the proposed predictions, both high and low R&D groups are further divided according to the sign of earnings (earnings change) for M5 (M6). This procedure generates four portfolios that match the cases represented by the four proposed predictions. Portfolio 1 (P1, hereafter) contains firm-years with positive earnings (positive change in earnings) in the high R&D group. As discussed previously, the sign of 2 Since the return-earnings specification requires calculations of changes in market value, book value and 11

12 ERC is predicted positive for this portfolio. Portfolio 2 (P2, hereafter) contains firm-years with negative earnings (negative change in earnings) in the high R&D group. The sign of ERC is predicted negative for this portfolio. Portfolio 3 (P3, hereafter) contains firmyears with positive earnings (positive change in earnings) in the low R&D group. The sign of ERC is predicted negative for this portfolio. The final portfolio (P4, hereafter) contains firm-years with negative earnings (negative change in earnings) in the low R&D group. The sign of ERC is predicted positive for this portfolio. Testing Models Under the market efficiency assumption, market value can be considered as the observed true value of equity. Therefore, I use market value to proxy for the true value of equity. Under this proxy, M5 and M6 are transferred into their empirical versions as below: MVT jt = β 0 + β 1 BVT jt +β 2 NIT jt + ε (1) R jt = γ 0 +γ 1 CBV jt +γ 2 CNI jt + ε (2) Where MVT jt is the market value of firm j at t deflated by beginning total assets; BVT jt is the book value of firm j at t deflated by beginning total assets; NIT jt is the earnings before extraordinary items of firm j in t deflated by beginning total assets; CBV jt is the change in BV jt deflated by beginning market value; CNI jt is the change in NI jt deflated by beginning market value; R jt is stock market return of firm j in t; and ε is the error term. BV and NI are defined as before. (Insert Table 1 Here) IV. EMPIRICAL RESULTS Descriptive Statistics Table 1 summarizes the descriptive statistics of the sample, with Panel A of the table displaying the statistics for Equation 1, and Panel B of the table displaying the same earnings, the sample period ( ) is one year shorter than the data collection period ( ). 12

13 but for Equation 2. Table 1, Panel A shows that the sample has a mean R&D intensity of 1.45, accompanied by a mean book-to-market ratio of.82 and a mean price-earnings ratio of The three values together indicate an overall under-recognition of book value. More than half firm-years (i.e., firm-years in P1 and P2) invest more than 21% of sales in their R&D projects, within which, based on the sample, 39.27% reports positive earnings, versus 17.41% reports negative earnings. In the low R&D group (i.e., firm-years in P3 and P4), also based on the sample, 28.55% reports positive earnings, versus reports negative earnings. P2 has the highest R&D intensity of 4.92, accompanied by the lowest book-to-market ratio of.28, versus the same measures being.36 and.35 in P1,.02 and 1.17 in P3 and.19 and 1.98 in P4, respectively. Comparing between the R&D groups, a higher R&D intensity is associated with a lower book-to-market ratio. Such comparison indicates the appropriateness of using R&D intensity as a proxy for the level of unrecognized true value of equity, given the market efficiency. The cross-portfolio differential magnitudes of the book-to-market and price-earnings ratios imply that earnings play heterogamous roles in equity valuation, depending on R&D intensity. Panel B of the table shows that the sample has a mean return of.33, accompanied by a mean change in book value of.07 and a mean change in earnings of.05. Based on the sample, 36.56% of the firm-years in the high R&D group reports a positive change in earnings, while 20.12% in the same group reports a negative change in earnings. The same percentages in the low R&D group are 22.83% and 20.49%, respectively. The same as the case shown in Panel A of the table, P2 has the highest R&D intensity (3.85) but lowest book-to-market ratio (.33), followed by P1, P4 and P3 in a descending order based on R&D intensity. Different from this ranking, P1 has the highest mean return, followed by P2, P3 and P4 in a descending order. (Insert Table 2 Here) Correlation Matrix Table 2 summarizes the correlation coefficients of the portfolios, with Panel A of the table reporting the correlation coefficients for Equation 1, and Panel B of the table reporting the correlation coefficients for Equation 2. This table reveals two important 13

