pp. 695–717
Discretionary Revenues as a Measure of Earnings Management
Stephen R. Stubben
The University of North Carolina at Chapel Hill
ABSTRACT: This study examines the ability of revenue and accrual models to detect simulated and actual earnings management. The results indicate that revenue models are less biased, better specified, and more powerful than commonly used accrual models. Using a simulation procedure, I find that revenue models are more likely than accrual models to detect a combination of revenue and expense manipulation. Using a sample of firms subject to SEC enforcement actions for a mix of revenue- and expenserelated misstatements, I find that, although revenue models detect manipulation, accrual models do not. These findings provide support for using measures of discretionary revenues to study earnings management.
Keywords: revenues; earnings management; discretionary accruals.
Data Availability: Data are available from public sources.
I. INTRODUCTION
T
his study examines the ability of revenue and accrual models to detect simulated and actual earnings management. Despite repeated criticisms of accrual models over the past 15 years (e.g., Dechow et al. 1995; Bernard and Skinner 1996; Guay et al. 1996; McNichols 2000; Thomas and Zhang 2000; Kothari et al. 2005), many studies have addressed and continue to address earnings management using these models, presumably because few viable alternatives exist.1 Accrual models have been criticized for providing biased and noisy estimates of discretion, which calls into question the conclusions from studies that use them (Bernard and Skinner 1996). The objective of this study is to evaluate a different measure of earnings management—discretionary revenues—that permits more reliable and conclusive inferences than existing models.
1 For example, between 2005 and 2008, The Accounting Review, Journal of Accounting and Economics, and Journal of Accounting Research published at least 40 articles that use a measure of discretionary accruals.
This study is based on my dissertation titled ‘‘The Use of Discretionary Revenues to Meet Earnings and Revenue
Targets.’’ I thank my dissertation committee of Mary Barth (co-chair), Bill Beaver (co-chair), and Maureen McNichols, as well as Steven Kachelmeier (the senior editor), Mark Trombley (the editor), two anonymous reviewers, Yonca Ertimur, Fabrizio Ferri, Wayne Landsman, and workshop participants at Stanford University, University of California, Los Angeles, The University of Chicago, Massachusetts Institute of Technology, Harvard Business School, The University of North Carolina at Chapel Hill, the 2005 Accounting Research Symposium at Brigham Young University, and the 2006 EAA Doctoral Colloquium for invaluable comments and suggestions.
Editor’s note: Accepted by Mark Trombley.
Submitted: June 2008
Accepted: July 2009
Published Online: March 2010
695
The most common approaches to estimating earnings management (i.e., the extent management exercises discretion over reported earnings) use aggregate accruals. However, several studies have suggested focusing on one component of earnings, which has the potential to provide more precise estimates of discretion (McNichols and Wilson 1988; Bernard and Skinner 1996; Healy and Wahlen 1999; McNichols 2000). Modeling a single earnings component permits incorporating key factors unique to that component, thereby reducing measurement error. In addition, focusing on earnings components provides insights into how earnings are managed. Revenues is an ideal component to examine as it is the largest earnings component for most firms and is subject to discretion. Dechow and Schrand (2004, 42) find that over 70 percent of SEC Accounting and Auditing Enforcement Releases involve misstated revenues. Furthermore, revenues are the most common type of financial restatement (Turner et al. 2001).
I model a common form of revenue manipulation—premature revenue recognition— and its effect on the relation between revenues and accounts receivable. I define prematurely recognized revenues as sales recognized before cash is collected using an aggressive or incorrect application of Generally Accepted Accounting Principles. My revenue model is similar to existing accrual models (Jones 1991; Dechow et al. 1995), but with three key differences.
First, I model the receivables accrual, rather than aggregate accruals, as a function of the change in revenues. Of the major accrual components, receivables have the strongest empirical and most direct conceptual relation to revenues. Explaining other working capital accruals by revenues alone contributes to the noise and bias that plague accrual models. Because I model receivables instead of aggregate accruals, the model is one of revenues rather than earnings.
Second, I model the receivables accrual as a function of the change in reported revenues, rather than the change in cash revenues (Dechow et al. 1995). Although this choice systematically understates estimates of discretion in revenues, it is less likely to overstate estimates of discretion for firms whose revenues are less likely to be realized in cash by year-end (e.g., growth firms). The modified Jones model (Dechow et al. 1995) treats uncollected credit sales as discretionary.
Third, I model the change in annual receivables as a linear function of two components of the change in annual revenues: (1) change in revenues of the first three quarters, and (2) change in fourth-quarter revenues. Because revenues in the early part of the year are more likely to be collected in cash by the end of the year, these have different implications for year-end receivables than a change in fourth-quarter revenues. Revenue and accrual models that fail to consider fourth-quarter revenues separately overstate (understate) discretion when fourth-quarter revenues are relatively high (low).
I also estimate a version of the model that allows the relation between receivables and annual revenues to vary depending on firms’ credit policies. Models that fail to incorporate differences across firms in the relation between revenues and receivables (or accruals) will misstate estimates of discretion.
Discretionary revenues is the difference between the actual change in receivables and the predicted change in receivables based on the model. Abnormally high or low receivables indicate revenue management. To benchmark against existing models, I compare the ability of the revenue model and commonly used accrual models (Jones 1991; Dechow et al. 1995; Dechow and Dichev 2002; Kothari et al. 2005) to detect combinations of revenue and expense management.
Findings indicate that measures of discretionary revenues do in fact produce estimates with substantially less bias and measurement error than those of accrual models. Using simulated manipulation (Kothari et al. 2005), I find that the revenue model produces estimates of discretion that are well specified for growth firms. Each of the accrual models tested exhibits substantial misspecification. The results for growth firms indicate a bias of over 2 percent of total assets for each of the accrual models.
The results indicate further that discretionary revenues can detect not only revenue management, but also earnings management (via revenues), whereas accrual models do not. Using a sample of firms targeted by SEC enforcement actions, I find that the revenue model is able to detect earnings manipulation, but accrual models are not. The simulation analysis reveals that the revenue model is more likely than accrual models to detect earnings management for equal amounts of revenue and expense manipulation. These findings suggest that the revenue model is less likely than accrual models to falsely indicate earnings management, and more likely than accrual models to detect earnings management when it does occur.
