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Discretionary Accruals: Model 3.1
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Accounting Analytics
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Big Data and Prediction Models
This week, we’ll use big data approaches to try to detect earnings management. Specifically, we're going to use prediction models to try to predict how the financial statements would look if there were no manipulation by the manager. First, we’ll look at Discretionary Accruals Models, which try to model the non-cash portion of earnings or "accruals," where managers are making estimates to calculate revenues or expenses. Next, we'll talk about Discretionary Expenditure Models, which try to model the cash portion of earnings. Then we'll look at Fraud Prediction Models, which try to directly predict what types of companies are likely to commit frauds. Finally, we’ll explore something called Benford's Law, which examines the frequency with which certain numbers appear. If certain numbers appear more often than dictated by Benford's Law, it's an indication that the financial statements were potentially manipulated. These models represent the state of the art right now, and are what academics use to try to detect and predict earnings management. By the end of this module, you'll have a very strong tool kit that will help you try to detect financial statements that may have been manipulated by managers.
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Brian J BusheeThe Geoffrey T. Boisi Professor
Accounting
Christopher D. IttnerEY Professor of Accounting
Accounting
Hello I'm Professor Brian Bushee.
Welcome back.
In this video,
we're gonna take a look at something called the Discretionary Accruals Model.
The idea of this model is to pick up earnings management when managers
are making tweaks to a bunch of different accounts instead of changing one account.
So for example, manager tweaks the estimate of an expense to reduce it,
recognizes a little bit of extra revenue, capitalizes some extra cost,
reduce that expense.
If we looked at the tools for each of those individual accounts,
the changes might not be big enough to pick up.
But together, they had a significant impact on the accruals or
noncash portion of earnings, and we can pick that up using this model.
The basic idea of the model is we're gonna use a regression analysis
to try to figure out what the level of accruals or
noncash earnings would be if the manager was not committing any manipulations.
Then any differences from that expected level
are potentially evidence of earnings management.
It's a really cool model.
Let's get started.
Before we talk about discretionary accruals models first let's take a step
back and review what we mean by accruals.
So you can think of a company's earnings, or
its net income as made up of cash earning and non-cash earnings.
Cash flow from operations is a measure of the cash earnings during the period.
The non-cash earnings are all the accruals,
all of the earnings that are recognized at a point different than the cash flow.
So things like sales made on account.
When you deliver the goods and recognize revenue but
haven't collected the cash yet.
Depreciation expense, where you spent the cash a long time ago on a building.
And now you're showing the expense through depreciation this period.
Warranty expense, which is an example of an expense that's recognized before you
actually pay the cash to fix the defective goods.
So in general, these accruals improve the measurement of firm performance by
tying the earnings to business activities, rather than to cash flows.
And that's why we've been using this model for
over 500 years because the accruals are informative about from performance and
they're also very informative about future performance.
But the problem is that accruals are also the easiest portion of earnings
to manipulate, because they're based on managerial judgment and estimates.
And we saw this a little bit last week with the revenue and
expense manipulations.
We talked about some ratios that could detect those manipulations.
But those ratios are only gonna work for bigger manipulations of revenues and
expenses, which also may be the easier ones for outsiders to detect.
So what would happen if managers made small manipulations
to a number of accounts?
Well, the discretionary accruals models are designed to
detect this very type of manipulation.
>> Nice explanation, except that I have no idea what you are talking about.
>> It's good to see that we're off to a great start.
I'm gonna give you a example of this later in the video.
So when we're going through and estimating these models we'll go in in one case and
manipulate a little bit of bad debt expense.
We'll delay a write-off, we'll tweak the warranty expense, and
individually they won't be big changes.
But collectively, they'll have a big impact on earnings and
one that we can pick up with these discretionary accruals models.
The model that we're gonna use for
discretionary accruals is called the Modified Jones Model.
It was first developed by Jennifer Jones
as part of her doctoral education at the University of Michigan in the early 1990s,
and then it was modified by subsequent research.
