Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values

Transcription

1 Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values Mary E. Barth William H. Beaver Graduate School of Business Stanford University John R. M. Hand Wayne R. Landsman Kenan-Flagler Business School University of North Carolina at Chapel Hill September 2004 We appreciate funding from the Financial Research Initiative, Graduate School of Business, Stanford University, Center for Finance and Accounting Research at UNC-Chapel Hill, Stanford GSB Faculty Trust, and Bank of America Research Fellowships. We also thank workshop participants at Lancaster University and the University of Utah for helpful comments, and Brian Rountree, Steve Stubben, Qian Wang, and Rui Yao for able research assistance. Corresponding author: William H. Beaver, Graduate School of Business, Stanford University, 518 Memorial Way, Stanford, CA , (650) ,

2 Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values Abstract This study uses out-of-sample equity value estimates to determine whether earnings disaggregation, imposing valuation model linear information (LIM) structure, and separate industry estimation of valuation model parameters aid in predicting contemporaneous equity values. We consider three levels of earnings disaggregation: aggregate earnings, cash flow and total accruals, and cash flow and four major components of accruals. For pooled estimations, imposing the LIM structure results in significantly smaller prediction errors; for by-industry estimations, it does not. However, by-industry prediction errors are substantially smaller, suggesting the by-industry estimations are better specified. Mean squared and absolute prediction errors are smallest when disaggregating earnings into cash flow and major accrual components; median prediction errors are smallest when disaggregating earnings into cash flow and total accruals. These findings suggest that (1) If concern is with errors in the tails of the equity value prediction error distribution, then earnings should be disaggregated into cash flow and the major accrual components; otherwise earnings should be disaggregated only into cash flow and total accruals. (2) Imposing the LIM structure neither increases nor decreases prediction errors, which provides support to the efficacy of drawing inferences from valuation equations based on residual income models that do not impose the structure implied by the model. (3) Valuation of abnormal earnings, accruals, accrual components, equity book value, and other information varies significantly across industries.

3 Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values 1. Introduction There is a large literature examining how accounting amounts, including earnings, and earnings disaggregated into cash flow and accruals, relate to contemporaneous equity values. 1 Ohlson (1995, 1999) and Feltham and Ohlson (1995, 1996) develop valuation models that link accounting amounts and equity values by assuming a link between equity values and the linear information structure of the accounting amounts. Although such models have been the subject of empirical testing, few studies test whether they aid in predicting equity values. The objective of this study is to determine whether and the extent to which disaggregation of earnings and imposing valuation model linear information structure aid in predicting contemporaneous equity values out of sample. We also determine whether and the extent to which basing such predictions on separate industry estimation of valuation model parameters affects their accuracy. A primary goal of financial reporting is aiding investors in making economic decisions. A primary economic decision investors make is assessing the value of firms in which they are invested or consider investing. The Financial Accounting Standards Board (FASB) recognizes this motivation for financial reporting by noting in Statement of Financial Accounting Concepts No. 1, paragraph 34, financial reporting should provide information that is useful to present and potential investors, and creditors, and other users in making rational investment, credit, and similar decisions. Although the FASB recognizes the importance to investors of financial statement amounts, the concepts statements provide little guidance as to how the amounts are to be used. In contrast, accounting-based valuation models incorporating accounting accruals based 1 Throughout we use net income and earnings interchangeably.

4 on the Feltham-Ohlson framework provide this guidance. We use this framework to provide empirical evidence on our research questions. The first empirical question we address is whether disaggregating earnings into cash flow and total accruals, and into cash flow and the major components of accruals, result in differences in equity value predictive ability. We do this because several studies find that cash flow and accruals differ in their ability to forecast future earnings and to explain cross-sectional variation in equity values. The second empirical question we address is whether accounting-based valuation models incorporating accruals aid investors in predicting equity market values. Accounting-based valuation models have been the focus of studies in several contexts, including examining whether such models are descriptively valid, and assessing the value relevance of accounting amounts. Some studies use accounting-based valuation models to predict equity values for purposes of exploiting differences between theoretical and actual equity values. However, they only consider aggregate earnings and do not address whether imposing the model s linear information structure affects predictability. The third empirical question we address is whether basing predictions on separate industry estimation of valuation model parameters affects equity market value predictions. Valuation parameters can differ across industries because the relative mix of accrual components can differ across industries, and because earnings forecastability or persistence of particular accrual components can differ across industries. To address our research questions, we use a sample of Compustat firms from 1987 to We predict contemporaneous equity market values using out-of-sample estimates, i.e., we use cross-sectional valuation equations that for each year exclude each firm from the equations used to predict its equity value that year. Hereafter, we use the term predictions to refer to these 2

