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Accrual duration
Ilia D. Dichev
Emory University
December 15, 2016
Abstract: Accrual duration can be defined as the length of time
between an accrual and its associated cash flow. This paper argues
that accrual duration is a key factor in understanding the
discretion in accruals. The function of accruals is to shift the
recognition of associated cash flows across time, usually working
in pairs of opening/closing accruals. By design, one side of the
accrual pair shifts the recognition of the associated cash flow
away from the period in which it occurs by recording an accrual
with the same magnitude but the opposite sign in the same period.
Thus, such zero-duration accruals are non-discretionary because the
timing and magnitude of the associated cash flow pin down the
timing and the magnitude of the concurrent accrual. The other side
of the accrual pair shifts the recognition of the associated cash
flow into some other time period(s), which involves using
forward-looking estimates over the duration of the accrual, and
therefore some discretion. In addition, accruals that have longer
duration are more discretionary because longer horizons of
estimation allow more discretion with respect to their timing and
magnitude. Summarizing, accrual duration and accrual discretion are
inextricably linked by the fundamentals of the accrual process. The
study concludes with some thoughts on how to practically use
accrual duration as a measure of accrual discretion.
I appreciate helpful comments from Hal White, Valeri Nikolaev,
Frank Zhang, Joseph Gerakos, Jim Leisenring, Yin Wang, Xiao Tian,
and workshop participants at Rice University, INSEAD, ESSEC
(Paris), University of Zurich, Tilburg University, Washington
University, University of Miami, Hong Kong Polytechnic University,
Chinese University of Hong Kong, UC – Berkeley, University of
Tokyo, Kobe University, University of Melbourne, University of New
South Wales, and Columbia University.
Contact: Ilia Dichev [email protected] (404) 727-9353
mailto:[email protected]
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1. Introduction
Recording accruals is at the heart of accounting, and thus there
has been much interest in
their function and characteristics. A major theme in this
interest is that there is considerable
discretion in recording accruals, and understanding the nature
of this discretion is a key to
understanding the utility and cost of using accruals. More
specifically, a prominent idea in this
literature is that accruals can be usefully split into
discretionary and non-discretionary
components. The motivation is that non-discretionary accruals
are driven by fundamentals like
business activity and growth, while discretionary accruals are
more subjective, and therefore
more prone to managerial biases and manipulation.1 The volume of
the discretionary accrual
literature is substantial. Studies using discretionary accrual
ideas or techniques certainly number
in the dozens, and likely in the hundreds (Dechow, Ge, and
Schrand 2010 and Francis, Olsson,
Schipper 2008). While this sustained effort has produced a
number of insights, the leading
discretionary accrual models have been criticized as inadequate,
and even misleading (Dechow,
Sloan and Sweeney 1995, Ball 2013).
Prompted by such criticisms, this study develops a new approach
to identifying the
discretion in accruals. The linchpin of this approach is closer
attention to how accounting works,
with a special emphasis on the mechanism and manifestations of
accrual discretion. The main
idea about the mechanism of accrual discretion is that recording
accruals involves using forward-
looking estimates, and it is the quality of these estimates that
determines the benefits and the
costs of using accruals. The manifestation of accrual discretion
is in shifting the recognition of
cash flows as components of income across time. Note that since
income trues up to the
corresponding cash flows, ultimately the only thing that
accruals do is re-shuffle the timing of the
recognition of cash flows over time. The implication is that
both the benefits and the costs of 1 Many studies also use the term
“abnormal accruals,” with a similar meaning.
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accruals relate to timing, where the benefits of using accruals
relate to recognizing cash flows
into the “right” periods, while the costs of using accruals
relate to recognizing cash flows into the
“wrong” periods. For example, the benefit of the Accounts
Receivable accrual is the more
timely recognition of income (Revenue) at the time of sale as
opposed to waiting for cash
collections from customers. The cost of the Accounts Receivable
accrual is that income may be
allocated in the “wrong” way, for example the Accounts
Receivable may be recorded too early or
it may be overstated at inception which could necessitate
restatements or write-downs later on.
As developed in more detail further on, such recording of income
into the “wrong” periods
represents timing errors, which introduces noise into the
measurement of income.
The difficulty in implementing these ideas is that the main
theoretical constructs,
forward-looking estimates and timing errors, are not readily
observable. To address this
difficulty, the study looks more closely into the fundamentals
of recording accruals. As is well-
known, accruals work in pairs, i.e., the recognition of a cash
flow in a period different from when
it occurs is accomplished by recording a combination of an
opening and a closing accrual.
Notice that by design one side of this accrual pair coincides in
time with the associated cash
flow, while the other side occurs in a different period. The
point is that shifting of the
recognition of a cash flow is a two-step process, it is a
shifting of a cash flow amount away from
some period and into another period.2
Using the Accounts Receivable example to clarify the difference
in the function and
characteristics of these two steps, notice that when cash comes
in from customers, the closing
2 For deferrals, the shifting away step comes with the opening
accruals (e.g., the capitalization of PPE and Inventory at
inception), and the shifting into another period step comes with
the closing accruals (recoding the expense of Depreciation and Cost
of Goods Sold). For accruals proper, the order of the two steps is
reversed – the shifting into another period step comes with the
opening accruals (e.g., the recognition of income at the inception
of Accounts Receivable and the recognition of expense at the
inception of Warranty Payable), and the shifting away step comes
with the closing accrual (the extinguishment of Accounts Receivable
with cash collections and Warranty Payable with cash payments).
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accrual of Accounts Receivable is merely a matter of bookkeeping
rather than discretion. For
example, if $100 of cash comes in, the Accounts Receivable has
to be reduced by $100, there is
no other way to record the collection. In other words, shifting
the recognition of a cash flow
away from a period is accomplished by recording an accrual with
the same magnitude and the
opposite sign in the same period. Thus, such accruals are
non-discretionary because the timing
and the magnitude of the concurrent cash flow pin down the
timing and magnitude of the
associated accrual.
In contrast, the opening accrual for Accounts Receivable is
discretionary because it can
be recorded sooner or later, and at larger or smaller amounts
depending on estimates about
satisfying the revenue recognition criterion and the future cash
collections from customers. For
deferrals like PPE and Inventory the sequence is reversed, the
opening accrual is non-
discretionary because it is merely the deferral of a known cash
flow at a known time, and it is the
allocation of these costs to later periods as depreciation or
cost of goods sold where the
discretion resides. The unifying point for deferrals and
accruals proper is that recording accruals
away from the periods of their associated cash flows always
involves using some kind of
forward-looking estimates (e.g., projected cash flows, useful
lives) and therefore it is these
accruals only that embody the notion of discretion in
accounting.
This intuition can be formalized and extended by introducing the
notion of accrual
duration. Accrual duration can be defined as the length of time
between an accrual and its
associated cash flow. The idea is that accrual duration captures
the horizon of accrual
estimation, and is therefore closely related to the discretion
of accruals. Specifically, accruals
that are concurrent with their associated cash flows have zero
duration, and also have zero
discretion because there is no estimation involved – as
discussed earlier, the timing and
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magnitude of the cash flow pin down the timing and magnitude of
its associated concurrent
accrual. But recording the other side of the relevant accrual
pair involves estimation of future
events, and is thus discretionary in timing and magnitude. Note
also that accruals that have
longer duration are more discretionary because estimation is
unavoidably less certain over longer
horizons. For example, recording the opening accrual for a
10-month Accounts Receivable is
likely to be more discretionary than that for a one-month
receivable. Summarizing, accrual
duration and accrual discretion are inextricably linked by the
fundamentals of the accrual
process.
The paper concludes with a discussion of the pros and cons of
the accrual duration
approach, and offers some observations on its possible empirical
applications. The major
attraction of this approach is that it applies to virtually all
possible accruals. The major difficulty
in implementation is the identification of the associated cash
flows and accruals because current
financial reporting provides only a patchwork of the necessary
data. When the associated
accruals and cash flows are available (e.g., for PPE, revenue
accruals), it is possible to derive
estimates of discretionary accruals using exact algebraic
derivations, avoiding the vexing
statistical and validity issues that plague existing
discretionary accrual models. Absence of clean
data necessitates reverting to statistical estimation, either at
the level of individual or aggregate
accruals.
