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ACCTMIS 7530—Using DuPont analysis to detect FFR
The idea
In DuPont analysis, a firm’s return on equity (ROE) and/or return on assets (ROA) are
decomposed into various components to evaluate a firm’s financial performance. A recent study 1 uses a
DuPont decomposition of ROA, focusing on operating assets and operating income, to investigate
earnings management. Their decomposition, which can be applied to FFR also, is as follows:
Return on operating assets = PM * ATO or
Sales

 Operating income   Operating income  
*
,

 = 

 Net operating assets 
Sales
 Net operating assets  



where net operating assets are defined as net assets less net financial assets, PM is profit margin (the ratio
of operating income to sales) and ATO is asset turnover (the ratio of sales to net operating assets). In a
stable operating environment, the authors submit that PM and ATO should remain relatively constant.
However, changes in PM and ATO, especially in opposite directions, could signal FFR. (This is because
the articulation of the income statement and balance sheet ensures that income-affecting FFR impacts
operating income and net operating assets in the same direction, thus causing PM and ATO to move in
opposite directions.) Specifically, an increase (decrease) in PM coupled with a decrease (increase) in
ATO is suggestive of income-increasing (-decreasing) FFR. This pattern of changes is correlated with the
likelihood that a firm will subsequently restate its earnings and also provides information about other FFR
indicators.
Types of FFR that are detectable
The pattern of changes is expected to hold for all types of expense FFR,2 assuming that there is no
change in business strategy and relatively constant growth in operating assets. For revenue FFR, however,
it is not as clear, because the numerators and denominators of both PM and ATO would change.
Considering for a moment only income-increasing revenue FFR, the patterns will hold if (1) the profit
margin on the fraudulent revenue is greater than the profit margin on the non-fraudulent revenue and (2)
the asset turnover of the fraudulent revenue is less than the asset turnover of the non-fraudulent revenue.
The first condition is likely satisfied but the second is not as clear-cut, as it depends on the relative effect
on turnover of any accrued expenses related to the fraudulent revenue.
1
Jansen, I., S. Ramnath, and T. Yohn. 2012. A diagnostic for earnings management using changes in asset turnover
and profit margin. Contemporary Accounting Research 29 (1): 221-251.
2
It is assumed that FFR does not involve cash-based manipulations.
Calculation of pattern of changes
(1) Calculate the basic variables:
Operating income = Sales – (COGS + SG&A expense + depreciation and amortization expense)
Net operating assets = Net assets – Net financial assets = Stockholders’ equity – (cash and equivalents –
(long-term debt + current maturities of long-term debt))
(2) Use the variables in (1) to calculate PM and ATO for the year being investigated (year t) and
the prior two years (years t-1 and t-2).
(3) Calculate ΔPMt-1 as (PMt-1 – PMt-2) and ΔATOt-1 as (ATOt-1 – ATOt-2).
If ΔPMt-1 > 0 and ΔATOt-1 < 0, then EM_UPt-1 = 1; otherwise EM_UPt-1 = 0.
If ΔPMt-1 < 0 and ΔATOt-1 > 0, then EM_DNt-1 = 1; otherwise EM_DNt-1 = 0.
(4) Calculate ΔPMt as (PMt – PMt-1) and ΔATOt as (ATOt – ATOt-1).
(5) The variables of interest are as follows:
EM_UPt = 1if ΔPMt > 0, ΔATOt < 0, and EM_DNt-1 ≠ 1.
EM_DNt = 1if ΔPMt < 0, ΔATOt > 0, and EM_UPt-1 ≠ 1.
EM_UPt = 1 is a signal of income-increasing FFR. Similarly, EM_DNt = 1signals income-decreasing
FFR. Note that in addition to different directions of change in PM and ATO in the current year (i.e., year t
minus year t-1), the EMt variables also require that the changes in PM and ATO in the prior year (change
from year t-2 to t-1) was not indicative of earnings management or FFR in the opposite direction. That is,
the EMt variables are designed to detect FFR (or earnings management) in the current period, not the
reversal of FFR (or earnings management) from the prior period. 3
Most of the time, neither of the EMt variables will signal FFR. In a sample of over 100,000 firmyears spanning the years 1971 through 2005, Jansen et al. (see footnote 1) report that 14.8% of the firmyear have EM_UPt = 1and 17.3% of the firm-years have EM_DNt = 1.
Although hit and false positive rates are not available for FFR firms, if one assumes that firms
subsequently restating earnings are fraudulent reporters and firms not restating are not, the LR (i.e., hit
rate / false positive rate) for EM_UP is .163/.138 = 1.2 and the LR for EM_DN = .293/.185 = 1.6.
3
Note that discretionary accruals regression models do not have this control and will therefore flag as FFR in the
current period reversals of FFR from prior periods.