5 out-of-sample equity market value predictions. To test whether earnings disaggregation affects equity value predictive ability, we predict equity values using three linear information valuation models (LIMs) employing three levels of earnings disaggregation. LIMs comprise forecasting equations for abnormal earnings and each earnings component considered separately, and an equity valuation equation. The LIM structure provides links between multiples in the valuation equation and those in the forecasting equations. The first LIM is based on aggregate earnings. The second, following Barth, Beaver, Hand, and Landsman (1999), disaggregates earnings into cash flow and total accruals. The third, introduced here, disaggregates earnings into cash flow and the four major components of accruals change in receivables, change in inventory, change in payables, and depreciation. We develop equity value predictions for each LIM using two estimation procedures. The first procedure is an equity valuation equation that includes accounting amounts as explanatory variables, but does not impose the structure of the LIM implied by the level earnings disaggregation. The second procedure imposes the LIM structure. To test whether earnings disaggregation aids in predicting equity values, we compare prediction errors across the three LIMs. To test whether imposing the LIM structure aids in predicting equity values, we compare mean and median squared and absolute prediction errors from estimations when the LIM structure is imposed to those from when it is not. To test whether basing predictions on separate industry estimations of valuation model parameters affects equity value predictions, we compare prediction errors from pooled and separate industry estimations for each LIM. The effect of imposing the LIM structure on out-of-sample prediction errors cannot be predicted. This contrasts with in-sample prediction errors, where for a given LIM, the errors obtained when the LIM structure is not imposed are guaranteed to be no larger than those 3

6 obtained when it is imposed. There are two reasons why imposing the LIM structure can result in smaller out-of-sample prediction errors. First, using knowledge of the interrelation of accounting amounts in structuring the LIM should, other things equal, enhance the equity valuation equation s ability to predict equity value. Second, imposing the LIM s structure mitigates the extent to which the equity valuation equation overfits the data. However, imposing the LIM structure can result in larger out-of-sample prediction errors because of inefficiency in estimating the additional forecasting parameters. One might also expect equity value prediction errors to decrease as the level of earnings disaggregation increases. This is because as the level of earning disaggregation increases, different components of earnings are permitted to have different valuation multiples. However, earnings disaggregation can be costly in terms of increasing prediction errors. First, out-ofsample prediction errors can increase as the level of earnings disaggregation increases because of the potential for data overfitting. Second, as the level of earnings disaggregation increases, so does the extent of structure imposed by the LIM on the forecasting and valuation relations. In other words, although earnings disaggregation relaxes constraints on valuation coefficients by permitting them to differ, it adds constraints on the valuation coefficients when the LIM structure is imposed. As a result, the predictive ability of each LIM relative to the others could differ depending on whether the LIM structure is imposed. Before addressing our first research question by comparing prediction errors based on different levels of earnings disaggregation, i.e., different LIMs, we address our second research question by comparing prediction errors within each LIM to determine whether imposing the LIM structure affects prediction errors. We find that for all three LIMs, imposing the LIM structure results in significantly smaller prediction errors for pooled estimations. However, 4

7 prediction errors do not differ significantly when the LIM structure is or is not imposed for the by-industry estimations. These finding support the efficacy of drawing inferences from valuation equations based on residual income models that do not impose the structure implied by the model because doing so neither increases nor decreases prediction errors. A striking result from the within LIM prediction error comparisons is that, consistent with our prediction relating to our third research question, prediction errors based on the by-industry estimations are substantially smaller than those based on the pooled estimations. This finding suggests that valuation of abnormal earnings, accruals, accrual components, equity book value, and other information varies significantly across industries. This finding also suggests that inferences relating to whether imposing the LIM structure reduces prediction errors should be based on byindustry estimation. Regarding our first research question, we find evidence of some reduction in mean prediction errors from disaggregating earnings into cash flow and total accruals, and some additional reduction from disaggregating total accruals into its four major components. Evidence from median prediction errors portrays a somewhat different picture. In particular, whereas mean prediction errors generally support disaggregation of earnings into cash flow and the four major accrual components, median prediction errors generally support disaggregation of earnings only into cash flow and total accruals. These findings suggest that if when predicting equity market values the concern is with errors in the tails of the prediction error distribution, then net income should be disaggregated into cash flow and the four major accrual components. However, if the concern is not with errors in the tails of the prediction error distribution, then earnings should be disaggregated only into cash flow and total accruals. Thus, accrual 5

8 components appear to provide additional information incremental to that in total accruals helpful to predicting equity values when considering firms with more extreme prediction errors. The remainder of the paper is organized as follows. Section 2 develops the research design. Section 3 describes the sample and data, and section 4 presents the findings. Section 5 summarizes and concludes the study. 2. Research Design 2.1 LINEAR INFORMATION MODELS Our tests of equity value prediction errors use equity value estimates from three linear information models (LIMs) based on the Feltham-Ohlson framework. Each LIM reflects a different level of earnings disaggregation. Our first research question is whether successively disaggregating earnings into cash flow and total accruals, and cash flow and four major accrual components aids in prediction equity values. Our second research question is whether imposing the LIM structure aids in predicting equity values. The first linear information model, LIM1, is based on Ohlson (1995), and comprises three equations. Equations (1a) (1c) are forecasting equations, and equation (1d) is the valuation equation implied by the linear information dynamics of the forecasting equations. For example, Ohlson (1995) shows that the abnormal earnings valuation coefficient in equation (1d), α 1, is a nonlinear function of ω 11 and the discount rate, r. a a NIit = ω 10 + ω11niit 1 + ω12bvit 1 + ω13ν it 1 + ε1 it (1a) BVit = ω 20 + ω22bv it 1 + ε 2it (1b) ν = + (1c) it ω30 + ω33ν it 1 ε 3it MVE = ν + it a α 0 + α1ni it + α 2BVit + α 3 it uit (1d) 6

