Measuring stockholder materiality.

SYNOPSIS: The Securities and Exchange Commission (SEC) has recently expressed concern that auditors' use of materiality allows misstatements to go uncorrected. Auditors do not require their clients to correct the financial statements for immaterial misstatements. According to the professional

standards, an immaterial misstatement is defined as one that has no effect on a typical or average users decisions. However, little is known about users' materiality perceptions, especially in relation to common materiality measures used by auditors, such as the percentage effect on earnings or the percentage effect on sales. To help clarify what is considered to be material from the stockholders point of view, we investigate empirically various quantitative factors that stockholders consider important in assessing whether earnings are materially misstated. For each factor, we identify a materiality threshold where potential misstatements exceeding the threshold are material.

Keywords: materiality; threshold; earnings-response; auditing.

INTRODUCTION

Auditors' applications of materiality are critical to earnings quality. The Securities and Exchange Commission (SEC) has recently expressed concern that liberal materiality standards might result in financial statements that are not fairly stated. Auditors do not require their clients to correct the financial statements for immaterial misstatements. Former SEC chairman, Arthur Levitt, contends that auditors do not sufficiently prohibit client firms from fabricating earnings in an attempt to attain earnings projections, which in turn may affect the firm's stock price. Levitt (1998) says, "In markets where missing an earnings projection by a penny can result in a loss of millions of dollars in market capitalization, I have a hard time accepting that some of these so-called non-events simply don't matter."

According to the Financial Accounting Standards Board (FASB), Statement of Financial Accounting Concepts (SEAC) No. 2 (AICPA 1984), an immaterial misstatement is defined as one that has no effect on a typical or average user's decisions. For example, an immaterial misstatement, if known to a stockholder, is not expected to result in a security price change. To help clarify what is considered to be material from the stockholder's point of view, we investigate empirically various quantitative aspects of earnings that stockholders consider important in assessing whether earnings are materially misstated. For each quantitative factor, we identify a materiality threshold beyond which potential misstatements are material.

Auditors have received little guidance in choosing materiality thresholds. Few court cases have rendered judgments defining materiality and definitions of materiality are not precise. The SEC defines materiality similarly to SFAC No. 2. Rule 1-02 of Regulation S-X describes a material misstatement as "information...about which an average prudent user ought reasonably be informed." The professional literature provides no quantitative guidelines and consequently, the choice of materiality involves auditor judgment. The SEC issued Staff Accounting Bulletin (SAB) No. 99 (SEC 1999) to provide more guidance concerning auditors' materiality decisions. However, SAB No. 99 does not suggest that all misstatements should be found and corrected, regardless of their size, because the related benefits do not exceed the costs. As in SFAC No.2 and Rule 1-02, SAB No. 99 does not provide any quantitative criteria for determining materiality.

In practice, auditors use materiality to identify the necessary precision of audit tests and to identify the amount of misstatement that requires adjustment in the financial statements. Auditors consider the size of misstatement that would cause a material misstatement of earnings and/or a material misstatement of a particular account. Prior research has identified three quantitative measures that auditors commonly use to determine materiality of an earnings misstatement. According to Ricchiute (1998, 45), these include: (1) percentage effect on net income, (2) percentage effect on sales or total revenues, and (3) percentage effect on total assets. For example, when sales is the materiality base, recorded sales is $100,000, and the auditor considers 2 percent of sales to be material, then the auditor requires financial statement adjustment for all identified earnings misstatements greater than $2,000.

These three criteria are also supported by various surveys and audit working paper analyses summarized in Kinney (2000, 186). Of the three measures, percentage effect on net income is the most widely used. Items less than 5 percent of net income are generally considered immaterial, while items greater than 10 percent are considered material. However, Kinney (2000) argues that the revenues-based and assets-based measures of materiality have three advantages over an earnings-based measure. First, revenues and assets are less variable over time than are earnings. Second, earnings are significantly influenced by expense accounting methods. Finally, earnings are highly susceptible to manipulation. Hence, "effect on total revenues" and "effect on total assets" are important measures of materiality. Ricchiute (1998) also suggests that auditors should use all three of these measures. (1)

In addition to the quantitative measures, auditors may also use qualitative factors that would normally cause a quantitatively immaterial item to become material, such as the reversal of an earnings trend. For example, if over several reporting periods net income has increased steadily by 10 percent per year, then the auditor would take into account how downward adjustments in net income would affect users' decisions based on the reversal of that trend.

Despite the measures auditors normally use, there is little information available concerning what information users consider to be material. Measuring user materiality is difficult because a user's decision process is unobservable. However, we can observe the market participants' reactions to financial information. Accordingly, we assess materiality by examining factors that influence investors' buy/sell decisions (O'Connor and Collins 1974), as reflected in stock price changes. In this spirit, a recent paper by Kinney et al. (1999) investigates the materiality of unexpected earnings. They find the average stockholders' materiality threshold for unexpected earnings is close to zero when earnings forecasts are not too dispersed. Our study extends that research.