While the accrual duration approach is flexible, and application
partly depends on
research goals, it is possible to make some general
recommendations. Essentially, the paper
argues for a two-stage approach in the investigation of
discretion in accruals. The first stage is
the split of total accruals into discretionary and
non-discretionary components along the lines
suggested above. The point is that non-discretionary accruals as
defined above have zero ability
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for discretion, and therefore motivations for discretion are not
in play either. Thus, such accruals
are usefully removed from total accruals before pretty much any
further investigation of
discretion. The remaining discretionary accruals can be further
stratified on relevant dimensions
of firm fundamentals and managerial incentives, consistent with
models in existing research (e.g.
Francis, LaFond, Olsson, and Schipper 2005). Accrual duration
itself can be used as another
such stratifying variable since accruals with longer duration
are more discretionary.
The remainder of the paper is organized as follows. Section 2
offers some observations
on the role of accruals in accounting, and introduces the
concept of timing errors in accruals and
income. Section 3 introduces the notion of accrual duration, and
outlines its relation to
discretion in accruals. Section 4 discusses the advantages and
limitations of the accrual duration
approach. Section 5 suggests some empirical applications.
Section 6 concludes.
2. Accrual discretion and errors of timing
2.1 The use of forward-looking estimates in accrual
discretion
I start with some observations on the nature of the accrual
process, which serve as a
springboard for the main theoretical ideas later. The essence of
accrual accounting is the use of
accruals. Accruals can be defined as adjustments to the
underlying cash flows, which shift their
recognition as components of income over time. 3 For example,
consider a company that makes
$100 of credit sales at time t, and the account is collected at
time t+1. The accounting system
records this transaction with the opening and closing of an
Accounts Receivable accrual:
Time t Accounts Receivable $100 Sales Revenue $100
3 Notice that this formulation is equivalent to the often-used
derivation of accruals as the changes in the assets and liabilities
of the firm because of the articulation between the balance sheet
and the income statement. The emphasis in this study is on the
income view of accruals because leading stakeholders view earnings
as the most important number in financial reports, and also because
of the desire to link earnings to cash flows.
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Time t+1 Cash $100 Accounts Receivable $100
Looking more closely at this example reveals that the mechanism
of accrual discretion is
through the use of forward-looking estimates. In the Accounts
Receivable example, the goal of
the accrual adjustments is to shift the recognition of Sales
Revenue (a component of income)
from the time of cash collections at t+1 to the point of sale at
time t. The accounting system
accomplishes this goal by recoding at time t a forward-looking
estimate of the expected future
cash collections.4
The notion of accrual discretion studied here is broad. Holding
other factors constant, it
is defined as the range of possible estimates that can be used
in a given transaction. For
example, if an Accounts Receivable with mean expected receipts
of $100 can be recorded
anywhere in a range of $98-$102 vs. a range of $95-$105, we can
say that there is more
discretion in the latter range. While this definition is quite
general and probably non-
controversial, it is clear that operationalizing it is
difficult. Especially for outside observers,
measures of the range of possible managerial estimates are
unavailable. But as shown later, it is
possible to derive some useful results that capture the spirit
of this notion of accrual discretion.
Notice that this notion of accrual discretion is also broad in
the sense that it encompasses
everything that may influence the range of possible estimates,
including fundamentals like
volatility of operations but also opportunistic managerial
motivations like hitting earnings
4 Note that accrual discretion is also governed by factors
beyond the use of estimates. For example, standard setting
specifies rules that prescribe or restrict the use of discretion in
accruals, e.g., U.S. GAAP mandates the capitalization and
depreciation of PPE but prohibits the capitalization of most
R&D costs even if estimates of future R&D benefits are
available. While such other determinants of discretion are
important, the emphasis in this study is on the role of
forward-looking estimates in accrual discretion. The reason is that
the use of estimates is at the heart of accrual discretion, and
insights about their role are universal, as seen in more detail
further on. In contrast, standard setting is shaped by more
idiosyncratic factors including consideration of the relative
importance of various firm stakeholders, which triggers the use of
compromises and even political meddling.
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benchmarks and control features like quality of the auditing and
corporate governance. For
applications that are interested in more focused notions of
discretion, existing research offers
some helpful techniques for splitting broad measures of
discretion into more focused
components, e.g., Francis, LaFond, Olsson, and Schipper (2005)
split total discretionary accruals
into fundamentals-driven vs. managerial components.
2.2 Errors of timing
Most accrual adjustments work as an associated pair of opening
and closing accruals,
where the opening accrual initiates the necessary adjustment,
and the closing accrual reverses
and extinguishes the initial adjustment. Thus, by the end of the
life of the transaction, the
cumulative net accrual is zero. This property can be stated more
formally using the expression:
Earningst = Cash Flowst + Accrualst (1)
Where summing up over the life of any transaction obtains:
∑Earningst = ∑Cash Flowst + ∑Accrualst
And since all accruals reverse over the life of the relevant
transaction, the sum of the associated
accruals over time is zero, which yields:
∑Earningst = ∑Cash Flowst (2)
which is true for any transaction, as long as “Earnings” and
“Cash Flows” are appropriately
defined.5 Since everything on the income statement and across
firm activities is additive, it is
clear that this expression applies to all components of earnings
(like specific revenues and
expenses, operating and net income, gains and losses), and for
any aggregation at the account,
division, and firm level. It also applies to all kinds of
transactions, including those with multiple
5 For example, if “Earnings” is Revenue, “Cash Flows” will be
Cash Collections from Customers. Cost of Goods Sold for a
merchandising firm will correspond to Cash Paid to Suppliers. Net
Income will correspond to Free Cash Flows to Equity Holders.
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cash flows, and multiple initiating and reversing accruals,
e.g., the accounting for Investments
under the equity method.
Of course, expression (2) in itself is nothing new to accounting
thought, it is the
expression that underpins well-known intuitions like “accounting
is self-correcting” and
“earnings true up to the corresponding cash flows”. But the
implications of this expression have
not been fully explored, as reflected in the following
observation:
Observation 1: Both the benefits and the costs of recording
accruals relate entirely to the
timing of the recognition of the associated cash flows into
earnings.
The benefits side is better-understood, and it is clear from
expression (2). Since the total
recognized magnitudes are the same across accrual and cash flow
accounting, the benefits from
the accrual process have to be in the timing pattern of
recognition. Consider, for example, the
following transaction, where the sequence of events and summary
implications are organized in
Table 1:
Time t - Company makes a sale for $300, to be collected in three
installments of $100 each over
the next three periods (with all discounting effects
ignored).
Time t+1 - Customer makes the scheduled $100 payment.
Time t+2 - Customer misses the scheduled $100 payment. The
company estimates that the
customer will make the final payment at t+3, and therefore
writes down the
receivable to its realizable value of $100 as of the end of
t+2.
Time t+3 - Customer makes an actual final payment of $120, and
thus the company realizes a
gain of $20.
In this example, total income (revenue) under cash accounting is
$220, equal to cash
collected from the customer. Total income (revenue) under
accrual accounting is also $220. The
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only thing that differs across the two systems of accounting is
the pattern of recognition over the
four periods, which is 0, 100, 0, 120 for cash accounting, and
300, 0, (100), 20 for accrual
accounting.
Thus, income under accrual accounting is the associated cash
flows, sliced and re-
distributed in a different timing pattern. And since the only
thing that differs across the two
systems is timing, it follows that the entire benefits of the
accruals process have to be somehow
related to timing as well. In this case, the benefit is the more
timely recognition of sales revenue
at the time of sale, presumably because that period more
accurately represents when the firm
completed its obligations in the sale.6 More generally, the
conclusion is that the benefit of using
accruals is in shifting the recognition of the associated cash
flows into the “right” periods, where
“right” is prompted by the logic of the business
transaction.
The cost side of Observation 1 is less clear, and I believe it
is either novel or at least not
widely understood in the accounting literature. On some basic
level, since expressions (1) and
(2) show that the only difference between earnings and
associated cash flows is the pattern of
recognition over time, it follows that the costs of the accrual
process have to be in the pattern of
recognition as well – there is simply nowhere else they can be.
But it is less clear what that
means, especially if one wants to operationalize this
intuition.
Further reflection on the four-period accounts receivable
example above provides some
clues. It is clear that the accruals in this example did not
work well because significant
collectability problems came up, and that prompted accrual and
income adjustments in the
follow-up periods. The company turned out to be too optimistic
in its initial accrual, and was too
pessimistic in the third-period write-down, which necessitated
adjustments later on. The main
6 Point is easier to see if there were no collectability
problems, with the firm booking $300 at time t, and collecting
three installments of $100 thereafter.