Finally, the results have implications for studies that use accrual models. First, the Jones model (Jones 1991) exhibits better specification than the modified Jones model (Dechow et al. 1995), which suggests including reported revenues, rather than cash revenues, in accrual models. Second, the Dechow-Dichev model (Dechow and Dichev 2002; McNichols 2002), which was originally developed to estimate earnings quality, exhibits greater misspecification than other accrual models when used to estimate discretionary accruals. I am unaware of any other study that evaluates the ability of the Dechow-Dichev model to estimate discretionary accruals. Last, the innovations I incorporate into the revenue model, including separating fourth-quarter revenues and allowing the relation between revenues and accruals to vary across firms, could improve the performance of accrual models.
II. MOTIVATION AND RELATED RESEARCH Earnings Management
Earnings management has received significant attention in the popular press and academic accounting literature (McNichols 2000). Recently, various accounting scandals (e.g., Enron, WorldCom, and Parmalat), and subsequent regulation (e.g., Sarbanes-Oxley) have fueled this attention.
As Beneish (1999, 24) writes, ‘‘The extent to which earnings are manipulated has long been of interest to analysts, regulators, researchers, and other investment professionals.’’ For analysts and investors, understanding the extent to which managers exercise discretion in earnings is important in assessing the quality of earnings. Understanding which firms manage earnings and how they do it is useful for standard-setters and regulators. Frequent earnings management warrants new standards or additional disclosures, and evidence on the specific accruals managed allows standard-setters to narrow their focus in this regard. Understanding the motives for earnings management allows the SEC to narrow its focus in enforcing standards. In each case, a reliable measure of earnings management and the specific accruals used is required.
Findings of Prior Literature
Accrual Models
Studies of earnings management around firm-specific events commonly use models of aggregate accruals. A variety of accrual models have been used in recent years. Most accrual models are some variation of the cross-sectional Jones model (Jones 1991; DeFond and Jiambalvo 1994). In these models, nondiscretionary, or normal, accruals are usually estimated as a linear function of change in revenues and gross property, plant, and equipment. The models are usually estimated by industry and year, and the residual is the discretionary accruals estimate. The modified Jones model (Dechow et al. 1995) uses change in cash revenues rather than change in total revenues because some credit revenues may be discretionary. Other models add additional conditioning variables, such as cash flows (Dechow and Dichev 2002; McNichols 2002).
Despite the prevalence of these models, they have been criticized for providing biased and noisy estimates of discretionary accruals (Dechow et al. 1995; Kang and Sivaramakrishnan 1995; Bernard and Skinner 1996; Guay et al. 1996; Thomas and Zhang 2000). Dechow et al. (1995) find that discretionary accrual models generate tests of low power for earnings management of economically plausible magnitudes and misspecified tests of earnings management for firms with extreme financial performance, which is frequently correlated with the earnings management incentive under investigation (e.g., IPOs and SEOs). The results in Guay et al. (1996) are consistent with the modified Jones model estimating discretionary accruals with considerable imprecision and/or misspecification. Thomas and Zhang (2000) assert that the commonly used models ‘‘provide little ability to predict accruals.’’
Inferences relating to earnings management depend on the researcher’s ability to accurately estimate discretionary accruals. As a consequence of accrual models’ poor performance, studies using accrual models have often produced mixed results. Burgstahler and Eames (2006) find that firms with small positive forecast errors have higher unexpected accruals using the Jones (1991) model, in contrast to the absence of such an association in Phillips et al. (2003), who employ the modified Jones model. Matsumoto (2002) finds evidence of firms using discretionary accruals to meet earnings forecasts in one specification, but not in another. Dechow et al. (2003) find similar magnitudes of discretionary accruals for small loss and small profit firms and conclude that if firms overstate earnings to report profits, then their accrual model is not powerful enough to detect it.
Specific Accruals
A limitation of aggregate discretionary accrual measures is that they do not provide information as to which components of earnings firms manage. These models do not distinguish discretionary increases in earnings through revenues or components of expenses. McNichols (2000) suggests that future progress in the earnings management literature is more likely to come from the examination of specific accruals (see also Bernard and Skinner 1996; Healy and Wahlen 1999; Beneish 2001).
The advantage of using specific accruals, such as loan loss reserves, is that they are material and a likely object of judgment and discretion. However, many accruals are industry specific (e.g., banking and insurance industries) and the analysis cannot be applied to firms outside the industry. In contrast, McNichols and Wilson (1988) examine discretion in the allowance for bad debts. This accrual is common across industries. However, bad debt expense is often only a small portion of reported earnings, so only a relatively small portion of the total amount of a firm’s discretion is likely to be captured. An ideal specific accrual for study is one that is (1) common across industries, (2) subject to discretion, and (3) represents a large portion of the earnings discretion available to firms. Based on these criteria, revenues is a natural candidate.
Revenues as a Means of Earnings Management
Three studies that examine revenue management are Plummer and Mest (2001), Marquardt and Wiedman (2004), and Caylor (2009). Plummer and Mest (2001) study the discretion in earnings components using distributional tests similar to those of Burgstahler and Dichev (1997), finding evidence suggesting firms manage earnings upward to meet earnings forecasts by overstating revenues and understating some operating expenses. They do not attempt to estimate discretionary revenues.
Marquardt and Wiedman (2004) estimate the unexpected portions of several accrual components, including receivables, to determine which components of earnings firms manipulate in certain settings. They find evidence that firms with small earnings increases understate special items but do not overstate revenues. They also find evidence that firms use discretion in revenues to increase (decrease) earnings prior to equity issuances (management buyouts). Caylor (2009) uses discretionary revenues to test their use for avoiding reporting negative earnings surprises and finds evidence that managers use discretion in revenues that affects both accounts receivable and deferred revenues to report positive earnings surprises. I seek to validate a measure of discretionary revenues that can be used to test hypotheses in studies such as these.
III. RESEARCH DESIGN
Discretionary revenues take a number of forms. Some involve the manipulation of real activities (e.g., sales discounts, relaxed credit requirements, channel stuffing, and bill and hold sales), and others do not (e.g., revenues recognized using an aggressive or incorrect application of Generally Accepted Accounting Principles (GAAP), fictitious revenues, and revenue deferrals). I model premature revenue recognition and its effect on the relation between revenues and accounts receivable. Premature revenue recognition includes channel stuffing and bill and hold sales, if customers do not pay cash for the inventory, and revenues recognized using an aggressive or incorrect application of GAAP.