We investigate how investors perceive various materiality measures used by auditors by estimating a model of stock price reactions. However, our model considers additional materiality criteria and employs a different methodology than Kinney et al. (1999). We use the standard relationship between abnormal returns and unexpected earnings and then partition unexpected earnings according to various quantitative materiality factors used by auditors. For each materiality factor, we identify a threshold percentage beyond which a significant stock price reaction to earnings is evident and below which there is no significant stock price reaction. We infer that the average investor materiality criterion for earnings is at least equal to this threshold level.

Guided by what auditors most often use to measure materiality, we test for materiality thresholds based on pretax earnings, total assets, and sales. We infer from our results that the average investor materiality threshold for pretax earnings is between 0.1 percent and 0.2 percent. For total assets, we estimate a materiality threshold between 0.01 percent and 0.025 percent.

For sales we consider two different types of materiality thresholds, one that applies to earnings generally, and one that is specific to sales. (2) To measure the first one, we use the same test as for pretax and total assets where sales is the base used to partition unexpected earnings. In this case, the materiality threshold is too close to zero for us to measure. To measure the second one, we estimate unexpected earnings as the sum of unexpected sales and unexpected expenses and then partition unexpected sales based on the percentage of sales. In this case, we detect a materiality threshold for sales between 0.01 percent and 0.025 percent. That is, when earnings information is divided between sales and expenses, then, for sales alone, our tests detect a threshold below which there is no significant price reaction. We also find that the materiality threshold is higher for sales decreases than sales increases. Finally, we find that the materiality threshold is relatively high for large earnings surprises and is lower for high-growth firms compared to low-growth firms.

The paper is organized as follows. In the next section, we discuss our research design and in the third section we present our empirical results. The final section provides conclusions, including possible extensions of this research.

RESEARCH DESIGN

The concept of materiality focuses on the use of financial statement information. In formulating an audit plan, the auditor selects materiality criteria based on the types of decisions he believes that financial statement users make. The problem with measuring what users consider material is that we cannot observe their decision processes. However, we can observe the effect of investors' decisions by observing stock prices movements.

We design a model that allows us to infer the average investor's materiality threshold based on their reactions to new earnings announcements. Researchers (e.g., Collins and Kothari 1989; Easton and Zmijewski 1989) typically use a variant of the following model to capture investors' reactions to earnings announcements:

Abnormal stock returns = F( Unexpected earnings). (1)

For each announcing firm, the abnormal stock return is the earnings announcement-period stock return in excess of the stock return that would be expected given the firm's size or market beta. Unexpected earnings are earnings in excess of a forecast that is either estimated from time-series models or obtained from security analysts.

We use Equation (1) as our base model, and then extend it by adding other quantitative factors that potentially alter how the market responds to earnings surprises. We use these altered responses, if any, to infer investors' materiality perceptions relative to each factor. The factors that we consider are percentage of pretax income, percentage of sales, and percentage of total assets.

Our measure of abnormal stock return is the cumulative abnormal return (CAR) for the three-day period centered at the quarterly earnings announcement date. The abnormal return is calculated as the announcing firm's raw return for the event period, minus the concurrent mean return on exchange-specific size decile to which the announcing firm belongs.

Following Brown et al. (1987), our proxy for unexpected earnings is actual earnings per share (obtained from Compustat) less the median forecast for earnings per share closest to the earnings announcement, as reported in the IIB/E/S database. (3) Thus, empirically, our base model is:

[CAR.sub.it] = [alpha] + [beta][SUE.sub.it] + [e.sub.it] (1a)

where:

[CAR.sub.it] = size-adjusted stock return for the three-day period centered around the quarterly earnings announcements; and

[SUE.sub.it] = earnings surprise, actual earnings per share less the consensus of analysts' forecasts deflated by the price at the beginning of the period.

Next, we expand the base model to incorporate our materiality criteria variables: (1) percentage of pretax earnings, (2) percentage of sales, and (3) percentage of total assets. Our objective is to determine whether and how users perceive materiality in terms of these variables. We design tests to detect a percentage level for each variable that splits the earnings-surprise sample into two groups: a material group (above the level) and an immaterial group (below the level). We use stock price reactions to guide our search. The material group comprises the range of information that results in a significant stock response. The immaterial group is the range for which no significant stock price behavior is evident. We then infer that the users' materiality threshold for a particular variable is the level that partitions the sample into material and immaterial groups.

There are many aspects of materiality that auditors consider when designing and evaluating their audit procedures. Typically an auditor determines a threshold amount of misstatement that is used as a guide in accumulating adjusting entries affecting earnings. Auditors may also "allocate" materiality among various accounts so that the materiality threshold for each account is different. This allows the auditor to perform the audit more efficiently by considering the importance of individual accounts within the context of the financial statements. In designing our empirical tests, we take each of these approaches into consideration. We design the first three test models to identify materiality thresholds that pertain to earnings generally, while the fourth focuses on identifying a materiality threshold specifically for sales.

Our test model for the "percentage effect on pretax earnings" criterion is as follows:

[CAR.sub.it] = [alpha] + [[beta].sub.1] [SUE.sub.it] * (Below_k%Earnings) + [[beta].sub.2][SUE.sub.it] * (Above_k%Earnings) + [e.sub.it] (2)

where:

Below_k%Earnings = 1, if Abs(UE/PTI), the absolute value of unexpected earnings (UE) divided by pretax income (PTI), is less than k percent, and 0 otherwise; and

Above_k%Earnings = 1 - Below_k%Earnings.