14 phenomena. First, the three perfect correlations described before in the model section do not exist, implying that book value and earnings are not redundant, and earnings do gain a role in equity valuation. Second, there appears to exist two types of correlations across portfolios, depending on the signs of earnings and earnings change. In P1 and P3 of Panel A of this table, market value is positively associated with both book value and earnings, for example, the correlation coefficients are.590 and.426, respectively, in P1; and earnings are positively associated with book value, for example, the correlation coefficient is.292 in P1. In contrast, in P2 and P4 of the same panel of this table, market value is positively associated with book value but negatively associated with earnings, for example, the correlation coefficients are.828 and -.838, respectively, in P2; but, earnings are negatively associated with book value, for example, the correlation coefficient is in P2. Panel B of this table reveals the same correlation pattern. The correlation pattern in the case of negative earnings is the same as that examined by Collins et al., (Insert Table 3 Here) Reconciling Role of Earnings To test the proposed reconciling role, equations 1 and 2 are estimated for each of the proposed portfolios. Table 3 summarizes the results, with Panel A of this table reporting the results for Equation 1, and Panel B of this table reporting the results for Equation 2. 3 In Panel A of this table, ERC is positive and significant (4.922, t = ) in P1, negative and significant in P2 (-1.576, t = ), negative and significant in P3 (-.171, t = ), and positive and significant in P4 (.046, t = 3.867). These results are fully consistent with the model predictions. In Panel B of the table, ERC is positive and 3 Reported results in all the tables are from the firm-year pooled sample. Firs-order autocorrelation in the estimation of Equation 1 is controlled by annual estimations. Results regarding the signs of ERCs in P1 and P2 from annual estimations are the same as reported in Table 3. ERCs in P3 and P4 have the predicted signs in 7 of 10 years, are insignificant in 2 years, and have opposite signs in one year. I allow the intercept to vary over time (the coefficients of the time variables are not reported). A GLS model is applied to get White-adjusted standard errors and t-statistics. A histogram of the standardized residual shows an approximate normal distribution of residuals. To control for the potential effect of multicollinearity in regression estimations, VIFs are calculated. All of them are below 2.08, indicating that multicollinearity is not an issue. The estimation of Equation 2 (i.e., the firs-order difference), along with allowing the intercept to vary overtime, can somewhat control for the omitted related variable issue. 14

15 significant in P1 (.511, t = ), negative and significant in P 2 (-1.693, t = ), positive and significant in P3 (.059, t = 7.407), and positive and significant in P4 (.177 t = ). These results are consistent with the model predictions except for those from P3. A positive ERC in P3, although economically meaningful, violates the reconciling role of earnings (i.e., the predicted sign is negative). This issue is addressed in the next part of the paper. (Insert Table 4 Here) Earnings Capitalization Following the sprit of Collins et al., 1999, Table 4 summarizes earnings capitalization in each portfolio, with Panel A of this table reporting for Equation 1 without book value and Panel B of this table reporting for Equation 2 without the change in book value. These estimations can further demonstrate the proposed reconciling role of earnings. In Panel A of this table, the signs of ERCs in P1 and P2 are the same as their counterparts in table 3. Differently, ERC is positive in P3 (1.479, t = ) but negative in P4 (-.968, t = ). They both are opposite to their counterparts in Table 3. Consistent with Collins et al., 1999, the addition of book value into the simple earnings capitalization model turns the negative sign of ERC in P4 (Panel A of Table 4) into positive (Panel A of Table 3). 4 Collins et al. argue that this is because book value proxies for the abandonment value. If their finding is descriptive, one should observe the same sign reversal in P2. As shown in Panels A of Tables 3 and 4, ERC in P2 is negative no matter book value is added or not, indicating that the finding by Collins et al. suffers from the omitted related variable issue. I argue that the omitted variable is the nature of the measurement error in book value. In fact, the sign reversal observed in P4 can be clearly explained by the reconciling role of earnings. That is, ERC is positive in P4 (Table 3, Panel A) because negative earnings bear a function to reconcile book value down to the true value of equity. In contrast, ERC in P2 (Table 3, the same panel) cannot be positive because negative earnings here bear a function to reconcile book value up to the true value of equity. Explaining economically by following the economic implications of 4 Collins et al. do not examine the case in P3. 15