I focus on premature revenue recognition because evidence suggests that it is the most common form of revenue management. For example, Feroz et al. (1991) find that more than half of SEC enforcement actions issued between 1982 and 1989 involved overstatements of accounts receivable resulting from premature revenue recognition. Other forms of revenue manipulation, such as sales discounts, could be profit-maximizing business decisions and not merely attempts manage revenues to meet a performance benchmark.
Model of Discretionary Revenues
Reported (i.e., managed) revenues (R) is the sum of nondiscretionary revenues (RUM) and discretionary revenues (RM):
Rit RitUM RMit .
A fraction, c, of nondiscretionary revenues remains uncollected at year-end, and I assume there are no cash collections of discretionary revenues. Thus, accounts receivable (AR) equals the sum of uncollected nondiscretionary revenues (c RUM) and discretionary revenues (RM):
ARit c RUMit RMit .
Discretionary revenues increase accounts receivable and revenues by the same amount; discretionary receivables equals discretionary revenues.
Because nondiscretionary revenues are not observable, I rearrange terms and express ending receivables in terms of reported revenues. I then take first differences to arrive at the following expression for the receivables accrual:
ARit c Rit (1 c) RMit .
The estimate of a firm’s discretionary revenues is the residual from the following equation: ARit Rit εit.
Because reported revenues include discretionary revenues, the amount of revenue management estimated by the revenue model will be understated by a factor of 1 c (see Jones 1991, footnote 31). The modified Jones model (Dechow et al. 1995) conditions on the change in cash revenues rather than total revenues, which avoids systematically understating the amount of earnings management. However, this approach introduces another problem: uncollected credit revenues are treated as discretionary. Firms with a higher than average portion of nondiscretionary revenues that are credit will have higher estimates of discretionary accruals. I condition on total revenues because this understates estimated earnings management, which biases against finding in favor of typical alternative hypotheses.
One limitation of accrual models is that by conditioning on annual revenues they treat revenues from early in the year the same as revenues from later in the year. Current accruals are generally resolved within one year. Thus, sales made late in the year are more likely to remain on account at year-end. Therefore, the revenue model I estimate allows the estimated portion of revenues that are uncollected at year-end to vary in the fourth quarter:
ARit 1 R1 3it 2 R4it εit. (1)
In Equation (1), R1 3 is revenues in the first three quarters, and R4 is revenues in the fourth quarter. Even though Equation (1) incorporates quarterly revenues, I estimate discretion on an annual level. Any revenue management in early quarters that reverses by year-end will not be captured.
Another limitation of accrual models is that cross-sectional estimation implicitly assumes that firms in the same industry have a common accrual-generating process. Dopuch et al. (2005) show that the relation between accruals and revenue changes depends on firmspecific factors such as credit and inventory policies. In cross-sectional estimation, deviations from the industry average credit policy, for example, would lead to nonzero estimated unexpected accruals. Therefore, to control for these deviations, I also estimate a version of the revenue model that allows the coefficient on revenues to vary with firms’ credit policies.
Petersen and Rajan (1997) review theories of trade credit and the determinants of accounts receivable. I use the implementation of the Petersen and Rajan (1997) credit policy model described in Callen et al. (2008). A firm’s investment in receivables is a function of its financial strength, operational performance relative to industry competitors, and stage in the business cycle. Firm size, measured as the natural log of total assets (SIZE), is a proxy for financial strength. Firm size and firm age (AGE), measured as the natural log of the firm’s age in years, are proxies for the firm’s stage in the business cycle. Following Petersen and Rajan (1997), I also include the square of firm age (AGE SQ) to allow for a nonlinear relation between age and credit policy. As proxies for the operational performance of the firm relative to industry competitors, I use the industry-median-adjusted growth rate in revenues (GRR P if positive, GRR N if negative) and the industry-median-adjusted gross margin (GRM) and its square (GRM SQ).
I refer to the following model as the conditional revenue model, as it is a cross-sectional conditional estimation of the revenue coefficient:
ARit 1 Rit 2 Rit SIZEit 3 Rit AGEit
4 Rit AGE SQit 5 Rit GRR Pit 6 Rit GRR Nit
7 Rit GRMit 8 Rit GRM SQit εit. (2)
As a benchmark for the revenue models, I estimate discretionary accruals using four common approaches: the Jones model (Equation (3) below; Jones 1991), the modified Jones model (Equation (4) below; Dechow et al. 1995), the Dechow-Dichev model (Equation (5) below; Dechow and Dichev 2002; McNichols 2002), and performance-matched estimates from the modified Jones model (Kothari et al. 2005). The Appendix summarizes the discretionary revenue and accrual estimates I use in this study.
ACit 1 Rit 2PPEit εit; (3)
ACit 1(Rit ARit) 2PPEit εit; (4)
ACit 1 Rit 2PPEit 3 Rit CFOi,t1 4CFOit 5CFOi,t1 εit.
(5)
Data and Descriptive Statistics
The sample period begins in 1988 because prior to that date cash flow from operations disclosed under Statement of Financial Accounting Standards No. 95 (FASB 1987) is unavailable. The sample period ends in 2003 but uses 2004 data for cash from operations. I exclude firms in regulated industries (financial, insurance, and utilities) because their revenues and accruals likely differ from those of other firms.
I obtain financial data from Compustat. I calculate accruals as earnings before extraordinary items less cash flow from operations. I obtain cash flow from operations and the change in receivables from the cash flow statement (Hribar and Collins 2002). Revenues of the first three quarters is the difference between annual revenues and fourth-quarter revenues. I deflate all revenue and accrual variables by average total assets. Annual earnings growth is the annual change in income before extraordinary items, deflated by average total assets. Revenue growth is the ratio of current to prior-year revenues. Gross margin percentage equals revenues less cost of revenues, divided by revenues. Firm age is the number of years since the firm’s initial appearance in the Compustat annual file with non-missing financial information. Industries are as defined in Barth et al. (2005). I winsorize at 1 percent each model input variable by industry and year.
Following Kothari et al. (2005), I estimate nondiscretionary accruals with scaled and unscaled intercepts (by assets), to control for scale differences among firms (Barth and Kallapur 1996). I exclude firms suspected of manipulation (e.g., firms targeted by the SEC) when estimating the model coefficients. I use the estimated coefficients to calculate discretionary revenues of suspected firms.