In Equation (2), the two indicator variables Below_k%Earnings and Above_k%Earnings, split the sample into two groups. Unexpected earnings are less (greater) than k percent of pretax income for the first (second) group. If k percent is the investors' materiality threshold for the "effect on pretax income" criterion, then [[beta].sub.1] should equal 0, whereas [[beta].sub.2] should be positive. If k is above the materiality threshold, then both [[beta].sub.1] and [[beta].sub.2] are positive and statistically significant. For example, if we find that both [[beta].sub.1] and [[beta].sub.2] are positive and significant when k equals 2 percent, then investors consider some deviations from expectations of less than 2 percent of pretax income to be material. However if we find that [[beta].sub.1] is insignificant and [[beta].sub.2] is significant when k equals 1 percent, then we infer that investors find no deviations from expectations of less than 1 percent of pretax income to be material.

In order to identify the threshold, we first estimate Equation (2) for a large k, and then repeat the estimation for sequentially decreasing values of k. For each estimation, we note the statistical significance of the coefficients [[beta].sub.1] and [[beta].sub.2] The value of k that yields the desired result ([[beta].sub.1] =0; [[beta].sub.2]>0) is inferred to be the lower bound on the average investor's materiality threshold for the "percentage effect on pretax earnings" criterion. We do not precisely estimate the materiality threshold because we estimate Equation (2) for discrete increments of k. Thus we identify an interval in which the materiality threshold lies.

We use similar methodologies to test for the "percentage effect on sales" and the "percentage effect on total assets" criteria. The model for the sales-based criterion is as follows:

[CAR.sub.it] = [alpha] + [[beta].sub.1][SUE.sub.it] * (Below_m%Sales) + [[beta].sub.2] [SUE.sub.it] * (Above_m%Sales) + [e.sub.it] (3)

where:

Below_m%Sales = 1, if Abs(UE/Sales), the absolute value of unexpected earnings divided by sales, is less than m percent, and 0 otherwise; and

Above_m%Sales = 1 - Below_m%Sales.

Similarly, the model for the assets-based criterion is as follows:

[CAR.sub.it] = [alpha] + [[beta].sub.1][SUE.sub.it] * (Be1ow_n%Assets) [[beta].sub.2] [SUE.sub.it] * (Above_n%Assets) + [e.sub.it] (4)

where:

Below_n%Assets = 1, if Abs(UE/TA) , the absolute value of unexpected earnings divided by total assets, is less than n percent, and 0 otherwise; and

Above_n%Assets 1 - Below_n%Assets.

Our final model examines materiality thresholds for an important component of earnings, namely, sales. In this model, we test investor response to sales information to determine whether material unexpected sales exceed a certain threshold percentage of sales. We use a percentage of sales criterion because it is the one most likely to be applied to unexpected sales.

The model is based on the following variant of Equation (la):

[CAR.sub.it] = [alpha] + [[beta].sub.1][SUSales.sub.it] + [[beta].sub.2][SUExpenses.sub.it] + [e.sub.it] (5)

where:

[SUSales.sub.it] unexpected sales, actual sales less forecast sales, deflated by the beginning-of-returns-period price; and

[SUExpenses.sub.it] = unexpected expenses, actual expenses less forecast expenses, deflated by the beginning-of-returns-period price.

Following Foster (1977), we use the seasonal random walk model to forecast sales. Unexpected sales thus equal sales for the current quarter q, minus sales for quarter q-4. Unexpected expenses are computed in a similar fashion. We standardize these variables by the beginning-of-returns period price, and incorporate the "percentage of sales" materiality criterion:

[CAR.sub.it] = [alpha] + [SUSales.sub.it] * (Below_p%Sales) + [[beta].sub.2][SUSales.sub.it] * (Above_p%Sales) + [[beta].sub.3][SUExpenres.sub.it] + [e.sub.it] (6)

where:

Be1ow_p% Sales = 1, if Abs(USales/Sales), the absolute value of unexpected sales divided by sales, is less than p percent, and 0 otherwise; and

Above_p%Sales = 1 - Below_p%Sales.

The coefficient on expenses, [[beta].sub.3], is expected to be negative.

Our models are similar to the ones used by Kinney et al. (1999), who examine the significance of investor reactions to earnings surprises within narrow ranges around zero. Our tests, by contrast, are designed to test investor reactions to earnings surprises within, as well as outside, narrow ranges around zero. We use this alternative design, because a materiality threshold implies no reaction within the threshold and a significant reaction above the threshold. One problem with our model is that other explanations cannot be ruled out for the insignificant investor reactions below our detected threshold. These explanations include transactions costs and low statistical power. However, our design ensures that actual thresholds are no higher than our detected thresholds.

Finally, we treat our examination of materiality thresholds purely as an empirical issue. Our purpose here is not to offer a theory of how users form their own materiality preferences, but, as a first step, to simply gather evidence that measures stockholder materiality in terms of a limited set of criteria identified in the auditing literature. Indeed, user materiality preferences may vary widely among users and involve factors other than those examined here.