16 negative earnings addressed in the model section, ERC of negative earnings is negative when negative earnings represent investments in intangibles, but positive when they represent operational failure. The reconciling role of earnings is also demonstrated in P3. ERC in P3 (table 4, Panel A) is positive, which is economically meaningful. However, after adding book value into the simple earnings capitalization model, it turns into negative (Table 3, the same panel), which is economically meaningless. 5 To my understanding, a reasonable explanation for this sign reversal can only be drawn from the reconciling role of earnings. That is, positive earnings in this case bear a function to reconcile book value down to the true value of equity. Therefore, the ERC has to be negative. Interestingly, Panel B of Table 4 does not exhibit the same sign reversals, i.e., all ERCs have the same signs as their counterparts in Table 3. It appears that the change in earnings may not be an appropriate proxy for the unrecognized true change in equity value. To mitigate, I replace the change in earnings by earnings in Equation 2. 6 Results from this replacement (not tabulated) are fully consistent with the model predictions. That is, ERC is positive in P1, negative in P2, negative in P3, and positive in P4. Moreover, they show the same sign reversals observed by comparing Panel As in Tables 3 and 4. This finding suggests that the opposite sign of ERC in P3 shown in Panel B of Table 3 may be caused by the inappropriateness of change in earnings as a proxy for the unrecognized true change of equity value. However, this proxy issue requires further empirical investigation. (Insert Table 5) Comparisons across Portfolios As mentioned before, the proposed model implies heterogeneous reconciling roles across the proposed portfolios. If R&D intensity can to a great degree reflect the extent to which book value is biased with respect to the true value of equity, earnings should play a more economically important and statistically significant reconciling role in a portfolio with higher R&D intensity. In comparing the economic importance, a direct look at the 5 It is hard to economically interpret a negative ERC of positive earnings. 6 To be consistent with the measures of return and change in book value in this equation, earnings are deflated by beginning market value. 16

17 magnitude of ERC across the portfolios is limited, as the signs of ERCs are opposite for earnings with the same sign but in different portfolios. However, by comparing the absolute values of ERCs, one can see obvious difference in the magnitude of ERC between the high R&D group and low R&D group. For example, in Panel A of Table 3, ERC is absolutely in P1, in P2,.171 in P3 and.046 in P4, indicating that earnings play a more economically important reconciling role in the high R&D group. For comparing the statistical significance, I design a measure of the relative significance, as one cannot directly compare t statistics across the portfolios. 7 The relative significance of earnings (RSE) is measured as the significance of earnings relative to the significance of book value in the following way: t statistic of earnings RSE = t statistic of book value RSE is defined purely based on the reconciling role of earnings. A more statistically significant reconciling role should be associated with a higher value of RSE. RSEs based on Table 3 are reported in Table 5, with Panel A of this table reporting for Equation 1 and Panel B of this table reporting for Equation 2. Panel A of this table shows that earnings in P2 have the highest relative significance level, followed by P1, P3 and P4 in an descending order. Panel B of this table also shows that earnings change in P2 has the highest relative significance level, followed by P1, P4 and p3 in a descending order. These results, along with the results regarding the economic importance, suggest that earnings (earnings change) play a more pronounced reconciling role when book value (change in book value) is biased downward in portfolios 1and 2. V. SUMMARY and CONCLUSIONS Summary of Empirical Results The heterogeneous associations between market value and earnings, especially between market value and negative earnings, reported by prior studies inspire the current study. To shed light on the understanding of this heterogeneity, the current study 7 Such comparison can be performed between variables within portfolios. 17

18 proposes a theoretical model that alternatively outlines the role of earnings in equity valuation. The proposed model defines a reconciling role for earnings under an imperfect and incomplete market including the biases in the accounting system. The reconciling role essentially suggests that the role of GAAP earnings in equity valuation can be interpreted as a mechanism to reconcile book value to the true value of equity. Based on this role, the model suggests signs of ERCs for different accounting measurement and economic situations. Specifically, it predicts that the sign of ERC jointly depends on the completeness in the recognition of the true value of equity in accounting books and the sign of earnings. When book value is under-recognized with respect to the true value of equity, ERC is positive for positive earnings but negative for negative earnings in order to reconcile book value up to the true value. When book value is over-recognized, ERC is negative for positive earnings but positive for negative earnings in order to reconcile book value down to the true value. Empirical results based on a sample of 46,999 firmyears during the period from 1993 to 2003 strongly support these predictions, thus validating the proposed reconciling role. Robust Check Hyan (1995) regresses market return on earnings per share deflated by beginning share price. I apply her specification to test the proposed reconciling role, and obtain similar results (not tabulated). Burgstahler and Dichev (1997) propose a model that indicates the convexity of the association between market value and earnings, which is determined by the size of earnings relative to book value. I also propose a non-linear cross-sectional association between market value and earnings, but this association is determined by the completeness of the recognition of the true value of equity in accounting books, i.e., the size of book value relative to the true value of equity. In order to ensure that the results from the current study do not overlap with the convexity identified by Burgstahler and Dichev, I apply their empirical price-earnings model (equation 6), and obtain similar results. That is, ERC is positive and significant in P1, negative and significant in P 2, negative but insignificant in P 3, and positive and significant in P 4. These results indicate that the non-linear cross-sectional association proposed by the current study is different from the non-linear cross-sectional association 18