Table 1 presents summary statistics. Panel A indicates that mean (median) accruals are 8 (6) percent of average assets. The mean and median change in receivables is 1 percent of average assets. Panel A also indicates that the mean (median) change in revenues is 9 (7) percent of average assets. On average, the revenue change is approximately evenly
Panel A: Descriptive Statistics TABLE 1
Sample Summary Statistics (n 70,580)
Variable Mean Std. Dev. Q1 Median Q3
AC 0.35 0.21 0.18 0.19 0.05 0.04
AR 0.40 0.48 0.38 0.49 0.04 0.07
R 0.26 0.50 0.94 0.67 0.02 0.09
R1 3 0.23 0.41 0.93 0.40 0.02 0.09
R4 0.24 0.54 0.72 0.50 0.01 0.05
PPE 0.14 0.04 0.01 0.01 0.01 0.23
CFO 0.25 0.06 0.14 0.14 0.10 0.28
AC 0.08 0.17 0.12 0.06 0.01
AR 0.01 0.07 0.01 0.01 0.04
R 0.09 0.37 0.04 0.07 0.22
R1 3 0.07 0.30 0.03 0.05 0.17
R4 0.03 0.13 0.02 0.02 0.07
PPE 0.30 0.24 0.11 0.24 0.44
CFO 0.03 0.19 0.01
Panel B: Pearson (above), Spearman (below) Correlations 0.06 0.13
AC AR R R1 3 R4 PPE CFO
Variables are deflated by average total assets. All correlations in Panel B are significantly different from zero (p 0.01).
Variable Definitions:
AC annual current accruals earnings before extraordinary items cash from operations;
AR end of fiscal year accounts receivable;
R annual revenues;
R1 3 revenues of the first three quarters;
R4 revenues of the fourth quarter;
PPE end of fiscal year gross property, plant, and equipment;
CFO cash from operations; and annual change.
distributed across quarters. The median change in revenues of the first three quarters is 5 percent of average assets (approximately 2 percent per quarter), and the median change in fourth-quarter revenues is 2 percent of average assets.
Panel B of Table 1 presents correlations. Because the Pearson and Spearman correlations are similar, I focus on the Pearson correlations. All correlations are significantly different from zero. Change in receivables is positively correlated with accruals (0.35), largely by construction because change in receivables is typically a large component of current accruals. However, the correlation between annual revenue change and change in receivables (0.48) is larger than the 0.21 correlation between annual revenue change and accruals. Additionally, change in receivables is more highly correlated with change in fourth-quarter revenues than with the change in revenues of the first three quarters (0.49 versus 0.38) or even change in annual revenues (0.49 versus 0.48). Taken together, these correlations suggest that estimates from models of receivables are less noisy than estimates from accrual models, and that using quarterly data to disaggregate annual change in revenues might lead to better specified models. However, I base my inferences on the tests presented in the next section.
IV. RESULTS Estimation of the Models
Table 2 presents results from the estimation of the revenue and accrual models. Panel A presents summary results of the revenue models. In revenue model (1), the coefficient on change in fourth-quarter revenues (0.21) is over four times higher than that of the change in revenues of the first three quarters (0.05), although both are significantly positive. In contrast, when conditioning on annual revenue change, the average coefficient is 0.08 and the adjusted R2 decreases from 0.28 to 0.21. The coefficient on revenues in model (2) varies significantly with size (SIZE), age (AGE), industry-adjusted revenue growth (GRR P and GRR N), and gross margin (GRM). The adjusted R2 increases from 0.21 to 0.28 over the model that does not allow for variations in credit policy.
Panel B of Table 2 presents summary results of the accrual models. The coefficient on revenue change in the Jones model (3) is 0.10, as compared to 0.06 for the modified Jones model (4). In addition, the adjusted R2 of the modified Jones model is lower (0.09) than that of the Jones model (0.12). In the Dechow-Dichev model (5), the coefficients on past and future cash flows (0.27 and 0.14, respectively) and the coefficient on current cash flows (0.46) are each significantly related to accruals. The adjusted R2 increases to 0.30 when adding cash flows to the Jones model.
Untabulated results reveal that, when estimating the Jones model after excluding receivables from accruals, the resulting coefficient on revenue change is 0.01 and is significantly positive in only 66 out of 285 industry-year groups. This finding indicates that the change in receivables drives much of the correlation between accruals and change in revenues. As expected, the relation between other accruals and revenue change is weaker than that of the receivables accrual and revenue change, leading to noisier estimates of discretion for accrual models.
Evaluation of the Models
I evaluate estimates of discretion from the various models by assessing the models’ abilities to detect simulated revenue and expense manipulation and by relying on actual earnings and revenue manipulation in a sample of firms known to have misstated their financial results.
Detection of Simulated Revenue Manipulation
Similar to Dechow et al. (1995) and Kothari et al. (2005; hereafter KLW), I use simulations to test the power and specification of discretionary accrual models in the presence of extreme performance. By comparing estimates of discretionary revenues and expenses
TABLE 2
Estimation of Revenue and Accrual Models Panel A: Estimation of Revenue Models
ARit 1 R1 3it 2 R4it εit
ARit 1 Rit 2 Rit SIZEit 3 Rit AGEit 4 Rit AGE SQit
R GRR P R GRR N R GRM (1)
it 7 it it
(2)
(2)
FM Mean FM
t-stat Estimate t-stat
33.03** 0.19 9.84**
R SIZE 0.01 6.20**
R AGE 0.04 2.80**
R AGE SQ 0.01 2.07*
R GRRP 0.02 5.12** R GRRN 0.07 7.70** R GRM0.04 3.83**
R GRMSQ 0.06 1.38
Adj. R2 0.28 0.21 0.28
Panel B: Estimation of Accrual Models
ACit 1 Rit 2PPEit εit (3)
ACit 1(Rit ARit) 2PPEit εit (4)
ACit 1 Rit 2PPEit 3 Rit CFOi,t1 4CFOit 5CFOi,t1 εit
(3) (4) (5) (5)
Mean FM Mean FM
Estimate t-stat Estimate t-stat
R 0.10 22.29** 0.10 24.09**
R AR 0.06 15.73**
PPE 0.07 15.55** 0.07 15.03** 0.07 18.07**
CFOt1 0.27 23.62**
CFOt 0.46 27.75**
CFOt1 0.14 13.98**
Adj. R2 0.12 0.09 0.30
*, ** Indicates the coefficient estimate is significantly different from zero at the 0.05 and 0.01 level, using a two-sided test.