EMPIRICAL RESULTS

Sample and Data Description

Our sample comprises 31,470 firm-quarters that satisfy the following selection criteria. First, we require data on quarterly earnings, income before taxes, sales, and total assets, and earnings announcement dates to be available on the 1998 Compustat PC-Plus CD. Second, we require earnings forecasts to be available on the I/B/E/S (January 1998) earnings forecast summary tape. Third, we require firm and portfolio returns to be available on CRSP Access 1998. Finally, we exclude observations for which the absolute value of SUE (actual earnings per share less the consensus of analysts' forecasts, deflated by the price at the beginning of the period) is equal to or greater than 1.

We report the summary statistics of our test variables in Table 1. The mean three-day cumulative abnormal return around sample earnings announcements is 0.15 percent. The standardized unexpected earnings variable, SUE, has a negative mean and median, suggesting that, on average, actual earnings trailed forecasts. Consistent with the negative mean SUE, mean standardized unexpected expenses (SUExpenses) slightly exceed mean standardized unexpected sales (SUSales). The distribution of the variable measuring the absolute value of unexpected earnings divided by pretax income, Abs(UE/P TI) , is skewed, although this is unlikely to affect the results because the variable is transformed into an indicator variable and is used interactively.

Regression Results for the Base Model

Table 2 contains estimation results for Equation (la), the base model. The coefficient on unexpected earnings, 0.2 197, is positive and statistically significant at the 0.001 level. The adjusted [R.sup.2] for the regression is 1.42 percent. These results are similar to those documented by prior studies on the earnings-stock returns relation. The results in Table 2 provide a benchmark to evaluate estimation results for Equations (2) through (4) and (6), discussed below.

Results for the "Percentage of Pretax Earnings" Criterion

Table 3 summarizes the results of the threshold search for the "percentage of pretax earnings" criterion. As described previously, this search involves estimating Equation (2) for several potential thresholds. Each row in Table 3 contains the estimation results for the corresponding test percentage specified in the first column of the table. Overall, the results indicate that, consistent with Freeman and Tse (1992), earnings response coefficients are decreasing in the magnitude of earnings surprise.

We start the experiment by estimating Equation (2) for a potential threshold of 2 percent of pretax earnings. The results for this estimation (the first row in the Table 3) indicate a significant stock price reaction to unexpected earnings that are less than 2 percent of pretax earnings. This suggests that investors' materiality threshold is lower than 2 percent. We next examine a potential threshold of 1 percent, then 0.5 percent, 0.3 percent, 0.2 percent, and finally, 0.1 percent. The final estimation, using a potential threshold of 0.1 percent, yields a stock price response that is insignificant in the "below" range, but positive and significant in the "above" range. Based on our evidence, we infer that the average investor's materiality threshold is between 0.1 percent and 0.2 percent of pretax income. Notably, this threshold is substantially lower than the 5-10 percent level discussed in the auditing pedagogical literature (e.g., Ricchiute 1998).

Of course, while this result suggests that auditors might want to rethink the materiality thresholds they use, it is not a prescription for auditors to employ a 0.1 percent materiality threshold on pretax earnings. Our purpose here is simply to investigate materiality perceptions for an important user-group consisting of investors. Further investigation into other characteristics of materiality, such as intentional versus unintentional misstatements or the effects of transactions costs, might lead to different thresholds for those characteristics.

Results for the "Percentage of Sales" Criterion

Table 4 presents the results of the threshold search for the "percentage of sales" criterion. We repeatedly estimate Equation (3) for potential thresholds ranging from 2 percent of sales down to 0.01 percent of sales. We are unable to identify a materiality threshold for the percentage of sales criterion. The coefficients on the "below" range are positive and significant for all our test thresholds. For instance, the last row of the table indicates that the estimate of [[beta].sub.1] is 1.5601 (p-value <0.001) for a test threshold of 0.01 percent. Evidently, investors consider earnings less than 0.01 percent of sales to be important.

Results for the "Percentage of Total Assets" Criterion

Table 5 presents the results of the threshold search for the "percentage of total assets" criterion. We estimate Equation (4) for thresholds ranging from 2 percent of total assets down to 0.01 percent of total assets. The coefficients on the "below" range variable are all positive and significant, with the exception of the last row. This evidence suggests that investors' materiality threshold for the "percentage effect on total assets" criterion is between 0.01 percent and 0.025 percent.

The regression for a threshold of 0.01 percent of total assets yields an estimate of [[beta].sub.1] of 8.7809, although this estimate is statistically insignificant. This estimate is the highest of all regressions in the table, suggesting that investors are the most responsive at this level. As discussed previously, the lack of significance may be attributable to low power. The sample distribution for this regression indicates that only 222 of the 31,470 sample observations fall below a threshold of 0.01 percent of total assets. Alternatively, the regression result may indicate that materiality thresholds vary with the magnitude of earnings surprise, an issue that we examine later in the section on additional analysis. In any case, the results in Table 5 provide evidence that the materiality threshold is less than 0.025 percent of total assets, which is substantially different from the level discussed in various auditing texts (1-2 percent total assets).