9 MVE is market value of equity, NI a is abnormal earnings defined as earnings minus the normal return on equity book value, BV, the ε k s and u are error terms, and the i and t subscripts denote firm and year. 2 ν, other information, is defined as MVE MVE 1, where MVE t 1 is the t t 1 t fitted value of MVEt 1 based on a version of equation (1d) that does not include ν t. Thus, ν t captures the extent to which the accounting variables do not explain market value of equity (Feltham and Ohlson, 1995; Ohlson, 1995). We include equity book value in equation (1a) and the abnormal earnings and component forecasting equations for LIM2 and LIM3 to enhance stationarity of the forecasting equations (Barth, Beaver, Hand, and Landsman, 1999). LIM1 implicitly assumes that all earnings components have equal weight in forecasting abnormal earnings and hence have equal weight in the valuation equation. We estimate LIM1 because it focuses on aggregate earnings and plays a prominent role in the empirical accounting literature. Several studies (Bernard, 1995; Lundholm, 1995; Barth, Beaver, Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999; Myers, 1999) find that LIMs using aggregate earnings are descriptively valid. In light of this, a rather robust literature uses specifications based on LIM1 to examine how accounting amounts relate to contemporaneous equity values to obtain inferences about these accounting amounts, i.e., their value relevance (Barth, Beaver, and Landsman, 2001; Holthausen and Watts, 2001). Other studies (Frankel and Lee, 1998; Lee, Myers, and Swaminathan, 1999) use models similar to LIM1 to estimate theoretical prices to exploit differences between theoretical and actual equity values to find mispriced securities. The second, LIM2, is that estimated in Barth, Beaver, Hand, and Landsman (1999). It relaxes the assumption that the total accruals, ACC, and cash flow components of earnings have 2 We use the same notation for coefficients and error terms across the three LIMs to facilitate exposition. They 7

10 the same model parameters. 3 LIM2 can be viewed as a version of the model in Ohlson (1999), which models the transitory component of earnings, although the model applies to any earnings component. LIM2 comprises four equations, where equations (2a) through (2d) are forecasting equations, and equation (2e) is the valuation equation implied by the linear information dynamics of the forecasting equations. Thus, relative to LIM1, by adding an additional forecasting equation, LIM2 imposes additional assumptions on the valuation parameters. a a NIit = ω 10 + ω11niit 1 + ω12 ACCit 1 + ω13bvit 1 + ω14ν it 1 + ε1 it (2a) ACCit = ω 20 + ω22accit 1 + ω23bvit 1 + ε 2it (2b) BVit = ω 30 + ω33bv it 1 + ε 3it (2c) ν = + (2d) it ω 40 + ω 44ν it 1 ε 4it MVE = ν + it a α 0 + α1ni it + α 2 ACC it + α 3BVit + α 4 it uit (2e) We estimate LIM2 because it focuses on the cash flow and total accrual components of earnings and several studies find that these components differ in their ability to forecast future earnings and to explain cross-sectional variation in equity values (Dechow, 1994; Sloan, 1996; Barth, Beaver, Hand, and Landsman, 1999; Barth, Cram, and Nelson, 2001). The third, LIM3, further relaxes the assumptions relating to earnings components by permitting the model parameters for four major accrual components to differ from one another as well as from those on other components of earnings, including cash flow. LIM3 comprises seven equations. Thus, relative to LIM2, by adding three additional forecasting equations, LIM3 imposes additional assumptions relating to the valuation parameters. a a it = ω 10 + ω11ni it 1 + ω12 REC it 1 + ω13 INVit 1 + ω14 APit 1 + ω15 DEPit 1 + ω16 BVit 1 + ω17ν it 1 + ε it NI 1 (3a) likely differ. 8

11 REC it = ω 20 + ω 22 REC it 1 + ω 23 INVit 1 + ω 25 DEPit 1 + ω 26 BVit 1 + ω 27ν it 1 + ε 2it (3b) INVit = ω 30 + ω 32 REC it 1 + ω 33 INVit 1 + ω 34 APit 1 + ω 35 DEPit 1 + ω 36 BVit 1 + ε 3it (3c) APit = ω 40 + ω 43 INVit 1 + ω 44 APit 1 + ω 46BVit 1 + ε 4it (3d) DEPit = ω 50 + ω55depit 1 + ω56bvit 1 + ε 5it (3e) BVit = ω 60 + ω66bv it 1 + ε 6it (3f) ν it = ω70 + ω77ν it 1 + ε7it (3g) it a α 0 + α1ni it + α 2 REC it + α 3 INVit + α 4 APit + α 5DEPit + α 6 BVit + α 7 it uit (3h) MVE = ν + REC is annual change in receivables, INV is change in inventory, AP is change in payables, and DEP is depreciation and amortization expense. We estimate LIM3 because it focuses on earnings disaggregated into cash flow and four major accrual components and findings in Barth, Cram, and Nelson (2001) indicate these components differ in their ability to forecast future cash flows and explain cross-sectional variation in equity values. In addition, Barth, Beaver, Hand, and Landsman (1999) finds that LIM2 may be mispecified, which suggests that disaggregating accruals into its major components could enhance our ability to predict equity values. Appendix A describes how we develop LIM3 and presents findings from estimating the LIM forecasting equations for all three LIMs. Appendix B develops the algebraic relation between the valuation coefficients and the forecasting equation coefficients for LIM3. As explained in Appendix B, the signs and magnitudes of the α j s in equation (3h) depend on the ωs in equations (3a) through (3g). The relations among the α j s and the ωs are complex because of the number of explanatory variables in equation (3h), each of which has its own forecasting 3 Note that permitting a different coefficient for total accruals in equations (2a) and (2e) implicitly permits the 9