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idea behind booking the effects of the sale into income at the
time of sale is that that it represents
a more timely recognition of the accomplishments of the company
in this transaction. But note
that the realized pattern in income over the four periods of the
transaction was $300, $0, ($100),
$20, which clearly deviates from an ideal pattern of total
revenue recognition at the time of sale
of $X, $0, $0, $0.
It is also worth thinking what this amount $X would be under an
ideal pattern of revenue
recognition at the time of sale. Ideally, the company would have
liked to recognize all relevant
revenue at the time of sale, which is equal to the total
realized cash collection of $220. In other
words, if the company had perfect foresight in this transaction,
it should have booked $220 as
revenue and opening receivable at the time of sale, and then the
cash collections would have
amortized the receivable, with no effect in income, with a
resulting pattern of income recognition
of $220, $0, $0, $0. Compared to that, the actual pattern of
recorded income of $300, $0, ($100),
$20 implies that the company booked $80 of income too much in
the first period, and then that
was corrected by a loss of $100 in the third period, and finally
zeroed out with a gain of $20 in
the fourth period. In other words, the costs of using accruals
in this example is that pieces of
income end up booked in the “wrong” periods. One can think of
income ending up in the wrong
periods as “timing errors”, as errors in the timing of
recognition of income.
Summarizing, the benefits of the accrual process are in shifting
the recognition of cash
flows into the “right” periods, where “right” is determined by
the business substance of the
transaction. The costs of the accrual process are in shifting
the recognition of cash flows into the
“wrong” periods, where “wrong” is again determined by the
business substance of the
transaction.
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The difficulty in using these conclusions is that typically it
is not clear what “right” and
“wrong” periods really means, especially for an outside observer
that does not have access to the
transactional records of the company. Notice also that even with
great records, the income
effects of transactions are only clear ex post, while evaluation
of accrual and earnings quality is
needed on an evolving and ex ante basis. In the accounts
receivable example above it is clear ex
post that the time-of-sale recognition of income was compromised
by unforeseen collectability
problems. But it is not clear whether something meaningful can
be said about these collectability
problems before they manifest. As an illustration of these
problems, notice that the initial
accrual of $300 at time t turns out ex post to be a jumble of a
“right” accrual of $220 and
“wrong” over-accrual of $80. The question again is whether some
meaningful differentiation
can be made on an ex ante basis, and for an outside
observer.
It turns out that although this problem is vexing, some progress
can be made by looking
more closely into the mechanism of accrual discretion discussed
earlier. The main insight is that
since accrual accounting moves the recognition of income across
time using forward-looking
estimates, it is the use of these estimates as opposed to actual
realizations which creates “timing
errors”, i.e., the problem of income ending up in the wrong
periods. The example above is a
good illustration of this insight. Booking revenue at the time
of sale seems warranted because it
more accurately reflects the fact that the benefits of the sale
transaction are mostly secured at the
time of sale rather than waiting for the cash collections to
roll in as in cash accounting. But this
benefit comes at the cost of booking revenue as a
forward-looking estimate of cash collections,
and the resulting difference between estimate and realizations
necessitates recording corrections
in income in later periods. These corrections are essentially
errors in the timing of the
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recognition of income, and constitute the cost or recording the
revenue accrual at the time of
sale.7
A closer look into the example also offers a way to
conceptualize this intuition. The idea
is that if one could construct a theoretical benchmark of
recoding accruals which avoids the
problem of using estimates and therefore avoids timing errors,
one would be left with only the
benefits of accruals, providing a clean split of accruals and
income into their “right” and “wrong”
components. In this case, there is a natural solution. Since the
problem is that forward-looking
estimates differ from their realizations, the solution is the
use of “perfect foresight” estimates. In
the accounts receivable example above, the “perfect foresight”
estimate is recording $220 at the
time of sale because that amount is a perfect foresight of the
expected cash collections. As
discussed above, the “perfect foresight” estimate of the
accounts receivable accrual of $220 at
time t also produces the “perfect foresight” pattern of revenue
recognition of $220, $0, $0, $0.
The perfect foresight accrual of $220 at time t also produces a
quantifiable measure of the
“timing errors” in this example, i.e., income ending up in the
“wrong” periods. Since Actual
Income = Perfect Foresight Income + Timing Errors for any given
period, it follows that:
Timing Errors = Actual Income – Perfect Foresight Income (3)
Using this expression, and recalling that the pattern of actual
income is $300, $0, ($100), $20 and
that for perfect foresight income is $220, $0, $0, $0, yields a
sequence of timing errors of $80,
$0, ($100), $20, also see a summary of income and timing error
effects in Table 1. This
sequence of timing errors correctly reflects the intuition that
the company overestimated the
initial receivable by $80 at time t, corrected the initial
mistake at time t+2 by recording a $100
write-down (so, ended up overshooting the right correction by
$20), and finally the series of
7 By “cost of using accruals” what is meant here is the cost of
using income as a performance metric. Otherwise, there are clearly
other costs of using accruals like procedural costs of running the
accrual accounting system, auditing, etc.
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errors and corrections was settled with a positive adjustment of
$20 at time t+3. Note that the
sequence of timing errors sums up to zero, consistent with the
intuition that accrual accounting is
self-correcting.
Summarizing, the derived sequence of timing errors is a measure
of the cost of using
accruals. The cost of using accruals arises from the necessity
of using forward-looking
estimates, and since the estimates differ from realizations, the
result is that recorded income
includes temporary and reversible errors of timing.
Introducing the concept of timing errors as the key cost of
using accruals offers two
decisive advantages over existing notions of accrual discretion
and accrual quality. First, it is
rooted into the fundamentals of the accrual process, which is
preferable to ad hoc models like
Jones (1990) and its extensions. Second, the notion of timing
errors applies to virtually all
accruals, which is preferable to other models, which typically
capture only one type of accruals
and/or one type of discretion. For example, the Dechow and
Dichev (2002) model captures the
discretion of only short-term accruals, where the opening
accrual precedes the associated cash
flow (i.e., accruals proper, for example one-period Accounts
Receivable and Warranty Payable).
In contrast, the notion of timing errors also applies to
deferrals, for example Inventory and PPE.
And the notion of timing errors accommodates both short-term and
long-term accruals, and
readily applies to all kinds of operating, investing, and
financing accruals.
A brief example using the long-term PPE/depreciation deferral
illustrates the universal
applicability of the timing error approach. Assume that a
company buys PPE for $100 at the end
of year t, expected to be depreciated straight-line over the
next four years, with no salvage value.
Accordingly, depreciation for year t+1 is $25. In year t+2,
however, the company determines
that the PPE is obsolete, and so records a total
depreciation/write-off of $75 to reduce its value to
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zero. The benefit from using accruals in this example is that
the cost of PPE is not immediately
expensed at inception but is rather spread out over the useful
life of equipment, which makes
sense given the economics of PPE investment. The discretion and
cost from using forward-
looking estimates here comes from the forward-looking estimate
of depreciable life. The
recorded pattern of depreciation expense (broadly defined to
include write-offs) is $25, $75 over
the two-year realized life of the equipment. The “perfect
foresight” estimate of depreciable life
would be two years, and correspondingly the “perfect foresight”
pattern of straight-line
depreciation expense is $50, $50. The resulting pattern of
timing errors in accruals and income
is ($25), $25, which correctly reflects the intuition that the
company recorded too little
depreciation in year t+1, and too much in year t+2. Note again
how the cost of using forward-
looking estimates in accruals manifests as temporary and
reversible timing errors in income.
From this example, it is also clear how the timing error
approach can be extended to other
deferrals, e.g., Inventory, Prepaid Expenses, Deferred Revenue,
etc.
To further understand the timing error approach, a comparison
with the Dechow/Dichev
(DD) model is instructive. Essentially, these two approaches
share the same underlying logic but
the timing error approach can be considered a more general
version of the DD model. The
reason is that the DD model is also a “perfect foresight”
approach, where the key intuition is that
the quality of accruals is determined by the extent to which
accruals map into their future cash
flow realizations. In other words, the DD approach uses perfect
foresight with respect to the
magnitude of the associated future cash flows as the benchmark
for “right” accruals. And since
the quality of accruals in DD is determined by the deviations of
accruals from the perfect
foresight forecast of the associated future cash flows, the
takeaway is that DD estimations errors
are one manifestation of the broader concept of timing
errors.
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In comparison, the timing approach is a more general version of
the DD approach
because it uses perfect foresight with respect to everything as
a benchmark for “right” accruals.
