Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values

Accruals, Accounting-Based Valuation Models, and the
Prediction of Equity Values





Mary E. Barth
William H. Beaver
Graduate School of Business
Stanford University

John R. M. Hand
Wayne R. Landsman
Kenan-Flagler Business School
University of North Carolina at Chapel Hill




September 2004





We appreciate funding from the Financial Research Initiative, Graduate School of Business,
Stanford University, Center for Finance and Accounting Research at UNC-Chapel Hill, Stanford
GSB Faculty Trust, and Bank of America Research Fellowships. We also thank workshop
participants at Lancaster University and the University of Utah for helpful comments, and Brian
Rountree, Steve Stubben, Qian Wang, and Rui Yao for able research assistance. Corresponding
author: William H. Beaver, Graduate School of Business, Stanford University, 518 Memorial
Way, Stanford, CA 94305-5015, (650) 723-4409, fbeaver@leland.stanford.edu

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Accruals, Accounting-Based Valuation Models, and the Prediction of Equity
Values



Abstract

This study uses out-of-sample equity value estimates to determine whether earnings
disaggregation, imposing valuation model linear information (LIM) structure, and separate
industry estimation of valuation model parameters aid in predicting contemporaneous equity
values. We consider three levels of earnings disaggregation: aggregate earnings, cash flow and
total accruals, and cash flow and four major components of accruals. For pooled estimations,
imposing the LIM structure results in significantly smaller prediction errors; for by-industry
estimations, it does not. However, by-industry prediction errors are substantially smaller,
suggesting the by-industry estimations are better specified. Mean squared and absolute
prediction errors are smallest when disaggregating earnings into cash flow and major accrual
components; median prediction errors are smallest when disaggregating earnings into cash flow
and total accruals. These findings suggest that (1) If concern is with errors in the tails of the
equity value prediction error distribution, then earnings should be disaggregated into cash flow
and the major accrual components; otherwise earnings should be disaggregated only into cash
flow and total accruals. (2) Imposing the LIM structure neither increases nor decreases
prediction errors, which provides support to the efficacy of drawing inferences from valuation
equations based on residual income models that do not impose the structure implied by the
model. (3) Valuation of abnormal earnings, accruals, accrual components, equity book value,
and other information varies significantly across industries.

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Accruals, Accounting-Based Valuation Models, and the Prediction of Equity
Values
1. Introduction
There is a large literature examining how accounting amounts, including earnings, and
earnings disaggregated into cash flow and accruals, relate to contemporaneous equity values.1
Ohlson (1995, 1999) and Feltham and Ohlson (1995, 1996) develop valuation models that link
accounting amounts and equity values by assuming a link between equity values and the linear
information structure of the accounting amounts. Although such models have been the subject of
empirical testing, few studies test whether they aid in predicting equity values. The objective of
this study is to determine whether and the extent to which disaggregation of earnings and
imposing valuation model linear information structure aid in predicting contemporaneous equity
values out of sample. We also determine whether and the extent to which basing such
predictions on separate industry estimation of valuation model parameters affects their accuracy.
A primary goal of financial reporting is aiding investors in making economic decisions.
A primary economic decision investors make is assessing the value of firms in which they are
invested or consider investing. The Financial Accounting Standards Board (FASB) recognizes
this motivation for financial reporting by noting in Statement of Financial Accounting Concepts
No. 1, paragraph 34, “financial reporting should provide information that is useful to present and
potential investors, and creditors, and other users in making rational investment, credit, and
similar decisions.” Although the FASB recognizes the importance to investors of financial
statement amounts, the concepts statements provide little guidance as to how the amounts are to
be used. In contrast, accounting-based valuation models incorporating accounting accruals based

1 Throughout we use net income and earnings interchangeably.

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on the Feltham-Ohlson framework provide this guidance. We use this framework to provide
empirical evidence on our research questions.
The first empirical question we address is whether disaggregating earnings into cash flow
and total accruals, and into cash flow and the major components of accruals, result in differences
in equity value predictive ability. We do this because several studies find that cash flow and
accruals differ in their ability to forecast future earnings and to explain cross-sectional variation
in equity values. The second empirical question we address is whether accounting-based
valuation models incorporating accruals aid investors in predicting equity market values.
Accounting-based valuation models have been the focus of studies in several contexts, including
examining whether such models are descriptively valid, and assessing the value relevance of
accounting amounts. Some studies use accounting-based valuation models to predict equity
values for purposes of exploiting differences between theoretical and actual equity values.
However, they only consider aggregate earnings and do not address whether imposing the
model’s linear information structure affects predictability. The third empirical question we
address is whether basing predictions on separate industry estimation of valuation model
parameters affects equity market value predictions. Valuation parameters can differ across
industries because the relative mix of accrual components can differ across industries, and
because earnings forecastability or persistence of particular accrual components can differ across
industries.
To address our research questions, we use a sample of Compustat firms from 1987 to
2001. We predict contemporaneous equity market values using out-of-sample estimates, i.e., we
use cross-sectional valuation equations that for each year exclude each firm from the equations
used to predict its equity value that year. Hereafter, we use the term predictions to refer to these