It starts with the premise that the accrual portion of earning should be
a function of revenue growth and tangible assets.
Revenue growth because growing sales causes working capital to grow.
So things like receivables and payables which should increase non-cash earnings.
And property plan equipment because higher property plan equipment is going to lead
to higher depreciation charges and non-cash earnings.
So the model is accruals should be a function of the cash revenue growth and
property plant and equipment.
We're going to define accruals as net income minus cash from operations, so
that non-cash portion of net income.
We're gonna define cash revenue growth as
the change in revenue minus the change in accounts receivable.
So, this tries to get at how much of the growth and revenue was in cash sales.
And we look at cash sales because,
of course, revenue on its own could be one of the things that's manipulated.
And so, to be able to pick up revenue manipulations,
we need to look at cash revenue growth to explain accruals.
And then the final component is property, plant, and
equipment which we measure as gross property, plant, and equipment.
So in other words, PP&E before you subtract out the depreciation.
>> More Greek letters!
Is this an accounting class or a classics class?
Are you also going to ask us to read the Iliad and the Odyssey?
>> Well I actually haven't read the Iliad and the Odyssey myself so
I'm not gonna ask you to read it.
Sorry for the Greek letters.
The convention with regression models is that for the theoretical
regression model you include Greek letters for the intercept, the coefficients.
You include an epsilon as an error term to recognize that
no model is gonna be perfect, there will always be error.
Then when you estimate the model using data, you go away from the Greek letters.
I should note at this point that if you've never seen regression before,
you should be okay.
Cuz I'm gonna present the material in a way, and give you resources so that you
actually don't have to understand how the regression works to be able to use it.
Think of it as some kind of magical statistical technique which
allows us to model what a company's results should look like
if the manager's doing no manipulation.
Then we can look for differences from that ideal level and
those differences could reflect earnings management.
So anyway, accruals that fit this model are gonna be normal accruals.
These are accruals that are explained by normal business activities.
In other words, if there was no manipulation activity at all by managers,
this is the amount of accruals we would expect to see.
Accruals that don't fit this model are called discretionary accruals and
these are the ones that are more likely to reflect earnings management.
But there's some caveats.
So changes in the business, so acquisitions,
divestitures, changes in segments, changes in strategy,
changes in the industry like technological innovation, or just bad model fit.
The model doesn't fit very well for
a given company could also create the appearance of discretionary accruals.
So we're gonna have to exercise some caution and do some additional
benchmarking and think about earnings management incentives before we can judge
that a discretionary accruals number is likely to reflect earnings management.
>> So you are saying that this model works quite well except, of course,
for all of the times it doesn't work.
>> Yeah, that is pretty much what I'm saying.
So we've talked about this in a lot of the videos that none of these tools provide
definitive evidence that a management team is 100% committing earnings management.
Instead it's just suggestive that something unusual is going on in
the numbers this year.
Then we have to look for
are their earnings management motives that the manager has?
Are the changes for the firm unusual given the industry?
So do we see similar discretionary accruals for competitors or not?
And then, are there any changes in the business which may either explain why
the discretionary accruals are really not discretionary?
They're part of the normal business, or
changes in policy which would help them facilitate manipulation.
So in other words,
these discretionary accrual models are not the end of your investigation into whether
companies committing earnings management, they're the start of your investigation.
Here's the approach we're gonna use to estimate discretionary accruals.
So we've got our model for explaining accruals as a function of
cash revenue growth and property plant & equipment.
We're gonna scale all these variables by prior total assets which means that we're
gonna divide them all by prior total assets.
This is gonna remove a firm size effect.
If we don't do this, then our model's gonna be messed up for
smaller firms because the larger firms are gonna dominate how it gets estimated.
Once we do that then we can estimate a regression to get parameters a, b and c.
So we replace the theoretical intercept alpha with
the intercept a that we estimated in a certain sample.
