ACCTMIS 7530—Case 4
Using discretionary accruals to detect fraud
When companies record fictitious revenue, income is increased, but cash flows
are not. Similarly, postponing the recording of expenses (not paid in cash) until future
accounting periods increases the current period’s income, but does not affect current
period’s cash flows. It is generally easier to commit (and hide) fraudulent financial
reporting by manipulating accruals as opposed to cash flows, and fraudsters take
advantage of this. It seems reasonable, then, that we may be able to develop more
powerful tests for detecting FFR if we focus on accruals.
To focus on accruals, we separate income before extraordinary items (IBEI) into a
cash component and an accrual component. Cash flow from operations (CFO) measures
the cash component, and the accrual component (designated total accruals or TotAcc) is
the difference between IBEI and CFO:
TotAcc = IBEI – CFO
For a given quarter or year, if TotAcc is positive, the company engaged in transactions
that increased income but not cash flows. Of course, not all of these transactions are
indicative of FFR (in fact, none of them may be fraudulent). On the other hand, if the
company is committing FFR by manipulating accruals to increase income, TotAcc will
likely be positive (or less negative than it would otherwise be). A simple first test, then,
is to determine whether TotAcc is significantly greater than 0 (benchmarks other than 0
can be used).
Although this first test (calculating and evaluating the sign and magnitude of
TotAcc), may be useful, it does not consider that some accruals are outside of
management’s control and, therefore, are unlikely to be used by management to
manipulate income. For example, a company’s accruals may reflect changes in the
economic conditions that the company faces, which are largely outside of management’s
control. We can refine the test by separating TotAcc into discretionary accruals (DA)
and nondiscretionary accruals (NDA). (DA are also called “abnormal” accruals and
NDA are also called “normal” accruals.) The idea is that NDA, because they are not
under direct short-term control of management, will not be used to manipulate the
financial statements. NDA relate to changes in the business environment that
management has little control over, or to items that cannot be changed in the short-term.
If we can remove this portion of accruals from TotAcc, then we might have a more
powerful test for FFR. That is, we focus our tests on accruals that can be used for shortterm manipulation of income (i.e., DA).
To measure NDA, we use two pieces of data: (1) the change in revenue between
accounting periods (deltaRev), which is used to measure the effects on working capital
accounts of changes in the business environment and (2) gross property, plant, and
equipment (grossPPE), which is used to measure the longer-term effects of changes in the
environment. To estimate the portion of TotAcc that is related to these two variables, we
use this equation:
NDA = a + b1(deltaREV) + b2(grossPPE),
where a, b1, and b2 are coefficients from a regression model (discussed below).
Estimating the regression coefficients
To develop the a, b1, and b2 coefficients to calculate NDA, we use the following
regression model:
TotAcct = a + b1(deltaREVt) + b2(grossPPEt) + prediction error,
where TotAcct = IBEI – CFO for year t,
deltaREVt = Revenue for year t minus Revenue for year t-1, and
grossPPE = Gross value of PPE at end of year t.
(If you would like a refresher on regression analysis and information on how to estimate
regressions in Excel, please see the files “regression to predict.doc” and “regression
example.xls” available on the course homepage.)
Here are some things to note about estimating the regression model:
1. The data to estimate the regression can be quarterly or annual, but annual data are
most often used.
2. The model can be estimated using data from the same firm (i.e., the company being
investigated) over a period of time. The specific year being investigated, however,
should not be used to estimate the model. For example, if you are investigating Raystar
for 1997, you could use data from 1986 through 1996 to estimate the model. This is a
time-series analysis.
3. The model can also be estimated using data from companies in the same industry (for
the same year or quarter) as the company being investigated. Again, do not include the
company being investigated in the model’s estimation. This is a cross-sectional analysis.
4. Although some authors suggest that at least 15 observations per independent variable
should be available to estimate a regression model, researchers have had success
estimating accruals models with as few as 10 (total) observations.
5. The variables are often scaled by Total Assets as of the beginning of the year. That is,
TotAcc, deltaREV and grossPPE for year t are all divided by Total Assets at end of year
t-1 and the resulting amounts are used to estimate the regression. It may be more
important to used scaled amounts for cross-sectional analyses than for time series
analyses.
6. You may have (correctly) deduced that the prediction error is also an estimate of DA.
The prediction error (also called “residual” or simply “error”) has a standard deviation
associated with it and we can use that to compute the statistical significance of estimates
of DA. (See “Running the test” below.)
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Running the test
You may complete the following steps to perform the test. Assume that you are
investigating a company for time period (year or quarter) t.
1. For a cross-sectional analysis, gather the following financial data for each company in
the industry to estimate the base regression model: (a) IBEI for period t, (2) CFO for
period t, (3) Revenues for periods t and t-1, (4) Gross PP&E at end of period t, and (5)
Total assets at end of period t-1. It is acceptable to use 2-, 3-, or 4-digit SIC codes to
identify companies in the industry.