Stock Price Response to Unexpected Sales Information

Table 6 presents estimation results for Equation (6). We estimate the model for values of p ranging from 2 percent down to 0.01 percent. The regressions yield adjusted [R.sup.2]s (1.02-1.03 percent) that are lower than those for the previous models. The coefficients on the unexpected sales variable in the "above" range and on the unexpected expenses variable have the predicted signs, and are significant. These coefficients indicate that an unexpected increase in sales (expenses) has a positive (negative) impact on stock returns. As discussed previously, the materiality threshold is identified by an insignificant estimate of and a significant, positive estimate of [beta]2. This result is obtained in the last two rows of the table. We do not detect a stock price response to sales information in the "below 0.01 percent" and the "below 0.005 percent" ranges. However, investors react positively to unexpected sales that exceed 0.01 percent of sales. This result suggests that investors' materiality threshold for the "percentage effect on sales" criterion is between 0.01 percent and 0.025 percent. In other words, when considering sales alone, we detect a non-zero materiality threshold but not when we use sales as a general materiality base for earnings.

We also examine whether different thresholds exist for positive and negative unexpected sales. The untabulated results indicate that the materiality threshold is lower for positive unexpected sales (between 0.01 percent and 0.025 percent, as for the full sample), than for negative unexpected sales (between 0.2 percent and 0.3 percent). One way to interpret "negative unexpected sales," from an auditing point of view, is that the forecast for sales was overstated. Likewise "positive unexpected sales" implies that the forecast for sales was understated. Thus, our results suggest a wider range of nonresponse and a higher materiality threshold for forecast overstatements.

Additional Analysis

We first examine whether the results presented in Tables 3 through 6 are sensitive to changes in the research design. We replicate our tests using beta-adjusted stock returns, with and without size as a control variable in the regressions. We also examine whether our results are sensitive to omission of outliers. Outliers are sample observations with studentized residual values of greater than 3 in the original regressions. The untabulated results for these two sets of tests are qualitatively similar to those presented in the paper. While the omission of outliers leads to marginal improvements in adjusted [R.sup.2]s and significance levels, the identified thresholds remain the same.

Finally, this study focuses on estimating the average investor's materiality threshold without regard to specific characteristics of forecast errors. We perform a series of additional analyses to explore how variations in our basic model might affect the average investor's materiality threshold. We consider whether the magnitude of unexpected earnings, firm growth, stock splits, and the sign of the earnings surprise affect our estimation of materiality threshold for pretax earnings.

The Magnitude of Unexpected Earnings

Our main tests focus on the average materiality threshold across all types of firms and sources of unexpected earnings. We estimate the smallest forecast error that produces a significant stock price reaction and, based on our results, there is a small nonresponse range around zero (i.e., the estimated materiality threshold is small). However, our model is likely to yield larger materiality thresholds for firms with extreme earnings surprises. Assuming the total market value of the firm is greater than pretax earnings [absolute value of PTI], partitioning the sample based on [absolute value of SUE]> K implies that [absolute value of UE/PTI] > K. Thus the materiality threshold for this partition should be greater than K. In order to investigate this possibility, we estimate Equation (2) on two subsamples that only contain high-magnitude earnings surprises: (a) [absolute value of SUE] > 0.005, and (b) [absolute value of SUE] > 0.01.

As reported in Table 7, we find that materiality thresholds are substantially higher for high-magnitude earnings surprises than for our entire sample. The "[absolute value of SUE] > 0.005" subsample contains approximately 37 percent of the original sample observations. For this subsample, our analysis yields a materiality threshold of between 1 percent and 2 percent of pretax income. Similarly, the threshold for the "[absolute value of SUE]> 0.01" subsample (which contains approximately 23 percent of the original sample observations) is between 2 percent and 2.5 percent of pretax income.

However, one limitation of our study is that we cannot systemically associate large unexpected earnings with particular firm characteristics. Furthermore, estimating the materiality threshold of a particular class of transactions, such as restructuring charges, would require a modification of our model to include stock price reactions to forecast errors for those transactions.

Firm Growth

Skinner and Sloan (2002) find that expected growth is a significant determinant of the magnitude of stock price response to earnings surprise. Accordingly, we examine whether the investor's average materiality threshold is a function of firm growth. We use market-to-book (M/B) and priceto-earnings (P/E) ratios to partition the sample into high-growth and low-growth firms. For each sample observation, the M/B ratio is computed as the quarter-end price divided by book value per share. The median MIB ratio for the sample is 1.55. We compute the PIE ratio as quarter-end price divided by the sum of earnings per share for the latest four quarters. For the P/E analysis, we exclude all observations with negative or zero earnings. The median P/E for this truncated sample is 17.98. For each of the two test variables, M/B and PIE, we use the median value to partition the sample into high and low groups, and investigate the materiality threshold separately for each group.

We find that high MIB firms have lower thresholds (between 0.2 percent and 0.3 percent of pretax income) than low MJB firms (between 0.5 percent and 1 percent of pretax income). However, we find no evidence that investors differentiate between high PIE and low PIE firms, which is consistent with the findings in Kinney et al. (1999). Our results suggest that the MIB ratio is a better proxy for investors' expectations of firm growth than the PIE ratio if growth matters in determining materiality.