Same thing with the coefficients beta and chi, we'll replace them with b and c,
which we estimate within a certain sample.
There's two approaches we're gonna use to form samples.
One is time series, so we're gonna use the past history for the company.
So, if we want to measure discretionary accruals this year, we'll take say,
the prior ten years of data and use those ten years to estimate a, b, and c.
The disadvantage of this approach is you can't do it for
younger firms cuz you need at least ten years of prior data.
Also you can have some bad model fit if the parameters change over time.
So if the company makes big acquisitions during this period,
the parameters won't necessarily carry over to the current period.
So the other approach we'll use is cross-sectional,
where we'll look at everyone in a firm's industry at the same point in time.
So this will allow us to look at younger firms.
It'll guard against the parameters changing over time cuz we're
estimating the parameters based on the same period.
The disadvantage of this approach is it's sensitive to the definition of industry.
If you include too many firms in the definition of industry that
are different from the firm you're looking at, again you could get bad model fit.
So there's pros and cons to each, we'll do them both ways initially.
The other thing to think about is we have to assume there's no manipulation
on average in the estimation sample.
So ideally we would estimate a, b, and c in a sample where there's no
manipulation going on which would allow us to detect manipulation out of that sample.
But if there is manipulation in the estimation sample it's just gonna
reduce our power to find manipulation.
Once we get a, b and c, then we are going to calculate normal accruals
as the intercept a + the coefficient b * cash revenue growth +
the coefficient c * properly plan equipment.
And then discretionary accruals are simply accruals- our estimate of normal accruals.
>> Dude, I am ready to run some regressions.
>> Dude, that's awesome.
Go find the Arfabark company spreadsheet on the course platform, and
let's go run some gnarly regressions.
The example we're gonna use to show how to do these models is Arfabark corp foration.
And we're interested in doing discretion accruals for 2009 and 2010.
First I'm gonna do a time series approach,
so I'm gonna pull in ten years of prior data for Arfabark.
And you can see in these first few columns is all the raw data that you need to
collect to do the model.
Then we get to the variables that we're going to run in the model.
Accruals divided by total assets, change in cash revenue divided by
prior total assets and property plant equipment divided by prior total assets.
Once those are calculated, we can do a regression.
If you want to do that in Excel, you can click Data Analysis > Regression.
You have to fill in the range for accruals, that's your y variable.
Make sure you stop at 2008, don't take the years that you're estimating.
Then do the same thing for the x range where we take cash revenue and PP&E.
Make sure Labels is checked so that you have the coefficients labeled.
Click Output Range, show Excel where you want the output, hit OK,
and voila, you get regression coefficients down here.
We're gonna take those coefficients and we're gonna put them in for
every single year cuz we're assuming the model is stationary for Arfabark.
Once we have the coefficients, then we can take the normal accruals as
a plus b times the change in cash revenue plus c times the PP&E,
you can see the formula if you click on that.
Once you get normal accruals,
then you take accruals minus normal accruals to get discretionary accruals.
And then what you can see is the two that are in red are the one we're
interested in, 2009 and 2010.
That's the amount for discretionary accruals.
Are they big or small?
Well, the way to check would be to compare it to the mean min and
max over the period that you're estimating it.
The mean is going to be zero if you're doing it within the sample cuz it's
a residual.
But notably, the 0.007 in 2009 is not greater than the max.
The value in 2010 is less than the min, so
that might be a suspect period in terms of manipulating earnings downward.
But there's no evidence in either year of manipulating earnings upward.
>> Professor, even a statistical neophyte like myself knows
that you should not use a coefficient that is insignificant from zero.
>> Yeah, you got me on that one.
If you don't know a lot about regressions you may want to go just get a drink right
now and skip this part.
Because it's fairly technical, or maybe if you do know regressions,
you should get a drink also so I don't get in trouble for what I'm doing.