12 equation. The complexity of the relations is exacerbated because equations (3a) through (3g) do not have a triangular structure. For example, with a triangular structure, the signs of α 1 and α 2 are determined solely by the signs of ω 11 and ω 22, respectively (Myers, 1999). Although it can be shown that the sign of α 1 is determined by the sign of ω 11, the sign of each of the remaining αs is not determined by any single ω. The third research question we address is whether estimating valuation parameters using separate industry estimation aids in predicting equity market values. Valuation parameters can differ across industries for two reasons. The first is that the relative mix of accrual components can differ across industries. For example, manufacturing firms have substantial investments in inventory, but service firms do not. With respect to LIM3, if this is the only difference, then all valuation and forecasting parameters will be the same across industries. However, because inventory is aggregated with other accruals in LIM1 and LIM2, valuation and forecasting parameters will differ across industries for these LIMs. The second is that earnings forecastability or persistence of particular accrual components can differ across industries. For example, manufacturing firms are likely to have more persistent receivables than retail firms. To the extent that firms within the same industry face similar economic conditions, including cost of capital, and have similar accounting practices, including level of conservatism, the valuation and forecasting parameters for firms within a given industry will be the same. But, the parameters can differ across industries as a result of differences in economic environment and accounting practices. Separate industry estimation permits all valuation and forecasting parameters to reflect systematic variation in economic and accounting environments across industries, e.g., coefficients on cash flow, i.e., ω 11 and α 1, to differ from those on accruals, i.e., ω 11 + ω 12 and α 1 + α 2. 10

13 differential persistence in abnormal earnings. It also permits the level of conservatism and the cost of capital associated with abnormal earnings to vary by industry OUT-OF-SAMPLE PREDICTION We use a jack-knifing procedure to generate contemporaneous out-of-sample equity market value predictions. The principal reason for using jack-knifing is that we seek to obtain equity value predictions for each firm without using that firm s data to generate its predicted equity value. 5 Jack-knifing also results in our obtaining statistics for hypothesis testing that do not rely on unknown parametric distributions, e.g., normality (Noreen, 1989). 6 The prediction of firm i s equity value in year t is the predicted value from the valuation equation in each LIM, i.e., equations (1d), (2e), and (3h), using estimated coefficients from the valuation equation and all firms data except firm i s in year t. Because firm i s data in year t are not used to estimate the coefficients, each prediction is out-of-sample. We set to zero negative predicted equity market values because equity market values cannot be negative. 7 Imposing the structure implied by the LIM constrains the estimated valuation coefficients to be related to the estimated forecasting equation coefficients in the manner specified by the particular LIM. When we impose the LIM structure, we exclude firm i s data in year t when 4 As explained in section 3.1, when we estimate equations pooling sample firms across industries, we use industry and year fixed-effects. This permits intercepts to vary across industries and years, but restricts slope coefficients to be the same. 5 Another motivation for using out-of-sample predictions is to help distinguish between two alternative interpretations for the finding in Barth, Beaver, Hand, and Landsman (1999) that imposing the structure of LIM2 results in greater in-sample equity value prediction errors. In particular, one interpretation of that finding is that LIM2 not correctly specified. Another is that LIM2 is correctly specified and it overfits the data. That is, it is possible that imposing the structure implied by LIM2 results in estimated valuation coefficients that are closer to unobservable valuation multiples at the expense of lower explanatory power relative to an estimation in which the structure is not imposed. It is difficult to determine which interpretation is correct without out-of-sample prediction tests. 6 The jack-knife procedure assumes that parameter estimates are generated from a sample that was collected randomly and that observations in the sample are independent. 11