Table 2 summarizes the results of separate estimations of revenue and accrual models for each of 285 industryyears. An intercept scaled by average total assets and an unscaled intercept are not tabulated. FM t-stat is the Fama and Macbeth (1973) t-statistic. Variables are deflated by average total assets.
(continued on next page)
TABLE 2 (continued)
Variable Definitions:
AR end of fiscal year accounts receivable;
AC annual current accruals earnings before extraordinary items cash from operations; R annual revenues;
R1 3 revenues of the first three quarters;
R4 revenues of the fourth quarter;
PPE end of fiscal year gross property, plant, and equipment;
CFO cash from operations;
SIZE natural log of total assets at end of fiscal year;
AGE age of firm (years);
GRR P industry-median-adjusted revenue growth ( 0 if negative);
GRR N industry-median-adjusted revenue growth ( 0 if positive);
GRM industry-median-adjusted gross margin at end of fiscal year; SQ square of variable; and annual change.
against a known quantity of manipulation, I am able to obtain evidence of the bias, specification, and power of competing models. I measure the bias of each model as the difference between the mean estimate of discretion and the amount of manipulation I induce. If the model is unbiased, then the difference will equal zero. I evaluate the specification of the models by computing how often tests reject the null hypothesis of no manipulation for samples with no manipulation induced. Finally, I evaluate the power of the models by computing how often tests detect induced manipulation.
I perform this simulation first using subsamples from the entire set of firms and then on subsamples of firms known to produce biased estimates of discretion—i.e., subsamples with high growth (McNichols 2000; Kothari et al. 2005). With the simulation on all firms, I compare the revenue and accrual models’ power in detecting combinations of revenue and expense manipulation. With the simulation on growth firms, I compare the specification of the revenue and accrual models in the presence of extreme performance.
I repeat the following steps 250 times (either drawing firms from the entire population or from the set of firms in each industry-year’s highest quartile of earnings growth):
(1) Draw a random subsample of 100 firm-year observations without replacement.
(2) Simulate revenue manipulation by adding 1 percent of average total assets to the change in revenues, the change in fourth-quarter revenues, and the receivables accrual, and 1 percent times the gross margin percentage to current accruals of these 100 firm-years; or simulate expense manipulation by adding 1 percent to current accruals.
(3) Estimate the models using all observations except the 100 subsample firm-years.
(4) Use each model’s coefficient estimates to calculate estimates of discretion for the 100 subsample firm-years.
(5) Calculate the mean estimate of discretion from each model and test whether the mean is significantly greater than zero.
Statistics from the 250 subsamples form the basis of the tests. I report the mean and standard error of the 250 estimates of discretion, as well as the percent of the 250 times that the model rejects the null hypothesis of no manipulation. A rejection rate of 5 percent is expected when manipulation is not introduced, and based on the 95 percent confidence interval, an actual rejection rate below 2 percent or above 8 percent indicates that the test is misspecified. When manipulation is introduced, however, the rejection rate should be 100 percent.
My procedure differs from that of KLW in three ways. First, I simulate combinations of revenue and expense manipulation to evaluate the models under different forms of earnings management. Second, I calculate accruals using items from the statement of cash flows rather than the balance sheet. Hribar and Collins (2002) find that the error in the balance sheet approach of estimating accruals is correlated with firms’ economic characteristics. As KLW note, this error not only reduces the models’ power to detect earnings management, but also has the potential to generate incorrect inferences about earnings management. Finally, I winsorize variables before, rather than after, estimating the models. This ensures that each model’s mean estimate of discretion is zero.
Table 3, Panel A, presents descriptive statistics from the simulation on subsamples drawn from the entire sample of firms. The table presents estimates of discretionary revenues and accruals based on four combinations of induced manipulation: no manipulation, revenue manipulation of 1 percent of assets, expense manipulation of 1 percent of assets, and both revenue and expense manipulation of 1 percent of assets.
TABLE 3 Bias, Specification, and Power of Revenue and Accrual Models Using Simulated Revenue and Expense Manipulation on All Firms
Panel A: Mean Bias and Standard Error of Discretionary Revenue and Accrual Estimates
% Manip: (Rev, Exp)
(0%,0%)
Mean
(0%,0%) Std. Dev.
Revenue (1) 0.05 0.55
Conditional Revenue (2) 0.06 0.64
Jones (3) 0.05 1.63
Modified Jones (4) 0.03 1.63
Dechow-Dichev (5) 0.21 1.66
Performance-Matched Modified Jones (6) 0.19 1.86
Panel B: Rejection Rates (Ha: Discretion 0) for Combinations of Induced Revenue and Expense Manipulation
% Manip: (Rev, Exp) (0%,0%) (1%,0%) (0%,1%) (1%,1%)
Rate
Rate
Rate
Rate
Revenue (1) 0.8%** 23.6%** 0.8%** 23.6%**
Conditional Revenue (2) 1.2%** 24.0%** 1.2%** 24.0%**
Jones (3) 5.6% 6.8% 13.6%** 11.6%**
Modified Jones (4) 5.2% 7.2% 13.2%** 14.0%**
Dechow-Dichev (5) 7.6% 8.8%** 18.8%** 19.2%**
Performance-Matched Modified Jones (6) 4.4% 6.0% 9.2%** 11.2%**
*, ** Indicates the rejection rate is significantly different from 5 percent at the 0.05 and 0.01 levels, respectively. Table 3 presents statistics on discretionary revenues and discretionary accruals from 250 random samples of 100 firms. ‘‘% Manip’’ is the percent of revenue or expense manipulation induced in each of 250 random samples of 100 firm-years—either 0 percent or 1 percent of average assets.
Panel A presents the mean (‘‘Mean’’) and standard deviation (‘‘Std. Dev.’’) of the 250 sample mean discretionary accrual or revenue estimates, expressed as a percent of average assets.
Panel B presents rejection rates (‘‘Rate’’), which is the percent of the 250 sample means that are significantly greater than zero ( 0.05).
The revenue models (Revenue and Conditional Revenue) and accrual models (Jones, Modified Jones, Dechow-Dichev, and Performance-Matched Modified Jones) are described in the Appendix.
Because mean discretionary revenues and accruals in the entire sample are zero by construction, the mean bias of each of the models should approximate zero. Table 3, Panel A, confirms this expectation. Table 3, Panel A, also presents standard errors. The standard errors from the revenue models are about one-third those of the accrual models. A model that produces estimates with lower standard errors is more likely to detect manipulation when it occurs.