The Effects of Stock Splits

We examine materiality thresholds for a sample of firms that have not split their stock in the sample period to test the robustness of our primary results. Small historical earnings surprises might be understated after split-related adjustments and rounding. We use cumulative split adjustment factors from CRSP to identify firms with stock splits. As presented in Table 7, our results are not sensitive to the exclusion of firms with stock splits.

Negative versus Positive Earnings Surprises

Skinner and Sloan (2002) also find a greater market response for negative earnings surprises than for positive earnings surprises. We examine materiality thresholds for these subsamples as well. However, we find no difference in the materiality thresholds for positive and negative earnings surprises, because both these subsamples have thresholds of between 0.2 percent and 0.3 percent of pretax income (see Table 7).

CONCLUSIONS

The Securities and Exchange Commission (SEC) has expressed concern over the auditor's use of materiality. They recently issued SAB No. 99 that suggests ways in which the auditor might alleviate those concerns. However, SAB No. 99 provides no quantitative guidance on materiality. For example, is a 5 percent overstatement of sales material? Or should auditors formulate their audit plans to detect a 3 percent overstatement in sales? Little is known regarding what size of financial statement error users would view as material.

We investigate empirically investors' perceptions of materiality in the context of several materiality criteria. These include percentage of pretax earnings, percentage of sales, and percentage of total assets. We cannot observe the user's decision process, but we can observe stock price reactions when unexpected information is revealed to stock market participants.

Based on the results from an earnings-response model, we infer that the average investor's materiality threshold using pretax income is between 0.1 percent and 0.2 percent and using total assets is between 0.01 percent and 0.025 percent. The earnings-based model does not yield a threshold for the "percentage effect on sales" criterion. However, a sales-response model, in which unexpected earnings is represented as the sum of unexpected sales and unexpected expenses, suggests that this threshold is between 0.01 percent and 0.02 percent of sales. Furthermore, when we consider negative and positive unexpected sales in separate models, the threshold for negative unexpected sales increases to between 0.2 percent and 0.3 percent.

Notably, all these materiality levels are substantially lower than those discussed in the pedagogical literature on auditing and those used in practice. The results of this study suggest that auditors might consider using lower materiality levels to avoid misleading investors.

We also view this study as a first step in our understanding of materiality and several extensions of our model would further that understanding. We derive our results from a sample of firms with a broad spectrum of characteristics. By contrast, user materiality may depend on specific firm characteristics not considered here, such as the proportion of net assets financed by debt or the nature of misstatement, intentional versus unintentional. Moreover, auditors' choices of materiality criteria depend not only on users' perceptions concerning the importance of information, but also the audit litigation exposure for nondetection of misstatements. For example, in most audit environments, auditors focus more on detection of overstatement errors because they expect users' losses and their litigation exposure to be larger for these types of misstatements. However, despite these additional features of materiality to consider in future research, our study provides valuable information about how investors generally pe rceive materiality.

TABLE 1

Summary Statistics

                                     Standard
Variable              Mean   Median  Deviation  Minimum  Maximum

CAR                 0.0015   0.0007   0.0738    -0.6628   1.0000
SUE                -0.0076  -0.0006   0.0399    -0.9427   0.4311
SUSales             0.0262   0.0183   0.1217    -3.0956   2.5024
SUExpenses          0.0296   0.0182   0.1245    -2.8823   2.4886
Abs(UE/PTI)         0.7397   0.1339   5.8457     0       50.5440
Abs(UE/Sales)       0.0277   0.0005   0.9329     0        9.0000
Abs(UE/TA)          0.0112   0.0032   0.0314     0        1.6711
Abs(USales/Sales)   0.0230   0.0053   0.6576     0       93.1640

CAR = the size-adjusted stock return for the three-day period centered
around the quarterly earnings announcements;

SUE = earnings surprise, actual earnings per share less the consensus of
analysts' forecasts, deflated by the price at the beginning of the
period;

SUSales = unexpected sales, computed as the forecast error from a
seasonal random walk model for sales, deflated by the price at the
beginning of the period;

SUExpenses = unexpected expenses, computed as the forecast error from a
seasonal random walk model for expenses, deflated by the price at the
beginning of the period;

Abs(UE/PTI) = he absoute value of unexpected earnings divided by pretax
income;

Abs(UE/Sales) = the absolute value of unexpected earnings divided by
sales;

Abs(UE/TA) = the absolute value of unexpected earnings divided by total
assets; and

Abs(USales/Sales) = the absolute value of unexpected sales divided by
sales.

TABLE 2

Base Model Estimation[CAR.sub.u] = [alpha] + [beta] [SUE.sub.it] +
[e.sub.it]

[alpha]           [beta]
(t-statistic)  (t-statistic)  Adjusted [R.sub.2]

0.0032            0.2197            1.42%
(7.71) *         (21.87) *

* Indicates significance at the 0.001 level.

The dependent variable is CAR, the size-adjusted stock return for the
three-day period centered around the quarterely earnings announcements.

SUE equals surprise, actual earnings per share less the consensus of
analysts' forecasts, deflated by the price at the beginning of the
period.