14 estimating all of the LIM s equations. For example, when generating the LIM1 prediction for firm i in year t without imposing the LIM structure, we estimate equation (1d) using the data for all firms except firm i in year t. When generating the LIM1 prediction for firm i in year t with imposing the LIM structure, we estimate equations (1a) through (1d) using the data for all firms except firm i in year t and restricting the coefficients in equation (1d) to equal those implied by equations (1a) through (1c), e.g., α = ω /( R 11 ) ω 2.3 PREDICTION ERROR TESTS For each LIM, we construct two distributions of prediction errors, one generated without imposing the LIM structure and one with. For each distribution, we calculate two commonly employed prediction error metrics, absolute percentage error, AE, and squared percentage error, SE: AE = abs( MVE predicted MVE )/ MVE and (4a) it it it SE = MVE predicted MVE )/ MVE ). (4b) (( it it it To assess the statistical significance of differences in prediction errors, we compare both means 2 and medians for AE and SE. 8 This results in a total of eight error metrics for each LIM. For tests comparing means, MeanAE and MeanSE, we assume unequal variances when tests of variance equality reject the null. For tests comparing medians, MedAE and MedSE, we use a nonparametric paired sign test that does not require symmetry of paired differences in the ranks. To address our first research question, whether earnings disaggregation aids in predicting equity values, we compare prediction errors across the three LIMs, when the LIM structure is 7 The number of negative predicted equity market values is approximately 10 percent in each estimated LIM. Not surprisingly, the firms with negative predicted equity values are concentrated among firms with small equity market values. 8 The term significant indicates statistical significance at the 0.05 level or less using a one-sided test for signed predictions, and a two-sided test otherwise. 12

15 imposed and when it is not. To address our second research question, whether imposing the LIM structure aids in predicting equity values, within each LIM, we compare predictions from estimations when the LIM structure is imposed to those from when it is not. To address our third research question, whether basing predictions on separate industry estimations of valuation model parameters affects equity value predictions, we compare prediction errors from pooled and separate industry estimations for each LIM, when predictions are based on imposing the LIM structure and when they are not. 3. Data and Descriptive Statistics 3.1 DATA We obtain data for from the Compustat Primary, Secondary, and Tertiary, Full Coverage, and Research Annual Industrial Files. Our sample period begins in 1987 because prior to that date cash flow from operations disclosed under Statement of Financial Accounting Standards No. 95 (FASB, 1987) is unavailable. To mitigate the effects of outliers, for each variable, by year and within each industry, we treat as missing observations that are in the extreme top and bottom one percentile (Collins, Maydew, and Weiss, 1997; Fama and French, 1998; Barth, Beaver, Hand, and Landsman, 1999), and observations for which the absolute value of any accrual component used in LIM3 divided by total revenue is greater than one. To avoid the influence of small firms, we restrict the sample to firms with total assets in excess of $10 million. To facilitate comparisons across LIMs, we require sample firms to have full data to estimate all forecasting and valuation equations, which results in a sample common across LIMs. All variables are measured as of fiscal year end, including equity market value, and are expressed in millions of dollars. 13

16 Net income, NI, is income before extraordinary items from the statement of cash flows. Although defining NI in this way violates the clean surplus assumption of Ohlson (1995), it eliminates potentially confounding effects of large one-time items and is consistent with prior research (e.g., Dechow, Hutton, and Sloan, 1999). 9 Findings in Hand and Landsman (2004) suggest that violating clean surplus should have little effect on our findings. In calculating abnormal earnings, NI a, we set R 1 r = 12%, the long-term return on equities (Barth, Beaver, Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999). 10 Totals accruals, ACC, equals NI minus cash flow from operations. We estimate all equations with untabulated year fixed-effects, and with untabulated industry fixed-effects, when applicable, pooling available firm-year observations from all sample years. We use data from the current and most recent four prior years when estimating valuation and forecasting equations. 11 Because lagged amounts appear as explanatory variables in the forecasting equations, estimation of these equations uses data from six years. This reflects a tradeoff between efficiency and parameter stationarity, where presumably the former (latter) is increasing (decreasing) in years included in the estimating equations. We base our industry classifications on those in Barth, Beaver, and Landsman (1998) and Barth, Beaver, Hand, and Landsman (1999), and include food; textiles, printing and publishing; chemicals; pharmaceuticals; extractive industries; durable manufacturers; computers; retail; and services. We subdivide durable manufacturing firms into seven industries: rubber; plastic, leather, stone, clay & glass; metal; machinery; electrical equipment; transportation equipment; instruments; and miscellaneous. We also subdivide retail firms into three industries: wholesale; 9 It also is consistent with one-time items having zero persistence with respect to future abnormal earnings (Ohlson, 1999). 10 None of our experimental inferences is affected by assuming alternative values for r, ranging from 8 to 14 percent. 14

17 miscellaneous retail; and restaurant. We subdivide the durable manufacturers and retail industries to increase the likelihood that parameters are the same within each industry, and to help balance the number of sample firms across industries. However, we exclude financial institutions and those firms in the insurance and real estate industries. We do so to ensure that the accrual components on which we focus are meaningful for our sample firms. For example, inventory is not a predictor of future earnings for financial institutions. We estimate all equations using unscaled data (Barth and Kallapur, 1996) DESCRIPTIVE STATISTICS Table 1 presents descriptive statistics for each variable used in the estimating equations. Panel A reports distributional statistics, panel B contains Pearson and Spearman correlations, and panel C describes the industry composition of the sample. Panel A reveals that, on average, the market value of equity exceeds the book value of equity, indicating that equity book value alone is insufficient to explain equity market value. Consistent with prior research, (Sloan, 1996; Barth, Beaver, Hand, and Landsman, 1999; Barth, Cram, and Nelson, 2001), panel A also reveals that, on average, total accruals is negative. This is attributable to depreciation expense being included in accruals, but capital expenditures being included in investing cash flows. In particular, mean depreciation and amortization expense, $27.45 million, is more than three times greater than mean change in receivables, $5.59 million, the next largest accrual component. To provide insight into the relative size of each accrual component, panel A also includes distributional statistics for the absolute value of each component divided by total revenue. Findings indicate that all four accrual components comprise a non-trivial proportion of total 11 As noted above, we exclude firm i s data in year t when predicting year t s equity market value. However, we use firm i s data for years prior to year t because they are known when predicting equity market value for year t. 15

