Historical cost measurement and the use of DuPont analysis by. market participants

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1 Historical cost measurement and the use of DuPont analysis by market participants Asher Curtis University of Washington Melissa F. Lewis-Western University of Utah This draft: October, Comments Welcome. Sara Toynbee University of Washington Abstract: We investigate whether historical cost measurement of assets appears to lower the usefulness of DuPont analysis. Specifically, we examine how variation in the age of a firm s assets affects the asset turnover ratio, the DuPont ratio most impacted by asset measurement. We find that asset turnover ratios are systematically higher and more persistent for firms with older assets. Forecast errors of asset turnover are systematically associated with the change in asset age, and these forecast errors are positively associated with future returns. Thus, changes in asset age provide information on asset measurement biases that investors do not appear to fully incorporate into contemporaneous returns. Sorting firm-years by both changes in asset age and asset turnover increases the differences in returns. Our results are consistent with investors being unable to ex ante disentangle the effect of historical cost measurement on prior asset turnover ratios when forecasting future asset utilization. Keywords: Mispricing, DuPont analysis, forecasting, historical cost bias, balance sheet growth. Corresponding Author: abcurtis@uw.edu. We gratefully acknowledge the helpful comments of an anonymous reviewer, Christine Botosan, Patricia Dechow, Peter Demerjian (FARS discussant), Victoria Dickinson, Michael Drake, Lucile Faurel, Mark Jackson (WAAA discussant), Christo Karuna, Sarah McVay, Scott Richardson (the editor), Terry Shevlin, Nemit Shroff, Richard Sloan, Greg Sommers, Vicki Tang (AAA discussant), and participants at the Fullerton CCRG-SEC Conference, AAA Annual Conference, Financial Accounting And Reporting Section meeting, and the Western Regional AAA meeting; and workshop participants from the University of Arizona, University of California - Berkeley, University of Michigan, Emory University, University of Utah, University of Tennessee, and TCU. This paper was previously circulated with the title The comparability of accounting rates of return under historical cost accounting. All errors remain our own responsibility.

2 1. Introduction The usefulness of financial statements for investors varies with how well disclosed current period data aids in the task of forecasting future economic outcomes. For example, equity investors are interested in using current period data to predict future outcomes that enable them to assess the value of equity. Investors are assumed to combine information about current period sales, current period margins, and current period asset utilization to forecast future sales, profitability, and assets of the firm. DuPont analysis provides a framework for forecasting future profitability using the product of profit margin (as a measure of profitability) and asset turnover (as a measure of asset utilization). 1 Soliman (2008) identifies an apparent lag in investors processing of changes in asset turnover but not of changes in profit margin. In this paper, we investigate how modified historical cost measurement of assets affects the properties of financial ratios, whether these effects help explain why investors appear to make forecast errors about asset utilization, and whether this links more generally to the potential mispricing of changes in assets. Ratios that use accounting inputs, such as the DuPont ratios, are a function of both economic forces and accounting measurement. As a result, one possible shortcoming of DuPont analysis, and other approaches to forecasting that use income statement data relative to assets, is that the inputs are not measured on the same monetary basis (e.g., Konchitchki, 2011; 2013). In particular, the income statement includes many items measured at current values, such as sales, while assets are measured using modified historical cost. These differences in measurement lead to a bias in reported asset-based ratios, complicating the important task of forecasting future 1 The DuPont decomposition is a well-known ratio analysis, which decomposes return on assets into profit margin and asset turnover. It has been used since the early 1900s and began gaining popularity following Pierre DuPont s successful turn-around of General Motors in the 1920s using the DuPont decomposition in their managerial accounting system. The DuPont decomposition remains a central element of ratio analysis and forecasting in current financial statement analysis textbooks. 1

3 outcomes. In the case of the asset turnover ratio, because assets are measured at modified historical cost, variation in asset turnover not only reflects economic forces, but also the effects of asset measurement. This makes it difficult for investors to forecast future profitability based on current period asset utilization (Konchitchki, 2011; 2013). 2 We hypothesize that the bias in asset turnover ratios induced by historical cost measurement provides a partial explanation for the documented association between changes in asset turnover and future returns over the subsequent 12 months (Soliman, 2008), as well as potentially contributing to broader asset growth anomalies. We measure the effect of historical cost on reported asset values by calculating the weighted average age of assets in years using the ratio of accumulated depreciation to depreciation expense (e.g. Revsine, Collins, Johnson, and Mittelstaedt, 2009). 3 To avoid significant industry differences in depreciation methods, we industry-adjust this measure prior to ranking our sample firms into asset age portfolios (hereafter, asset age). We find a significant positive relation between asset age and asset turnover, with firms in the highest asset age group (i.e., those with relatively older assets) having significantly higher asset turnover than firms in the lowest asset age group (i.e., those with relatively younger assets). In contrast, we find the firms in the highest asset age group are significantly less profitable, as measured by profit margin and return on net operating assets, than firms in the lowest asset age group. Collectively, these results provide preliminary evidence that 2 Specifically, Konchitchki (2011, 2013) finds evidence that investors underreact to unrealized gains and losses due to inflation, consistent with investors being unable to accurately incorporate unrecognized changes in value. 3 We assume that differences between modified historical cost and current values are more severe for firms with older assets. Also implicit in our use of this measure is the assumption that the salvage value for all assets is zero and that all firms employ the straight-line deprecation method. Providing some support for this assumption, Accounting Trends and Techniques (AICPA, 2007) finds that the most common depreciation method is straight-line. 2