TABLE 3

Threshold Search for the Percentage of Pretax Earnings
Criterion[CAR.sub.it] = [alpha] + [[beta].sub.1] [SUE.sub.it] *
(Below_k%Earnings) + [[beta].sub.2] [SUE.sub.it] * (Above_k%Earnings)+
[e.sub.it]

        [alpha]     [[beta].sub.1]  [[beta].sub.2]  Adjusted
k    (t-statistic)  (t-statistic)   (t-statistic)   [R.sub.2]

2.0     0.0028          2.4222          0.2104        2.18%
       (6.55) *       (16.81) *       (20.34) *
1.0     0.0030          2.3266          0.2187        1.69%
       (7.02) *        (9.54) *       (21.12) *
0.5     0.0032          1.4178          0.2224        1.49%
       (7.55) *        (3.82) *       (21.49) *
0.3     0.0032          3.2947          0.2231        1.49%
       (7.58) *        (3.33) *       (21.56) *
0.2     0.0032          2.3723          0.2234        1.47%
       (7.66) *        (2.04) ***     (21.59) *
0.1     0.0032          1.2747          0.2235        1.46%
       (7.67) *        (0.99)         (21.60) *

*, *** Indicates significance at the 0.001 and 0.05 levels,
respectively.

The dependent variable is CAR, the size-adjusted stock return for the
three-day period centered around the quarterly earnings announcements.
SUE equals earnings surprise, actual earnings per share less teh
consensus of analysts' forecasts, deflated by the price at the
beginnings of the period. Below_k%Earnings equals 1, if the absolute
value of unexpected earnings divided by pretax income is less than k,
and 0 otherwise. Above_k%Earnings equals 1 minus Below_k%Earnings.

TABLE 4

Threshold Search for the Percentage of Sales Criterion

[CAR.sub.it] = [alpha] + [[beta].sub.1] [SUE.sub.it] * (Below_m%Sales) +
[[beta].sub.2] [SUE.sub.it] * (Above_m%Sales) + [e.sub.it]

         [alpha]     [[beta].sub.1]  [[beta].sub.2]  Adjusted
m     (t-statistic)  (t-statistic)   (t-statistic)   [R.sup.2]

2.0      0.0035          0.3304          0.1640        1.65%
        (8.31) *       (19.35) *       (12.80) *
1.0      0.0035          0.3629          0.1790        1.65%
        (8.34) *       (17.59) *       (15.16) *
0.5      0.0036          0.4216          0.1924        1.65%
        (8.45) *       (15.48) *       (17.37) *
0.05     0.0035          0.8936          0.2164        1.62%
        (8.23) *        (9.71) *       (20.83) *
0.01     0.0033          1.5601          0.2222        1.52%
        (7.80) *        (5.28) *       (21.47) *

* Indicates significance at the 0.001 level.

The dependent variable is CAR, the size-adjusted stock return for the
three-day period centered around the quarterly earnings announcements.
SUE equals earnings surprise, actual earnings per share less the
consensus of analysts' forecasts, deflated by the price at the beginning
of the period. Below_m%Sales equals 1, if the absolute value of
unexpected earnings divided by sales is less than m%, and 0 otherwise.
Above_m%Sales equal 1 minus Below_m%Sales.

TABLE 5

Threshold Search for the Percentage of Total Assets Criterion

[CAR.sub.it] = [alpha] + [[beta].sub.1] [SUE.sub.it] * (Below_n%Assets)
+ [[beta].sub.2] [SUE.sub.it] * (Abo_n%Assets)+ [e.sub.it]

          [alpha]     [[beta].sub.1]  [[beta].sub.1]  Adjusted
  n    (t-statistic)  (t-statistic)   (t-statistic)   [R.sup.2]

 2.0      0.0040         0.8327          0.1767         2.37%
          (9.51) *      (22.54) *       (16.59) *
 1.0      0.0037         1.1287          0.1972         2.23%
          (8.86) *      (19.43) *       (18.89) *
 0.5      0.0034         1.3665          0.2115         1.90%
          (8.07) *      (14.17) *       (20.39) *
0.05      0.0032         3.3638          0.2232         1.48%
          (7.58) *      (3.04) **       (21.56) *
0.025     0.0032         5.3754          0.2234         1.47%
          (7.64) *      (2.11) ***      (21.59) *
0.01      0.0032         8.7809          0.2235         1.46%
          (7.66) *       (0.98)         (21.60) *

*, **, *** Indicates significance at the 0.001, and 0.05 levels,
respectively.

The dependent variable is CAR, the size-adjusted stock return for the
three-day period centered around the quarterly earnings announcements.
SUE equals earnings surprise, actual earnings per share less the
consensus of analysts' forecasts, deflated by the price at the beginning
of the period. Below_n%Assets equals 1, if the absolute value of
unexpected earnings divided by total assets is less than n%, and 0
otherwise. Above_n% Assets equal 1 minus Below_n% Assets.