The first column of Table 3, Panel B, reports results on the specification of the models under the null hypothesis of no discretion. None of the models over-rejects the null hypothesis; however, the revenue models under-reject. Rejection rates for the revenue and conditional revenue models are 0.8 and 1.2 percent. Rejection rates for the Jones, modified Jones, Dechow-Dichev (DD), and performance-matched modified Jones (PM) models are 5.6, 5.2, 7.6, and 4.4 percent, respectively.
The next three columns of Table 3, Panel B present evidence on the power of the models. The revenue and conditional revenue models detect revenue manipulation of 1 percent in 23.6 and 24.0 percent of samples. The rejection rates for the Jones, modified Jones, DD, and PM models are a substantially lower 6.8, 7.2, 8.8, and 6.0 percent, respectively. By construction, the revenue models do not detect expense manipulation. The Jones, modified Jones, DD, and PM models detect expense manipulation of 1 percent in 13.6, 13.2, 18.8, and 9.2 percent of samples, respectively. The revenue and conditional revenue models detect a combination of revenue and expense manipulation in 23.6 and 24.0 percent of samples. The Jones, modified Jones, DD, and PM models detect the same combination of manipulation in only 11.6, 14.0, 19.2, and 11.2 percent of samples, respectively. The low rejection rates of the PM model relative to the modified Jones model indicate that performance matching reduces the power of accrual models.
Table 4 presents results from the simulation on firms in the highest quartile of earnings growth. Panel A of Table 4 reveals that each of the six models produces a positive estimate of discretion for growth firms with zero induced manipulation, which indicates a positive bias for growth firms. However, the bias is smaller for the revenue models than for the accrual models. The revenue and conditional revenue model estimates are 0.41 and 0.40 percent of assets, respectively; accrual model estimates are 2.39, 2.75, 3.71, and 2.07 percent of assets for the Jones, modified Jones, DD, and PM models, respectively. The larger estimates for the accrual models are consistent with accruals other than receivables not being explained by the change in revenues alone, and the factors omitted from the models being correlated with growth. For example, it is likely that growth firms invest in inventory beyond what would be predicted by the change in current revenues alone.
Results in Table 4, Panel A, indicate that the modified Jones model is more biased than the Jones model. This finding is consistent with growth firms having more uncollected credit sales, which are treated as discretionary in the modified Jones model. The DD model exhibits the greatest bias of all models tested. Although performance-matching reduces the bias of the modified Jones model, the bias remains more than five times the amount from either of the revenue models. Performance matching by income as suggested by KLW does not fully correct for growth-related model bias.
Table 4, Panel A, also presents standard errors across models. The standard errors from the revenue models are less than half of those of the accrual models. Of the accrual models, the PM model produces estimates with the largest standard errors. Thus, the reduction in bias accomplished by performance matching comes at a cost in efficiency.
TABLE 4 Bias, Specification, and Power of Revenue and Accrual Models Using Simulated Revenue and Expense Manipulation on Growth Firms
Panel A: Mean Bias and Standard Error of Discretionary Revenue and Accrual Estimates
% Manip: (Rev, Exp) (0%,0%) (0%,0%)
Mean
Std. Dev.
Revenue (1) 0.41 0.64
Conditional Revenue (2) 0.40 0.70
Jones (3) 2.39 1.99
Modified Jones (4) 2.75 2.07
Dechow-Dichev (5) 3.71 1.56
Performance-Matched Modified Jones (6) 2.07 2.41
Panel B: Rejection Rates (Ha: Discretion 0) for Combinations of Induced Revenue and
Expense Manipulation
% Manip: (Rev, Exp) (0%,0%) (1%,0%) (0%,1%) (1%,1%)
Rate
Rate
Rate
Rate
Revenue (1) 7.3% 44.4%** 7.3% 44.4%**
Conditional Revenue (2) 7.2% 41.2%** 7.2% 41.2%**
Jones (3) 35.6%** 31.2%** 52.4%** 46.8%**
Modified Jones (4) 43.6%** 38.4%** 58.0%** 52.0%**
Dechow-Dichev (5) 68.8%** 59.6%** 84.4%** 76.4%**
Performance-Matched Modified Jones (6) 20.0%** 18.4%** 37.2%** 34.4%**
*, ** Indicates the rejection rate is significantly different from 5 percent at the 0.05 and 0.01 levels, respectively. Table 4 presents statistics on discretionary revenues and discretionary accruals from 250 random samples of 100 growth firms. Growth firms are those in the highest quartile of change in earnings before extraordinary items deflated by average total assets, where quartiles are determined by industry and year. ‘‘% Manip’’ is the percent of revenue or expense manipulation induced in each of 250 random samples of 100 firm-years—either 0 percent or 1 percent of average assets.
Panel A presents the mean (‘‘Mean’’) and standard deviation (‘‘Std. Dev.’’) of the 250 sample mean discretionary accrual or revenue estimates, expressed as a percent of average assets.
Panel B presents rejection rates (‘‘Rate’’), which is the percent of the 250 sample means that are significantly greater than zero ( 0.05).
The revenue models (Revenue and Conditional Revenue) and accrual models (Jones, Modified Jones, Dechow-Dichev, and Performance-Matched Modified Jones) are described in the Appendix.
The first column of Table 4, Panel B, reports results on the specification of the models under the null hypothesis of no discretion. Only the revenue models produce well-specified tests of manipulation for growth firms. Rejection rates for the revenue and conditional revenue models are 7.3 and 7.2 percent, respectively. Each of the four accrual models overrejects the null hypothesis of no manipulation. Rejection rates for the Jones, modified Jones, DD, and PM models are 35.6, 43.6, 68.8, and 20.0 percent, respectively.
The next three columns of Panel B, Table 4 present evidence on the power of the models. The revenue and conditional revenue models detect revenue manipulation of 1 percent in 44.4 and 41.2 percent of samples. The rejection rates for the Jones, modified Jones, and DD models are 31.2, 38.4, and 59.6 percent, respectively. However, these rejection rates largely reflect the general tendency of biased models to over-reject even when no manipulation is induced. The PM model, which exhibits the least misspecification of the accrual models, detects revenue manipulation in only 18.4 percent of samples. By construction, the revenue models do not detect expense manipulation. The PM model detects expense manipulation of 1 percent in 37.2 percent of samples. The revenue and conditional revenue models detect a combination of revenue and expense manipulation in 44.4 and 41.2 percent of samples. The PM model detects the same combination of manipulation in only 34.4 percent of samples.