4 asset age is linked to a measurement bias, which lowers assets (and thus increases assetdenominated ratios), rather than a competitive advantage, which would be reflected in higher sales. 4 We hypothesize that historical cost measurement of assets will lead to biases in the persistence of the asset turnover ratio due to differences in the monetary basis of sales and assets. Consistent with prior research, when we estimate persistence for each of the DuPont ratios individually we find that asset turnover is more persistent than profit margin and return on net operating assets (e.g., Fairfield and Yohn, 2001; Nissim and Penman, 2001; Penman and Zhang, 2002; Soliman, 2008). One explanation for the higher persistence in asset turnover relative to profit margin is that economic rents from physical assets are harder to expropriate than knowledge assets (i.e., Romer, 1986). We extend these results and document that the persistence of asset turnover is significantly higher for firms with older assets than for firms with younger assets. Thus, it appears that asset age introduces an effect that could be considered in part as an artificial barrier to entry. We also explore whether asset age affects profitability forecasts by examining how changes in asset turnover interact with sales growth. We follow the method outlined in Richardson et al. (2006) and find that asset turnover is generally more important in forecasting future profitability than sales growth. We also find that asset turnover and sales growth are both statistically more important determinants of future profitability for firms with the oldest assets than firms with younger assets. This evidence is consistent with both asset measurement (via measurement error in asset turnover) and diminishing marginal returns (via declining sales growth) likely playing a role in the differences in future profitability of older and younger asset firms. 4 Furthermore, we also find that the future profitability of firms in the highest and lowest quintiles of asset age is not significantly different, thus the linkage between the asset turnover ratio and competitive advantages, at least those that end in realized earnings, are unlikely to be correlated with asset age. 3

5 We next examine the association between DuPont ratio forecast errors and changes in asset age. We investigate two approaches to forecasting - a random walk model (i.e., the change in asset turnover) and an out-of-sample model that estimates future asset turnover using lagged estimates of persistence from asset age portfolios. 5 We find that both of these forecasting approaches yield forecast errors that are the most negative for the firms where asset age has declined the most and the most positive for the firms where asset age has increased the most. One interpretation of these results is that when firms purchase new assets at current values (decreasing the firm s average asset age), asset turnover falls because prior asset turnover was inflated due to unrecognized appreciation of assets measured at their modified historical cost. Similarly, firms that do not purchase significant new assets see an increase in asset turnover as the gap between market value and modified historical cost widens over time. Overall, these results provide evidence that older asset firms have temporarily inflated asset turnover ratios, which is systematically linked to forecast errors when assets change. Turning to whether stock market participants appear to understand the temporary inflation in asset turnover induced by historical cost measurement, we document that asset turnover forecast errors are positively associated with future cross-sectional stock returns, consistent with Soliman (2008). We also find some evidence that the association between forecast errors and future stock returns varies with changes in asset age. Specifically, across most portfolios of asset turnover forecast errors, returns are higher for increasing asset age firms and lower for decreasing asset age firms. As such, the link between the mispricing of asset turnover varies with changes in asset age. 5 Specifically, we assign all firms annually to five portfolios based on asset age in year t to estimate the association between asset turnover at time t, and lagged asset turnover. We use the coefficients from this regression to estimate an out of sample forecast of asset turnover at time t+1. We also estimate these forecasts for profit margin and return on net operating assets. 4

6 That is, changes in the historical cost bias in asset values affect the extent to which asset turnover forecasts are mispriced by investors. In additional analyses we first provide some preliminary international evidence to generalize our findings and to investigate the role of inflation, which, based on Konchitchki (2011, 2013), likely increases the mispricing effects related to asset age biases. Consistent with this, we find that future returns have a higher association with changes in asset age and changes in asset turnover in high inflation countries relative to low inflation countries. Second, we examine whether changes in asset age are associated with the magnitude of returns to asset growth based trading strategies (Richardson et al., 2005; Cooper et al., 2008). We find some evidence that the return spreads and alphas for these strategies are greater for firms in the extreme changes in asset age. We contribute to the literature in the following ways. First, we document an important role of accounting measurement in understanding persistence. Prior literature has generally attributed the higher persistence of asset turnover solely to the barriers of entry associated with movements of capital (e.g., Romer, 1986). Our results suggest another reason that asset turnover has higher persistence. Specifically, measuring assets at historical cost but sales at current values creates the appearance of a barrier to entry, i.e., an artificial barrier to entry. This finding is important as it provides evidence of one consequence of differences in the measurement of accounting inputs on the income statement and balance sheet a lower degree of usefulness of accounting ratios to forecast future profitability and asset utilization. Second our findings help explain why market participants may appear to misprice information about widely used accounting metrics; they appear to misunderstand the implications of historical cost accounting, one of the most well-known measurement features of financial accounting. Thus, our results should be of interest to a wide audience, following calls by Kothari 5