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out-of-sample equity market value predictions. To test whether earnings disaggregation affects
equity value predictive ability, we predict equity values using three linear information valuation
models (LIMs) employing three levels of earnings disaggregation. LIMs comprise forecasting
equations for abnormal earnings and each earnings component considered separately, and an
equity valuation equation. The LIM structure provides links between multiples in the valuation
equation and those in the forecasting equations. The first LIM is based on aggregate earnings.
The second, following Barth, Beaver, Hand, and Landsman (1999), disaggregates earnings into
cash flow and total accruals. The third, introduced here, disaggregates earnings into cash flow
and the four major components of accruals?change in receivables, change in inventory, change
in payables, and depreciation.
We develop equity value predictions for each LIM using two estimation procedures. The
first procedure is an equity valuation equation that includes accounting amounts as explanatory
variables, but does not impose the structure of the LIM implied by the level earnings
disaggregation. The second procedure imposes the LIM structure. To test whether earnings
disaggregation aids in predicting equity values, we compare prediction errors across the three
LIMs. To test whether imposing the LIM structure aids in predicting equity values, we compare
mean and median squared and absolute prediction errors from estimations when the LIM
structure is imposed to those from when it is not. To test whether basing predictions on separate
industry estimations of valuation model parameters affects equity value predictions, we compare
prediction errors from pooled and separate industry estimations for each LIM.
The effect of imposing the LIM structure on out-of-sample prediction errors cannot be
predicted. This contrasts with in-sample prediction errors, where for a given LIM, the errors
obtained when the LIM structure is not imposed are guaranteed to be no larger than those

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obtained when it is imposed. There are two reasons why imposing the LIM structure can result
in smaller out-of-sample prediction errors. First, using knowledge of the interrelation of
accounting amounts in structuring the LIM should, other things equal, enhance the equity
valuation equation’s ability to predict equity value. Second, imposing the LIM’s structure
mitigates the extent to which the equity valuation equation overfits the data. However, imposing
the LIM structure can result in larger out-of-sample prediction errors because of inefficiency in
estimating the additional forecasting parameters.
One might also expect equity value prediction errors to decrease as the level of earnings
disaggregation increases. This is because as the level of earning disaggregation increases,
different components of earnings are permitted to have different valuation multiples. However,
earnings disaggregation can be costly in terms of increasing prediction errors. First, out-of-
sample prediction errors can increase as the level of earnings disaggregation increases because of
the potential for data overfitting. Second, as the level of earnings disaggregation increases, so
does the extent of structure imposed by the LIM on the forecasting and valuation relations. In
other words, although earnings disaggregation relaxes constraints on valuation coefficients by
permitting them to differ, it adds constraints on the valuation coefficients when the LIM structure
is imposed. As a result, the predictive ability of each LIM relative to the others could differ
depending on whether the LIM structure is imposed.
Before addressing our first research question by comparing prediction errors based on
different levels of earnings disaggregation, i.e., different LIMs, we address our second research
question by comparing prediction errors within each LIM to determine whether imposing the
LIM structure affects prediction errors. We find that for all three LIMs, imposing the LIM
structure results in significantly smaller prediction errors for pooled estimations. However,

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prediction errors do not differ significantly when the LIM structure is or is not imposed for the
by-industry estimations. These finding support the efficacy of drawing inferences from
valuation equations based on residual income models that do not impose the structure implied by
the model because doing so neither increases nor decreases prediction errors. A striking result
from the within LIM prediction error comparisons is that, consistent with our prediction relating
to our third research question, prediction errors based on the by-industry estimations are
substantially smaller than those based on the pooled estimations. This finding suggests that
valuation of abnormal earnings, accruals, accrual components, equity book value, and other
information varies significantly across industries. This finding also suggests that inferences
relating to whether imposing the LIM structure reduces prediction errors should be based on by-
industry estimation.
Regarding our first research question, we find evidence of some reduction in mean
prediction errors from disaggregating earnings into cash flow and total accruals, and some
additional reduction from disaggregating total accruals into its four major components. Evidence
from median prediction errors portrays a somewhat different picture. In particular, whereas
mean prediction errors generally support disaggregation of earnings into cash flow and the four
major accrual components, median prediction errors generally support disaggregation of earnings
only into cash flow and total accruals. These findings suggest that if when predicting equity
market values the concern is with errors in the tails of the prediction error distribution, then net
income should be disaggregated into cash flow and the four major accrual components.
However, if the concern is not with errors in the tails of the prediction error distribution, then
earnings should be disaggregated only into cash flow and total accruals. Thus, accrual