18 revenues, with depreciation and amortization expense being the largest component (mean = 5.98% of total revenues), and change in inventory being the smallest (mean = 2.36% of total revenues). Panel B reveals that most of the variables are highly correlated with each other. Panel C reveals that industries with the largest concentrations of firm-year observations are Computers, 15.32%, Textiles, printing & publishing, 9.49%, and Services, 9.18%. 4. Results 4.1 SUMMARY STATISTICS FROM LIM ESTIMATIONS Table 2, panels A through C, present regression summary statistics for the equity market value equations for the three LIMs, equations (1d), (2e), and (3h). 13 These statistics are not based on the jack-knifing procedure described in section 2.2. We present these statistics to provide descriptive evidence on the magnitudes and signs of the valuation parameter estimates and the effects on the estimates of imposing the LIM structure, and to facilitate comparison with prior research. The first two lines in each panel report statistics based on pooling all observations. The remaining lines report statistics from industry-by-industry estimations, specifically means, minimums and maximums, number of industries for which coefficients are significantly positive and negative, and number of industries for which the coefficients estimated with and without imposing the LIM structure differ significantly. For example, the mean α 1 estimate in table 2, panel A, 6.82, is an average of the 17 industry mean values. The test of 12 Untabulated findings from regressions using a variety of controls for scale differences across firms result in inferences similar to those from the tabulated findings. 13 We employ seemingly unrelated regressions when estimating each system of equations. Thus, parameter estimates from the valuation equations reflect the effects of permitting regression errors from each of the forecasting equations to be correlated with those in the valuation equation. 16

19 whether each mean coefficient differs from zero is based on the standard deviation of the 17 industry means (Fama and MacBeth, 1972). The findings relating to LIM1 in panel A are consistent with prior research (Barth, Beaver, Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999). In particular, the valuation coefficients on abnormal earnings and equity book value, α 1 and α 2, are significantly positive in the pooled sample and in all industries (and therefore the mean coefficients across industries are also significantly positive), both with and without imposing the LIM structure. The valuation coefficient, α 3, on other information, ν, also is always significantly positive. For example, without imposing the LIM structure, the pooled estimation coefficient estimates (tstatistics) for α 1, α 2, and α 3 are 9.45, 2.52, and 0.69 (69.75, , and 80.38). The large range in coefficient estimates across the 17 industries, as evidenced by the minimums and maximums, suggest equity predictions based on separate industry estimation rather than pooled estimation may be more accurate. For example, without imposing the LIM structure, estimates of α 1 across industries range from 2.02 to Panel A also reveals that the valuation coefficients, α 1, α 2, and α 3, estimated with and without imposing the LIM structure differ significantly for virtually all industries. For example, for 8 (7) industries, α 1 estimates are significantly larger when the LIM structure is not (is) imposed, leaving only two industries for which the α 1 estimates do not differ significantly. This raises the possibility that predictions of equity market value based on coefficients estimated with and without imposing the LIM structure could differ significantly. Turning to LIM2, the findings in panel B also are consistent with prior research (Barth, Beaver, Hand, and Landsman, 1999). In particular, for the pooled sample and for all industries, the valuation coefficients on abnormal earnings and equity book value, α 1 and α 3, are 17

20 significantly positive. The incremental valuation coefficient on total accruals, α 2, is significantly negative in most (all) industries when the LIM structure is not (is) imposed. The means across industries of α 1, α 2, and α 3 without imposing the LIM structure are 7.43, 2.18, and 2.10, which compare to means across industries of 8.95, 1.94, and 1.87 in Barth, Beaver, Hand, and Landsman (1999). The fact that the coefficient on total accruals differs from that on other components of abnormal earnings suggests that disaggregating earnings into cash flow and total accruals can enhance equity valuation prediction. As for LIM1, the valuation coefficient for other information, α 4, is significantly positive in all cases. Panel B also reveals that the valuation coefficients estimated with and without imposing the LIM structure differ significantly for almost all industries. For example, for 10 (5) industries, α 2 estimates are significantly larger when the LIM structure is not (is) imposed, leaving only two industries for which the α 2 estimates do not differ significantly. As with LIM1, this again raises the possibility that predictions of equity market value based on coefficients estimated with and without imposing the LIM structure could differ significantly. Findings in panel C relating to LIM3, which permits separate coefficients for the four accrual components, indicate substantial differences in coefficients across the components, as well as substantial inter-industry differences in coefficients for each component. Regarding cross-component differences, results from the pooled estimation without imposing the LIM structure indicate each of the incremental coefficients on change in inventory, change in payables, and depreciation, α 3, α 4, and α 5, is positive, and that on change in receivables, α 2, is negative. However, only the incremental coefficient on change in payables is significantly different from zero. The pooled α 2, α 3, α 4, and α 5 coefficient estimates (t-statistics) are 0.22, 0.48, 1.20, and 0.21 ( 0.68, 1.15, 3.34, and 1.10). 18