For example, perfect foresight could mean correct estimation of
not only the magnitude of future
cash flows but also of depreciable lives and salvage values for
PPE, of future construction costs
for revenue recognition under the percentage-of-completion
method, of estimates of future
profitability in accruing incentive compensation expense, of the
timing, magnitude, and discount
rates for anticipated cash flow related to contingent
liabilities and legal settlements, and so on.
For the interested reader, Appendix A provides additional
information and examples on the
comparison between the DD model and the timing error
approach.
Summarizing this section, the benefit of using accruals is the
more timely recognition of
income, which makes it a better measure of firm performance. The
cost of using accruals arises
from the need to make forward-looking estimates, which
introduces timing error noise in the
recognition of income. These main ideas are reflected
graphically in Figure 1. Figure 1
compares the anchor case of cash flow accounting to the
benchmark case of accrual accounting
under perfect foresight, and the actual accrual accounting using
forward-looking estimates. The
difference between cash flow accounting and perfect foresight
accounting establishes the
benchmark maximum possible benefit from using accrual
accounting. The difference between
perfect foresight accounting and actual accrual accounting is
errors of timing, which are the cost
of using estimates in accruals. The difference between cash flow
accounting and actual accrual
accounting establishes the net benefit from using accrual
accounting.
3. Accrual duration
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16
While the notion of timing errors has intuitive appeal,
operationalizing it is non-trivial.
In some cases, it may be possible to measure timing errors
directly. For example, actuarial gains
and losses in pension accounting are clearly timing errors, and
they can be identified from
footnote disclosure. Income effects from changes in depreciable
lives also represent timing
errors, and they are disclosed in the footnotes as well. Most
timing errors, however, are difficult
to identify because they result from all kinds of realizations
differing from estimates, and most
such data are not available to outside users.
As a solution, this paper proposes a further development and
reformulation of the
estimates and timing error approach, which relies on closer
attention to how the accrual process
works. As is well-known, accruals generally work in pairs, where
the combination of an opening
and a closing accrual shifts the recognition of a cash flow into
income to a period different from
when the cash flow occurs. For an example for deferrals,
consider a firm that buys $100 of
merchandise inventory for cash. The corresponding accrual pair
will be reflected in the
following two journal entries, which occur at two different
points in time:
Inventory $100 Cash $100 Cost of Goods Sold $100 Inventory
$100
The opening accrual for Inventory defers the recognition of the
cash outflow away from
the period in which the purchase occurs, and the closing accrual
shifts the recognition of that
cash outflow in the form of Cost of Goods Sold into the period
in which the Inventory is sold.
Similar patterns are observed for other deferrals like PPE,
Prepaid Rent, and Deferred Revenue.
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17
For accruals proper, the opening accrual occurs before the
associated cash flow, and it is
the closing accrual that coincides with that cash flow. For
example, for $50 of Accounts
Receivable (and assuming no collectability problems for now),
the journal entries are:
Accounts Receivable $50 Sales $50
Cash $50
Accounts Receivable $50
Similar patterns are observed for other accruals proper,
including all kinds of receivables
and payables like Interest Receivable, Accounts Payable, and
Warranty Payable.
The unifying message across these two examples is that no matter
whether we are dealing
with deferrals or accruals proper, by design one side of the
accrual pair coincides with the
associated cash flow, and the other side occurs in some other
period. This is, of course, not
accidental because moving the recognition of a cash flow into
income across periods involves
two steps, one is moving the recognition of the cash flow away
from a period, and the other one
is moving the recognition of the cash flow into another period.
As the two examples above
illustrate, the accrual that coincides with the associated cash
flow is the device that moves the
recognition of a cash flow away from that period, and the
associated accrual that occurs in some
other period is the device that moves the recognition of the
cash flow into this other period.
One key implication is that the timing and magnitude of the
underlying cash flow pin
down the timing and the magnitude of its associated concurrent
accrual. This exact
correspondence obtains by construction - if the recognition of a
cash flow of a certain magnitude
is to be moved away from a certain period, the only way to do
that is by recording an accrual
with the same magnitude and the opposite sign in that same
period, so that the net effect on
income is zero. Thus, such accruals are non-discretionary. In
the Inventory example above, the
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18
opening accrual is non-discretionary because if a firm pays $100
for Inventory (negative cash
flow), it has to put this Inventory on the books for $100
(positive accrual of $100); thus,
recording this accrual is simply a matter of bookkeeping, and
not really of a matter of estimation
or discretion. This point is easy to see using the
representation Earnings = Cash Flows +
Accruals, which for the opening accrual of Inventory is:
Cost of Goods Sold = Cash Spent on Inventory + Inventory
0 = -$100 + $100
In other words, since accrual accounting suggests that the cost
of Inventory should be deferred
until sold rather than immediately expensed at purchase, the
only way to defer the cost of
purchase until some future period is to record an Inventory
accrual with the same magnitude but
the opposite sign in the period of the associated cash flow.
This is a bookkeeping identity rather
than a matter of discretion.
Using the terminology of this paper, it is also easy to see that
accruals that coincide with
their associated cash flows have no discretion. The reason is
that the cash flow and the
associated concurrent accrual coincide in time, and so the time
horizon of estimation for that
accrual is zero. The implication is that the actual recorded
accrual and the “perfect foresight”
accrual are the same, and so there is no estimation or
discretion or timing errors for such
accruals.
The other side of the Inventory accrual, however, is where the
estimation and the
discretion is. Depending on whether the firm is using FIFO or
LIFO, periodic or perpetual
inventory system, and whether there are inventory write-downs,
the realization of the Inventory
cost into income could take a number of different trajectories,
and there is real managerial
discretion in charting these trajectories. In other words, there
is a time horizon of estimation, and
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19
so there is a difference between recorded and perfect foresight
accruals, and so there is both
discretion and possible timing errors in accruals. Summarizing,
accruals that are concurrent with
their associated cash flows are non-discretionary, while
accruals that occur in a period away
from their associated cash flows are discretionary.
Note that this intuition applies to virtually all accruals. With
Accounts Receivable, the
opening accrual is the discretionary one because management has
discretion with respect to both
its timing and magnitude, while the receipt from customer
automatically triggers both the timing
and the magnitude of the closing accrual. Warranty Payable is an
accrual proper, and indeed the
recording of warranty expense, which is the opening accrual for
Warranty Payable is where the
discretion is, while the payment of warranty claims pins down
the timing and the magnitude of
the closing accrual; similar reasoning applies for all kinds of
reserve accounts like provisions for
environmental remediation, provisions for workforce reductions,
provisions for taxes, provisions
for integration of acquired businesses, and so on. PPE is a
deferral, which implies that the
opening accrual should be non-discretionary, while the closing
one is discretionary. Indeed, the
timing and the magnitude of cash spent for PPE pin down the
opening PPE accrual, while
management has considerable latitude with respect to the timing
and magnitude of the (series of)
closing PPE accruals of Depreciation Expense, and possibly PPE
write-downs.
A way to formalize and extend this intuition is to introduce the
notion of accrual
duration. Accrual duration can be defined as the length of time
between an accrual and its
associated cash flow. For example, for a $1,000 accounts
receivable that is opened on March 1,
and is closed at the receipt of customer collections on June 1,
the accrual duration for the
opening accrual is three months, and for the closing accrual it
is zero. It is immediate that
accruals that are concurrent with their associated cash flows
have zero duration. And since such
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20
accruals have zero estimation and discretion, there is a tight
link between accrual duration and
accrual discretion at the focal and common point of zero
duration.
Further consideration reveals that the relation between accrual
duration and accrual
discretion extends to the full range of accrual duration, where
the discretion in accruals increases
in accrual duration. Everything else equal, recording warranty
expense on three-year contracts is
likely to produce more discretionary accruals than those for
one-year contracts. Depreciation
expense on PPE with projected life of 20-30 years is likely to
be more discretionary than that for
PPE with a one-year life. The reason is straightforward, longer
duration implies longer horizon
of estimation, and longer horizons unavoidably bring more
uncertainty and discretion for the
resulting estimates.8 We also have some evidence that
forecasting horizon is rather strongly
related to uncertainty in business, e.g., the predictability of
earnings and growth deteriorates fast
with forecast horizon (Chan, Karsecki, and Lakonishok 2003).
Thus, there are reasons to believe
that accrual duration is a powerful determinant of discretion in
accruals.