7 (2001) and others to investigate the underlying reasons that returns appear predictable based on accounting information. Our approach is based on a practical forecasting perspective. Specifically, our results are consistent with the practical application of DuPont ratios using unadjusted assets to measure asset utilization. As these measures are biased upwards by historical cost, they are poor predictors of asset utilization for the assets firms acquire in subsequent periods, and thus in these future periods, investors revise their expectations of the firm s ability to efficiently utilize assets to generate sales. 2. Background and empirical predictions 2.1. Linking historical cost with asset turnover persistence Ratios that use accounting inputs, such as the DuPont ratios are a function of both economic forces and accounting measurement. In terms of economics, margins are considered measures of pricing power and asset turnover measures of asset utilization. Changes in asset turnover can be indicative of changes in the productivity of assets, and to the extent that returns on assets are not easily imitated by competitors, these changes in productivity are likely to be persistent. 6 Attributing all of the variation in asset turnover to economic forces, however, implicitly assumes that the financial information is measured at its current economic, or market, value. It is well understood that historical cost lowers the book-value of net operating assets, as historical cost does not allow for the recognition of appreciation in asset values over time. In contrast, sales are recorded at current values. We formalize the expected effect of differences in measurement bases in this section. We start by defining both sales ( ) and net operating assets ( ) in their current dollar values as functions of reported values and unobserved appreciation: 6 Dickinson and Sommers (2012) also find that many competitive advantages do not lead to a sustainable increase in return on net operating assets. 6

8 =, (1) = +, where 0. (2) The superscript c refers to current dollar values, the superscript r refers to reported values (i.e., book value of net operating assets), and the superscript u refers to values that remain unrecognized by the accounting system. Because accounting standards require impairments to be recognized when asset values are lower than their reported amounts, this implies that must be positive. That is, the current value of assets must be at least as high as the reported value. Dividing Equation (1) by (2) yields a measure of asset turnover (hereafter ATO) with assets measured at current values, which is a measure of economic efficiency: =, (3) Equation (3) can be written in terms of the ATO derived from reported values and a bias attributable to historical cost measurement: = 1+. (4) As Equation (4) illustrates, if investors calculate ATO using reported values ( ) then they will have a biased measure of economic efficiency ( ). The bias is given by the term 1+, which measures the ratio of unrecognized appreciation in assets to recognized assets. This bias is increasing in the appreciation of NOA not captured by the accounting system ( ). Because of depreciation and asset appreciation, will be increasing in the amount of time since the assets were originally recorded on the balance sheet, what we term asset age. On the other hand, when new assets are purchased (i.e., increases), average asset age declines and the bias is lower. Thus, the bias in reported in ATO is higher when the average asset age is higher. This leads to our first hypothesis, which we state in alternate form: 7

9 H1: Reported asset turnover is positively associated with asset age. We will not find evidence consistent with our hypothesis, however, if the magnitude of the bias in ATO due to asset appreciation is too small, if the variation in the asset-age bias across firms within an industry is too small, or if the proportion of appreciable assets on the average firm s balance sheet is too small to have a measurable impact on reported ATO ratios. Competition is expected to force profitability to mean-revert, or to be less persistent. Among others Nissim and Penman (2001) provide evidence that ATO has higher persistence, or is more slowly mean-reverting, than profit margins. Based on Equation (4), persistence in is a function of the persistence in both true asset utilization ( ) and the bias induced by historical cost accounting 1+. Only true asset utilization is expected to be mean-reverting due to competitive forces (i.e., no firm can capture infinite sales increases without increasing assets), whereas, absent impacting capital expenditures, competitive forces are not expected to affect the historical cost bias in. Consequently, because the bias term is not expected to be meanreverting, this dampens any mean reversion in reported ATO, making more persistent than. 7 Thus, all else equal, the greater the bias, the more persistent reported ATO will be. Following H1, we predict that the bias in reported ATO is increasing in asset age. This leads to our second hypothesis, which we state in alternate form: H2: The persistence of reported asset turnover is positively associated with asset age. 7 Technically, any ratio of two nonstationary (i.e., trending variables) like sales and assets are unlikely to yield a meanreverting ratio unless they are cointegrated. Economic theory suggests that sales and assets are cointegrated as it is difficult to increase sales over an extended period of time without increasing assets. If a ratio excludes a trending term such as unrecognized increases in the value of an asset, then these ratios will become more like a random walk, which increases persistence, see for example Chapter 19 of Hamilton (1994). 8