21 Results from the pooled estimation with imposing the LIM structure indicate that the incremental coefficients on change in payables and depreciation, α 4, and α 5, are significantly positive, and those on changes in receivables and inventory, α 2, and α 3, are significantly negative. The pooled α 2, α 3, α 4, and α 5 coefficient estimates (t-statistics) are 1.40, 2.70, 1.17, and 0.84 ( 7.63, 11.69, 5.90, and 4.61). In addition, untabulated findings from a test of equality of coefficients across the four accrual components indicate the coefficients differ significantly from each other. These findings indicate that the total coefficients on depreciation and changes in receivables, inventory, and payables significantly differ from those on the cash flow and other accrual components of earnings when the LIM structure is imposed. Thus, relating to our first research question, these findings suggest that disaggregation of total accruals into its four major components can aid in predicting equity values when the LIM structure is imposed. Relating to our second research question, finding different coefficients with and without imposing the LIM structure raises the question of whether equity value prediction is enhanced when the LIM structure is imposed. Turning to the separate industry estimations, table 2 reveals that inferences relating to the mean coefficients across industries differ from those from the pooled regressions. In particular, when the LIM structure is not imposed, none of the incremental accrual component coefficient estimates of α 2, α 3, α 4, and α 5 is significantly different from zero. When the LIM structure is imposed, only the coefficient on change in inventory, α 3, is significantly different from zero. Also, table 2, panel C, indicates there is substantial cross-industry variation in the coefficients on each accrual component. For both with and without LIM structure-imposed estimations, the incremental valuation coefficient, α j, on each accrual component is significantly positive for some industries and negative for others. For example, when the LIM structure is not 19

22 imposed, the coefficient on change in payables, α 4, is significantly positive in five industries, and significantly negative in five industries. This contrasts with the coefficients on the other components of abnormal earnings, which includes cash flow, α 1, equity book value, α 6, and other information, α 7, which are significantly positive in all industries. The incremental valuation coefficients on change in receivables, α 2, and change in payables, α 4, are more consistently positive than those on change in inventory, α 3, and depreciation, α 5, which are more evenly split as to their signs. Collectively, table 2, panels A, B, and C, yield three key findings that potentially have implications for equity value predictions. First, the valuation coefficient on net income differs from that on total accruals, and the valuation coefficients on the major accrual components differ from each other. Second, the signs and magnitudes of the accrual component valuation coefficients depend on whether the LIM structure is imposed. Third, accrual component valuation coefficients differ across industries. The next section examines the extent to which these differences affect equity value prediction. 4.2 COMPARISON OF OUT-OF-SAMPLE EQUITY VALUE PREDICTIONS Within LIM comparison of equity value prediction errors Table 3 presents mean (median) squared and absolute errors, MeanSE and MeanAE (MedSE and MedAE), for equity market value predictions obtained from estimations in which model parameters are estimated with and without imposing the LIM structure, using the jackknifing procedure described in section 2.2. Significant differences are denoted by boldface font. For each comparison, table 3 presents findings based on prediction errors from pooled and separate industry estimations. Two comparisons are presented for the industry estimations. The first is based on aggregating all errors from separate industry estimations. The second is based 20

23 on the mean and median error metrics for each of the 17 industries. Table 3 also lists the number of industries for which the error metrics differ significantly. Panels A, B, and C present the findings relating to LIM1, LIM2, and LIM3. Findings relating to pooled estimations for all three LIMs reveal that imposing the LIM structure results in significantly smaller MeanSEs, MeanAEs, MedSEs, and MedAEs. For example, for LIM1, panel A reveals that imposing the LIM structure significantly reduces the MeanSEs (MeanAEs) from to (2.72 to 2.64) based on pooled estimation. However, for LIM1 and LIM2, this finding does not obtain in the by-industry estimation. In particular, with one exception, all four error metrics based on by-industry estimations are significantly larger when the LIM structure is imposed. For example, for LIM1, panel A reveals that imposing the LIM structure significantly increases the MeanSEs (MeanAEs) from to (1.76 to 1.79). For LIM3, the results are mixed in that when the LIM structure is not imposed, median prediction errors are significantly larger, but mean prediction errors are significantly smaller. However, for all three LIMs, none of the error metrics relating to the mean (median) of industry means (medians) differs significantly when the LIM structure is or is not imposed. Consistent with this, for all three LIMs, the number of industries for which MeanSEs (MeanAEs) are significant smaller with or without imposing the LIM structure is approximately the same, although there is some evidence that imposing the LIM structure is marginally beneficial for LIM2. Taken together, these findings suggest that imposing the LIM structure neither consistently increases nor consistently decreases prediction errors. Thus, these findings support the efficacy of drawing inferences from valuation equations based on residual income models that do not impose the structure implied by the model. 21