4. Discussion
This section provides a discussion, and some extensions and
clarifications of the theory in
the paper. A broad advantage of the accrual duration approach is
simply a better understanding
of the nature and function of accruals, which allows new
conceptual clarity into some long-
standing issues. As an illustration of this advantage, consider
the example of a steady-state
company with no changes in assets and liabilities. Can such a
company have a change in its
accrual quality over a given period? Intuitively, the answer
must be “yes.” But the traditional
8 For Accounts Receivable, the estimate is how much cash will be
collected, for Warranty Payable the estimate is how much cash will
be paid out in claims, for Depreciation the estimate is about the
length of useful life, for Revenue under the
percentage-of-completion method the estimate is about the remaining
costs to complete the project, and so on.
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21
understanding of accruals as changes in assets and liabilities
will be flummoxed by this question,
because a steady-state company has no change in net assets, and
so it does not have accruals, and
therefore cannot have a change in accrual quality.
In contrast, the approach advocated here handles such a question
with ease. Take
Accounts Receivable, for example, that has no change over a
given period. The accrual duration
approach will point out that although the net change in Accounts
Receivable is zero, there are
new gross accruals recorded during the period, specifically the
old Accounts Receivable have
been collected, and there have been an equal amount of new
Accounts Receivable created by the
new credit Sales (see also White 2012 on this point). And since
the new Accounts Receivable
can be of lower quality than the old Accounts Receivable, it is
clear that accrual quality can
change for steady-state firms. The key point is that the accrual
duration approach makes a sharp
distinction between the reduction of receivables due to the
collection of cash (a non-discretionary
accrual) and the origination of new receivables (a discretionary
accrual), while the traditional
approach essentially treats them as the same accrual but with
opposite signs. This is a
consequential distinction.
Another example of enhanced conceptual clarity is the question
of the contemporaneous
correlation between accruals and cash flows. Many studies have
explored this question,
generally finding a negative correlation (Dechow 1994), which
has been decreasing over time
(Bushman, Lerman, and Zhang 2016), while some studies have
pointed out that this correlation
can be positive in certain environments (e.g., recessions
trigger poor cash flow from operations
coupled with write-offs of assets as in Ball and Shivakumar
2006). There has also been much
debate about the magnitude and interpretation of the negative
correlation between cash flows and
accruals, with some authors interpreting it as a beneficial sign
of resolving timing and
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22
mismatching problems in the cash flows (Dechow 1994), and others
interpreting it as evidence of
opportunistic managerial smoothing of income (Leuz, Nanda and
Wysocki 2003).
While a full reconciliation of extant evidence and views is
beyond the scope of this study,
the accrual duration framework yields some key observations that
can be helpful in
understanding the theoretical and empirical correlations between
cash flows and accruals. Most
importantly, it is clear that the correlation for associated
contemporaneous cash flows and
accruals is negative, and in fact it is -1 if both variables are
appropriately defined. Note also that
this negative correlation obtains before any value-laden
functions of accruals are posited, it is
simply the unavoidable outcome for any accrual system that moves
the recognition of cash flows
across periods because that requires recording contemporaneous
accruals with the same
magnitude and the opposite sign of the associated cash flow. If
one is going to capitalize the
cash cost of PPE of $100, there is no other way to do that than
by debiting an asset, a positive
accrual, which will be perfectly negatively correlated with the
corresponding contemporaneous
cash outflow of $100.
Thus, one conclusion from these considerations is that the
negative correlation between
cash flows and contemporaneous accruals is an unavoidable and
necessary property of accruals.
This impression is further strengthened by the point that such
accruals are non-discretionary, as
one can recall from the analysis presented earlier in the paper.
Of course, things become more
complicated when one is using non-associated cash flows and
accruals. But that is precisely the
point – a major takeaway from this study is that there has to be
better care in the definition of
cash flows and accruals used in a given specification. Many
examples are possible here, e.g.,
Cash Flow from Operations from the Statement of Cash Flows is
not really “cash flow from
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23
operations” because it includes many non-operating items, and
this contamination has likely
become worse over time because of the proliferation of
non-operating items.9
It is also useful to point out that while the preceding
theoretical framework uses the
simplifying notion of “accrual pairs,” the main ideas of the
study generalize to more complicated
accrual situations. For example, consider the accounting for
equity investments, which for
similar securities could be under the cost or the equity or one
of the fair value methods. For all
these methods, the initial accrual for the purchase of the
investment and the final accrual for the
sale of the investment are non-discretionary because they are
pinned down by the concurrent
cash flows. But accounting for the intervening years can take
very different trajectories, with no
entries (except for dividends) under the cost method, following
book profitability under the
equity method, and following market values under the fair value
methods. And that is precisely
the point, all of these intervening entries are discretionary
because there are no associated
concurrent cash flows. Similar considerations apply for other
more involved accrual situations,
for example, booking accounts receivable with a bad debt expense
provision, and the subsequent
collection and write-offs of receivables. Appendix B provides
examples of some common
accounting situations, and how the accrual duration approach
applies to them.
The notion of accrual duration is also appealing because it
provides a conceptual
generalization for some existing techniques and measures in
accounting. For example,
accounting texts point out that high value of Days Receivables
Outstanding is a sign of low-
quality Accounts Receivable. As is probably clear, Days
Receivables Outstanding, defined as
9 The accrual duration approach also offers insights about the
correlation between non-contemporaneous cash flows and accruals.
For associated cash flows and accruals, most non-contemporaneous
correlations will be positive because the non-contemporaneous
accruals are essentially accruing the effect of the associated cash
flow into income in another period, and so they have to be of the
same sign. In fact, if there is only one non-contemporaneous
accrual, and there are no timing errors, the correlation will be 1.
But the correlation will be lower, and possibly much lower, if the
non-contemporaneous accrual is split into several periods (like in
depreciation) and there is timing error noise.
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24
Average Accounts Receivable/(Annual Sales/365), is a close kin
of accrual duration of the
Accounts Receivable accrual at the account-year level. In fact,
the only difference is that Days
Receivables Outstanding measures the number of days it will get
all outstanding Receivables to
get collected, while accrual duration for the average Receivable
will be half that. Similar
considerations apply for Days Inventory Outstanding, Days
Payables Outstanding, and
Depreciable Life. While such measures are widely used, to my
knowledge there has been little
attempt to conceptualize and generalize them in a meaningful
way.
Finally, it is also helpful to be clear about the boundaries of
the accrual duration
approach. The main point here is that this approach takes the
accruals as given, i.e., as
mentioned earlier, this approach does not address questions like
whether the accruals should
have been recorded in the first place, e.g., in capitalization
vs. expensing decisions for R&D, or
standard-setter questions like whether GAAP should capitalize
all leases. Further reflection
suggests that this limitation is mild. For one thing, the very
same caveat applies to all existing
accrual models, including Jones (1991) and Dechow and Dichev
(2002), and their variations and
extensions. The other consideration has to do with utility. On
some level, all accruals are
“discretionary” because firms can in theory use cash flow
accounting, and eliminate all accruals.
But such an extreme perspective is not helpful. The point is
that GAAP already mandates
accruals, and thus in practice there is no way for firms to
avoid recording them. Therefore, the
emphasis in this paper is on the pragmatic - since accruals are
already being recorded, the
pragmatic question is whether one can perform a meaningful split
of total recorded accruals into
more or less discretionary components. And that is the question
that this paper answers.
It is also worth considering that standard setting-type issues
are notoriously tricky
because they reflect things like balancing the needs and
preferences of different societal groups
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25
(e.g., equity vs. debt investors vs. government authorities vs.
general public), and thus they
inevitably tend to lean to the compromise and to the political.
In contrast, the main features of
the approach advocated here apply regardless of what the present
GAAP rules may be, and how
they may change in the future. The reason is that accrual
duration approach focuses on the
mechanism and consequences of making forward-looking estimates,
which applies to any
plausible accrual system.10
5. Possible empirical applications
The accrual duration approach has wide reach, and so specific
empirical implementations
depend on the goals of different investigations. Nevertheless,
it is useful to offer some broad
observations on possible empirical applications.
As an immediate suggestion, this paper advocates a two-stage
approach to investigating
the discretion in accruals. The first stage splits accruals into
discretionary and non-discretionary
along the lines discussed above. The non-discretionary accruals
are the no-estimation, zero-
duration accruals, whose timing and magnitude are pinned down by
the timing and magnitude of
their concurrent associated cash flows. Such accruals are really
bookkeeping placeholders,
shifting the recognition of cash flows away from the period in
which they occur, and setting the
stage for the other side of the accrual entry where the real
discretion in accruals is exercised.