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components appear to provide additional information incremental to that in total accruals helpful
to predicting equity values when considering firms with more extreme prediction errors.
The remainder of the paper is organized as follows. Section 2 develops the research
design. Section 3 describes the sample and data, and section 4 presents the findings. Section 5
summarizes and concludes the study.
2. Research Design
2.1
LINEAR INFORMATION MODELS
Our tests of equity value prediction errors use equity value estimates from three linear
information models (LIMs) based on the Feltham-Ohlson framework. Each LIM reflects a
different level of earnings disaggregation. Our first research question is whether successively
disaggregating earnings into cash flow and total accruals, and cash flow and four major accrual
components aids in prediction equity values. Our second research question is whether imposing
the LIM structure aids in predicting equity values.
The first linear information model, LIM1, is based on Ohlson (1995), and comprises three
equations. Equations (1a) – (1c) are forecasting equations, and equation (1d) is the valuation
equation implied by the linear information dynamics of the forecasting equations. For example,
Ohlson (1995) shows that the abnormal earnings valuation coefficient in equation (1d), ?1, is a
nonlinear function of ?11 and the discount rate, r.
a
a
NI = ? + ? NI
+ ? BV + ? ?
+ ?
it
10
11
it 1
?




(1a)
12
it 1
?
13 it 1
?
it
1
BV = ? + ? BV
+ ?
it
20
22
it 1
?






(1b)
2it
? = ? +? ?
+ ?
it
30
33 it 1
?







(1c)
3it
a
MVE = ? + ? NI + ? BV + ? ? + u
(1d)

it
0
1
it
2
it
3 it
it

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MVE is market value of equity, NIa is abnormal earnings defined as earnings minus the normal
return on equity book value, BV, the ? s and
k
u are error terms, and the i and t subscripts denote
firm and year.2 ? , other information, is defined as MVE ? MVE , where MVE is the
t
t 1
t 1
?
?
t 1
?
fitted value of MVE based on a version of equation (1d) that does not include ? . Thus, ?
t 1
?
t
t
captures the extent to which the accounting variables do not explain market value of equity
(Feltham and Ohlson, 1995; Ohlson, 1995). We include equity book value in equation (1a) and
the abnormal earnings and component forecasting equations for LIM2 and LIM3 to enhance
stationarity of the forecasting equations (Barth, Beaver, Hand, and Landsman, 1999). LIM1
implicitly assumes that all earnings components have equal weight in forecasting abnormal
earnings and hence have equal weight in the valuation equation.
We estimate LIM1 because it focuses on aggregate earnings and plays a prominent role in
the empirical accounting literature. Several studies (Bernard, 1995; Lundholm, 1995; Barth,
Beaver, Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999; Myers, 1999) find that
LIMs using aggregate earnings are descriptively valid. In light of this, a rather robust literature
uses specifications based on LIM1 to examine how accounting amounts relate to
contemporaneous equity values to obtain inferences about these accounting amounts, i.e., their
value relevance (Barth, Beaver, and Landsman, 2001; Holthausen and Watts, 2001). Other
studies (Frankel and Lee, 1998; Lee, Myers, and Swaminathan, 1999) use models similar to
LIM1 to estimate theoretical prices to exploit differences between theoretical and actual equity
values to find mispriced securities.
The second, LIM2, is that estimated in Barth, Beaver, Hand, and Landsman (1999). It
relaxes the assumption that the total accruals, ACC, and cash flow components of earnings have

2 We use the same notation for coefficients and error terms across the three LIMs to facilitate exposition. They

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the same model parameters.3 LIM2 can be viewed as a version of the model in Ohlson (1999),
which models the transitory component of earnings, although the model applies to any earnings
component. LIM2 comprises four equations, where equations (2a) through (2d) are forecasting
equations, and equation (2e) is the valuation equation implied by the linear information dynamics
of the forecasting equations. Thus, relative to LIM1, by adding an additional forecasting
equation, LIM2 imposes additional assumptions on the valuation parameters.
a
a
NI = ? + ? NI
+ ? ACC + ? BV + ? ?
+ ?
it
10
11
it 1
?



(2a)
12
it 1
?
13
it 1
?
14 it 1
?
it
1
ACC = ? + ? ACC
+? BV + ?
it
20
22
it 1
?






(2b)
23
it 1
?
2it
BV = ? + ? BV
+ ?
it
30
33
it 1
?