24 A striking result in table 3 relates to the comparison of findings between the pooled and the by-industry estimations. First, consistent with our prediction that the relation between equity market value and accounting amounts differs across industries, each of the four error metrics is significantly and substantially larger based on the pooled estimation. 14 For example, the MeanSEs and MeanAEs based on the pooled estimation are almost twice as large as those based on by-industry estimation. Recall that the pooled estimations include industry fixed-effects. Had we restricted the intercept to be the same across industries in the pooled estimations, the differences between the pooled and by-industry estimations likely would be even greater. Second, inferences relating to whether imposing the LIM structure reduces prediction errors differ depending on whether the inferences are based on comparisons of error metrics from pooled or by-industry estimation. Whereas the error metrics based on pooled estimation are significantly smaller when the structure is imposed, the reverse is true in the by-industry estimation Cross-LIM comparisons of equity value prediction errors Table 4 presents comparisons of the four error metrics across the three LIM estimations. Panel A (B) presents comparisons of MeanSE and MeanAE without (with) imposing the LIM structure; panel C (D) presents analogous statistics for MedSE and MedAE. Significant differences between (1) LIM1 and LIM2, (2) LIM1 and LIM3, and (3) LIM2 and LIM3 error metrics are denoted by an asterisk (*), italics font, and boldface font, respectively. For each pairwise comparison of the LIMs, table 4 also lists the number of industries for which the error metrics differ significantly. 14 MeanSE, MeanAE, MedSE, and MedAE values for pooled estimations are significantly larger than each comparable industry-based value at less than the level. Consistent with these findings, Barth, Beaver, Hand, and Landsman (1999) provides descriptive evidence that accrual and cash flow earnings components vary across 22

25 Comparison of MeanSE and MeanAE based on LIM1 and LIM2 in panels A and B reveals that disaggregation of earnings into cash flow and total accruals aids in predicting equity market values. In 11 of 12 comparisons, the error metrics for LIM2 are smaller than those for LIM1. However, only four of these differences are significant, three of which obtain when the LIM structure is imposed. In particular, panel B reveals that when the LIM structure is imposed, three of six error metrics are significantly smaller for LIM2 than LIM1, and none is significantly smaller for LIM1. The significant reductions are in MeanSE, to 58.13, based on pooled estimation, and in MeanAE, 2.64 to 2.58 and 1.79 to 1.76, based on pooled and by-industry estimation. In addition, there is a greater number of industries for which LIM2 results in a reduction in MeanSE (MeanAE), 4 versus 3 (7 versus 5). Regarding comparison of prediction errors from LIM2 and LIM3, panels A and B reveal that LIM3 evidences smaller prediction errors than LIM2 when the LIM structure is not imposed. For example, panel A reveals that when the LIM structure is not imposed, disaggregating earnings into cash flow and the four major accrual components significantly decreases MeanSE from to based on by-industry estimation, and MeanAEs from 2.69 to 2.66 and 1.75 to 1.68, based on pooled and by-industry estimation. However, panel B reveals that when the LIM structure is imposed, MeanSEs and MeanAEs increase significantly when using LIM3, from to and 2.58 to 2.63, based on pooled estimation. For only MeanAE based on by-industry estimation is there a significant decrease in prediction error from LIM2 to LIM3 when the LIM structure is imposed. In addition, table 4, panels A and B reveal that the efficacy of disaggregating total accruals into its four major components appears to be industry-specific. In particular, when the industries, but does not test whether constraining the components coefficients to be the same across industries is binding. 23

26 LIM structure is not imposed, panel A reveals there are 2 (3) industries for which LIM2 results in significantly smaller MeanSEs (MeanAEs), and 4 (7) industries for which LIM3 results in significantly smaller MeanSEs (MeanAEs). When the LIM structure is imposed, panel B reveals the number of industries for which LIM2 or LIM3 has significantly smaller MeanSEs and MeanAEs is evenly split. Although comparison of error metrics based on LIM2 and LIM3 fails to reveal a consistent benefit to additional disaggregation of earnings into cash flow and the four major accrual components, comparison of mean prediction errors from LIM1 and LIM3 reveals a somewhat clearer picture. In particular, in all 12 possible cases, error metrics for LIM3 are smaller than those for LIM1. When the LIM structure is (is not) imposed, 4 of 6 (2 of 6) of the differences are significant. For example, panel A reveals that when the LIM structure is not imposed, there is a significant reduction in MeanSE (MeanAE) from to (2.72 to 2.66), based on pooled estimations, and from to (1.76 to 1.68), based on by-industry estimations. Panel B reveals that when the LIM structure is imposed, there are significant reductions in MeanAEs only, from 1.79 to 1.71 based on pooled estimations, and from 1.72 to 1.64, based on by-industry estimations. Also, table 4, panels A and B, reveal that the efficacy of disaggregating earnings into cash flow and the four major accrual components appears to be compelling for a greater number of industries, whether or not the LIM structure is imposed. In particular, panel A reveals that whereas there are 3 (8) industries for which LIM3 results in significantly smaller MeanSEs (MeanAEs) when the LIM structure is not imposed, and panel B reveals there are 8 (9) industries when it is, there are only 1 (2) industries for which LIM3 results in significantly larger MeanSEs (MeanAEs) when the LIM structure is not imposed, and 2 (3) industries when it is. 24