The point is that such accruals are usefully expunged as a first
screen no matter what the specific
10 Another caveat about the approach of this paper is that it
does not reflect discretion with respect to the management of real
activities and cash flows. Partly, this is simply beyond the scope
of the study; and this caveat applies to all other accrual models.
But in terms of practical import, it is helpful to point out that
the conclusions of the study apply regardless of whether there is
real earning management. This point is clear for management of cash
flows that enter income directly, e.g., cutting R&D to boost
income, because there is no interaction with accruals. And it also
applies for management of real activities with interaction with
accruals, e.g., using an end-of-period sales incentive to boost
credit Sales. Notice that whether the sales boost is artificial or
not, the same conclusions apply for the accruals produced (Accounts
Receivable or Deferred Revenue) – one side of these accrual pairs
is tightly determined with respect to timing and magnitude while
the other one is not, and the discretion increases in the horizon
of the accruals.
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26
further investigation is about because if the ability for
accrual discretion is not there, specific
motivations like hitting earnings benchmark cannot be in play
either. Given that this first stage
would potentially remove up to 50% of accrual variation
(roughly, as removing the variation
from one side of accrual pairs), it is easy to see how this
first stage would make a difference.
If the relevant cash flow and accrual data are available, the
application of the first stage is
exact, avoiding the need for problematic statistical
estimations. Using the expression:
Discretionary Accruals = Total Accruals - Non-discretionary
Accruals
and having in mind that:
Non-discretionary Accruals = - Concurrent Associated Cash
Flow
because non-discretionary accruals shift the recognition of
concurrent associated cash flows by
recording the same amount with an opposite sign yields:
Discretionary Accruals = Total Accruals + Concurrent Associated
Cash Flows (4)
In expression (4), accounts appear with their algebraic sign
given by the way they affect
income. Specifically, cash inflows appear as positive and cash
outflows appear as negative, and
increases in assets appear as positive accruals, while increases
in liabilities appear as negative
accruals, with the converse for decreases in assets and
liabilities.
While this decomposition is simple, there has to be some care in
its application. The
difficulty is that while the effects analyzed above are clear at
the level of the individual
transaction, such granular data are not available to outsiders.
Broadly speaking, the least
aggregated data available to outsiders is at the account-period
level. The challenge in using such
aggregated data is in constructing the right “associated”
accrual and cash flow variables.
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27
For some situations, the application is straightforward. For
example, assume that Net
PPE goes up by $10 for period t, and purchases of PPE are $100
during period t with no sales of
PPE. These data yield:
Total PPE accrual = ΔPPE = $10
Associated Cash Flow = Purchases of PPE = - $100
Discretionary PPE accrual = Total PPE accrual + Purchases of PPE
= - $90
The -$90 answer represents Depreciation Expense for the period,
which makes sense
because Depreciation is where the discretion resides in the PPE
accruals; the sign is negative
because Depreciation Expense reduces income. To recap, note that
by the end of this example,
the PPE accrual has been cleanly split into a discretionary and
non-discretionary component,
with no need for any statistical estimation. This is a powerful
advantage considering that
existing discretionary accrual models suffer from major
estimation and statistical noise problems,
e.g., the Jones model and its variations, see Dechow, Sloan and
Sweeney (1995), Dechow, Ge,
and Schrand (2010) and Ball (2013).
For other situations, it is trickier to figure out what
“associated” cash flows and accruals
implies – but as long as the right data are available, exact
answers still obtain. The following
example for Accounts Receivable illustrates this point. Suppose
that beginning Accounts
Receivable is $30, ending Accounts Receivable is $50, and Sales
are $300 during that period
(assume all on credit). What is the Discretionary Accrual for
this period? Note that there are no
cash flows associated with the ending balance of Accounts
Receivable, and the cash flows
associated with the beginning Accounts Receivable are $30, which
represents the collection of
the receivables outstanding at the beginning of the period, also
corresponding to the closing non-
discretionary accrual of these receivables. Using this argument
and expression (1), the estimate
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28
is Discretionary Accruals = $20 + $30 = $50, which is also the
ending balance of Accounts
Receivable. This answer makes sense because it indeed captures
the discretion in newly-
originated Accounts Receivable during a period, which are not
resolved by cash collections by
the end of that period. Using similar logic, this same answer is
also suggested in White (2012),
linking the discretion in working capital accruals to their
ending balances rather than to their
changes.
In many cases, however, there will be no clear identification of
the associated cash flows
and accruals, e.g., for various aggregate specifications like
working capital or total accruals. In
such cases, the solution is to revert to some kind of
statistical estimation. Specifically, using the
main theoretical conclusion that discretionary accruals are
those that are not associated with
concurrent cash flows, the exact theoretical expression (4) is
then proxied by the following
regression specification:
Accrualst = b0 + b1*Associated Cash Flowst + εt (5)
where the key to successful identification is to define accruals
and cash flows as closely as
possible to their theoretical counterparts in expression (4).
Discretionary accruals for time t are
given by the residual term εt, and non-discretionary accruals
for time t are calculated as Accrualst
– εt. For example, for the most popular working capital accrual
specification, Accruals can be
defined as change in non-cash working capital (ΔWC), and the
closest correspondence to
Associated Cash Flows is Cash Flow from Operations (CFO) or some
modification which purges
it from non-operating items. It is possible that the accrual
duration approach can be adapted to
other aggregate specifications, including those for all accruals
of the whole firm or even at the
level of the industry or the entire economy. Note that the
change in working capital version of
expression (5) has already been used in existing research,
variations of it have appeared for
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29
example in Ball and Shivakumar (2006) and Bushman, Lerman, and
Zhang (2016), usually
motivated by the noise reduction role in accruals suggested by
Dechow (1994) and Dechow,
Kothari, and Watts (1998). In that sense, the specification in
expression (5) is an affirmation of
existing practices in accruals research - but is also a call for
careful specification of the
associated variables.
Whether the derivation is exact or statistical, the end result
of the first stage is a split of
total accruals into discretionary and non-discretionary
components. Note that the discretionary
accruals are derived entirely at the level of the firm/account
and the period, avoiding the need for
multiple periods and forward-looking information like in
Dechow/Dichev applications. Finally,
the discretionary accrual is signed, which is superior to
unsigned approaches.
The second stage depends on the goals of the investigation. One
way to describe the
broad intuition here is that nearly all existing studies of
accrual discretion and accrual quality can
be run as a second stage on the discretionary accruals derived
after the first stage above. For
example, one can use proxies for firm fundamentals like size,
incidence of losses, and CFO and
sales variability as in Francis, LaFond, Olsson, and Schipper
(2005) to split the discretionary
accruals derived in the first stage into fundamentals-driven vs.
manager-driven components.
Further, the manager-driven components can be used to test
theories of earnings management to
beat benchmarks, and influence capital market and contractual
outcomes.
The second stage can also benefit from further stratification on
accrual duration because
longer accrual duration unavoidably implies more accrual
discretion. Note that the accrual
duration approach centers on the ability for accrual discretion,
so it is perhaps a natural
complement to most existing research, which emphasizes the
motivation for accrual and earnings
malfeasance. In some cases, the calculation of accrual duration
presents no problems. Using
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30
well-known techniques from financial statement analysis, it is
easy to compute accrual duration
for the discretionary accruals of Depreciation and Accounts
Receivable, for example. Assuming
straight-line depreciation and negligible residual values:
Accrual duration for Depreciation = Depreciable life of
PPE/2
Where Depreciable life of PPE estimated as Gross
PPE/Depreciation Expense, and depreciable
life is scaled by 2 since depreciation is an annuity rather than
a single closing accrual. As
mentioned earlier, for Accounts Receivable accrual duration at
the account/year level is given by
the Days Receivables Outstanding/2.11
An advantage of the accrual duration approach is that it allows
more focused
investigations of accruals, which can potentially improve
research design. For example, we
know that revenue recognition problems are the most prominent
form of earnings malfeasance,
present in about half of firms with AAERs (Dechow, Ge, Larson,
and Sloan 2011), and so some
studies focus on this particular area of accounting discretion
(Peterson 2011, Altamuro, Beatty,
and Weber 2005). Existing financial data allows using the
accrual duration approach to build
empirical measures at the level of the Revenue account, and its
most closely associated accruals,
Accounts Receivable and Deferred Revenue. One can use such
information to derive Cash
Collections from Customers, and thus one would have both the
relevant cash flow and its
associated accruals, which allows splitting the revenue accruals
into discretionary and non-
discretionary components, and deriving measures of accrual
duration.