19 proposed by Burgstahler and Dichev. Conclusions Prior studies raise an important question for accounting research. That is, given the fact that accounting earnings are not well defined economically, how do we accounting researchers understand the role of earnings in equity valuation, especially the role of negative earnings? Ohlson (1995) implicitly bases the explanation of market value on book value, leaving earnings a complementary valuation role. Up to today, no research has realized that the role of earnings in equity valuation can be better understood in the context of reconciling book value to the true value of equity. Under this reconciling role, one can alternatively understand the evidence on the value relevance of earnings, especially the mixed evidence on the sign of the ERC of negative earnings. Hyan (1995) suggests the separation of positive earnings from negative earnings in the valuation models based on Ohlson s study (1995). Nemours empirical studies follow this suggestion. The current study demonstrates that it is not sufficient. Earnings should be further divided based on the nature of the measurement error in book value. 19

20 References Amir, E. and B. Lev Value-relevance of non-financial information: The wireless communications industry. Journal of Accounting and Economics 22: Burgstahler, C.D. and I. D. Dichev Earnings, adaptation and equity value. The Accounting Review 72: Collins.D., M. Pincus, and H. Xie Equity valuation and negative earnings: the role of book value of equity. The Accounting Review 74: Collins, D. and S. Kothari An analysis of intertemporal and cross-sectional determinants of earnings response coefficients. Journal of Accounting and Economics 11: Easton, P. and T. Harris. (1991). Earnings as an explanatory variable for returns. Journal of Accounting Research 29: Easton, P. and M. Zmijewski Cross-sectional variation in the stock market response to accounting earnings announcements. Journal of Accounting and Economics 11: Hayn, C The information content of losses. Journal of Accounting and Economics 20: Ohlson, J Earnings, book value, and dividends in equity valuation. Contemporary Accounting Research 11: Penman, S The articulation of price-earnings ratios and market-to-book ratios and the evaluation of growth. Journal of Accounting Research 34: Scott, W Financial Accounting Theory. Prentice Hall Canada Inc. 20

21 Table 1 Descriptive Statistics Panel A Price-earnings Specification (M5) Sample P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R&D and positive NI P4: Low R&D and negative NI Means Std. D. Means Std. D. Means Std. D. Means Std. D. Mean Std. D. s MVT BVT NIT R&D BM PE ROE TA t Obs % of obs Panel B Return-Earnings Specification (M6) Sample P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R& and positive NI P4: Low R&D and negative NI Means Std. D. Means Std. D. Means Std. D. Means Std. D. Means Std. D. R CBV CNI R&D BM PE ROE MV t Obs % of obs Notes: MVT is the market value of firm j at t deflated by beginning total assts; BVT is the book value of firm j at t deflated by beginning total assets; NIT is earnings before extraordinary items of firm j in t deflated by beginning total assets; R&D is R&D expenditure over sales of firm j in t; BM is book-to-market ratio of firm j at t; PE is market-toearnings ratio; ROE is earnings over end-of-period book value of firm j at t; TA t-1 is beginning total assets of firm j; R is stock market return from t-1 to t; CBV is the change in book value of equity in the period from t-1 to t, deflated by beginning market value; CNI is the change in earnings from period t-1 to period t, deflated by beginning market value. MV t-1 is beginning market value of firm j. 21