10 Our first two hypotheses suggest that historical cost measurement introduces a bias into the measurement of ATO, and this bias is persistent. This persistent bias is due to how historical cost measurement affects assets in the denominator of the ratio. However, as the proportion of newer assets increases, the bias falls as older assets become a smaller portion of the asset base. That is, the difference between reported asset utilization,, and true asset utilization will be decreasing when new assets make up a higher proportion of the asset base (i.e., through purchases of new assets at market value, and disposals of older assets) and increasing as the assets age (naturally as a function of time and increasingly when newer assets are disposed of). Thus, changes in the bias will affect investors ability to forecast because the extent of the bias is difficult to observe until the asset base changes and subsequent unexpected ratios are reported providing information on the portion of attributable to economic performance ( ) and accounting measurement 1+. Thus, our third hypothesis, stated in alternate form, is: H3: Asset turnover forecast errors are positively associated with changes in asset age Linking accounting rates of return to stock prices Accounting rates of return are linked to stock prices as they provide information about future cash flows. We formalize the link in this section. Finance theory describes stock returns over the period t 1 to t, as the change in the price from t 1 to t plus dividends paid during the period t 1 to t: #$%&' = ( +) ( +,, (5) 9

11 Where #$%&' is the dollar return to an investment at the purchase price ( +,, the closing price is ( and ) is the sum of all net dividends paid over the period t 1 to t. Edwards and Bell (1961), Peasnell (1982) and Ohlson (1995) show that clean-surplus earnings and book values can replace dividends in a valuation model. In particular, the cleansurplus relation means that all changes in the book value of equity (- ) can be captured by net income (. ) and dividends, i.e., clean-surplus is the relation that - = - +, +. ). Substituting the clean-surplus relation into Equation (5) yields: #$%&' =. +/(( - ) (( +, - +, )], (6) Writing Equation (6) as an expected return over the period t + 1 at time t yields: 1 (#$%&', ) = 1 (., )+1 / (( - )], (7) Equation (7) highlights that expected returns include the change in the expected difference between price and book value. Rearranging the price-level residual income model yields ( - = = 1 ( ): 78;< >?,, and substituting into Equation (7) suggests that: (, 9 ) 8 = 1 (#$%&', ) = 1 (., ( ): 78;< >?, A. (8) (, 9 ) 8 Equation (8) illustrates that according to the residual income model, expected changes in return on equity (ROE) are associated with expected returns. To isolate the role that historical cost measurement has on accounting ratios, we decompose ROE following prior literature. Nissim and Penman (2001) highlight that ROE is affected by capital decisions and show that it is useful to abstract away from the effects that financial leverage has on ROE using return on net operating assets (RNOA): # 1 = # +/BC1D (#1) ]. (9) Where BC1D is financial leverage, or net financial assets, and (#1) is the (net) rate of return on net financial assets. Hence, # captures the firm s operating profitability after removing the 10

12 effects of financial leverage. Fairfield and Yohn (2001) and Soliman (2008) further decompose # using the DuPont formula: # = (F, (10) Operating Income Where PM = Sales and ATO = Sales Net Operating Assets expectations of changes in ATO are positively associated with stock returns.. Combined, Equations (8)-(10) illustrate that Miller and Rock (1985) suggest that rational investors will price new information that changes beliefs about future cash flows as a function of the persistence of that information. Prior literature, however, find results consistent with investors underreacting to new information, as their price responses do not appear to fully reflect the persistence in earnings (Kormendi and Lipe 1987; Bernard and Thomas 1990), accruals (Sloan 1996), special items (Burgstahler et al. 2002), and asset turnover ratios (Soliman 2008). As we argue above, changes in reported asset turnover will in part be attributable to changes in economic performance and in part to changes in the measurement bias in assets. We expect that both of these factors are likely to be persistent as Romer (1986) suggests that returns to physical assets are difficult to expropriate making asset utilization persistent and as older assets lead to a persistent bias in reported asset turnover. Although this effect on the value of assets is well-known, Konchitchki (2011, 2013) finds evidence that unrealized gains and losses due to inflation are underreacted to by investors, consistent with investors not being able to accurately incorporate unrecognized changes in value. For these reasons, we conjecture that investors do not undo the measurement bias in prior asset turnover ratios. We also anticipate that investors may underreact to asset turnover forecast errors, leading to predictable future returns. This is because although changes in the asset base will provide some information about the extent of the bias in asset turnover ratios, the bias is unlikely to be completely revealed in a single period. Therefore, as future investments are made, the persistent effects of the 11