But if you look at the t statistics and p values, those are ways to
test whether the coefficients are what's called significantly different from zero.
So, does that mean do we have confidence that the coefficient is actually different
than a coefficient of zero?
And, in a lot of cases they won't be statistically significant.
And that's because we use pretty small samples when we run these regressions.
But we find that these models work anyway because the coefficient estimate we
get even though it is noisy, is better than nothing.
And we're gonna end up with a discretionary accruals model that's
sort of the best estimate we can come up with.
Again it won't be 100% accurate, none of these statistical techniques are.
But it's at least evidence that we can
use to try to figure out whether a company's manipulating or not.
So we didn't find any evidence of manipulation for Arfabark, but
we didn't really suspect any in those two years.
This was just an example where I pulled the data, but
we didn't necessarily expect there was any reason for them to manipulate earnings.
So just to show you the model does work in the next tab I did some manipulations.
So for 2009 I cut bad debt expense, I delayed a write-down,
cut warranty expense, and manipulated earnings upward.
I changed all the other variables that would change as a result.
And voila, the Discretionary Accruals model gives us a value of
0.062 in 2009 which is much, much greater than the max during the estimation period.
And would suggest evidence of earnings manipulation.
In the next tab I also did it with just a sales manipulation.
So I just manipulated revenue, changed all the variables that would also change.
You get a discretionary accruals number of 0.058, which again,
is greater than the max in the period that we estimated the model and
would lead you to suspect earnings manipulation.
Again, as long as you had some other basis to think that there were incentives
to manage earnings during the period.
But I just wanted to show you if you inject a manipulation into this data,
you can pick it up with the discretionary accruals models.
Now let me show you the cross-sectional regression approach.
So the first step is to pull in all of the company's data that's in
the same industry as Arfabark.
Their SIC code was 2670.
I grab just the first two digits and took all the firms that were in SIC codes
starting with 2, 6 to get as big f sample as possible.
And I came up with 51 companies.
So then for 2009, I have all the data for those 51 companies and
then I would run the regression, data analysis regression,
I wanna highlight the y column.
Highlight the two columns for x, make sure Labels is clicked,
choose my output range, hit OK, and I get coefficients.
Now those coefficients are just for 2009.
So I'll carry those over into another tab.
In this tab all the data is the same out to where you get to the coefficients and
then the coefficients are what I get from the cross sectional model.
Notice that they vary by year which means that I had to run
the industry regression every year to get different coefficients for every year.
After doing that, then I can do the normal accruals and
the discretionary accruals the same way.
I get discretionary accruals of 0.019, which is small, but again,
we don't suspect any manipulation.
In the next two tabs,
which you can check out in detail on your own, I inject multiple manipulations.
Again, the bad debt write downs and warranty expense.
And discretion accruals jumps up from 0.09 to 0.072.
And if I just do the sales manipulation I can also pick it up, it jumps up to 0.070.
>> I am a busy kid.
I do soccer, chess, dance, pottery, swimming and judo after school.
I don't have time to run all of these regressions.
What do you propose I do with all of this?
>> Yeah, I know that's a lot of different ways to do it.
The most common way that people will do this is what we just looked at with
the cross-sectional regression.
So in other words the industry regressions by year.
And then apply those coefficients to all the firms in the industry.
And people tend to do it that way because you can usually get more observations of
firms within the industry than you can number of years in a company's history.
And then you can also apply this to younger firms.
You don't need a long time history to do the regressions.
What I'm going to do to make this easier for you cuz I do realize you have judo and
jazz and dance and all that stuff also in your life
is on the course platform I'll give you a spreadsheet of coefficients.
So I will run these regressions by industry by year.
And make all the coefficients available to you on a spreadsheet so
all you have to do is pull them off the spreadsheet, and
then you can use it without having to run these regressions yourself.
Now that we've seen how to estimate these models what we'll do in the next video
is try them out on three different cases to see how well they work.
I'll see you then.
>> See you next video.
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