In summary, simulation analysis on all firms indicates that the revenue models are more likely than accrual models to detect an equal combination of revenue and expense manipulation. The simulation analysis on growth firms indicates that, although performance matching improves the specification of the accrual models, only the revenue models are well-specified with or without performance matching. Again, the revenue models are more likely than the PM model to detect an equal combination of revenue and expense manipulation.
Detection of Actual Revenue Manipulation
The second procedure I use to evaluate revenue and accrual models assesses the ability of these models to detect revenue and expense manipulation in a sample of firms that are known to have misstated their financial results. The known manipulators are a sample of 250 firm-years that were investigated by the SEC for accounting irregularities between 1995 and 2003.
I divide sample firms into two groups: those that manipulated revenues and those that manipulated expenses only. For each sample firm, I group observations into four time periods: the manipulation period, the year before the manipulation, the year after the manipulation, and all other years. I assume that sample firms overstate revenues and understate expenses during the manipulation period. If the models are powerful, then mean discretionary revenue and accrual estimates should be significantly positive during the manipulation period. Assuming no manipulation took place the year prior to the manipulation period, if the models are correctly specified, then mean discretionary revenue and accrual estimates should not differ from zero.
When studying SEC enforcement actions, one concern is selection bias. For this reason, I present results after adjusting discretionary revenues and accruals of the SEC sample firms by those of control firms chosen from the same industry and year. In the first case, I choose a control firm for each sample firm from the same industry and year with the closest return on assets, which is analogous to the performance matching approach suggested by KLW.
In the second case, I choose a control firm from the same industry and year with the closest revenue growth in the prior year. Prior research documents that firms targeted by SEC enforcement actions tend to be firms with high revenue growth (Beneish 1999).
Table 5, Panel A, displays the distribution of sample firms through event time. Revenues were manipulated over 173 firm-years and expenses were manipulated over 77 firmyears, consistent with revenue manipulation being the most common form of earnings management.
Panel B provides results based on the entire sample of both revenue and expense manipulators. When choosing control firms based on profitability, evidence indicates that the Jones, modified Jones, and DD models are misspecified for the sample of SEC firms. Discretionary accruals before the manipulation period are estimated to be higher than control firms by 6.30, 7.05, and 5.49 percent of assets, respectively. If these discretionary accruals represented actual manipulation, however, then it is likely that they would have been included in the alleged manipulation period. The evidence indicates the performancematched revenue models are well specified.
The revenue and conditional revenue models detect discretion significantly higher than that of control firms during the event period (1.80 and 1.63 percent of assets when matching on profitability; 1.16 and 1.15 percent of assets when matching on growth). Each of the performance-matched accrual models fails to detect discretion during the event period— discretionary accruals are not significantly higher than those of control firms.
Panel C of Table 5 provides results based on the entire sample of firms that manipulated revenues alone or revenues and expenses. Each of the performance-matched accrual models is misspecified. Before the manipulation period, the Jones, modified Jones, and DD models produce discretionary accruals that are significantly higher than those of control firms by 9.07, 10.18, and 7.92 percent of assets when matching on profitability and by 6.86, 6.96, and 5.47 percent of assets when matching on growth. The revenue models are well specified.
Only the revenue models detect manipulation during the event period. Discretionary revenues from the revenue and conditional revenue models are significantly higher than those of control firms by 2.19 and 1.82 percent of assets when matching on profitability and 1.56 and 1.43 percent of assets when matching on growth. The performance-matched accrual models fail to detect manipulation.
Panel D of Table 5 provides results based on the sample of firms that manipulated expenses. As expected, the performance-matched revenue models do not detect discretion in the sample of firms that did not manipulate revenues. However, neither do the accrual models. Discretionary accruals during the manipulation period are not significantly different than those of control firms. Because the sample studied in Table 5, Panel D is restricted to expense manipulators, the accrual models should be more powerful than the revenue models. However, neither the accrual nor revenue models detect manipulation by this subset of SEC firms.
V. CONCLUSION
This study provides evidence on the reliability of discretionary revenues and various measures of discretionary accruals by assessing their ability to detect both simulated and actual manipulation. The results indicate that the revenue model is less biased and better specified than accrual models, such that estimates from revenue models could be useful as a measure of revenue management or as a proxy for earnings management.
Although revenue models do not detect discretion in expenses, findings suggest that accrual models have difficulty detecting discretion in expenses as well. The state-of-the-art
TABLE 5 Detection of Revenue and Expense Manipulation by Firms Subject to SEC Enforcement Actions
Panel A: Number of Sample Firm Observations through Event Time
No Revenue Revenue
Event Year Manipulation Manipulation
1 25 54 0 77 173
1 28 69
Total 130 296
Panel B: Mean Discretionary Revenues and Accruals by Event Year—All Firms
Event Year 1 Event Year 0 Event Year 1
Adjusted for Control Firms (matched on profitability) t-stat
t-stat
t-stat
Revenue (1) 0.86 0.90 1.80 2.99** 1.14 1.10
Conditional Revenue (2) 1.71 1.72 1.63 2.93** 1.10 1.02
Jones (3) 6.30 2.57* 0.89 0.70 4.98 2.32*
Modified Jones (4) 7.05 2.89** 1.39 1.08 5.07 2.35*