22 Table 2 Correlation Matrix Panel A Price-Earnings Specification (M5) P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R&D and positive NI P4: Low R&D and negative NI MVT BVT NIT MVT BVT NIT MVT BVT NIT MVT BVT NIT MVT BVT.590** 1.828** 1.963** 1.998** 1 NIT.426**.292** ** -.538** 1.147**.142** ** -.480** 1 Panel B Return-Earnings Specification (M6) P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R&D and positive NI P4: Low R&D and negative NI R CBV CNI R CBV CNI R CBV CNI R CBV CNI R CBV.800** 1.531** 1.918** 1.971** 1 CNI.446**.581** ** -.331** 1.523**.588** ** -.746** 1 Notes: * and ** are 0.05 and 0.01 significance levels, respectively. MVT is the market value of firm j at t deflated by beginning total assts; BVT is the book value of firm j at t deflated by beginning total assets; NIT is earnings before extraordinary items of firm j in t deflated by beginning total assets; R is stock market return from t -1 to t; CBV is the change in book value of equity in the period from t-1 to t, deflated by beginning market value; CNI is the change in earnings from period t-1 to period t, deflated by beginning market value. 22

23 Table 3 Reconciling Role of Earnings Panel A Price-Earnings Specification MVT jt = α 0 +β 0 BVT jt +β 1 NIT jt + ε (1) P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R&D and positive NI P4: Low R&D and negative NI Intercept ( ***).813 (3.291***) (-3.014***) (-2.592**) BV (83.79***) (34.63***) ( ***).891 ( ***) NI (43.207***) ( ***) (-10056***).046 (3.867***) Adj.R 2 (%) Predicted sign of ERC Panel B Return-earnings specification R jt = α 0 +β 0 CBV jt +β 1 CNI jt + ε (2) P1: High R&D and positive NI P2 : High R&D and negative NI P3: Low R&D and positive NI P4 : Low R&D and negative NI Intercept.537 (47.509***).198 (12.343***).133 (15.767***) ( ***) CBV.772 (40.761***).968 (33.166***).132 (33.978***).178 (29.506***) CNI.511 (24.088***) ( ***).059 (7.404***).177 (17.818***) Adj.R 2 (%) Predicted sign of ERC Notes: numbers not in the parentheses are estimated parameters. Numbers in the parentheses are t-statistics and significance levels. *** is significant at.001level, ** is significant at.05 level. MVT is the market value of firm j at t deflated by beginning total assts; BVT is the book value of firm j at t deflated by beginning total assets; NIT is earnings before extraordinary items of firm j in t deflated by beginning total assets; R is stock market return from t-1 to t; CBV is the change in book value of equity in the period from t-1 to t, deflated by beginning market value; CNI is the change in earnings from period t-1 to period t, deflated by beginning market value. 23

24 Table 4 Earnings Capitalization Panel A Price-Earnings Specification MVT jt = α 0 + β 0 NIT jt + ε (1) P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R&D and positive NI P4: Low R&D and negative NI Intercept (35.068***) (17.22***).442 (103123***).324 (19.517***) NI (61.924***) (42.08***) (45.949***) ( ***) Adj.R 2 (%) Panel B Return-earnings specification R jt = α 0 +β 0 CNI jt + ε (2) P1: High R&D and positive NI P2 : High R&D and negative NI P3: Low R&D and positive NI P4 : Low R&D and negative NI Intercept.593 (50.465***).237 (14.000***).131 (14.807***).198 (29.606***) CNI.732 (34.121***) ( ***).158 (20.241***).162 (15.592***) Adj.R 2 (%) Notes: numbers not in the parentheses are estimated parameters. Numbers in the parentheses are t-statistics and significance levels. *** is significant at.001level, ** is significant at.05 level. MVT is the market value of firm j at t deflated by beginning total assts; NIT is earnings before extraordinary items of firm j in t deflated by beginning total assets; R is stock market return from t-1 to t; CNI is the change in earnings from period t-1 to period t, deflated by beginning market value. 24

25 Table 5 Comparisons Between Portfolios Panel A Price-Earnings Specification P1: High R&D and positive NI P2: High R&D and negative NI P3: Low R&D and positive NI P4: Low R&D and negative NI Relative significance Panel B Return-Earnings Specification P1: High R&D and positive NI P2 : High R&D and negative NI P3: Low R&D and positive NI Relative significance P4 : Low R&D and negative NI 25

26 26