Ilia D. Dichev
July 26, 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, and Chinese University of Hong Kong.
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. 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 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.
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 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 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 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.  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 tAccounts 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.
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 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. 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 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 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. 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.