Table 6

Threshold Search for the Percentage of Sales Criterion Using Stock Price
Response to Sales Information

[CAR.sub.it] = [alpha] + [[beta]. sub.1] [SUSales.sub.it] * (Below_p
%Sales) + [[beta].sub.2] [SUSales. sub.it] * (Above_p%Sales) +
[[beta].sub.3] [SUExpenses.sub.it] + [e.sub.it]

          [alpha]     [[beta].sub.1]  [[beta].sub.2]  [[beta].sub.3]
p      (t-statistic)  (t-statistic)   (t-statistic)   (t-statistic)

2.0       0.0016          0.1557          0.1515         -0.1383
         (3.63) *        (16.31) *       (17.17) *       (-16.76) *
1.0      0.0015           0.1594          0.1514         -0.1383
         (3.59) *        (14.85) *       (17.56) *       (-16.75) *
0.5      0.0015           0.1632          0.1517         -0.1381
         (3.58) *        (12.63) *       (17.75) *       (-16.72) *
0.05     0.0016           0.1876          0.1528         -0.1383
         (3.69) *         (3.54) *       (18.09) *       (-16.76) *
0.025    0.0016           0.1966          0.1529         -0.1383
         (3.73) *         (2.08) ***     (18.10) *       (-16.76) *
0.01     0.0016          -0.0857          0.1531         -0.1384
         (3.81) *        (-0.36)         (18.12) *       (-16.77) *

       Adjusted
p      [R.sub.2]

2.0      1.03%

1.0      1.03%

0.5      1.03%

0.05     1.02%

0.025    1.02%

0.01     1.03%


*, *** Indicates significance at the 0.001 and 0.05 levels,
respectively.

The dependent variable is CAR, the size-adjusted stock return for the
three-day period centered around the quarterly earnings announcements.
SUSales equals unexpected sales, computed as the forecast error from a
seasonal random walk model for sales, deflated by the price at the
beginning of the period. SUExpense equals unexpected expenses, computed
as the forecast error from a seasonal random walk model for expenses,
deflated by the price at the beginning of the period. Below_p%Sales
equals 1, if the absolute value of unexpected sales divided by sales is
less than p%, and 0 otherwise. Above_p%Sales equals 1 minus
Below_p%Sales.

TABLE 7

Additional Analysis of the Materiality Threshold: Summary Results

                                  Sample   Identified Threshold
Subsample Criterion                Size   (% of Pretax Earnings)

a. Full sample (Table 3 results)  31,470  Between 0.1% and 0.2%
b. Extreme Earnings
   (i) \SUE\>0.005                11,599  Between 1% and 2%
   (ii) \SUE\>0.01                7,169   Between 2% and 2.5%
c. Market-to-Book
   (i) High: M/B>1.55             15,735  Between 0.2% and 0.3%
   (ii) Low: M/B<=1.55            15,735  Between 0.5% and 1%
d. Price-to-Earnings
   (i) High: P/E>17.98            13,072  Between 0.2% and 0.3%
   (ii) Low: P/E<=17.98           13,073  Between 0.2% and 0.3%

e. Sign of Earnings Surprise
   (i) Positive SUE               13,999  Between 0.2% and 0.3%
   (ii) Negative SUE              17,469  Between 0.2% and 0.3%
f. Firms with no stock splits     16,631  Between 0.2% and 0.3%

The analysis presented in this table uses Equation (2):

[CAR.sub.it] [alpha] + [[beta].sub.1] [SUE.sub.it] * (Below_k%Earnings)
+ [[beta].sub.2] [SUE.sub.it] * (Above_k%Earnings) + [e.sub.it]

where:

CAR = the size-adjusted stock return for the three-day period centered
around the quarterly earnings announcements

SUE = earnings surprise, actual earnings per share less the consensus of
analysts' forecasts, deflated by the price at the beginning of the
period

Below_k%Earnings = 1, if the absolute value of unexpected earnings
divided by pretax income is less than k%, and 0 otherwise; and

Above_k%Earnings = 1 minus Below_k%Earnings.

Materiality thresholds are identified by repeatedly estimating Equation
(2 for sequentially declining values of k, and by examining the
significance of [[beta].sub.1], which we require to be insignificant at
the lower bound, and [[beta].sub.2], which we require to be positive.
The Market-to-Book (M/B) ratio is computed as quarter-end price divided
by book value per share, and the Price-to-Earnings (P/E) ratio is
computed as quarter-end price divided by the sum of earnings per share
for the latest four quarters. The P/E ratio analysis excludes all
observations with negative or zero earnings.

(1.) See Tuttle et al. (2002) for further discussion and for an experimental study of materiality thresholds.

(2.) Auditors often use multiple materiality measures, one of which applies to earnings in general. However, in testing a specific account, such as sales, an auditor may define materiality, or tolerable misstatement, that is different from the one applied to earnings in general. Sometimes this is the result of "allocating" materiality to specific accounts or it may arise from the auditor's understanding of users' concerns about a specific account. For example, in a growth industry, users may be particularly concerned about fluctuations in sales in addition to fluctuations in earnings.

(3.) Our measure of earnings surprise is likely to be influenced by analyst forecasting ability and by earnings management. We do not investigate these implications.

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Seong-Yeon Cho is an Assistant Professor at Drexel University, Robert L. Hagerman is a Professor at the State University of New York at Buffalo, Sandeep Nabar is an Assistant Professor at Oklahoma State University, and Evelyn R. Patterson is an Assistant Professor at the State University of New York at Buffalo.

We acknowledge the helpful comments of Ron Huefner, Jim Largay, Kevin Sachs, two anonymous reviewers, and especially, the editor, Patricia Dechow. This paper is dedicated to the memory of Vie Pastena.