13 measurement bias are likely to lead to asset turnover forecast errors in future periods. As the measurement bias is unobservable, we expect that investors cannot disentangle the measurement bias from changes in asset utilization completely, and we expect this will lead to an underreaction to asset turnover forecast errors on average. This leads to our final hypothesis: H4: Forecast errors of reported asset turnover are positively associated with future returns. 3. Data and variable measurement We obtain financial data from the Compustat database and stock returns from CRSP for fiscal years from We include all common shares (CRSP share codes 10 and 11) listed on the NYSE/AMEX and NASDAQ (CRSP exchange codes 1, 2 and 3). We exclude financial firms (with SIC codes between ), as the DuPont ratios are not meaningful for these firms and to maintain consistency with prior research. We also remove utilities due to the possible regulation of capital expenditures and firms who are classified into the Other category in Fama and French (1997) as it is a noisy industry grouping. Consistent with Konchitchki (2011), we delete observations with total assets, sales, or market value of equity less than ten million dollars to avoid problems associated with using a small denominator. We also delete firms with a closing price less than one dollar per share at the end of fiscal year t to remove firms with poor liquidity. We separate firm-years where a loss was reported from our main sample for three reasons. First, accounting ratios are typically less meaningful for loss firms. Second, we are interested in whether historical cost accounting inflates accounting based rates of return, but for loss firms, accounting based rates of return are deflated (i.e., look less negative) when the asset base is larger. Third, we are interested in linking persistence to historical cost and accounting based metrics and 12

14 loss firms tend to have lower persistence at least for earnings variables. Combined with other sample restrictions relating to variable construction, which are discussed below, these restrictions yield a sample of 56,300 profitable firm-year observations for our primary set of analysis The DuPont decomposition Following Soliman (2008), we measure RNOA as operating income (OIADP) divided by average net operating assets (NOA) where NOA is operating assets less operating liabilities. Operating assets (OA) is total assets (AT) less financial assets (FA). 8 FA is cash and short-term investments (CHE) plus investments and advances (IVOA). Operating liabilities is calculated as total liabilities (TL) less the current and long-term portion of long-term debt (DLC+DLTT). Asset turnover (ATO) is sales (SALE) divided by average NOA, profit margin (PM) is operating income (OIADP) divided by sales (SALE). We restrict our analysis to firms with non-missing operating income, total assets, common equity, net operating assets, and gross and net property, plant and equipment and positive sales. All other variables are set to zero when missing. Because we require these variables in both levels and changes, we require that the ratios can be computed for year t and year t - 1 for the observation to enter the sample Asset age We measure asset age as the ratio of accumulated depreciation to depreciation expense. This is a simple estimate of the age of a firm s assets that is advocated by financial analyses texts (e.g., Revsine, Collins, Johnson, Mittelstaedt 2011). 9 We measure accumulated depreciation as the difference between gross property plant and equipment and net property plant and equipment 8 Note that total assets reported by Compustat aggregates net property, plant and equipment. 9 Although we anticipate that more precise measures, for example by the method of Konchitchki (2011), would increase the power of our tests, we do not expect any systematic bias resulting from using our simple measure. 13

15 (PPEGT PPENT). In order to isolate depreciation expense, we calculate the difference between depreciation, depletion and amortization (DP) and amortization (AM), where missing values of amortization are set to zero. We identify and remove observations where asset age appears to be a data error. Specifically, we eliminate observations where: (i) asset age is negative, (ii) asset age is greater than the age of the firm, and the (iii) accumulated depreciation is greater than gross property plant and equipment. Finally, we industry-adjust our asset age variable based on the Fama-French 48 industry classifications. We report the unadjusted means for each industry in Appendix A, as expected, average asset age varies significantly by industry, highlighting the need for industry adjustments to this variable Concurrent and future returns We calculate average buy-and-hold size-adjusted abnormal returns for each portfolio over holding periods of 12, 24, and 36 months beginning five months after the end of the fiscal year. Buy-and-hold returns for firms that delist during our sample period are adjusted for delisting returns following Beaver et al. (2007). We also calculate concurrent returns using returns for the 12 months ending four months after the end of fiscal year t (Ret). 4. Empirical results 4.1. Descriptive statistics In Table 1, we provide mean values for the variables used in our study, both for the full sample, for loss firm-years separately, and by quintiles of asset age (excluding loss firms). We report differences between the mean characteristics of firms with the oldest asset age and the mean characteristics of firms with the youngest asset age in the final column. All financial ratios are 14

16 winsorized at the 1 st and 99 th percentile to reduce the impact of outliers on the means. The average return on net operating assets is Average asset age is 6.103, the average asset turnover ratio is 2.676, and the average profit margin is 0.060, similar to Soliman (2008). The average firm in our sample has a market value of equity of 2,586 million, consistent with these companies being larger and reflects our removal of smaller firms in our sample screens. Asset turnover is significantly higher for the portfolio of firms with the highest asset age. Specifically, asset turnover is for firms with the youngest assets (in Q1) and for firms with the oldest age (in Q5). The difference of is statistically significant at the 1% level. 10 Thus, we find evidence consistent with H1, which predicts a positive association between ATO and asset age. 11 We also report the average values of other accounting ratios and performance indicators. We find significant differences in profit margin (PM) and return on net operating assets (RNOA) between the oldest and youngest asset firms. However, we find that firms with the youngest assets have significantly higher PM and RNOA than those firms with the oldest assets. To the extent that RNOA is driven more by PM than ATO (Amir et al., 2011), these results suggest that relation between asset age and ATO is not driven by asset age reflecting factors correlated with economic performance, as we would find similar relations between asset age and both RNOA and PM. 12 Rather, these results suggest that asset measurement impacts reported ATO ratios, with olderasset firms reporting more upwardly biased ATO ratios We estimate the statistical significance of the difference in the mean values between the extreme quintiles after accounting for both cross-sectional and time-series correlation. 11 We confirm the robustness of this result to several controls for determinants of economic performance. We discuss this analysis further in section Related to this observation, Konchitchki and Patatoukas (2014) find that the relation between RNOA and future real GDP growth is driven by PM, not by ATO. 13 Throughout our analyses, we industry-adjust asset age and changes in asset age due to significant variation across industries in this measure, which could be attributable to differences in depreciation methods across industries. In untabulated analyses, we also confirm the robustness of our results to industry-adjusting the accounting ratios. Inferences are unchanged with these adjustments (not tabulated). 15