2. For a time-series analysis, gather the following data (for as many years or quarters as
possible before time period t) for the company being investigated: (a) IBEI, (b) CFO, (c)
Revenues, (4) Gross PP&E, and (5) Total assets (if you desire to scale).
3. For the company under investigation in time period t, gather the following financial
information: (a) IBEI for period t, (2) CFO for period t, (3) Revenues for periods t and t1, (4) Gross PP&E at end of period t, (5) Total assets at end of period t-1, and (6)
Accounts receivable at end of time periods t and t-1. Note the addition of the Accounts
receivable item.
4. Calculate the variables needed for the regression.
5. Estimate the regression using Excel or another program.
6. For the company under investigation in period t, use the coefficients a, b1, and b2 from
the estimated regression model to calculate NDA as follows:
NDAt = a + b1(deltaREVt – deltaARt) + b2(grossPPEt),
where deltaARt equals Accounts receivable at end of period t minus Accounts receivable
at end of period t-1 and the other variables are the same as above.
Then calculate DA for period t as follows:
DAt = TotAcct – NDAt
7. Use the Standard Error of prediction from the regression model output to calculate a zscore for the DA computed in step 6, as follows 1:
z = DA / Standard Error of Prediction.
8. Assess whether z is significantly positive (use whatever standard for significance you
deem appropriate; see “Empirical evidence” below for some ideas). If it is significantly
positive, the evidence favors the company overstating income.
9. If you have the time and desire, you may run a test on TotAcc by calculating the mean
and standard deviation for the industry (or time series) and assessing whether the
company under investigation has TotAcc that are significantly higher than the mean.
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As noted in the “regression to predict.doc” file, for small samples, this formula provides for a liberal
approximation of z, but is probably well-suited for fraud investigations.
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Empirical evidence
Accounting researchers have studied the use of accruals to identify firms that
commit FFR. The Appendix contains excerpts from one such study. Pay particular
attention to the second and third plots in Figure 1. These plots show that fraudulentlyreporting firms have higher TotAcc and DA amounts than similar-sized non-fraudulent
firms in the periods of fraudulent reporting, but lower TotAcc and DA amounts after the
period of fraudulent reporting. This suggests that TotAcc and DA may be useful in
distinguishing FFR firms from other firms.
In another article (“Detecting Earnings Management,” The Accounting Review 70,
2 (April 1995), pp. 193-225 by Patricia M. Dechow, Richard G. Sloan, and Amy P.
Sweeney), the authors reported hit rates and false positive rates, as follows:
Test level (one-tailed)
1%
5%
Hit rate
12.5%
28.1%
False positive rate
1.3%
5.9%
The hit rates are defined as P(DA>0 | FFR present) and false positive rates are P(DA>0 |
FFR absent). “DA>0” means that DA is statistically significantly greater than 0. The test
levels in the table are the significance levels used for determining whether DA is
significantly greater than 0, using a one-tailed test. That is, the z-values for the 1% and
5% levels are 2.326 and 1.645, respectively.
Respond to the following:
1. Even though it is generally easier to commit FFR by manipulating accruals as opposed
to cash flows, not all frauds are perpetrated using accruals.
a. Why is it generally easier to commit FFR by manipulating accruals as opposed
to manipulating cash flows?
b. Provide an example of an income-increasing FFR that does not involve the
manipulation of accruals.
2. Identify and discuss some strengths and weaknesses in using DA to test for FFR.
3. Based on the hit rates and false positive rates reported above, which test level (1% or
5%) provides stronger evidence that FFR exists? Would you use that test level in a fraud
investigation? Explain.
4. The Excel file “raystar2.xls” (on course homepage) includes time series data and
cross-sectional data for Raystar and the companies in its industry. Perform the DA test
specified above. I have done steps 1-3 for you. Note that for the time series data, even
though there are only 9 observations, you should still perform the analysis (the mechanics
are the same no matter how many observations there are). Do the analyses indicate that
Raystar is engaging in FFR? Explain.
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Appendix: Excerpts from “Causes and Consequences of Earnings Manipulation: An
Analysis of Firms Subject to Enforcement Actions by the SEC,” Contemporary
Accounting Research 13, 1 (Spring 1996), pp. 1-36, by Patricia M. Dechow, Richard G.
Sloan, and Amy P. Sweeney.
The authors of this study gathered data on firms that were identified by the SEC as
violating Section 13(a) of the Securities Exchange Act of 1934 (specifically, filing
financial statements that did not conform to GAAP). The 92 firms were the subject of
Accounting and Auditing Enforcement Releases (AAERs) issued between 1982 and 1992
and are designated as “SEC firms” or the “SEC sample” in the following excerpts. In
addition, for comparison purposes, the authors identified 92 “matching” firms (called the
“control firms” or the “control sample” in the following) that were of similar size and in
the same industry (measured by 3- or 2-digit SIC code) as the SEC firms. For our
purposes, we are particularly interested in the behavior of total accruals and discretionary
(i.e., abnormal) accruals of the SEC firms versus the control firms. The “modified Jones
(1991) model” is the model used in this case.
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