Dechow-Dichev (5)
Adjusted for Control Firms
(matched on growth) 5.49 2.40* 0.92 0.68 3.85 1.52
Revenue (1) 0.36 0.35 1.16 2.02* 2.17 2.36*
Conditional Revenue (2) 1.24 1.07 1.15 1.97* 2.10 2.01*
Jones (3) 3.95 1.57 0.20 0.11 8.43 3.50**
Modified Jones (4) 4.16 1.66 0.43 0.25 8.94 3.72**
Dechow-Dichev (5) 2.61 0.95 0.92 0.59 3.81 1.57
Panel C: Mean Discretionary Revenues and Accruals by Event Year—Revenue Manipulators
Event Year 1 Event Year 0 Event Year 1
Adjusted for Control Firms (matched on profitability) t-stat
t-stat
t-stat
Revenue (1) 1.32 0.98 2.19 2.75** 2.04 1.51
Conditional Revenue (2) 1.86 1.39 1.82 2.51** 1.95 1.39
Jones (3) 9.07 2.85** 0.77 0.48 5.37 1.92
Modified Jones (4) 10.18 3.21** 1.55 0.95 5.50 1.95
Dechow-Dichev (5)
Adjusted for Control Firms
(matched on growth) 7.92 2.64* 0.02 0.01 3.68 1.12
Revenue (1) 0.06 0.05 1.56 2.14* 1.67 1.58
Conditional Revenue (2) 0.11 0.08 1.43 1.89* 1.77 1.45
Jones (3) 6.86 2.30* 1.11 0.54 9.05 3.02**
Modified Jones (4) 6.96 2.32* 1.33 0.64 9.53 3.19**
Dechow-Dichev (5) 5.47 1.78 0.26 0.13 5.62 1.78
(continued on next page)
TABLE 5 (continued)
Panel D: Mean Discretionary Revenues and Accruals by Event Year—Expense Manipulators
Event Year 1 Event Year 0 Event Year 1
Adjusted for Control Firms (matched on profitability) t-stat
t-stat
t-stat
Revenue (1) 0.52 0.47 0.91 1.16 1.02 0.81
Conditional Revenue (2) 1.95 1.46 1.14 1.41 0.95 0.70
Jones (3) 0.66 0.21 1.17 0.59 4.02 1.41
Modified Jones (4) 0.80 0.26 1.06 0.53 4.00 1.44
Dechow-Dichev (5)
Adjusted for Control Firms
(matched on growth) 1.76 0.72 2.73 1.59 4.43 1.24
Revenue (1) 1.05 0.59 0.26 0.29 3.41 1.86
Conditional Revenue (2) 3.62 1.56 0.53 0.59 2.95 1.47
Jones (3) 2.43 0.54 1.96 0.64 6.88 1.75
Modified Jones (4) 2.01 0.46 1.69 0.54 7.46 1.90
Dechow-Dichev (5) 4.83 0.89 2.23 0.99 0.61 0.20
*, ** Indicates a significant difference from zero at the 0.05 and 0.01 levels, respectively, using a one-sided test in event year 0 and a two-sided test otherwise.
Table 5 presents mean discretionary revenue and accrual estimates before, during, and after SEC enforcement actions.
‘‘Revenue Manipulation’’ indicates whether the alleged violations involved a revenue misstatement. Event years include –1, the year preceding the first year of the manipulation, 0, one or more years during the manipulation, and 1, the first year after the manipulation.
Panels B through D present mean (‘‘Mean’’) estimates of discretion from models described in the Appendix, expressed as a percent of average assets. Mean estimates presented under ‘‘Adjusted for Control Firms (matched on profitability)’’ (‘‘Adjusted for Control Firms (matched on growth)’’) use discretionary revenue and accrual estimates after adjusting for a control firm from the same industry and year with the closest return on assets (revenue growth). The t-statistics represent a paired t-test of discretionary revenues or accruals of sample firms versus control firms.
performance-matched modified Jones model (Kothari et al. 2005) detects simulated expense manipulation in only 9.2 percent of samples of firms, and it fails to detect expense manipulation by firms subject to expense-related SEC enforcement actions. Still, the success of the revenue model at detecting earnings management depends on the relative frequency of revenue versus expense manipulation. For equal amounts of simulated revenue and expense manipulation across the entire sample, the revenue model outperforms each of the accrual models. The revenue model also detects earnings management by firms subject to SEC enforcement actions, but the performance-matched accrual models do not. Overall, the revenue model outperforms accrual models both in detecting and failing to detect earnings management, as appropriate. Thus, revisiting research settings with the revenue model could shed light on whether significant results were driven by misspecification of accrual models or whether insignificant results were driven by the accrual models’ lack of power.
Measures of discretionary revenues can also be useful by providing evidence on how firms manage earnings or for studying revenue management. On the whole, relatively little research has been conducted in the area of discretion in revenues. Although revenues is a logical first step in examining individual components of earnings, future studies could model discretion in various expense components of earnings.
Finally, this study has implications for studies that use accrual models. First, the Jones model (Jones 1991) exhibits better specification than the modified Jones model (Dechow et al. 1995), which suggests including reported revenues, rather than cash revenues, in accrual models. Second, the Dechow-Dichev model (Dechow and Dichev 2002; McNichols 2002), which was originally developed to estimate earnings quality, exhibits greater misspecification than other accrual models when used to estimate discretionary accruals. Last, separating fourth-quarter revenues and allowing the relation between revenues and accruals to vary across firms could be applied to accrual models to improve their performance.
APPENDIX SUMMARY OF DISCRETIONARY REVENUE AND ACCRUAL ESTIMATES Revenue Model
Discretion ARit ˆ ˆ1 R1 3it ˆ2 R4it.
Conditional Revenue Model
Discretion ARit ˆ ˆ1 Rit ˆ2 Rit SIZEit ˆ3 Rit AGEit ˆ4 Rit AGE SQit ˆ5 Rit GRR Pit ˆ6 Rit GRR Nit ˆ7 Rit GRMit ˆ8 Rit GRM SQit.
Accrual Models
Jones Model (Jones 1991)
Discretion ACit ˆ ˆ1 Rit ˆ2PPEit.
Modified Jones Model (Dechow et al. 1995)
Discretion ACit ˆ ˆ1(Rit ARit) ˆ2PPEit.
Dechow-Dichev (DD) Model (Dechow and Dichev 2002; McNichols 2002)
Discretion ACit ˆ ˆ1 Rit ˆ2PPEit ˆ3CFOi,t1 ˆ4CFOit ˆ5CFOi,t1.
Performance-Matched (PM) Modified Jones Model (Kothari et al. 2005)
Discretion ACit ˆ ˆ1(Rit ARit) ˆ2PPEit, less the same measure for the firm from the same industry and year with the closest return on assets.
where:
AR end of fiscal year accounts receivable;
AC annual current accruals earnings before extraordinary items cash from
operations;
R annual revenues;
R1 3 revenues of the first three quarters;
R4 revenues of the fourth quarter;
PPE end of fiscal year gross property, plant, and equipment;
CFO cash from operations;
SIZE natural log of total assets at end of fiscal year;
AGE age of firm (years);
GRR P industry-median-adjusted revenue growth ( 0 if negative);
GRRN industry-median-adjusted revenue growth ( 0 if positive);
GRM industry-median-adjusted gross margin at end of fiscal year; SQ square of variable; and annual change.
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