17 We also provide evidence that our measure of asset age captures changes in the asset base. Specifically, we use a broad measure of investment following Richardson (2006) and compare investment as a proportion of total assets for firms in each asset age quintile. Specifically, we measure total investment as the sum of capital expenditures, research and development expenditures, and acquisitions, less the sale of property, plant and equipment, plus amortization and depreciation (CAPX + XRD + AQC SPPE + DPC). The results illustrate that firms with the youngest assets invest significantly more than firms with the oldest assets. Older asset age firms are also typically value firms with higher book-to-market ratios and are on average significantly older than firms with the youngest assets. 14 Similarly, we also find that firms with the youngest assets have significantly higher sales growth and accruals ( NOA) than firms with the oldest assets. As asset turnover is lower for these firms with higher sales growth our results are consistent with conservatism and growth being substitutes (Rajan et al., 2007). Finally, consistent with asset age capturing accounting measurement effects as opposed to economic forces, we find no significant differences in the change in future profits over the period t to t+3 between the highest and lowest asset age quintiles The association between the persistence of the DuPont ratios and asset age Hypothesis 2 predicts a positive association between the persistence of asset turnover and asset age. To test this hypothesis, we estimate the following persistence regressions for each of the five portfolios ranked by asset age: # > = K +, # >+, + (11) > = L K +L, >+, +, (12) 14 Note however, that the market value of equity suggests that the extreme asset age firms are smaller on average. 16

18 (F > = M K +M, (F >+, + (13) The regressions in Equations (11) (13) are standard in the accounting literature and measure the average persistence for equally-weighted portfolios. Sorting on asset age allows us to test whether the average persistence of RNOA, ATO, PM is higher for firms with older assets. We predict that asset age will increase the persistence of asset turnover but we do not make any ex-ante predictions regarding the persistence of PM or RNOA. Specifically, hypothesis 2 predicts L, will be higher for firms with older assets. We estimate Equations (11) (13) by asset age quintiles and present the results of the pooled estimates that correct for cross-sectional and time-series correlation in Table 2 (Petersen, 2009). 15 We also present results separately for the full sample (including loss firms) and for loss firm-years separately. In Panel A, we provide the estimates of the RNOA. The persistence of RNOA in our sample varies across the asset age groups, but is not significantly different between the oldest and youngest asset firms. In Panel B, we report the persistence of asset turnover. In this case, consistent with hypothesis 2, we see a clear increase in the persistence of asset turnover as asset age increases. Specifically, the persistence of asset turnover for firms with the youngest assets is equal to 0.715, whereas the persistence of asset turnover for firms with the oldest assets is 0.836, where the difference is significant at the 1% level. 16 Thus variation in asset age appears to make asset turnover less comparable, as it biases the asset turnover of older asset firms upwards. This comparability concern will be persistent until the bias in the asset base is removed, either by disposals of older assets or purchasing newer assets. 15 Our inferences are unchanged when estimating Equations (11)-(13) by year and asset age quintiles and obtaining the t-statistics based on the distribution of the parameter estimates (untabulated). 16 Results are robust to estimating persistence by quintiles of the average asset age in t and t-1 (untabulated). 17

19 In Panel C, we report the persistence coefficients for PM. The results are similar to those of the RNOA where we find evidence of an inverted U-shape in the persistence of PM across the asset age quintiles. Furthermore, the bottom and top quintiles of asset age do not differ significantly in the persistence of PM. Thus, asset age does not have a systematic effect on the persistence of the PM, which provides further support that asset age captures an accounting measurement effect rather than differences in economic forces across the firms in the different quintiles. Given the lower persistence of loss firm-years, we exclude these firm-years in our remaining analyses, unless stated otherwise Forecasting RNOA using additional decompositions Because forecasting financial statement elements is typically undertaken jointly, we also investigate two decompositions of RNOA, which highlight how asset turnover contributes to forecasting RNOA. We present the results of these decompositions in Table 3. In Panel A, we examine the DuPont decomposition and find a marginal increase in the association between lagged asset turnover and RNOA for firms with older assets. However, the difference in the coefficients between Q5 and Q1 is not significant at conventional levels. Consistent with Amir et al. (2011), we also find that PM appears to have stronger predictive power for forecasting future RNOA than ATO even though ATO is individually more persistent. This result also provides some descriptive evidence as to why the persistence of RNOA is more similar to PM than ATO in Table 2. In Panel B, we use a decomposition of RNOA based on long-term accruals provided by Richardson et al. (2006). This decomposition illustrates that long-term accruals can be decomposed into sales growth, the change in asset turnover, and the interaction of the two terms. We estimate the model in Richardson et al. (2006) for the full sample, loss firm-years and by quintiles of asset 18