In other cases, there may be a natural focus on specific
accruals, especially if the requisite
data are available. For example, required disclosure in the
property-casualty insurance industry
provides information about the provision for claims, balances of
unpaid claims, and cash paid for
11 This formulation assumes that all Sales are credit sales. If
that is not the case, one should instead use credit sales only, if
that information is available.
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31
claims (Petroni 1992, Beaver and McNichols 1998), which allows
constructing measures of
discretionary accruals and accrual duration for the most
important accrual for such firms.
Pension and OPEB disclosure about the associated cash flows and
accruals can be used to derive
measures of Pension and OPEB discretionary accruals.
6. Conclusion
This paper argues that making estimates is at the heart of using
accruals, and that the
quality of these estimates unavoidably depends on the horizon of
estimation. This idea is
embodied by the concept of accrual duration, defined as the
length of time between an accrual
and its associated cash flow. There are two main results from
the analysis of accrual duration.
First, accruals act in pairs, using an opening and a closing
accrual to shift the recognition of cash
flows across time. The point is that to shift the recognition of
a cash flow away from a period,
by construction one side of the accrual pair has to occur in the
same period with the associated
cash flow, and have the same magnitude and the opposite sign.
Thus, such zero-duration and
zero-estimation accruals are non-discretionary; essentially,
they are bookkeeping placeholders in
the accrual process, setting up the stage for the real
discretion in accruals, which is contained in
the other side of the accrual pair. Second, for accruals that
shift the recognition of cash flows
into another period, longer duration implies longer horizons of
estimation, and therefore more
discretion in the timing and magnitude of recorded accruals.
These two results can be used to
derive empirical measures of discretion in accruals. The
principal advantage of this approach is
that it applies to pretty much all accruals.
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Appendix A: Further comparison of the Dechow/Dichev and the
timing error approach
The main advantage of the Dechow/Dichev (DD) approach is that
future cash flow realizations provide a crisp benchmark for whether
accounting records the “right” accruals. The disadvantage is that
the DD approach only reflects the discretion in accruals where the
opening accrual precedes cash flow realization, e.g., accruals
proper like Accounts Receivable and Accounts Payable, and does not
capture the discretion in accruals where the cash flow realization
coincides with the opening accrual, e.g., deferrals like PPE and
Inventory. In addition, the DD approach is designed for working
capital accruals, while it is clear that there is much discretion
in longer-term accruals. Finally, even in accruals proper there is
a timing discretion that is not reflected in the DD approach. For
example, premature revenue recognition is not detected by the DD
approach as long as the recorded Accounts Receivable is an accurate
predictor of cash collections.
The main advantage of the timing error approach is that it
applies to all accruals and captures all discretion related to
using estimates. The disadvantage is that the timing error approach
lacks a natural crisp benchmark for the “right” accruals.
Otherwise, the DD and the timing error approach have a common logic
because both are “perfect foresight” approaches. In DD, perfect
foresight is with respect to the future cash flow realizations. In
the timing error approach, perfect foresight is with respect to
everything (future cash flow realization, future costs for the
percentage-of-completion revenue recognition method, future income
in recoding incentive compensation accruals today, depreciable
lives, residual lease values, interest rates, etc.), which is of
course more general – but harder to operationalize.
A brief example helps in comparing and contrasting these two
approaches. Assume that a firm books $100 in Accounts Receivable at
time t but only collects $80 in t+1, which triggers a write-off of
$20 in t+1. This is a classic DD situation dealing with the
discretion for accruals where the opening accrual precedes the cash
flow realization. The DD model interpretation of this situation is
that the opening Accounts Receivable accrual had an estimation
error of $20 ($100 receivable - $80 cash flow realization), which
implies a fairly low quality of the Accounts Receivable accrual at
time t. The timing error approach reaches a similar conclusion but
couches it in different terms. First, the timing error approach
points out that total cash flow income over the two periods is $80,
and total accrual income is $80 as well ($100 credit revenue at
time t - $20 write-off at time t+1). In other words, while there is
a mismatch between the opening accrual at time t and cash flow
realization at time t+1, there is no mismatch between the total
magnitude of accrual and cash flow income over the life of the
transaction. The only difference between accrual and cash flow
income is the timing pattern of realization. Since the example is
simple, it is also intuitively clear what the problem is:
essentially, the firm booked $20 of income “too much” at time t but
will also have $20 of income “too little” at t+1, when the inflated
receivable is written off as a loss. In other words, the
mis-estimation of the opening receivable is just a timing error of
$20 of income appearing at time t rather than at time t+1. Or in
the language of this paper, the actual pattern of accrual income
was $100, ($20) over the two periods. The pattern of “perfect
foresight” accrual income is $80, 0, which implies a pattern of
reversible timing errors of $20, ($20). Thus, DD estimation errors
represent a type of timing error – which is not surprising because
perfect foresight with respect to cash flow realizations represents
one type of perfect foresight.
Note that the more general timing error approach captures
additional aspects of discretion and accrual quality even for
accruals proper, which are the natural forte for the DD model. For
example, consider premature recognition of revenue. Booking $100 of
revenue prematurely in period t vs. t+1 is not captured in the DD
model if the recorded receivable is otherwise an accurate predictor
of cash collected from customers. In the timing error approach,
though, this situation produces a sequence of timing errors of
$100, ($100) over the two periods, given by the actual income
sequence of $100, 0 minus the perfect foresight income sequence of
0, $100.
It is also helpful to reconcile the key analytical expressions
between the two approaches. The key expression in Dechow and Dichev
(2002) is their equation (3):
Et = CFt-1t + CFtt + CFt+1t+ εt+1t - εtt-1
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which says that earnings at time t is the sum of cash flow
components from times t-1, t, and t+1 plus an adjustment for
estimation errors and their corrections. Expanding DD equation (3)
with the corresponding expressions for earnings for the two
adjacent periods, t-1 and t+1 yields:
Et-1 = CFt-2t-1 + CFt-1t-1 + CFtt-1+ εtt-1 - εt-1t-2 Et = CFt-1t
+ CFtt + CFt+1t+ εt+1t - εtt-1 Et+1 = CFtt+1 + CFt+1t+1 + CFt+2t+1+
εt+2t+1 - εt+1t Summing up the left and the right hand side across
the three equations and re-organizing the cash
flow terms by the periods in which they occur produces: Et-1 +
Et + Et+1 = CFt-2t-1 + (CFt-1t-1 + CFt-1t) + (CFtt-1 + CFtt +
CFtt+1) + + (CFt+1t + CFt+1t+1) + CFt+2t+1 + + εtt-1 - εt-1t-2 +
εt+1t - εtt-1+ εt+2t+1 - εt+1t Notice that CFtt-1 + CFtt + CFtt+1 =
CFt , and that four of the error terms cancel out, which yields:
Et-1 + Et + Et+1 = CFt-2t-1 + (CFt-1t-1 + CFt-1t) + CFt + (CFt+1t +
CFt+1t+1) + CFt+2t+1 - εt-1t-2 + εt+2t+1 From this expression, it
is clear that as the time interval expands, the cash flow terms
start to
aggregate to actual period cash flows, and the error terms will
continue canceling out, so that over the life of a transaction or
the firm:
∑Et = ∑CFt
which is the same as the key expression in equation (2) of this
paper. Summing up, the main insight from this reconciliation is
that the DD approach emphasizes that accruals that forecast cash
flow realizations contain an estimation error, which can be
considered the cost of using accruals. The timing error approach
emphasizes that such estimation errors reverse, and so the cost of
using accruals is the introduction of timing errors, which
represent reversible noise in the measurement of income. The
advantage of the timing error approach is that it accommodates the
discretion with respect to all estimates, and not just those
related to future cash flow realizations.
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Appendix B
Examples of some common accrual situations, illustrating the
applicability of the accrual duration approach
1. Accounts Receivable with Allowance for Uncollectibles
Consider the following series of accounting entries. Underlying
data not explicitly spelled out but should be clear from the
entries themselves. At time t: Accounts Receivable $200 Sales $200
Bad Debt Expense $10 Allowance for Uncollectibles $10 At time t+1
Cash $174 Accounts Receivable $174 Allowance for Uncollectibles $7
Accounts Receivable $7 In a nutshell, the accrual duration approach
says that accruals that are contemporaneous with the associated
cash flows are non-discretionary, and all others are discretionary.