20 age separately. Our results illustrate that both the change asset turnover and sales growth are significantly more negatively associated with future RNOA for older asset firms than for younger assets firms. These results suggest that the historical cost bias in asset measurement creates accounting distortions, which contribute to the lower persistence of accruals (e.g., Richardson et al., 2006). Additionally, the difference in the effect of sales growth on future RNOA by asset age quintiles suggests a significant role of diminishing marginal returns, as sales growth has a lower effect on persistence for firm-years with older assets. Finally, we also present the F-statistic comparing the coefficients for sales growth and the change in asset turnover in Panel B. Except for the highest quintile of asset age, we find a significant difference in the coefficients for each subsample examined. Overall, the results in Panel B suggest that both asset measurement and diminishing marginal returns likely play a role in the differences in forecasting RNOA for older and younger asset firms Correlation between asset turnover forecast errors and changes in asset age Hypothesis 3 predicts that forecast errors of asset-based ratios are positively associated with changes in asset age. We calculate forecast errors for each DuPont ratio based on two different forecasting models. First, we forecast each ratio as a random walk, where the forecast error is simply the change in the ratio from year t-1 to year t. Second, we calculate forecast errors based on the AR(1) models described in Equations (11) - (13). Specifically, we subtract from the actual realizations of each DuPont ratio the predicted value, where the predicted values are calculated using parameter estimates from the asset age portfolio that the firm belonged to in the prior year Thus, the AR(1) forecast errors are out of sample forecast errors and are estimated from

21 We present the average value of these forecast errors as well as additional variables for quintiles sorted on the basis of the industry-adjusted change in asset age in Table 4. Consistent with expectations, in Panel A, we find the mean random walk forecast error for firms in quintile 1 is and the mean forecast error for firms in quintile 5 is The difference between these mean forecast errors is and is significant at the 1% level. The AR(1) forecast errors are presented in Panel B and although the forecast errors are smaller than the random walk forecast errors, we continue to observe a similar pattern in the forecast errors and document a similarly significant difference in the AR(1) forecast errors between the highest and lowest change in asset age quintiles. These results suggest that when firms make more investments in assets or dispose of older assets, thus reducing the average age of their assets, forecasts of ATO overestimate the persistence of the ratio. In contrast, when firms asset base increases in average age, forecasts of ATO underestimate the persistence of the ratio. Thus, consistent with hypothesis 3, we find evidence of a positive relationship between ATO forecast errors and changes in asset age. We also find evidence of significant differences in the random walk forecast errors for PM and RNOA for firms in the highest and lowest quintiles of changes in asset age, suggesting that asset age effects may also be correlated with future profit margins. Overall, Table 4 provides evidence consistent with the notion that changes in asset age are systematically associated with ATO forecast errors, consistent with our third hypothesis. We present additional descriptive statistics for quintiles sorted on the basis of the industryadjusted change in asset age in Panel C. First, we illustrate that firms whose average asset age has declined the most (i.e., Q1) made significantly greater investments (TI/TA) and experienced significantly greater sales growth during the year than firms whose average asset age has increased 20

22 the most (i.e., Q5), and this difference is significant at the 1% level. 18 This provides additional support for our asset age variable. As changes in asset age provide information about the removal of a bias in asset measurement, we expect these changes to be associated with poor stock price performance. Consistent with this prediction, we find that both contemporaneous and future returns are significantly greater for firms with the largest increases in asset age (Q5) relative to firms with the greatest declines in asset age (Q1). As we see similar patterns in future returns over longer horizons, suggesting that investors do not immediately impound the information in changes in asset age The correlation between stock returns, asset turnover forecast errors, and changes in asset age Our fourth hypothesis predicts that asset turnover forecast errors are positively associated with concurrent and future returns. In Table 5, we report the mean buy-and-hold returns for various portfolios over several horizons. Specifically, we measure concurrent returns (Ret) as buy-and-hold returns for 12 months ending four months after the end of fiscal year t. Future size-adjusted buyand-hold abnormal returns are held at 12, 24 and 36 month, beginning five months after the end of the fiscal year t. We report statistical significance of the hedge returns to the extreme portfolios after adjusting for cross-sectional and time-series correlation (Petersen, 2009; Gow et al., 2010). In Panel A, we report the raw returns to portfolios formed on the basis of the random walk forecast errors for ATO (i.e., changes in ATO). In the year over which ATO is realized and reported, returns are increasing across quintiles. However, consistent with Soliman (2008), we find evidence that investors fail to fully incorporate the effect of changes in asset turnover ratios, as the returns subsequent to the realization of the asset turnover are significantly greater for the firms with 18 We also find consistent results when examining only capital expenditures as a measure of investment (untabulated). 21

23 positive changes in asset turnover relative to the firms with the lowest changes in asset turnover. We also report returns over longer horizons and find that the returns are increasing over the holding period, suggesting that the incorporation of forecast errors into stock prices occurs over a relatively long horizon. Nonetheless, the majority of the future returns are realized within the first year after portfolio formation. This is consistent with market participants calibrating their estimates of the magnitude of the bias over time as subsequent ATO ratios are reported. In Panel B, we report returns to portfolios sorted on the forecast errors generated from the AR(1) forecast model in which firm-years are assigned based on membership in the asset age portfolio in year t-1, and the forecast errors being the difference between time t asset turnover and the predicted value of the ratio. This method generates slightly greater hedge returns than the random walk specification. Specifically, the raw hedge return is or 7.6% spread over the 24 months after portfolio formation, is approximately 2.2% higher than the random walk model. 19 In Panels C and D, we report the average value of one-year ahead size-adjusted buy-andhold abnormal returns to portfolios formed by independent double sorts on the basis of the change in asset age and ATO forecast errors. Here we examine whether the returns associated with asset age vary by the change in asset age. We expect that the returns will be lower for firms in the lowest asset age quintile within each change in asset turnover quintile. In Panel C, we find some evidence consistent with this expectation, as in each column the returns appear higher in the highest change in asset age (Q5) portfolio than in the lowest change in asset age (Q1) portfolio. Other than in Q3 of the change in asset age, however, the results are typically not statistically significant. When we 19 In untabulated analyses, we estimate the hedge returns to portfolios formed on the basis of AR(1) forecast errors in PM and RNOA. As expected, we find that the concurrent hedge returns are significantly positive, suggesting that firms with higher than predicted PM and RNOA have significantly higher future returns than firms with lower than predicted PM and RNOA. However, in contrast to the results in Table 5, future returns to a hedge portfolio based on AR(1) forecast errors of PM (RNOA) are significantly (insignificantly) negative. 22

24 examine the two most extreme portfolios in Panel C (i.e., firm-years in the lowest quintiles for both the change in asset age and forecast errors and those in the highest quintiles for both the change in asset age and forecast errors), we see a significantly positive return spread (0.055), which we confirm is statistically significant and robust to controlling for various proxies for risk. We find similar results in Panel D, although these results are statistically significant in the predicted direction within four of the five quintiles of the change in asset turnover. Overall, the evidence in Table 5 provides evidence in support of hypothesis 4. In addition, the out-of-sample forecast errors based on prior levels of persistence have a greater association with future returns and have a greater ability to sort future returns within each portfolio, which is consistent with investors being unable to disentangle changes in asset measurement effects from the change in asset turnover Multivariate analysis of future returns In Table 6 we examine the association between one-year ahead size-adjusted buy-and-hold returns, changes in asset age, and asset turnover ratio forecast errors, controlling for known sources of variation in returns. We follow the methodology of Doyle et al. (2003) and rank the independent variables into quintiles ranging from 0 to 4 and divide the rank by 4. We also include controls for sales growth and the change in net operating assets, as well as the ratio of total investment to total assets from Richardson (2006). We also calculate a number of variables that aim to control for firmcharacteristics and risk in our tests. Specifically, for each firm we calculate market capitalization (MVE) at the end of the fiscal year as the product of shares outstanding and the closing price (CSHO*PRCC_F), the book-to-market ratio (BM) as common equity divided by MVE (CEQ / 23

25 MVE), lagged annual beta from the market-model using the CRSP value-weighted index (beta), lagged annual idiosyncratic risk using the variance of the market model residuals (Sigma). We report these results in Table 6. In column (1) we report results using the random walk forecast errors. After controlling for various firm and risk characteristics, we find a positive association between these forecast errors of asset turnover and future returns, although this association is not significant at conventional levels. Untabulated analyses reveal that including the change in net operating assets in the model subsumes the predictive power of the change in asset turnover. Furthermore, we find no evidence of an association between changes in asset age and future returns. In column (2) we investigate the forecast errors generated by the AR(1) model, and find evidence of a positive and significant association between asset turnover forecast errors and future returns (p<0.01). These results suggest that the future market prices are predictably related to the errors resulting from forecasts using biased prior asset turnover. We next examine whether there are differences in the apparent mispricing of asset turnover between firms with the largest and smallest changes in asset age. Specifically, we examine the model in column (2) of Table 6 for the bottom and top quintiles of the change in asset age separately and report results in columns (3) and (4) of Table 6 respectively. We find no evidence of mispricing for asset turnover for firms whose average asset age has declined the most (Q1) but we continue to document a significant positive association between the asset turnover forecast errors and future returns for firms whose average asset age has increased the most (Q5). Despite visual evidence of an economically greater coefficient, we find that this difference is not statistically significant at conventional levels (two-sided p-value = 0.183; untabulated). 5. Additional Analyses 24