In this example, the only accrual contemporaneous with the
associated cash flow is the collection of the Accounts Receivable,
and indeed this accrual is non-discretionary. Since the
uncollectability of receivables is reflected through an Allowance
account in this example, there is no discretion with respect to
that in the opening accrual for Accounts Receivable. But that
accrual is still somewhat discretionary in timing, especially for
certain businesses and transactions, like for sales with material
performance obligations or rights of return that may or may not be
completed at the time of sale. The opening accrual of the Allowance
account is clearly discretionary with respect to the estimated
value of uncollectibles. The closing accrual of the Allowance
account is also discretionary because it is likely triggered by
some company rule like “write off Accounts Receivable older than 4
months”, and such a rule is discretionary. As explained in the
text, accrual duration for Accounts Receivable can be estimated as
Days Receivable Outstanding/2 – although it is probably better to
use Cash Collections rather than Sales in the denominator if one
uses net Accounts Receivable in the numerator (as compared to
gross). It is an interesting question whether one can calculate a
separate accrual duration for the Allowance accrual. The answer
seems to be affirmative, with an estimate of (Average
Allowance/Write-offs)/2. Summarizing, this example conforms very
closely to the insights from the accrual duration approach. 2.
Warranties Consider the following two accounting entries, occurring
in two consecutive periods: Warranty Expense $150 Warranty Payable
$150 Warranty Payable $125 Cash $125
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This example is a straightforward application of the accrual
duration approach. The opening accrual for warranty payable is
discretionary because it is an estimate of future warranty claims.
The closing accrual is non-discretionary because it is pinned down
by the amount of warranty claims paid out. The average duration of
the Warranty Payable account for a given period can be estimated as
(Average Warranty Payable/Cash Paid out for Warranties)/2, and it
is clear that discretion in recording Warranty Payable increases in
the duration of this accrual. If the business is simple, the
duration of the Warranty Payable can also be potentially estimated
from specific disclosure about warranty coverage. For example, for
a company that produces only watches with warranty of 2 years,
assuming warranty claims are even throughout warranty life implies
an average duration of Warranty Payable of 1 year. 3. Prepaid Rent
Prepaid Rent $100 Cash $100 Rent Expense $24 Prepaid Rent $24 The
opening entry is clearly non-discretionary. The closing entry is
often not really discretionary for a simple case with constant
monthly rent, for example. But rent expense can be discretionary as
well in cases where rent expense is tied to sales volumes, and thus
quarterly rent expense assumes projections about annual sales. It
can be also discretionary in cases where there is an accrual for
projected rental penalties specified in the rental contract. The
accrual duration for Prepaid Rent is calculated as (Average Prepaid
Rent/Rent Expense)/2. 4. Deferred Revenue Cash $800 Deferred
Revenue $800 Deferred Revenue $475 Sales Revenue $475 The opening
entry is a non-discretionary deferral of cash received until
delivery of goods or services. Depending on the type of good or
service provided, the closing entry can be quite discretionary,
especially for contracts with complicated performance obligations,
multiple deliverables, rights-of-return, etc. The accrual duration
for Deferred Revenue is (Average Deferred Revenue/Sales
Revenue)/2.
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References:
Altamuro, Jennifer, Anne L. Beatty, and Joseph Weber, 2005, The
effects of accelerated revenue recognition on earnings management
and earnings informativeness: Evidence from SEC Staff Accounting
Bulletin No. 101, The Accounting Review 80 (2), 373-401.
Ball, Ray, 2013, Accounting informs investors and earnings
management is rife: two questionable beliefs, Accounting Horizons
27 (4), 847-853.
Ball, Ray, and Lakshmanan Shivakumar, 2006, The role of accruals
in asymmetrically timely gain and loss recognition, Journal of
Accounting Research 44 (2), 207-242.
Beaver, William H., and Maureen F. McNichols, 1998, The
characteristics and valuation of loss reserves of property casualty
insurers, Review of Accounting Studies 3 (1-2), 73-95.
Bushman, Robert M., Alina Lerman, and X. Frank Zhang, 2016, The
changing landscape of accrual accounting, Journal of Accounting
Research 54 (1), 41-78.
Chan, Louis K.C., Jason Karsecki, and Josef Lakonishok, 2003,
The level and persistence of growth rates, The Journal of Finance
58 (2), 643-684.
Dechow, Patricia M., 1994, Accounting earnings and cash flows as
measures of firm performance: The role of accounting accruals,
Journal of Accounting and Economics 18, 3-42.
Dechow, Patricia M., and Ilia D. Dichev, 2002, The quality of
accruals and earnings: the role of accrual estimation errors, The
Accounting Review 77 (S-1), 35-59.
Dechow, Patricia M., Weili Ge, Chad R. Larson, Richard G. Sloan,
2011, Predicting material accounting misstatements, Contemporary
Accounting Research 28 (1), 17-82.
Dechow, Patricia, Weili Ge, and Catherine Schrand, 2010,
Understanding earnings quality: A review of the proxies, their
determinants and their consequences, Journal of Accounting and
Economics 50, 344-401.
Dechow, Patricia M., S.P. Kothari, and Ross L. Watts, 1998, The
relation between earnings and cash flows, Journal of Accounting and
Economics 25, 131-214.
Dechow, Patricia M., Richard G. Sloan, and Amy P. Sweeney, 1995,
Detecting earnings management, The Accounting Review 70 (2),
193-225.
Dichev, Ilia D., John R. Graham, Campbell R. Harvey, and Siva
Rajgopal, 2013, Earnings quality: Evidence from the field, Journal
of Accounting and Economics 56, 1-33.
Francis, Jennifer, Ryan LaFond, Per Olsson, and Katherine
Schipper, 2005, The market pricing of accruals quality, Journal of
Accounting and Economics 39 (2), 295-327.
Francis, Jennifer, Per Olsson, and Katherine Schipper, 2008,
Earnings quality, Now Publishers Inc. Jones, Jennifer, 1991,
Earnings management during import relief investigations, Journal of
Accounting
Research 29 (2), 193-228. Leuz, Christian, Dhananjay Nanda, and
Peter Wysocki, Earnings management and investor protection: an
international comparison, Journal of Financial Economics 69 (3),
505-527. Peterson, Kyle, 2011, Accounting complexity, misreporting,
and the consequences of misreporting,
Review of Accounting Studies 17 (1), 72-95. Petroni, Kathy Ruby,
1992, Optimistic reporting in the property-casualty insurance
industry, Journal of
Accounting and Economics 15 (4) 485-508. Richardson, Scott A.,
Richard G. Sloan, Mark T. Soliman, and Irem Tuna, 2005, Accrual
reliability,
earnings persistence, and stock prices, Journal of Accounting
and Economics 39 (3), 437-485. Sloan, Richard G., 1996, Do stock
prices fully reflect information in accruals and cash flows about
future
earnings?, The Accounting Review 71 (3), 289-315. White, Hal,
2012, Accruals, deferrals, cash flows, and earnings: Articulation
implications for earnings
management models and a suggested alternative, Working paper,
Penn State University, also available on ssrn.com.
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Figure 1 Schematic representation of the benefits and costs of
the accrual process as reflected in the
timing of accruals and income
Definitions: Cash flow accounting: Cash inflows are revenues and
income, cash outflows are expenses and losses Actual accrual
accounting: Income = Cash flows + Accruals; accruals are recorded
using real-time
forward-looking estimates Perfect foresight accounting: Income =
Cash flows + Accruals; accruals are recorded under perfect
foresight Maximum potential benefits from using accrual
accounting: Difference between Cash flow accounting
and Perfect foresight accounting” Costs of using accrual
accounting: Making timing errors in income, which are the
difference between
actual recorded income and income under perfect foresight Net
benefits of using accrual accounting: Difference between Cash flow
accounting and Actual accrual
accounting; More timely recognition of income at the cost of
making timing errors
Cash flow accounting Actual accrual accounting Perfect foresight
accounting
Net benefits from using accrual accounting Cost of using
accruals: Timing errors
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Table 1 Summary of income and timing error effects for the
four-period sales transaction example
Sequence of events in sales transaction: Time t - Company makes
a sale for $300, to be collected in three installments of $100 each
over the next
three periods (with all discounting effects ignored). Time t+1 -
Customer makes the scheduled $100 payment. Time t+2 - Customer
misses the scheduled $100 payment. The company estimates that the
customer will
make the final payment at t+3, and therefore writes down the
receivable to its realizable value of $100 as of the end of
t+2.
Time t+3 - Customer makes an actual final payment of $120, and
thus the company realizes a gain of $20.
Summary of income effects over time:
Time t t+1 t+2 t+3 ∑ Incom